Neutrino exploration of the earth

NEUTRINO EXPLORATION OF THE EARTH

A. De RUJULA

CERN, Geneva, Switzerland S.L. GLASHOW

Lyman Laboratory of Physics, Harvard University, Cambridge, MA 02138, U.S.A. R.R. WILSON

Physics Department, Columbia University, New York, N Y 10027, U.S.A. G. CHARPAK

CERN, Geneva, Switzerland

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NORTH.HOLLAND PUBLISHING COMPANY-AMSTERDAM

PHYSICS REPORTS (Review Section of Physics Letters) 99, No. 6 (1983) 341-396, North-Holland Publishing Company

NEUTRINO EXPLORATION OF THE EARTH* A. De RI]JULA CERN, Geneva, Switzerland

S.L. GLASHOW Lyman Laboratory of Physics, Harvard University, Cambridge, MA 02138, U.S.A.

R.R. WILSON Physics Department, Columbia University, New York, NY 10027, U.S.A.

and G. CHARPAK CERN, Geneva, Switzerland Received May 1983

Contents: 1. Introduction 2. Accelerator design 2.1. The Geotron 2.2. A Tevatron-like Geotron 2.3. A more up-to-date Geotron 2.4, Buried pipes and robots 2.5. More about magnets 2.6. Injector system 2.7. Costs 2.8. A seaborne Geotron 2.9. The external proton beam: The snout 2.10. A prototype 3. Neutrino beams

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4. Sound generation by particles interacting with matter 4.1. Possible mechanisms 4.2. The thermoacoustic model 4.3. Experimental tests of the thermoacoustic model 4.4. The sonic neutrino antenna 5. Background seismic noise 6. GENIUS vs. other methods of seismic research 7. GEMINI: Geological Exploration with Muons Induced by Neutrino Interactions 8. GEOSCAN: The density profile of the Earth 9. Directions of future research and development 10. Conclusion References

* Research supported in part by the National Science Foundation under Grant No. PHY-82-15249.

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Abstract: We show how the neutrinos produced by a multi-TeV proton synchotron may be used for purposes of geological research. Project GENIUS (geological exploration by neutrino-induced underground sound) is designed to search for deposits of oil and gas at large distances from the accelerator. It depends upon the coherent sound signal produced at depth by millions of neutrino interactions along the underground neutrino beam. Surface measurements of the acoustic pulse provide a remote underground probe. Project GEMINI (geological exploration with muons induced by neutrino interactions) is designed to search for distant deposits of high-Z ores. It depends upon the surface measurement of neutrino-induced muons which were produced in the last few kilometers of the neutrinos' underground voyage. Project GEOSCAN is a flux-independent procedure to determine the vertical density profile of the Earth, and especially its core. It depends upon the angle and energy dependence of the attenuation as the neutrino beam traverses the whole Earth.

I. Introduction Much of what we know about the fundamental structure of matter comes from the study of collisions of very energetic particles. Such particles are occasionally found in cosmic rays, but are far more copiously produced by particle accelerators. These machines are of many kinds and may be designed to accelerate protons, electrons, or atomic nuclei. However, the highest laboratory energies are provided by protons which have been accelerated by proton synchrotrons. Over the past decades, larger and larger proton synchrotrons were built to provide ever larger energies. Within a year, the Tevatron will make available protons of a TeV per particle. Every few minutes, a pulse of ~ 1 0 1 4 protons with a total kinetic energy of megajoules will be extracted from the machine. In fig. 1.1, we show the rapid evolution of the energy of proton synchrotrons with time. The considerations of this paper concern a future generation of proton synchrotrons capable of producing extracted beams of protons with energies of 3-30 TeV. At present, large proton synchrotrons are facilities which are totally dedicated to the pure and noble science of elementary particle physics. Technological spin-off from the construction and utilization of those machines has been significant in many applied disciplines such as fast electronics, cryogenics, superconductivity, and computer science. The economic value of spin-off far exceeds the capital cost of

1TeV

I00 GeV

/Asf NAL

10 Ge~ BEVATRON ' COSMOTRON

I GeV

I

I

]960

]970

I 1980

Fig. 1.1. Rapid growth of maximum energies produced by proton synchrotrons. An energy of 10 TeV should become available during the 1990's.

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the machines. High-technology pump priming can induce the rebirth and revitalization of our industrial society. Nonetheless, the raison d'etre for the construction of high-energy accelerators has always been the pursuit of science for science's sake. We believe that future accelerators can be of direct commercial and technological importance. We envisage the construction of one (or more) large proton synchrotrons for purposes which may loosely be termed "WHOLE E A R T H TOMOGRAPHY". It is the purpose of this paper to explore the nature and feasibility of such a project. We shall refer to the accelerator dedicated to geological exploration as the GEOTRON, presumably a proton synchrotron with a beam energy - 1 0 TeV. Some considerations on the construction of the GEOTRON are given in section 2. T h e high-energy protons must be aimed towards a distant site of geological interest. Immediately after extraction, the protons collide with a target, producing an intense and highly collimated beam of mesons. These mesons pass through a long decay tunnel, wherein they generate a neutrino beam. The complex system of proton beam transport, target, and decay tunnel must be capable of being redirected with great precision towards remote sites. We refer to this novel construction as the SNOUT of the GEOTRON. The nature of the neutrino beam which is produced at the GEOTRON complex is discussed in section 3. The collimated neutrino beam, when it reaches the remote site to be explored, undergoes secondary interactions with the underground medium. This leads to the production of a detectable signal whose interpretation can provide useful information. The neutrino beam can be used in at least three different ways to reveal information about the subsurface. Project GENIUS stands for Geological Exploration by Neutrino Induced Underground Sound. In this scenario, the neutrino beam is deployed at a shallow angle of declination so as to emerge from the Earth at a distant site. For example, at a declination angle of 4.5°, the point of emergence of the beam is 1000 km distant from the accelerator and its maximum depth is 20 km. As the neutrinos pass through the Earth they undergo occasional interactions wherein their energy is converted into ionizing radiation. With a proton synchrotron of energy Ep = 10 TeV, the amount of ionization produced by the neutrino beam is ~ 100 ergs/cm. At a distance from GEOTRON of 1000 km, the radius of the region of energy deposition by the neutrinos is ~ 10 m. The density of energy deposition per GEOTRON burst is e ~ 3 x 10-5 ergs/cm 3. Some of this energy is converted into elastic energy which propagates to the surface as a sonic pulse. The production of this sound signal at depth is considered in detail in section 4. The local overpressure produced by the energy deposition can be dimensionally estimated to be

(Kc2/Cp)e

(1.1)

where K is the coefficient of thermal expansion, c is the velocity of compressional sound waves and Cp is the specific heat per unit mass. At depth, the dimensionless parameter (Kc2/Cp) is of order unity. Thus, the magnitude of the bipolar pressure pulse is 43 x 10-5 dynes/cm2. If the neutrino beam is at a depth of one km, the surface acoustic signal is only several microdynes/cm2. The radius of the region of energy deposition corresponds to a quarter wavelength, so that the characteristic acoustic frequency is -100 Hz. One such acoustic pulse accompanies each neutrino pulse, which takes place roughly once each minute. On the surface below which the neutrinos pass is placed a large array of geophones or hydrophones, constituting an antenna designed to detect the acoustic signal in the presence of background seismic noise. The detectability of the signal under these circumstances is considered in section 5. Here, our

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considerations on signal/noise ratios are only order of magnitude estimates, likely to be overpessimistic. This is because the generation of sound by ionizing radiation in inhomogeneous media under strong pressure (the signal) has not been experimentally studied, and we must rely on information for homogeneous liquid media. Moreover, the coherence and directionality of microseismic noise at f - 10 to 100 Hz (essential to the analysis of the noise) are also unknown, and we must pessimistically rely on estimates based on uncorrelated noise. The acoustic signal can be interpreted in terms of the physical properties of the subsurface. The neutrino beam takes milliseconds to travel from the accelerator to the underground site under study, and the acoustic signal takes hundreds of milliseconds to propagate to the surface. This travel time (hence, the mean sound velocity) can be measured with great precision. Scanning of the neutrino beam determines the vertical profile of sound velocity to a depth - 10 km and over a potential area - 10 6 km 2. Further information about the subsurface is provided by the time-structure of the pulse and by its magnitude. This information can be used to search for commercially important deposits, particularly of oil and gas. A comparison of Project GENIUS with other methods of seismological research is given in section 6. Project GEMINI stands for geological exploration by muons induced by neutrino interactions. Here again, the neutrino beam is deployed at small angles. What is measured is the flux of muons which accompany the neutrinos at their point of emergence from the Earth. Project GEMINI is examined in detail in section 7. We estimate the magnitude of the muon flux at a point ~ 1000 km from a - 1 0 TeV accelerator, where the radius of the neutrino beam is - 1 0 m. Each pulse of the accelerator will yield - - 1 0 1 3 neutrinos, whose mean energy is ~0.5TeV. The emergent neutrino flux will thus be -101° neutrinos/m2 burst. The flux of accompanying muons is proportional to the neutrino flux. The dimensionless constant of proportionality is essentially the product of the neutrino cross section, the muon range, and the density of nucleons. Explicitly, it is - 1 0 - 6 ((E~)/TeV)2. Thus, the emergent muon beam should consist of several thousand muons per square meter per burst. The intensity of the surface muon flux is sensitive to the presence of high-Z ore bodies at vertical depths of several hundred meters. Underground deposits of copper or iron at a level of one ton per square meter of land area can be detected by observing a corresponding suppression of the surface muon flux. The sensitivity to very high-Z materials such as lead or uranium is four times greater. We imagine the simultaneous implementation of Projects GEMINI and GENIUS in order to optimize the utilization of the accelerator facility. A third method for neutrino exploration of the Earth is Project GEOSCAN. It is designed to measure the vertical profile of the density of the Earth, and most particularly that of the Earth's core. It is examined more closely in section 8. In traversing an Earth diameter, a neutrino beam encounters 101° g/cm 2 of matter, and is thereby attenuated by several percent. This attenuation can be measured no more precisely than the neutrino flux can be monitored. We circumvent the difficulty by measuring the emergent muon flux at two locations, one at the center of the beam and one at its periphery. Because the muons at the center are the most energetic ones, and because attenuation is energy dependent, this strategy provides a self-normalizing procedure for measuring the projected mass density of the Earth. We demonstrate that a 2 TeV proton accelerator is sufficient to yield several percent accuracy over a period of several days of operation. Of course, such a GEOTRON must be equipped with magnets to deflect the protons to a vertical inclination, and with a vertically deployed decay tunnel. Project GEOSCAN requires a specially designed SNOUT. This paper considers only a few of the technical questions and related scientific questions associated with a neutrino beam used as a remote sensor. In section 9, we identify several promising

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directions for future research and development related to this Project. Finally, we offer our conclusions in section 10. Briefly, the Project seems to us to be technically feasible, but it is not evidently commercially feasible at this time. Further work is clearly called for. Perhaps the next major scientific accelerator program, which is likely to be a 10 TeV or 20 TeV proton-proton or proton-antiproton collider, can also be used as a prototype GEOTRON. Thus, it must be a high-intensity accelerator equipped with an extracted beam and a modestly mobile SNOUT. With such a machine, the practitioners of pure and applied science can once again be brought together.

2. Accelerator design 2.1. The Geotron The technology of building accelerators has advanced enough so that it is now feasible to construct a synchrotron capable of producing an intense beam of 10--20 TeV protons. Such an accelerator could be used for the exploration of the deeper depths of the atom: it could also be used to explore the deeper depths of the Earth. For the latter application, which concerns us here, a narrow beam of high energy neutrinos is to be produced by the proton beam when it is directed at a target. It is the highly penetrating character of this radiation which will allow us to examine the interior of the E a r t h - all the way to the center. The neutrino beam will also allow us to probe closer to the surface for minerals and hydrocarbons, but yet deeper than with present prospecting techniques. It would be best for prospecting purposes to be able to move the accelerator about on the surface of the Earth. We will discuss a method of doing exactly that by floating the accelerator in the sea. However, because building a seaborne accelerator would be a considerably more adventuresome project than building one on firm land, we will first consider a land-based accelerator, and then indicate what changes would be necessary in order to put out to sea. In any case, the accelerator on land could be built close to the area to be prospected, and close to shore, so that the proton beam could be transported to the water. In the sea it should be possible to install a device, a kind of a snout to be described later, by which the proton beam could be directed downward, or indeed in any direction. The neutrino beam maintains rather closely the direction of the protons as they strike the target, hence we point the neutrinos by pointing the protons. 2.Z A Tevatron-like Geotron Let us discuss a 10 TeV proton synchrotron which for simplicity we will refer to as the "Geotron". It will be easy to scale it up or down to a not-too-different energy. Thus, a 20 TeV Geotron would have about twice the radius and, apart from the injector, would cost about twice as much. For orientation, we will first consider a Geotron which might be built using only Tevatron components, i.e., the same magnets in the same lattice arrangement, in the same kind of tunnel, with the same refrigerators, etc., that were used in constructing the 1 TeV proton synchrotron just being finished at Fermilab [1]. The radius of the Tevatron is 1 km, so the 10 TeV Geotron would have a radius of 10 km. We might even use a copy of the Tevatron itself as the injector of 1 TeV protons into the Geotron Main Ring. This overly conservative exercise allows us to estimate costs with some degree of reliability: it also allows us to identify where simplifications and cost savings might be made. The 400 GeV Fermilab accelerator cost about 150 million dollars in 1970, so it might cost about 400

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million dollars today. roughly an additional Tevatron to be about might cost about 2000

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The Energy Saver part, i.e., the superconducting part of the Tevatron, cost 150 million dollars a few years ago, so we might estimate the whole cost of the 600 million dollars in 1983 dollars. This implies that the Tevatron-like Geotron million dollars, more or less depending on circumstances.

2.3. A more up-to-date Geotron

The design of the Tevatron was essentially finished in 1977. Surely, we can do better today for less money. Such possibilities were discussed at the 1982 DPF Summer Physics Study of Future Accelerators held at Snowmass, Colorado [2]. A principal variable in any design is the value of the magnetic field which can be used in the bending magnets. At Snowmass, fields between 2 and 10 Tesla were advocated. A low field of 2 or 3 Tesla, such as "superferric magnets" would produce, implies large costs associated with the large radius, but cheap and reliable magnets. A high field implies a small radius with all the concommitant savings in utilities, tunnels, etc., but expensive magnets. It was the conclusion of the study that, for present technology, the cost would be essentially independent of the magnetic field, the high-field magnet costs just about balancing the savings due to the consequent reduction in the size of the ring. However, the Geotron should be as compact as possible, consistent with reliability, hence we should choose the highest practical field that we can project to the probable time of construction. The Tevatron magnets, indeed all the superconducting magnets being built in laboratories all over the world, now easily reach 5 T using Nb-Ti superconductor. The Japanese have recently produced a variant, Ni-Ti-Ta, which appears to be significantly better- in some respects almost twice as good [3]. On the basis of this and of developments in the art of making Nb-Sn, we can be conservative in choosing 7.5 T as a future operating field value. Higher fields have been reached in short magnets, but it has not yet been demonstrated for them that the energy stored in the field can be safely removed in a "quench", wherein for some reason the superconductor becomes a normal conductor. Nor have questions about fatigue in the collars been adequately investigated. Synchrotron radiation by the protons also begins to become significant at these high energies, especially as a heat load on the refrigerators. This effect also tends to favor a lower magnetic field. Let us tentatively decide on 7.5 T for the magnetic field, implying a radius of about 6 km. The optimum lattice for this radius will require a longer length of bending magnets between quadrupole focusing magnets than is the case for the Tevatron. In this regard we must decide whether the accelerator will be used all the time as a Geotron to accelerate an intense beam of protons, or whether it might be used part of the time as a colliding beam facility-just as the Tevatron is to be used as a collider in its "Tevatron-l" mode. The latter would imply a somewhat less etticient bending-toquadrupole length ratio than would a machine which would be used only for accelerating protons. However, we should keep in mind the possibility that the costs of the accelerator might be shared with those who would like to use it for particle physics. Indeed, the geophysicists might even find it expedient to become secondary users. The above discussion adds up to a lattice in which the length of the bending magnet would be about 15 meters and for which the quads would be about one meter long. To this length we should add another two meters or so of free space at each quad for beam-position detectors, correction coils, magnet leads, etc. Six long straight sections, each about 17 meters in length, would also be inserted in the lattice for beam injection, beam extraction, RF acceleration, beam aborts, colliding beam experiments, etc., to give the roughly 24 mile perimeter already mentioned. Of course, the above parameters are educated guesses which would later be subjected to more sophisticated calculation.

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2.4. Buried pipes and robots A major item is the cost of the tunnel. This can be significantly reduced by placing the magnets, etc., in a pipe about one meter in diameter buried about two meters beneath the surface of the ground. Such a scheme was suggested at the Snowmass Study in relation to a superferric magnet system. We would also adopt the suggestion made there of using robots for positioning the magnets, and we will examine the possibility of using the robots even for installing the magnets. All this can be of great application when we come to the seaborne accelerator. Figure 2.1 illustrates the buried pipe, or culvert, the magnet within, and a robot hovering about it, ready to adjust its position, or, together with some husky fellow-robots, to disconnect the magnet, lift it up, and carry it to an access point for removal from the tunnel. The sheer size of the ring mandates an army of servile robots, robots who could inhabit a claustrophobic and hostile environment, bask in a climate of intense radiation, and work 24 hours a day to get and keep the Geotron going.

Fig. 2.1. Buried pipe, about one meter in diameter, containing the superconducting magnet and the artist's conception of robot capable o[ positioning the magnet.

2.5. More about magnets Let us now discuss the magnets in more detail because considerable simplifications in their construction can be made on the basis of new ideas. They would differ from the Fermilab superconducting magnets in being much longer and by not having the rather heavy iron outer-yoke which provides magnetic shielding between the Main Ring magnets and the Tevatron magnets which are only a few inches apart. The outer-yoke also provides a slight amount (about 10%) of extra field strength, but that can be made up to some extent by extra current in the coil. The proposed magnet is shown in cross section in fig. 2.2. The advantage of doing away with the yoke, apart from the savings in not having to buy, fabricate, and install a large amount of steel, is that the cryogenic losses would be vastly reduced. This is because the heat leak into the cold inner-magnet of

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rIUl|~¢

Fig. 2.2. A proposed sketch of the design of a Geotron magnet.

the Tevatron is due in large part to the conduction of heat through the supports of the inner-magnet. The heat leak through the supports is large because the supports must be strong to resist a large force due to magnetic moments induced in the iron yoke. No yoke, no induced moments; less force, less heat leak. This is not a trivial matter because the refrigeration costs are a substantial part of the total cost. Making the magnets much longer can also reduce the cost. This is because the ends of the coils tend to be complicated and expensive- about half the cost of each of the Tevatron magnets can be ascribed to the coil ends and to the end boxes where individual magnets are joined together. Thus instead of having four separate bending magnets each about six meters long between quads as in the Tevatron, we might have only one magnet about 40 m long between quads in the Geotron. Details of just how this might be accomplished are described in the Snowmass report. Synchrotron radiation by the protons has already been mentioned. Were the proton intensity high and were the radiation not intercepted on warm fingers protruding into the donut, the radiation would add significantly to the refrigeration load. Indeed, the power radiated by N protons moving in an orbit of radius of curvature R is P = 6 x IO-14NE4/R2

(2.1)

where P is in watts, E in TeV; and R in km. As an example, with R = 6 km, E = 10 TeV, and N = 1015 protons, the radiated power is 16 kilowatts. The same proton intensity in a 20 TeV accelerator of twice the radius produces 64 kilowatts of synchotron radiation, which in this case is about three times the static heat load.

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2.6. Injector system We need not spend much time on the injector. Many of the improvements discussed above could also be incorporated in the injector rings and bring about considerable cost savings. The new injector might start with a 1 GeV Linac which could include the improvements developed at Los Alamos; it would be cheaper than the 200 MeV Linac used at Fermilab and would provide a brighter beam. This might be followed by a double-stage booster accelerator. The first stage could be a fast-cycling 10 GeV synchotron made using conventional magnets. The second stage booster could be located in the same tunnel and might be a 400 GeV superconducting synchrotron - both having a radius of about 300 m. Z Z Costs Costs, seemingly so prosaic, are in reality utterly romantic, and in every sense of the word. We have seen that the idiot's delight we started with might cost two billion dollars. With a better design, the Geotron as just described might cost about one billion dollars. By more ingenious people, it might cost less; but it might cost very much more if built under the loving supervision of present day bureaucrats. The construction could well be drawn out in a jobs-for-all Nirvana, for years and years as the costs double and then double again. This sobering pitfall for projects is not, experience informs us, the exception. But let us take the optimistic view; the cost will be of the order of one billion dollars, and it will be built in three years after funding. This does assume that we do have a few very committed physicists on board.

2.8. A seaborne Geotron Can we really put an accelerator out to sea or is this just another technical chimera? The first part is easy. We will just float the pipe containing the magnets and robots, etc. at a depth of about five fathoms where the wave motion will be very small most of the time. During large storms, the accelerator would be shut down. The robots with their magnets in hand will gain entry to the pipe through snorkels and air locks in a manner already rather well worked out in the last century. But the ocean currents, what can stand up to them? Cables. Stainless steel cables fastened to the bottom might hold the pipe in position-perhaps to within several centimeters of where it should be. The cables would be most effective if the water were not too deep. This suggests that the Geotron be located over a submerged coral reef of the kind that is found encircling a desert island. The booster ring in that case might be placed in a sheltered lagoon within the reef. The linac and control center could be placed on the island itself. But we must face up to the main reason for skepticism about floating the accelerator in the sea. Here-to-fore much has been made of the necessity of extremely solid and stable supports for a synchrotron and for the accuracy by which magnets must be p l a c e d - t o a few tenths of a mm. O f course, we cannot expect to achieve any such solidity- let alone any such accuracy- by means of our cables. The alternative we wish to invoke is to provide an automatic magnetic correcting system, a dynamic one which will sense the position of the proton beam at each quadrupole magnet and respond by aiming the beam at the center of the next lquadrupole. This is exactly what is done in the Tevatron at injection with the correction coils progided, but in that case the correction is steady because the positions of the magnets are steady. In the case of the Geotron in the sea, in spite of the cables, the magnets will pitch about slightly even during the acceleration process. One thing we do know now is how to respond electronically to the position of a beam. For example, the stochastic cooling devices

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used at CERN and Fermilab respond within nanoseconds to measurements of beam positions. Our problem is vastly simpler in one sense, for the movement of the magnets will take of the order of seconds to occur, or even much longer depending on the cause of the motion. It will take aldout 0.1 msec for the proton to make one turn of the ring, hence we can expect to sense the displacement of the beam on one turn and respond on the next. Thus as the magnets slowly pitch and yaw, the beam will remain dynamically centered in the magnetic aperture. The above discussion assumes that the magnets have been placed more or less in the right position by adjusting the cables as the acceleration process is started, say to within several cm over a distance comparable to a Betatron wavelength (a few hundred meters), the distance over which the beam would be most sensitive to magnet misalignments. The wave motion should be small and the forces due to ocean currents should change only slowly with distance and time. It is not difficult to imagine a survey system (radar, optical and sonar) which could be used to position the tube to the necessary accuracy by adjusting the cables (the robots will help). For short distances the stiffness of the tube will help to keep the magnets in alignment. Until the correction coil system has captured the beam and locked it onto the center of the aperture, the intensity of the beam should be cut down so that it will not be able to damage the magnets or create too much of a heat load for the refrigerators. Correction magnets are provided for all large synchrotrons, the only difference in this sense is that these correction magnets will be programmable and will be responsive during the whole acceleration cycle. If we can by the use of the above dynamic correction system keep the beam in the aperture, then most of the other problems at sea will not be too much different from those encountered on dry land. The power supplies, refrigerators, survey stations, and controls could be housed in barges which could be connected to the tube below through a snorkel-like device. The amount of radiation released to the water should be small compared to natural sources and to cosmic rays-except near the target where special measures would be taken. People and fish might be warned away from the vicinity of the accelerator by an intense sonic signal as well as by more prosaic devices. The water would make for effective (and free) shielding. We cannot expect to have a stiff power line on our island, yet the amount of electrical energy stored in the magnetic field can be rather large. The happiest solution to this problem would be to have two rings, possibly intersecting part of the time. One of the rings could slowly be energized using a flux pump, and then the energy might be caused to slosh back and forth between the two rings. Another problem is the large amount of energy and momentum, stored in the beam itself. There is the possibility of containing as many as 1015 protons in the accelerator. This would be a prodigious amount of energy, ~ 109 joules for the above example. This amount of energy could vaporize almost any obstacle it should inadvertently strike. This problem already exists to some extent at Fermilab with the Main Ring, not to mention the Tevatron. It also exists to a much more serious degree in our automobiles which come hurtling at us from every direction with much more energy. We are careful with our cars, and very very seldom is it that we are hurt by one. The beam at Fermilab is just not allowed to depart from the center of the aperture, and very very seldom hits the donut - and so it would be with the Geotron. Incidentally, the huge momentum of the beam implies a longitudinal tensile force in the magnet ring of about 1 ton weight. Of course, especially cooled targets can be prepared to withstand the heating produced by even the most intense beams, but it's not easy. The radioactivity produced by neutrons near the target could be contained in huge plastic bags that could be towed away for disposal elsewhere. Moving to a new underwater site would be a matter of closing a few bulkheads, breaking the

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magnet-containing tube, and then of having some tugs tow the now nearly linear magnet tube to the new location where it would be pulled into a circle again. It should be emphasized that the Geotron does not depend on most, indeed on any, of the romantic ideas put forward here. Most of the suggestions have been made for reasons of economy. Should the narrow pipe and the robots not appeal to one, then a larger pipe into which human workers could enter and carry out their construction in the usual manner would still be an alternative, albeit a more expensive one. Another alternative would be to fasten the magnet tube solidly to the reef by means of frequently placed concrete pylons or steel towers. If we can float an accelerator over a reef, can we float an accelerator out in the ocean where the water might be too deep to fasten it to the bottom? Well, we could talk about "sailing" the magnet tube into position by means of frequently spaced propellors, and holding it in position by those propellors just as some oil drilling rigs are held over the drilling point. But we would suggest that we creep before we walk, and we learn the simpler shallow water technology on the reef first. Eventually we shall build an accelerator that sails "twenty thousand leagues beneath the sea", and then we shall build one twenty thousand times larger out in space. So much for Jules Verne. 2.9. The external proton beam : The snout

The proton beam in the accelerator will be extracted very much as it is in the Tevatron, where the beam can be extracted in one turn, or over several seconds, or for about any time between. The Geotron needs only the fast extraction mode, i.e., in one turn (0.2 sec). This is the simplest mode of extraction for the beam is just knocked out of the accelerator by a single magnetic pulse. Although getting the beam out may be straightforward, aiming the protons downward in the desired direction will require a new device that would be located in deep water. We can envisage a train of superconducting magnets in a flexible tube that could be held in a downward curve by a network of cables. The proton beam would be directed into this magnet chain. Depending on the sharpness of the bend of the magnet chain, it would be possible to deflect the beam through any angle up to 90 degrees. By rotating the plane of the device, let's call it a "snout", about the direction of the initial beam, the emergent beam could be pointed in any direction downwards or sidewards. Restricting the amount of angular deflection required would of course decrease the length and cost of the snout in proportion. The technology for making the snout would be less demanding than that for the accelerator tube because the beam need only pass through the magnet chain once so that small-aperture high-field (10 Tesla) magnets could be used. The cables which would hold the snout in place would be adjusted by computer-directed changes in their relative lengths. At the bottom of the magnet chain the protons would strike a dense target. The resultant nuclear collisions would produce a narrow secondary beam of zr and K mesons which would then enter a long vacuum tube having the same orientation as the incident protons. As the mesons pass along the tube, they decay in flight into neutrinos, and it is this intense beam of neutrinos that will be used to probe the Earth, as will be elucidated in the following sections. 2.10. A prototype

It is likely that the next large U.S. accelerator project will be the construction of a very large hadron coilider (either pp or p~) with a beam energy of at least 10 TeV. Such a machine would be constructed primarily as a high-energy physics facility. If this accelerator were provided with an extracted proton beam, it could serve as a prototype for the Geotron. A neutrino snout with even very limited mobility

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could survey thousands of square kms. The extra facilities needed to equip the large collider to purposes of geological exploration would modify its cost by only a few percent. The feasibility of neutrino exploration of the Earth can thereby be evaluated at relatively low cost. Ideally, the prototype will be successful in detecting and measuring known and new hydrocarbon deposits far from the accelerator. Interested parties may then consider the construction of a Geotron dedicated to geological surveying.

3. Neutrino beams

High-energy protons, of energy Ep, are extracted from the proton synchrotron and aimed in the direction of the distant geological site of interest. They are made to strike a dense target where their collisions with atomic nuclei produce a forward secondary beam consisting mainly of mesons called pions (It) and kaons (K). The secondary particles of given charge are further focused by means of a "magnetic horn", after which they enter a long evacuated "decay tunnel". Some of the particles in the collimated secondary beam will decay by such processes as ~r+-~/z++ u~, and K+-~/.t++ u,,, thus producing the desired neutrino beam. At existing high-energy facilities, only a few percent of the 7r's and K's have time to decay before coming to the end of the decay tunnel and entering the shielding which absorbs all incident particles but neutrinos. The neutrino flux produced by such an arrangement [4] at the CERN-SPS accelerator (the "wide-band beam") is shown in fig. 3.1. The units are numbers of neutrinos per GeV energy interval and per machine pulse. The primary proton beam has an energy Ep = 0.4 TeV, the number of protons per machine pulse is - 4 × 1013 protons, and the mean neutrino energy is - 2 2 GeV. To simplify the succeeding analysis, we approximate the neutrino flux by an exponential fit, &(E,,) ~ 2.5 x 10~° exp - (Ed(Ev)) (GeV) -1 ,

(3.1)

which is shown as a dotted line in fig. 3.1. This fit overestimates the flux of very low-energy neutrinos, but these play no role in our considerations. I

>

I

I

I

!

10I°

(.9

\

~) I0e Z OC

IO s Z

10 7 n~W nn :D Z

_

",,N,. ","N

10s

" 50I I00I 150I 200I \~I250 ~ Eu(GeV) Fig. 3.1. Neutrino flux per burst at the 400 OeV SPS "wide-band-beam". Solid line shows actual flux, while the dotted line shows the exponential approximation of eq. (3.1).

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Notice that the total energy in a proton pulse is - 1 . 6 x 1013TeV while the total energy of the neutrino pulse is - 1.2 x 101° TeV, some three orders of magnitude smaller. Because only a few percent of the pions have time to decay, and because the average neutrino energy is only about a quarter of the average pion energy, a two order of magnitude inefficiency is intrinsic. Better design of the neutrino facility might increase the total neutrino flux by a factor of ten, at the very most. We must estimate the neutrino flux that will become available at envisaged higher energy accelerators. The number Np of protons per pulse that may be accelerated increases linearly with the primary proton energy [5]:

Np ~ 1015(Ep/10 TeV).

(3.2)

This leads to a similar increase in the yield of secondary mesons. In our estimate of the neutrino flux, we assume that the same fraction of these particles decay into neutrinos as at existing neutrino facilities (CERN or FNAL) where the decay tunnel length is -300 m. Thus, we scale the length of the proposed neutrino decay tunnel with the primary proton energy (tunnel length) ~ 7.5 km(Ep/10 TeV).

(3.3)

The mean energy of the secondary mesons, and hence of the neutrinos, is also expected to increase linearly with Ep, (Ev) ~ Ep/18.

(3.4)

An exponential fit to the neutrino flux which incorporates (3.2), (3.3) and (3.4) is a straightforward extrapolation of (3.1): &(Ep, Ev) ~- 2.5 x 10 '3 e x p -

(Ed(Ev))(TeV)-'.

0.5)

Equation (3.5) is our educated guess for the neutrino flux produced at a future neutrino facility. We are interested in the number of neutrino interactions per centimeter which take place along the beam as it traverses material with density p. Let trvN be the total neutrino-nucleon interaction cross section. This cross section is measured to be proportional to neutrino energy at energies up to 100 GeV, and is theoretically understood. The linear extrapolation of the interaction cross section up to energies of several TeV, tr~N(Ev) -----10-35 cm2(EJTeV),

(3.6)

should be entirely justified. The range in Earth of a TeV neutrino is about 1011 cm, and is far larger than the Earth's radius. Attenuation of the neutrino beam is small. When a neutrino in the beam does suffer a collision, about 90% of its energy, on the average, will ultimately be deposited in the target material in the form of ionization. (The small loss is mostly due to secondary neutrinos produced in "neutral current" interactions.) The number of interactions per cm, produced by a single machine burst is dN/dy =

pNAf dE~O(Ep, E~) ¢~N(E~),

(3.7)

A. De Rt~jula et al., Neutrino exploration of the Earth

where NA = 6 x

355

is Avogadro's number. From (3.5) and (3.6), this result becomes

10 23

dN/dy "=-46(p/(g/cm3))(Ep/10 TeV) 2 .

(3.8)

With a 10TeV accelerator, the neutrinos produce -100 interactions/cm along their underground voyage. It is the coherent effects of these many interactions that may produce a detectable and commercially significant acoustic signal. To accomplish our purpose of geological surveying, the neutrino beam must be narrow at large distances from the accelerator. Hence, it must be well collimated in angle. There are two sources of angular divergence. Even if the protons are perfectly collimated, the secondary mesons (whose decays produce the neutrinos) will not be. Their mean production angle will be 0p,~ - 0.3 GeV/(E,,) - 1.2 × 10-4(10 TeV/Ep).

(3.9)

This divergence can be reduced by means of magnetic focusing of the secondary mesons. However, there is an intrinsic angular divergence of the neutrino beam characteristic of the decay scheme of the mesons. For the dominant process 7r÷ ~ # + + u,,, the mean decay angle is 0,~ - 0.03 GeV/(E~) - 0.5 x 10-4 (10 TeV/Ep).

(3.10)

With good magnetic focusing, 0p,~< 0,~ and the overall divergence of the neutrino beam is dominated by the neutrino decay angle. Equation (3.10) implies that the radius of the neutrino beam of a 10 TeV machine at a distance of 1000 km from the accelerator is -50 meters. In order to study the acoustic signal generated by the beam of neutrinos, we need to know the profile of energy deposition in the vertical plane defined by the neutrino beam and the microphone, d2W/dx dy. The total energy deposition per cm along the beam is d W / d y = NAp J- E~ t~(Ep, E~) Or,,N(Ev)dE~

(3.11)

o

where p is the density of the medium, and $ and tr are given by (3.5) and (3.6). Thus, d W/dy = 82p(g/cm 3) (Ep/10 TeV) 3 ergs/cm,

(3.12)

which corresponds to an energy deposition of -200 ergs/cm in Earth for Ep = 10 TeV. We calculate the transverse (vertical) profile (x-dependence) of the energy deposition under conditions of good magnetic focusing. The pion production angle is smaller than the decay angle, so that the angular dispersion of the pion beam is neglected. Consider first a perfectly focused monoenergetic pion beam of energy E. This produces neutrinos uniformly distributed in energy in the range (1- m 2~,/m 2,,)E >- E~ >-0. The neutrino energy is correlated with the decay angle. At the small angles where all of the high-energy neutrinos are found we have 02

m 2,~ _

m 2~, EE~

m 2,~ E2 •

From this information, we deduce the differential neutrino flux projected onto the x-y plane:

(3.13)

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d2N 1 f~2 n.12 ~2 ,..2)-1/2 oc--1J ' " ~ ~ ' " ~2-'" ~ - ~-:-t dx dE~ E [ EE~ E 2 L2J

(3A4)

where L is the distance to the accelerator and x is the vertical distance to the center of the neutrino beam. This flux of neutrinos passing through the Earth produces the distribution of deposited energy If 2 ~ m 2 - m 2 m~ x2"[-1/2 -~ j E~dE~ [ EE~ E2 ~-~j ,

dW(E)

dx

(3.15)

where one factor of Ev reflects the linear dependence of o'~N(E~), and the other takes into account the energy deposition of each neutrino. The integration is carried out over the kinematically allowed range of neutrino energies to give

dW(E)/dx

oc E - 4 ( m 2 / E 2 + x 2 ] L 2 ) -7/2 "

(3.16)

This is the energy deposition profile produced by a neutrino beam originating from a perfectly collimated beam of monochromatic pions. Next, we determine the energy spectrum f(E) of collimated pions which reproduces the shape of the observed neutrino energy spectrum (3.1). A beam of pions of energy E yields a normalized neutrino spectrum given by

10(E'- Ev) S(E, E~) = -~

(3.17)

where O(x)= l for x>O and O(x)=O for x
f f(E) S(E, E~) dE ~ exp(Ed(Ev)) ,

(3.18)

0

and find

f(E) ocE exp- (E/E,,)

(3.19)

E,~ = rn,~(E~)/(m,~2 2 m 2,,).

(3.20)

From (3.16) and (3.19) we deduce the energy deposition due to a neutrino beam with the correct energy distribution (3.1) generated by a well focused pion beam: eo

dW/dx oc f f ( E ) ~ x ( E dE. 0

(3.21)

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A. De Rzijula et al., Neutrino exploration of the Earth

This integral may be re-expressed as d W / d x oc ~ ~" e-C (1 + A2~'2)-7/2 dsr

(3.22)

0

where (3.23)

,~ = xE,,/Lm~,.

Equation (3.22) is recognized to be a Struve function. It is plotted in fig. 3.2 as a solid line. The right-hand side of (3.22) is well approximated by the expression 24/(1 + (10A)2),

(3.24)

as is shown by the dashed curve in fig. 3.2. We adopt this approximation for the sake of analytic simplicity. Finally, we gtve our result for differential energy deposition of the neutrino beam of the proposed facility with perfect pion focusing: 25

I

I

I

d W/d X

2(3

l

I

0,1

I

0.2

I

0.3

X

I

Fig. 3.2. Profile of energy deposition due to neutrino interactions produced by a focused pion beam. The abscissa is given by eq. (3.23). The solid line is the exact expression eq. (3.22), while the dotted line is our simple approximation eq. (3.24). The vertical unit is arbitrary.

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d W/dx dy = g(x ) d W/dy

(3.25)

where d W/dy is the energy deposition along the beam direction as given by (3.12) and g(x) is a properly normalized version of (3.24) giving the transverse profile of the energy deposition 1 1 g(x) - 7to" 1 + (x/tr) 2

(3.26)

with oo

f g(x) dx = 1

(3.27)

x/o-= 10A.

(3.28)

and

The effective radius of the region of energy deposition is o" = 0.1 Lm,dE,~,

(3.29)

with E,, given by (3.20). We obtain the half-width at half-maximum of the energy deposition O" ~ - - ~ "-

2 tm,~mj,2

where successive parenthetical levels utilize eqs. (3.29), (3.20) and (3.4). More succinctly we write cr

=

(10.8 meters)

L {10 TeV'~ (100-0-km) \ E p ,/"

(3.31)

The primary results of this section are: eq. (3.12) for the differential energy deposition along the beam direction, eq. (3.25) for its transversely projected profile, and eq. (3.31) for the transverse radius of the energy deposition. These results are needed to compute the magnitude and spectral distribution of the neutrino-induced acoustic signal.

4. Sound generation by particles interacting ,with matter 4.1. Possible mechanisms The collision of a high-energy particle, such as a neutrino, with an atomic nucleus in matter produces a forward-moving shower of many charged and neutral particles. The shower develops and dies as the charged particles in it ionize the medium, and as the neutral ones (mainly pions) decay to produce

A. De Rt~jula et al., Neutrino exploration of the Earth

359

additional ionizing radiation. In consequence, the energy of the original particle is deposited as a narrow cone of ionization. This sudden deposition of energy produces an acoustic signal. The generation of sound by beams of high-energy particles moving through liquid media has been well studied both experimentally and theoretically. A recent motivation for these studies is the proposed DUMAND project [6]. A version of this project would be an attempt to detect extremely high energy cosmic-ray neutrinos with a very large array of underwater microphones. Several mechanisms have been proposed to explain how part of the original particle's energy ends up in the form of sound. (i) The implosion of microbubbles formed at the ionization centers along particle tracks. This phenomenon, presumably relevant only to liquids or to solids made plastic under strong pressure, is known not to contribute significantly to sound generation in liquids. Sound generated by this mechanism would depend on pressure (bubble size) and on the ionic content of the medium (density of nucleation sites). Such effects have not been observed in liquids exposed to particle beams, but may have been observed in the case of laser beams [7]. (ii) Molecular dissociation and ion mobility in the high electric fields produced by ionizing particles [8]. This mechanism predicts strongly enhanced sound production in certain liquids, like CCL. These effects have not been observed. However, mechanisms (i) and (ii) may be relevant to sound production in solids. (iii) The thermoacoustic process of sudden local heating produced by the ionizing tracks [9]. A theory based upon this simple process alone gives a correct description of the sound produced by particle beams traversing liquid targets. We shall examine this theory in detail. The comparison of theory and experiment for solid targets is inconclusive. Sound generation has been observed in several experiments, but quantitative conclusions are not easy to draw.

4.2. The thermoacoustic model

This model has been developed by Askarian, Dolgoshein [7, 9], Bowen [10] and Learned [11]. Its predictions have been checked in liquid targets by Sulak et al. [12]. We present a brief description of the model in the "time domain" (as opposed to the "frequency domain"). This is best suited to our purposes and follows the work of Learned. We are concerned with acoustic frequencies so low that absorption (at least, in a homogeneous medium) may be neglected. We return later to the question of losses due to reflections within a layered medium. The local heating of a medium by an ionizing particle is ultimately due to the 6-rays (short electron tracks) that the particle produces in its voyage. This process is instantaneous on the scale of thermal diffusion and sound propagation. Assume, as the data will justify a posteriori, that no nonlinear effects, like shock waves, play a role. Let the sound wave be described by its pressure amplitude p(r, t) and let c be the sound velocity, K be the volume coefficient of thermal expansion (with the dimensions of inverse degrees) and Cp be the heat capacity of the medium, or specific heat at constant pressure (i.e., calories per degree and gram). Let E(x, t)d3x dt denote the energy deposition within the medium. For longitudinal (irrotational) waves of velocity c, one must then solve the wave equation [13] (c2W_ 02/c9t2)p =

Kc 2 1 (1 + o-) OE Cp 3 ( 1 - o ' ) Ot "

(4.1)

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A. De Rfijula et al., Neutrino exploration of the Earth

The solution to (4.1) with an instantaneous point-like source E = Eo 6(r) 5(0

(4.2)

is a spherically symmetric infinitely narrow bipolar pulse

p(r, t) = gc2E° 1 (1 + tr) 6'(r - ct)

(4.3)

47rrCp 3 (1 - or)

where 6' is the derivative of a 6 function. The expression ~(1 + tr)/(1- tr), depending upon Poisson's ratio ~r, is generally near to but somewhat smaller than one. Notice that the "figure of merit" of a given material

Kc2 = __7_Y A =47rCp 47r

(4.4)

is a dimensionless quantity. Multiplied by 47r, it is simply Grueneisen's parameter y. The values of A for various materials are given in table 1. The figure of merit is largest for rock salt, and is considerably smaller for other materials such as are found in the Earth's crust. For purposes of geological survey, we must know the parameters of merit for composite materials at conditions that apply at depths of one or more kilometers. We are unable to take into account the effects of composite structure, high temperature, high pressure, and anisotropic stress. However, it is known that the velocity of sound increases significantly with depth [14] and that stressed material produces an enhanced thermoacoustic signal [15]. For purposes of acoustic neutrino surveying, the figure of merit may be considerably larger than is indicated in table 1. An advantage of working in the time domain, as emphasized by Learned, is that it is trivial to take into account the effects of a source that is distributed in space and time, like an interaction shower, the ensemble of many interaction showers, or a succession of interactions spread over the beam spill time of an accelerator. The pressure pulse is then a simple convolution of E(x, t) with the elementary pulse (4.3):

p(r, t) = A f d3x dt' E(x, tr- xlt') 6,(i r - x l - c ( t - t'))

(4.5)

Table 1 Thermal properties of various materials

Material

Cp (cal/g°C)

104K (I/°C)

c (km/s)

A

Rock salt Marble Granite Petroleum Ice (0*C) Brick Natural gas Water (20°C)

0,21 0.21 0.20 0.50 0.49 0.20 0.49 1.00

1.2 0.7 0.3 10.0 1.5 0.3 40.0 2.0

4.7 3.8 6.0 1.4 3.2 3.7 0.5 1.5

0.25 0.09 0.10 0.07 0.06 0.04 0.04 0.01

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361

We will be interested in cases where the energy deposition time (beam spill) is negligible relative to the sound travel time across the transverse dimensions of the ionizing showers or shower ensembles. In this approximation E(x, t) = d(x) 6(0, with the pulse occurring at time zero, and

p(r, t) = A f d3x Ir - xl-ld(x)

8'(Ir- xl- ct) .

(4.6)

The meaning of (4.6) is best illustrated in a one-dimensional example. Let the energy deposition function be a Gaussian and the total energy deposited be E0: d(x)=

Eo e_X2/=2

(4.7)

Choose the size of the deposition region o" to be negligible compared to the distance at which the pressure is measured, r ,> o'. Then, the pressure is

p(r, t ) - 2AEo ( r - ct] e_(,_c,~,=2"

(4.8)

The Fourier transform of p(r, t) is #(r, t o ) - to e -t'°/~°)~

(4.9)

where the characteristic frequency and wavelength are

tOo= 2c/tr ;

Ao = mr.

(4.10)

The signal has a broad spectrum peaked at a wavelength characteristic of the size of the region in which the energy is deposited. In the case of neutrino surveying, the role of this parameter will be played by the radius of the neutrino beam as given by eq. (3.31). In the preceding simple example, the energy deposition was assumed to be continuous and Gaussian. In actual practice, the energy deposition is in the form of tracks of ionization due to the charged particles in the many showers produced by the particle beam. We argue that the thermoacoustic signal does not depend essentially upon this fine structure of the energy deposition, but only upon the averaged energy deposition. The intended neutrino survey beam has a radius - 1 0 meters. Within the beam profile, there are -105 individual showers per pulse. Each of these has a radius of order one meter and a length of several meters. It follows that the individual showers overlap sufficiently to produce a smooth energy deposition over a scale of centimeters. In the calculation of the thermoacoustic radiation from such a source, we shall treat the energy deposition as a smooth function. This is a valid approximation for sound waves longer than a few centimeters, which includes all frequencies of relevance to seismic prospecting.

4.3. Experimental tests of the thermoacoustic model Sulak et al. [12] have conducted a series of experiments to observe the sound generated by beams of

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362

protons of various energies traversing liquids. We summarize this work to give an idea of how well the phenomenon is understood in liquids, and we comment briefly on the critical but poorly studied question of sound generation in solids. Further experimental work on sound generation by particles traversing inhomogeneous solids (such as oil, gas, or water bearing rock at high pressure) is mandatory. Many of the consequences of the thermoacoustic model have been tested by experiment. There is agreement between experiment and theory to a precision of about 15%. The most significant results were obtained with beam-spill times shorter than the transit time of sound waves across the transverse size of the proton beam. The following predictions of the thermoacoustic model have been verified: (a) The acoustic signal is observed to be a bipolar pulse, as given by eq. (4.8). Other experiments have been done with a spill time longer than the sound transit time across the energy deposition region. The signal is observed to be the convolution of the bipolar pulse with the function defining the beam profile in time, in accordance with eq. (4.5). (b) The period of the bipolar pulse depends linearly upon the beam diameter, as in eq. (4.10). (c) The frequency spectrum of the acoustic pulse agrees with eq. (4.9). (d) The observed acoustic pressure depends linearly upon the amount of energy deposited. (e) In various liquids, the magnitude of the acoustic signal is roughly in agreement with the predictions of the thermoacoustic model. This indicates that mechanisms other than thermal expansion are not significant. (f) The dependence of the acoustic pressure amplitude on the figure of merit A (see eq. (4.4)) has been checked in water, olive oil, isopropanol , acetone, and C C l 4. (g) The acoustic signal is independent of pressure and ion concentration in water. (h) Accurate measurements of sound production by ionizing radiation have been performed on water. The results indicate several small departures from the thermoacoustic model. The absolute magnitude of the acoustic signal measured at 20°C is about 15% smaller than is expected. Moreover, the dependence of the acoustic signal upon water temperature was studied. In the thermoacoustic model, a null signal is expected at 4°C where the coefficient of thermal expansion of water vanishes. Such a null signal is seen, but it appears at a temperature of 6.0-0.2°C. Aside from this displacement, the temperature dependence of the signal is as expected. In the succeeding paragraph, we offer a modification of the thermoacoustic model which may explain these discrepancies. The point is that the energy deposition is initially in the form of ionization, rather than heat. Since ionic volumes are not in general equal to molecular volumes, the ionization will produce an immediate strain in the medium preceding thermal expansion. This can be accounted for by means of an additional ionization-related contribution to the expansion coefficient [16],

INa where I is the ionization energy of the material (12 eV/molecule, for water) and (NA/M)is the number of molecules per gram. The parameter 8 is a measure of the relative ionic and molecular volumes 8 = ( V i - V,.)/Vm

which, for water, is expected to be negative. For water, we obtain AK = 7 x 10-58. The value V,, - 2 Vi would explain the observed anomalies. Further experimental work is necessary to justify this approach, and to determine whether volume-changing effects due to ionization are relevant to the production of an acoustic signal by the neutrino beam.

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363

To summarize, experiments done in the U.S.A. confirm the thermoacoustic model to an accuracy of 15%. For water, this has been established at temperatures of 0-50°C and at pressure of 2 × 10-2 to 102 bar. However, some experiments done in the Soviet Union [17] are in disagreement with the American experiments. They report sound signals considerably larger than expected, and they find evidence for sound production by other mechanisms in addition to what is generated thermoacoustically. Our present knowledge of sound generation by particle beams in solids is negligible, compared with the situation for liquids. Pioneering work in the U.S.A. was conducted by Hofstadter's colleagues with electron beams exciting the resonant modes of metal cylinders [18]. The authors conclude "the results seem to agree with a 'hot rod' model". On the other hand, experiments at Brookhaven National Laboratory with proton beams on salt gave sound signals smaller than expected [19]. The authors believe "this is largely explained by the attenuation due to impedance mismatches". Clearly much remains to be done to understand sound generation in solids by energetic particle beams. 4.4. The sonic neutrino antenna

We are interested in the sound pressure signal produced at a point at or near the Earth's surface by a neutrino beam travelling underground at depth R, as in fig. 4.1a. Let o', as in eq. (3.31), be the characteristic vertical dimension of the region in which the beam interactions deposit energy. The depth of the sound-emitting region ranges in the domain Ix - R [ - tr, its length along the beam in the domain GEOPHONE ARRAY

(o)

GEOPHONE .

.

.

.

.

.

1 BEAM

y L dx

5_/_

I

j,

--#---I2o"

(b) Fig. 4.1. (a) The neutrino beam is shown traversing the Earth. At the site of interest, its radial dimension is tr and its depth is R. (b) In this detailed view, the geometry relevant to the computation of the surface pressure pulse is illustrated.

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A. De R~jula et al., Neutrino exploration o/the Earth

- ~ < y < ~, and its width in the domain Izl - tr. Let r be the distance from an elementary sound-emitting point to a microphone placed at or near the Earth's surface at the origin of the coordinate system. In practice, we envisage situations for which R >>tr. Thus, the effects of the beam width in the z direction are negligible [O(o-2/R2)] in the calculation of r. The problem is two-dimensional and it suffices to project the radial energy deposition of the beam onto a plane defined by the beam axis and the microphones as we have done in eq. (3.26). From that result, and from the magnitude of the energy deposition of eq. (3.12), we write E~ 3 __p___ dW = 8 2 [ 1 0 T e V ] [g/cm3] [c_~] rr1 1 + (x/tr) 1 2 dx dy

(4.11)

or = 1080 cm [ 1 0 L k m ] [10 TeV] I_ Ep J"

(4.12)

Here, as usual, p is the Earth density, Ep the accelerator energy, tr the characteristic beam dimension, L the distance to the accelerator, and d W/dx dy is given in ergs/cm 2. The elementary pressure pulse (in a uniform, nonabsorptive medium) produced at the microphone position by the instantaneous (t = 0) heating of the "volume" dx dy (see eqs. (4.3) and 4.4)) is:

dp2/dx dy = A r -~ 8'(r - ct) d W/dx dy.

(4.13)

Let the angle 0 be the inclination of the line from this volume element to the microphone, as shown in fig. 4.1b. The total pressure pulse is p = f dx d y A r -1 8 ' ( r - ct) dW/dx dy

(4.14)

which becomes, with the insertion of (4.11), ~r/2

dW A

P=dy

f 2do f 0

dr 8'(r - ct) 1 ,~ (l+(rcosO_R)2/o.2)

(4.15)

--oo

where d W/dy is given by eq. (3.12). Introduce the dimensionless parameters

B = R/o" >>1

y = (ct - R)/tr,

and

(4.16)

and perform the r-integration to obtain p = 4(d W/dy) A R -1/2 tr -3/2 I(B, y)

(4.17)

where the dimensionless function I is given by ¢r/2

1 B1/2 ~yy d f dO {1 + B2[(1 + y/B) cos 0 - 112}-1 . I(B, y) = - ~-~ 0

(4.18)

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365

We are interested in values of I(B, y) at the times ct = R + O(o'), for which the parameter y/B is of order B -1 and certainly small. In this time domain, the integral in (4.18) is dominated by small angles for which the approximation cos 0 = 1-02[2 is adequate. We deduce the result that I(B, y) is independent of B in this time domain:

I(B, y) ~ I ( y ) -

xdf

27r dy

dz [1+ ( y -

Z2/2)21-1

.

(4.19)

0

This integration may be performed, and yields (1 - y2 _ yX/1 + y2) I(Y) = 8(1 + y2)3/2 (y + X/i-+" y2)m"

(4.20)

Equations (4.17) and (4.20) are our result for the pressure signal at the surface geophone due to the linear sonic neutrino antenna at a distance R below. A few simple properties of this expression are: (1) The magnitude of the sonic amplitude depends upon g -1/2 a s may be anticipated for a linear antenna. This is to be contrasted with the R -1 dependence of a signal arising from a localized sound source at depth. The major part of the signal is generated by a section of the neutrino beam of length - R . The weak dependence of the signal upon depth implies that our surveying procedure, if feasible at any depth, is feasible at great depth. (2) The magnitude of the sonic signal depends sensitively upon the energy of the primary proton beam, and hence upon the size (and cost) of the accelerator facility. Besides the explicit dependence upon Ep in (4.17), there is an implicit dependence upon the beam width tr - Eg 1. Overall, the pressure signal depends upon Ep4.5. A factor of two in accelerator size is worth a factor of 23 in signal amplitude! (3) The signal is a bipolar pulse with a characteristic period of tr/c, independent of depth R. Thus, the dominant acoustic frequency is determined by the sound transit time across the neutrino beam. Measurement of the shape or spectral form of the acoustic signal can determine the local sound velocity at depth. (4) The time interval between the essentially instantaneous neutrino pulse and the arrival of the acoustic pulse can be measured as a function of depth at a given site. This provides an independent determination of the vertical profile of the local sound velocity. (5) The magnitude of the sonic signal depends upon the nature of the medium through which the neutrinos pass. The signal is proportional to pA, a combination of physical properties. This parameter can vary significantly in different media, and can perhaps distinguish between rock and oil, gas, or water bearing strata. (6) In fig. 4.2, we illustrate I(y) as given by eq. (4.20). The bipolar pulse is seen to fall off very rapidly for times much less than R/o, as it must for reasons of causality. The fall-off for times larger than R/o, is slower because of the contributions from distant parts of the neutrino-antenna. (7) In fig. 4.3, we show the contributions to (4.18) with B = 10 from the various angular intervals. The wider is the angle, the later is the arrival time, the wider is the bipolar pulse, as expected from geometrical considerations. The bulk of the signal comes from the angular region [01 < 20°, since the other contributions interfere destructively. A single microphone "listens" to a section of the neutrino beam of an effective length 2 (sin 20°)R ~ 0.4R. Let us now consider the order of magnitude of the acoustic signal. From fig. 4.2, we see that

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A. De Rtijula et al., Neutrino exploration of the Earth

0.14 0.12

I(y)

0.10

0.08 0,06 0.041 0.02 0

I

I

0

-5

I

'

I

10

y

-0.02 -0.04

-o,01 -o,1(

Fig. 4.2. The time dependence of the pressure pulse as given by eq. (4.20) with y = (ct- R)/~r.

5 a5 0.05

~ ....'"''-,. •

h

35

:

I(lO, y)

11 "

'¢~----T

-3

.....

-2

r ....

-I

',

~'k

i/

~

~

I".,"

I

i

I

"

t\

2 ~

%

t

~

"

"

tL

\

t

5

•"

.."

1 / i / / "

-0.05

Fig. 4.3. Contributions to eq. (4.18) from various angular intervals, with B = 10. The curve labeled 5 is for 0 < 10° < 101<2if', etc.

101<

10°, the curve labeled 15 is for

(/max -- Imin)/2 ~ 0.11, and from (4.17) A p =_ (pmax - p m i . ) / 2 ~ 0 . 4 4 ( d W / d y )

A tr-3/2 R -'/2 .

Substituting the value for or given by eq. (4.12), and the value of dW/dy of eq. (3.12), we obtain

(4.21)

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A. De Rgt/ula et aL, Neutrino exploration of the Earth

__g___ ( 10Ep Ap= 3"2x lO-6A (g/cm3) TeV}]9/z(lOO~km)3/z(J---~)

(4.22)

for the magnitude of the pressure signal in dynes/cm 2. Consider, for example, a medium with the acoustic properties of rock-salt: A = 0.25, p = 2.2 g/cm 3. Let the machine energy Ep be 10 TeV, the machine to microphone distance L be 1000 km, and the depth R of the beam be 1 km. We obtain a pressure signal Ap of 1.8x 10-6dynes/cm 2. For a 20TeV accelerator, Ap~-4.1 x 10-5 dynes/cm z. To ascertain whether such a small signal can be disentangled from the pervasive background of the Earth's seismic activity, we must turn our attention to the frequency spectrum of the signal. The spectral distribution of the acoustic signal is given by the Fourier transform of which is computed from (4.19) to be

p(t),

/~(~o)- 0),/2 e-,O/~o

(4.23)

c/o.

where ~Oo= Negligible error is incurred by our use of the approximation (4.19) rather than the exact form (4.18). The maximum value of/~(w) is at OJo/2, and

AO) = [(0) 2) --

(0)) = 1.50OJo] (t°z) = 3"75¢°°21 " (0))211,2 = 1.22OJo

(4.24)

The characteristic frequency in Hertz is given by )Co= °~---2°- c 27r 2fro""

(4.25)

From (4.12), (4.24) and (4.25) we obtain c

/¢,

( f ) = 23(1 km/sec)(100~___km)(10 TeV)"

(4.26)

For a typical situation (L = 1000 kin, Ep = 10 TeV, c = 4.74 km/sec as in rock salt), we find a mean frequency (f) = 109 Hz and a band width Af = 89 Hz.

5. Background seismic noise The acoustic signal induced by a single short machine pulse of neutrinos has a wide band frequency spectrum extending from a few Hz to a few hundred Hz. In this frequency region, the principal source of bakground is the ambient Earth motions or seismic noise. It is necessary to show that the neutrino-generated signal can be extracted from the seismic noise. The motion of the Earth's surface, in the frequency range of interest, is a continuous stochastic process but for transient microseisms or earthquakes. Its level depends very much upon location, proximity to rivers or surf, local wind conditions, season of the year, and local human activities. Most of the background at the surface is in the form of surface waves which are often directional and have a

368

A. De Rt~jula et al., Neutrino exploration of the Earth

velocity of propagation much slower than volume acoustic waves. Such surface waves may be suppressed with a phased array of geophones, and need not constitute a serious source of background. It is important to know how much of the surface noise consists of harmless surface waves, and to know the angular distribution and degree of coherence of the remainder. Such data is available at low frequencies (smaller than 5 Hz) from the Large Aperture Seismic Array [20]. Analysis of these data shows that in the 0.1->0.6 Hz interval the seismic noise consists primarily of coherent propagating noise, in the form of surface Rayleigh and Love waves, and body waves from a variety of localized sources. In the 0.6-->2.0 Hz band, on the other hand, the noise consists primarily of nonpropagating, incoherent noise, believed to be caused by local effects, such as atmospheric pressure fluctuations and wind. However, at the higher frequencies which interest us, all that we have are data obtained by means of a single detector. The analysis of the coherence and directionality of these data, based on evidence furnished by orbital motion calculations, is less reliable than the results obtainable with an array of geophones. Nonetheless, the conclusion reached by Frantti [21], from single directional-seismometer data, is that in the 2-~ 20 Hz interval a substantial portion of the noise originates in the Earth's surface and follows a path at, or near, the surface. Similar conclusions have been reached by Akamatu and Wilson [22], in the 1 -~ 100 Hz domain. Studies of seismic noise with geophone arrays in the 1 -~ 200 Hz frequency range are mandatory, if geological surveying via neutrino-produced acoustic signals is to be seriously pursued. This is because, with the available data, we cannot confidently take into account the noise suppression that may be feasible with an array of antennae capable of filtering out coherent and directional noise sources or surface waves. The considerations of the rest of this section, based on the worst-case hypothesis that the seismic noise is incoherent, are no doubt unduly pessimistic. The continuous line in fig. 5.1a shows the spectrum of the mean-square surface displacement (a 2) as a

I

I

I

I

L

I

120

10.5

100

10.7

80

I0 -°

60

10"u

I0"11

40

lO-,a

I0"la

20

10-15

I0 "is

0

lO-rr

10"1"1' -20

~_

0

' \g '

10-7

_'..

"i- 10"o

V

I

I

10.3

10-o N

I

GROUND

GROUND

,,\

-

~'.._ I

I

0.01 0.1

(a)

I

1

I

I

0.01 0.1

I

1

10

I

I

I

SEA

3~

-J u.I

_m

\ ,,,, , ,

%%°.o°° I

I

I

io

lo2

lo 3

I Io 4

f

",, 10 100 t

(b)

(c)

Fig. 5.1. (a) Spectrum of mean-square surface displacement per Hz as a function of frequency. The continuous curve is from Fix, whilst the dotted curves correspond to observations by Bruce and Oliver at noisy (I), average (II), and quiet (III) location. (b) Power-law fits to Bruce and Oliver data at average (II') and quiet (III') locations for frequencies greater than 0.1 Hz. Fix data are shown for reference. (e) Noise levels at shallow depths in the sea. Curves I and II correspond to maximum and minimum prevailing noise. The dotted line shows thermal noise. The dashed lines are extrapolations of Ir and III' in (b).

A. De R~jula et al., Neutrino exploration of the Earth

369

function of the frequency interval

d(a2)ldf

in cm2/Hz

(5.1)

as measured by Fix [23], at a very quiet location 130 m underground in Las Cruces, NM. The three curves labelled I, II, III are from data gathered by Bruce and Oliver [24]. They correspond, respectively, to noisy, average, or quiet surface situations. The quiet surface measurements of Bruce and Oliver agree with the Fix measurement at depth. We assume that these correspond to the true background noise, with surface waves subtracted, and we use this data for our signal-to-noise estimates. An "average" site is about one order of magnitude noisier in sonic amplitude than a "quiet" site. In fig. 5.1b we show again the Fix data, and a power-law fit at average and quiet surface sites. For the quiet location, the fit is

d(a2)/df

= 10-14(Hz/f)

4.4

cm2/Hz.

(5.2)

In fig. 5.1c, we show observations of noise levels at shallow depths in the sea [25]. These are of interest in view of possible applications of our methods to the geological exploration of off-shore sites, and because they extend to higher frequencies. The curves labelled I and II correspond to maximal and minimal prevailing noise levels. What is plotted is (noise level/Hz) in "decibels" = 10 loglo d

2) [2 x 10-4 dynes/cm2]

(5.3)

where d(p 2) is the mean-squared sonic pressure in the frequency interval dr. The dotted line is thermal noise. The dashed lines are the extrapolations of the fits of fig. 5.1b converted to units appropriate to eq. (5.3),

d(P 2) = (27rpc) 2

df

[)a(a2)]

(5.4)

where p and c are the density and sound velocity in water. The fall-off of the noise levels in the sea as a function of frequency is seen to follow approximately the same power behavior as in the ground, up to a few hundred Hz. Noise levels at sea decrease exponentially with depth and are 5-10 times smaller in amplitude at a depth of 3 km than at the sea surface in the relevant frequency domain [26]. We now estimate the signal-to-noise ratio for the acoustic signal produced by the neutrino beam at the Earth's surface. Since our signal is a wide band signal, we define a root-mean-square background noise in a frequency window f2 > f > fl: h

''2

(5.5) fl

Using (5.2), (5.4) and (5.5), we obtain

___e__

c

p(f,,f2) = 3.4X 10-z (g/cm3) ( ~ ) \ - f - T ]

[1_ \fz' J'a

(5.6)

A. De R(~]ula et al., Neutrino exploration of the Earth

370

for the rms background noise in dynes/cm 2. The window (f2, f~) should include most of the signal whose average frequency (f) and band width are given by (4.23) and (4.25). The signal is given by Ap in (4.22), and its mean frequency (f) in (4.26). In estimating the signal-to-noise ratio R, we put fl = (f)/2 and neglect f~/f2, to find

Ap = R =P(f,,f2) 5.2×

10-4A

(~)°3

( Ep "~52(lOOO_km'~Z2(k_~f/2. \10TeV]

\

L

(5.7)

}

In rock salt, with A = 0.25 and c = 4.74 km/sec, and the remaining parentheses set equal to unity, the signal-to-noise ratio is R = 8.2 × 10-5. With a larger 20 TeV accelerator, R increases to 3 x 10-3. Thus far, we have neglected acoustic attenuation in the Earth. In a homogeneous solid, absorption of sound in the 100 Hz range is significant over distances of a few km. However, there will be partial reflections and scattering due to inhomogeneities which are comparable or larger than the characteristic wavelength of the signal. Because the ratios of acoustic impedance of the various layers are usually near unity, we do not anticipate attenuation by this mechanism to exceed an order of magnitude in sonic pressure. After all, the 1-100 Hz frequency domain is successfully employed by conventional reflective seismological surveying procedures using explosives or mobile vibrators. The signal-to-noise ratio at a single microphone from a single pulse of neutrinos is very small, of order 10 -3 to 10 -s. Implementation of our method of geological surveying requires the use of many microphones and the accumulation of data from many machine bursts. We proceed to discuss some of the improvements in signal-to-noise ratio that may be anticipated. It takes a significant time to accelerate protons to their maximum energy in a large proton synchotron. The repetition rate for such a machine is linear in Ep and approximately equal to [2, 5] Rep. rate ~- 1 minute (Ep/10 TeV).

(5.8)

The acoustic signals reach the detectors at precisely known time intervals, giving rise to a signal which increases linearly in amplitude with the number of bursts. The noise amplitude on the other hand, is stochastic and increases with the square root of the number of bursts. Since microphones can be displayed over many kilometers of the neutrino antenna, it is practicable to run the beam in a fixed orientation for several days. The statistical gain in signal/noise amplitude in ND days is

S(No) ~- 38X/N-DD(10 TeV/Ep) '/2 .

(5.9)

For ND = 7, Ep = 10 TeV, S = 100, we obtain two orders of magnitude improvement in the signal-tonoise ratio. Note that the signals last for a fraction of a second and are spaced minutes apart. Most of the time, the microphone array can be used to analyze the background noise, or to gather complementary information by means of conventional reflective seismology. We contemplate the detection of the sonic neutrino signal with an array of microphones deployed on the surface along the direction of the underground neutrino beam, as in fig. 5.2. For uncorrelated noise, the improvement in signal/noise with NM microphones is of the order of N ~ 2. Should the noise be correlated surface noise in the frequency interval of interest, the improvement may be much greater. A microphone antenna array like that in fig. 5.2 may be used to focus on signals from the angular domain transverse to the beam direction (x in the figure) and/or to improve on the spatial resolution in the beam direction (y in the figure).

A. De R~jula et al., Neutrino exploration of the Earth

371

"~-~ o 00°0°°3°0°0 c t ~ ' 0 ~ " ~ ;~o°O o o o o o o o N

0

OoOOoOooOo

O-OOnO 0

0 0 0 0 0

0 0 0

BEA~ 2o

Z

Fig. 5.2. Microphone array contemplated in the GENIUS Project.

The sonic neutrino signals are bipolar pulses whose expected characteristics are roughly known a priori. For signals of known shape, it is possible to establish the presence of a signal within a very large noise background, a fact that is successfully exploited in seismic research with vibrator-induced signals. Other known methods of signal/noise enhancement conventionally used in seismography, like time varying single pass filtering or the bunching or chirping of the signal could also be useful for GENIUS. Finally, our calculations are based upon a neutrino beam whose energy spectrum is not optimized for seismic research. In the following paragraphs, we give a simple example of beam modification leading to an improvement of the signal/noise ratio. Our calculations of the signal/noise ratio are based upon an optimally focused pion beam whose energy spectrum, extrapolated from existing facilities, is given by eq. (3.19). We now examine the effect upon the signal and the noise that results from removal of the lower energy pions from thebeam. Let us consider an idealized pion focusing system which perfectly focuses pions with energies greater than AE~ and excludes from the beam pions with lesser energy. The parameter E,~, defined in eq. (3.20), is half of the mean pion energy. Truncation of the pion beam leads to a modified and reduced neutrino flux which may be computed from eqs. (3.17) and (3.18). This is inserted into eq. (3.11) to obtain the effect upon the rate of energy deposition along the neutrino beam:

d W/dy[A] = e-A(1 + A + A2/2 + A3/6) d W/dy[O].

(5.10)

Another consequence of pion energy truncation is a reduction of the size of the region of energy deposition. The angular dispersion of the neutrino beam results primarily from the process of pion decay: the greater the pion energy, the less is the dispersion. Elimination of the lower energy pions results in a smaller value of o-, the effective width of the energy deposition as given by eq. (3.29). This effect is computed from eq. (3.22), with ~"constrained to be greater than A. We find

A. De R~/ula et al., Neutrino exploration of the Earth

372

1+ A ]1/2 o-[A] = 1 + A ~JA272+ A~/3J o-[0].

(5.11)

It can be seen from eq. (4.17) that the magnitude of the acoustic signal depends upon the product o--3/2 dW/dy, and from eq. (5.6) that the noise depends upon o-°7. Thus, we find Signal[A] = e-A(1 + A + A2/2 + A3/6) L75 (1 + A) -°75 Signal[0]

(5.12)

Noise[A] = (1 + A) °35 (1 + A + A2/2 + A3/6) -°3~ Noise[0].

(5.13)

Both signal, noise, and their ratio are shown in fig. 5.3. Observe that an improvement in signal/noise ratio of a factor of 2.4 is obtained for a value of A of 3 to 4. It is seemingly paradoxical, yet true, that a reduction of the neutrino flux yields an increase of the signal (as well as a reduction of noise).

2.5

2.0

1.5

1.0 ~'--

~

N(A)IN(O)

"'"..

0.5

I 1

I 2

I 3

I 4

I 5

I 6

I 7

8

A Fig. 5.3. Normalized signal, noise and signal/noise for a pion beam that is defocused at energies below AE,,.

The optimisation of the signal/noise problem with all its many variables (proton energy, beam focusing, layout of microphone arrays, computer analysis of data and economic boundary conditions, etc.) is certainly a formidable task. A large enough accelerator, run for a long enough time, with a large enough geophone array will produce a meaningful and measurable signal. More detailed analysis is needed to translate "enough" into dollars and sense.

6. GENIUS versus other methods of seismic research

Geological exploration with neutrino induced underground sound could complement, rather than replace, conventional techniques for remote sensing of the underworld. For this reason we give a brief account of the conventional approach. For the sake of definiteness, and practical motivation, we

A. De Rtijula et al., Neutrino exploration of the Earth

373

concentrate on the example of seismic exploration for commercially useful oil and gas deposits. We borrow heavily from two excellent reviews by P.N.S. O'Brien [27]. A typical oil or gas deposit is shown in fig. 6.1 with the interesting material characteristically trapped under an impermeable dome and occupying some 20% of the dome rock volume. Known methods of exploration (other than drilling holes) cannot really detect the presence of oil or gas, but provide a vertical cross section of the layered structure. A dome in potentially oil-rich sedimentary rocks is a hint that may justify exploratory drilling. The most common method of land exploration consists in detonating explosives at the surface or a few meters underground and detecting the reflected waves from layer interfaces with surface geophones. At sea, a similar method is used, with explosives detonated close to the water surface and the reflections at the sea bottom and below detected by an array of hydrophones towed by the ship. The acoustic impedance contrast at the interfaces between layers are typically not very sharp, so that only a fraction of a percent of the signal is reflected upwards for detection. This is a disadvantage in the sense that it calls for the use of powerful explosions, and an advantage, in the sense that lots of power continues to move downwards toward deeper layers. The power per unit surface from a pointlike explosion decreases as R -2 in its downward voyage and the power reflected from an interface again decreases as R -2 in its upward voyage. Typical wavelengths of the useful signal are in the range of 50 to 100 meters. The method works because of the relative simplicity of formations of sedimentary rock which, but for the sought-for dome-like formations, consist of uniform and horizontal specularly reflecting strata. A disadvantage of the explosive method is that the shape of the signal is not known, so that the deconvolution needed to recover the reflection coefficients (acoustic impedance contrasts) between the different layers is not trivial. To obtain the shape of the signal from the data itself, one must assume that the distribution of reflection coefficients is white, random, stationary and deep. In land exploration this disadvantage can be overcome by the use of chirped vibrators, rather than explosives. (Here the signal, as in 5-50

km

P

SURFACE

HORIZONTAL SEDIMENTARY LAYERS

l-Skm

t

t

WATER, OIL AND GAS

t EP,NG U WA DS

Fig. 6,1. Typical oil or gas deposit,

t

t

t

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A. De R~jula et al., Neutrino exploration of the Earth

CHIRP radar, is a wave train with time-varying frequency). At sea one can measure the primary signal from an explosion or an "air gun" with a nearby sturdy hydrophone. Many simplifying assumptions are used in the analysis of reflection data. Among them: (1) The Earth is a fluid (shear waves are ignored). (2) Signals reflected more than once from deep layers are neglected, without good justification. Signals multiply reflected from superficial levels are identified and subtracted with considerable effort. (3) The reflecting interfaces are assumed unrealistically to have no dip. The most serious limitation of the standard method of reflective seismology is that it provides a picture of the underground in time, not in depth. To give a realistic cross sectional picture of the terrain the sound velocity as a function of depth must be assumed, a painful and dubious procedure accomplished by computer time consuming trial and error. About 800 seismic reflection crews operate in the "western world", gathering data at a rate of 3 x 1014 bits (year). We proceed to discuss the type of information that GENIUS could gather, which would be complementary and in several aspects superior to the information obtained by the conventional methods of geological exploration. As in section 5, we envisage the deployment of a surface array of detectors extending along the neutrino beam direction for as many kilometers or hundreds of kilometers as may be economically feasible. The beam would be shot at increasing depths in a vertical plane as in fig. 6.2a or in zigzagging downwards pattern as in fig. 6.2b, depending upon the relative difficulty of redirecting the neutrino beam horizontally or vertically. The time of passage of the burst of neutrinos can be precisely monitored at the accelerator since the neutrinos travel at the velocity of light. Thus the arrival time of the first signal at the microphones (o) SURFACE

® ® I

®

(b) SURFACE

/ @--.® z" ©-'@ ®

Fig. 6.2. Transverse profiles of neutrino beam deployment in GENIUS research, relevant to a mapping of sound velocities.

A. De Rdjula et al., Neutrino exploration of the Earth

375

precisely measures the average speed of sound from a certain depth. Multiple reflections are not a problem since they would typically give rise to delayed signals orders of magnitude smaller than the leading one. The simple detection of the signal, combined with a downward scan, would therefore directly provide a mapping of sound speed as a function of depth. An independent determination of the sound velocity at depth is provided by the time structure of the observed signal. The expected sonic signal is bipolar in nature, as shown in fig. 4.2. The width of the peaks (or the peak-to-peak delay time) is proportional to o/c, with or the known width of the beam and c the speed of sound at the sound source. GENIUS could provide a second contrast mapping of the underground material, beyond that of sound speed as a function of depth. Consider a simple situation, as depicted in fig. 6.3. Recall the expressions eqs. (4.2) and (4.4) for the primary pressure amplitude: (6. la)

z~p oc A p Kc 2

A -= 4~rG

(6.1b)

with p, c, K and Cp the density, sound speed, volume coefficient of thermal expansion and specific heat at constant pressure of the sound-generating medium. The measured sound pressure amplitudes at the positions A and B in the figure would be proportional to px ~ W12Axpl

(6.2a)

pa ~A2p2

(6.2b)

Wlzo~.

(6.2c)

2p2c2 P2C2 + P1¢1

where the subindices label the sound generating materials as in the figure, and W12is the transmission coefficient, that we have written for normal incidence, for simplicity of exposition. The ratio of observed

A ~PA

SURFACE

B IP8

Fig. 6.3. A profile of the neutrino beam in GENIUS, relevant to a mapping in terms of relative pressure signals.

376

A. De Rdjula et al., Neutrino exploration of the Earth

peak pressure amplitudes, therefore, gives a contrast map of the quantity

PA = Pa

2plc2

A_.__!1

(6.3)

p2C2q- plCl A2

whose boundaries should coincide with the independent velocity map. To summarize, the features of GENIUS that are superior to the conventional methods of seismic prospection are: (1) Depths are known, and need not be guessed with velocity trial functions. (2) Sound velocities are measured in two complementary ways. (3) Direct signals of known shape are used, thereby simplifying computer work and interpretation. (4) Two independent mappings can be obtained. (5) Many kilometers of land can be surveyed simultaneously with the beam in the same general direction. (6) The energy in the signal decreases with depth as R -1, as opposed to the R -4 power law in reflective seismology. On the other hand, the GENIUS procedure requires enormous capital and operating costs. Although the GENIUS project seems to be technically feasible, it is unclear to us whether it is at present economically sensible.

7. GEMINI: Geological Exploration with Muons Induced by Neutrino Interactions In Project GENIUS, a neutrino beam is used to implant an acoustic source at depth to serve as a probe of the nature of the subsurface medium. Project GEMINI is an alternative utilization of the neutrino beam which employs the highly-penetrating energetic muons which are produced by, and which accompany, the neutrino beam along its underground path. These muons are detected and counted at the point of emergence of the neutrino beam from the Earth. This technique can detect deposits of high-Z minerals at distances of thousands of kilometers from the accelerator and at depths of several hundred meters. Projects GENIUS and GEMINI are complementary utilizations of the same accelerator facility. The angle of emergence of the neutrino beam from the Earth is given by 0 = arcsin(L/D) where L is the distance along the beam to the accelerator and D is the Earth's diameter. When GEMINI is used to explore a region within several thousandki!emeters of t h e accelerator,_the neutrino_ decay tunnel must be precisely aimed at the site of interest. Its declination angle, which equals the angle of emergence of the neutrino beam from the Earth, is given by 0 - 4.5 ° (L/1000 km). The GEMINI mode is compatible with simultaneous implementation of GENIUS. Figure 7.1 shows the neutrino beam emerging from land at a shallow angle. The accompanying muons are being counted by an array of truck-mounted muon detectors, each probably consisting of layers of track chambers with an effective detection area of several square meters. Suppose that the neutrino beam intercepts a subterranean ore body lying a distance l "upstream" of the surface muon detector in the direction of the accelerator. We shall refer to ! as the "slant depth" of the ore body. An ore body is detectable by GEMINI only if its slant depth is not much greater than the mean range of the accompanying muons. For plausible accelerator energies, this range is several kilometers. The true depth of the ore body is given by I sin 0. Thus, for L = 1000 km, the sensitivity of

A. De R~jula et aL, Neutrino exploration of the Earth

377

(lO-3Om)

i/"I _

~

I z " !ex_. fJ

( (~ ~ l

EARTHSURFACE

I

(O to 200m)

Fig. 7.1. GEMINI's truck-mounted muon detectors.

GEMINI is limited to ore bodies not more than several hundred meters underground. On the other hand, GEMINI is very sensitive to the lateral extent of the ore body, which is generally a measure of its commercial significance. The effect of an ore body containing high-Z material is to cause a small reduction of the surface muon flux, perhaps by as little as a tenth of a percent. This is the signal being searched for by GEMINI. An array of muon detectors is required since the magnitude of each neutrino pulse cannot be monitored with great accuracy. What is important is the pattern of fluxes measured at many detectors, not the absolute muon flux at any one. The spatial resolution of the procedure is excellent in the directions perpendicular to the neutrino beam. In the direction along the beam, the spatial resolution is nil, but the magnitude of the signal is a measure of the lateral extent of the lode in slant depth. While GEMINI cannot distinguish between a large lode of copper or manganese and a smaller lode of lead or mercury, it is nonetheless a new and perhaps powerful method of remote surveying. It can be used for the discovery of new lodes, or for determining the extent of known ones. We must first compute the intensity of the neutrino beam as it approaches the muon detector at a distance L from the accelerator. In the approximation that the neutrinos arise from the decays of perfectly collimated pions with an energy spectrum f(E), we obtain

dNddE~ d A = L -2 f dE f(E) (EdEt,) 8(E - Ev - E~,)

(7.1)

where the energy of the muon in the decay zr-~/~ + v is kinematically determined

E 2= E ,2+ m E,, + p 2 - 2 p E v c o s a

(7.2)

with p (E 2 - m 2)1/2 the pion momentum. The neutrino is produced at the angle a relative to the pion momentum. If the muon detector is placed precisely at the beam axis, then the angle a must be put equal to zero. We shall assume that is the case. Insert eq. (3.19) for f(E) into eq. (7.1) with its normalization chosen to give the correct total neutrino flux given by eq. (3.5). Integration over pion energies then yields the result =

A. De R~jula et aL, Neutrino exploration o[ the Earth

378

F (E~) E 34 exp(-E,,/(E,,)) dNddE~ dA - 3!

(7.3)

where m2 1 2.5 1013 F = 3!(Ev) 2 ( m E _ m~)2L 2 7r TeV"

(7.4)

Notice that the central neutrino flux is much hotter than the total neutrino flux. On the beam axis the mean neutrino energy is 4(E~). The parameter F is the integrated central neutrino flux F = 2.4 x 109 (1000 km/L); (Ep/10 TeV) 2 neutrinos/m Eburst.

(7.5)

When one of the neutrinos in the beam interacts with an atomic nucleus, it produces a high-energy muon about 80% of the time by virtue of charged-current weak interactions. The remaining 20% of the neutrino interactions are of the neutral-current type. The production cross section of the muons is given by

dtr/dE, = 0.8 o'vs(E~) O(E~- E~,)/E~,

(7.6)

where E,, and E~ are the muon and neutrino energies, the total neutrino-nucleon cross section o'~N at high energy is given by eq. (3.6), and O(x)= 1 for positive argument, O(x)= 0 for negative argument. The flat energy distribution of the muons and the dependence of o'~, on energy are predictions of weak-interaction theory which are approximately verified by experiments at neutrino energies up to 0.5 TeV. There is every reason to believe the theoretical predictions up to neutrino energies of order 10 TeV. The muons are produced in the forward direction and they remain confined within the neutrino beam. Once produced, the muons suffer electromagnetic collisions with intervening atoms and are degraded in energy. The effects involved include ionization, pair production, bremsstrahlung, and nuclear collisions. We define R(E)= -dE/dx to be the average energy loss of the muon per unit length of its trajectory. An approximate formula for R(E) is obtained from experimental data and theoretical calculation [28]: R (E) ~ pro(1 +

BE)

Ro = 2.12 (MeV/cm) (2Z/A) B = 0.125 Z/TeV,

(7.7a) (7.7b)

(7.7c)

where p is the density relative to water of the medium through which the muons pass. Let us consider the muon flux ~bo(E~,,Ev) produced by a neutrino flux of unit strength and of energy Ev. It satisfies the differential equation

Oqbo(E~,,E~)lOx = R(E) O~po(E,,,Ev)IaE,, + pNA &r/dE,,

(7.8)

where NA is Avogadro's number. The first term on the r.h.s, takes into account the energy degradation of the muon beam, while t h e second term describes the production of new muons by the neutrinos.

A. De Rfqula et al., Neutrino exploration of the Earth

379

Within a few kilometers from the accelerator, and in a homogeneous medium, equilibrium is established between muon production and energy loss, so that O&o/OX= 0. The muon flux is then given by the monotone function Ev

&o(E,, E~) = f pNA (do-/dE)R-I(E) dE

(7.9)

E~

with do~dE given by eq. (7.6). The total muon flux is given by multiplication of &o by the neutrino flux and integration over neutrino energy,

dN,,/dE~ dA = f dEv ~bo(G, E~) dNddE, dA ,

(7.10)

with dNddE~ dA given by eq. (7.3) at the center of the neutrino beam. Detectors on the surface of the Earth count all emergent muons whatever their energy. Thus, we must compute the integrated muon flux, the integral of (7.10) over muon energies, the equilibrium number of muons per unit area and per burst, which accompany the neutrinos:

dN,,/dA -~ F (0.8NAO'~N/E~) B -2 Ro ~ [4B(E~) - ln(1 + 4B(E~))].

(7.11)

For a soil material with effective Z = 10, A = 20, and with the substitutions (Ev) = (18)-1Ep, trvN/Ev = 10 -35 cm2/TeV, we obtain

dN,ddA -~ 3.2 x 103 (t - tn(1 + t)) (Ep/10 TeV)3 (1000 km/L)2/m 2 burst

(7.12a)

t = 2.8 (Ep/10 TeV).

(7.12b)

At a distance from the accelerator of L = 1000 km, the muon flux of eq. (7.12) in muons per square meter per burst is

dN~,/dA =

0.1 at Ep= 20 Ep = 5000 Ep = 105 Ep =

1TeV 3 TeV 10 TeV 20 TeV.

(7.13)

Thus far, we have examined the muons produced in a homogeneous subsurface medium. We must compute the effect upon this flux of an intervening subterranean ore body. In the GEMINI project, the effect of the ore body is the signal of interest, while the background muon flux given by eq. (7.13) is the

noise.* As an idealized illustration, we consider a homogeneous medium with density p, neutrino scattering

* A simple detector may not distinguish pions from muons. In this case, there is a small correction to the noise, from primary and secondary pions produced sufficiently close to the surface to emerge from it. The correction is small, since the range of muons is orders of magnitude bigger than the range of pions.

380

A. De Rzijula et al., Neutrino exploration of the Earth

cross section o" and energy-loss function R. Within this medium is located an ore body with material parameters p', o-' and R'. Suppose that the neutrino beam intercepts the ore body at slant-depth (i.e., distance to the detector) given by l, and that the thickness of the ore body in slant-depth is hl. We must calculate the effect of the ore body upon the surface muon flux. In order to accomplish this, we must return to the differential equation, eq. (7.8), and to the muon production cross section, eq. (7.6), and perform the substitutions

po---, po- + (p' cr'- pa) 8(1 - x) At I R(E)--, R(E) + (R'(E)- R(E)) 8(1 - x) al J ¢o(E~,, Ev)--> ¢o(E~,, E,) + ¢~(E,,, E , x) At 0(1 - x)

(7.14)

At slant-depths greater than l, the muon flux has its equilibrium value, while at shallower depths ¢1 describes the perturbation due to the presence of the ore body. Integrating eq. (7.8) across the singularity at x = l, we obtain ¢,(E~, E~, Z) = e(E~,) NAp do/dE,,.

(7.15)

The dependence of 61 upon the nature of the ore body is contained in the multiplicative factor

e(E)= p'po" o" R' R "

(7.16)

The basis of the GEMINI project lies in the fact that e is large for ore bodies rich in high-Z atoms. Each term in eq. (7.16) depends upon the chemical composition of the ore body. It is an empirical fact that the neutrino--neutron cross section at high energy is about 50% higher than the neutrinoproton cross section. Thus, we may write for the average cross section o" - 1.5(A - Z)/A + Z/A, and hence

p'~r' = p'A 3 A ' - Z' po- pA' 3A - Z

(7.17)

where A, Z, A', Z' are the mean atomic weights and atomic numbers of the two media. Using eq. (7.7), we may similarly rewrite the second term in eq. (7.16) so as to obtain

e(E) = p'A [ 3 A ' - Z' oA' L 3 A - Z

Z' (1 + Z'E/8 TeV)] -Z (I+ ZE/8TeV) I"

(7.18)

Let us return to eq. (7.15) and integrate over the neutrino spectrum as given by eq. (7.3). The result

6(dN~,/dA dE~.) = f ~bl(E~,, E~,l) (dNJdE. dA) dE.

(7.19)

gives the perturbation of the muon flux caused by the ore body at depth. Carrying out the integration over neutrino energies we find

A. De Rfijula et al., Neutrino exploration of the Earth

381

6(dN'`/dA dE,,) = e Alp(O.8NAO',N/E,) F e -x (1 + x + x2/2+ x3/6)

(7.20)

where x = EJ(E,,). While eq. (7.20) does give the muon signal at slant]depth l, it does not yield the muon signal as observed at the detector. Only those "signal muons" whose range in Earth exceeds the slant-depth reach the surface detector. The surface muon signal is given by integration of eq. (7.20) over muon energies exceeding

E(t) = (exp(BRopZ)- 1)/B

(7.21)

where the energy-loss parameters B and Ro are defined in eq. (7.7). Taking p = 2.5, Z = 10, and A = 20 for typical Earth properties, we find

E(1) = 0.8 TeV[e °'66' - II,

(7.22)

where l is measured in kilometers. The surface muon signal is given by

Signal= f

6(dN'`/dAdE'`)dE'`.

(7.23)

E(t)

Our analysis is completed with the computation of the signal-to-noise ratio which is obtained from eqs. (7.23) and (7.11). This is the fractional change in the surface muon signal caused by the ore body: Signal . . . . (at) Noise

B(E.)

BRop Al (4B(E~) - In(1 + 4B(E~)) I(e)

(7.24)

where the integral I(e) is given by oe

I(e) = f dx e -x (1 + x + x2/2+ x3/6) e(x(E.))

(7.25)

Xl

with

x, = E(I)/(E~).

(7.26)

We proceed to examine the detectability of this signal for realistic ore deposits, and for various accelerator energies. For a measure of the extent of an ore deposit, we adopt as our basic unit "one kg/cm2'' of material in question deposited along the direction of the neutrino beam. For a horizontal layer of ore at a distance L = 1000 km from the accelerator, one kg/cm2 along the oblique slant-depth corresponds roughly to a lode of one ton per square meter of land area. The S/N ratio resulting from a deposit of one kg/cm2 of a material of intrinsic density p' is obtained from eq. (7.24) by the replacement of Al by 10 meters/p'. A good numerical approximation to the S/N ratio in a background material with Z - - 10, A = 20 is

382

A. De Rtijula et al., Neutrino exploration of the Earth

S/N(1 kg/cm 2) = ~7(7.4 x 10-3) (Ep/10 TeV) (t - In(1 + t))-' [1 + 3xd4 + x214 + xf/24] e -x'

(7.27)

with t as in eq. (7.12b), xl as in eq. (7.26) and the material dependence given by 7? = (10/A') [3A_~ Z'

[Z'~ Ls7] \10] J"

(7.28)

Numerical values for 7/for representative high-Z materials are given by r/fie) = -1.0,

r/(Pb) = -3.6,

r/(Cu) = -1.2,

r/(U) = -4.0.

The negative values of r/ indicate that high-Z minerals lead to a decrease in the surface muon flux. Figure 7.2 shows the S/N ratio of eq. (7.27) for one kg/cm= deposits of copper and uranium as a function of the slant-depth of the lode. Results are given for accelerator energies of Ep = 3, 10 and 20 TeV. It is unlikely that S/N ratios less than 10 - 3 c a n be successfully extracted from the data. This limits the maximum slant depth at which significant ore bodies can be revealed to - 1 km for Ep = 3 TeV, - 2 km for Ep= 10TeV, and - 3 km for Ep= 20TeV. A more significant measure of the performance of GEMINI is the time required to detect, with adequate statistics, a given ore body. Let the repetition rate of the accelerator be as in eq. (5.8), and let "adequate statistics" be defined as a three-standarddeviation signal. The required time is given by Time = (Ep/10 TeV) A

9 (S/N) -2 minutes, dN~,IdA

(7.29)

with A the collection area of the detector, and the "noise" given by eq. (7.13). In fig. 7.3 we show Time ,

cu

/

M

105

u

i l=2km/i/N ....... / I - . . . . /

i I1,,'/ •

~ 1 ......

,,o, ! ,

II/I 165

0

1

~

2 3 t(km) (o)

~

4

I

0

,

1

I

,

2 3 l(km) (b)

'

4

3

10 Ep (TeV) (c)

20

Fig. 7.2. Signal/Noise ratios for a I kg/cm2 in slant-depth of two high-Z materials as given by ¢qs. (7.27, 28). The materials are Cn and U in (a) and (b) respectively, where S/N is shown as a function of slant depth for Ep = 3, 10, 20 TeV. In (c) the S/N for U is shown as a function of E v for four different slant depths. Also shown as a dashed line is the Noise, whose magnitude is to be read in the dashed scale, and is given by eq. (7.12).

A. De Rf~jula et al., Neutrino exploration of the Earth

383

10 5 -

~j 10 2 z :E z hi

I---

/\E

p--2o o 2s

1

I

i

I

I

I

0.5

1

1.5

2

2.5

3

~(km) Fig. 7.3. Time required to detect a i kg/cm 2 (in slant-depth) lode of uranium, as a function of its slant-depth. The proton energies and detector sizes used are (3 TeV, 10 m2), (10 TeV, 1 m2), (20 TeV, 0.25 mE).

as a function of slant-depth for a one kg/cm 2 deposit of uranium at a distance L = 1000 km. For a 3 TeV accelerator we employ A = 10 m 2 detectors, for E~ = 10 TeV we put A = 1 m 2, and for Ep = 20 TeV we put A = 0.25 m 2. Shallow lodes at slant depths of a few hundred meters can be detected in a few minutes with an accelerator as small as Ep = 3 TeV. However, deposits at a slant-depth of - 1 km require the use of an Ep = 10 TeV accelerator for rapid detection. The 1 TeV accelerator "Tevatron" that will soon be completed at Fermilab, if it is provided with a steerable neutrino decay tunnel, is sufficient to begin the implementation of the GEMINI project, and to assess the practicality of a more ambitious program. (Unfortunately, the same cannot be said of the GENIUS Project which demands an even larger machine.) With a preliminary feasability study at the Fermilab facility, GEMINI may well develop into a cost-effective probe for the discovery or for the assessment of commercially important mineral deposits. If a larger facility is constructed, we can imagine each neutrino pulse being used by both a sonic survey team (searching for oil or for gas via GENIUS) and a muon survey team (searching for high-Z material via GEMINI). Finally, we consider the radiation burden for a worker exposed to the muon radiation of GEMINI. From the total muon flux (7.13), the repetition rate of the accelerator (5.8), and the effective radius of the beam, we compute an on-site muon flux of

f-

104 ( E p '~3 (100Okm'~2 muons/cm2 week \10 TeV] \ L ]

(7.30)

This corresponds to a whole-body radiation dose D=

03 E~ 3 (100_0Lkm)2 . (10TeV) mrem/week,

(7.31)

384

A. De Rtijula et al., Neutrino exploration of the Earth

which is to be compared with the maximum permissible occupational dose of 100 mrem/week. GEMINI presents no significant radiation hazard.

8. GEOSCAN: The density profile of the Earth The determination of the density of the Earth as a function of depth is a subject of considerable interest. Much of what is known results from analyses of the propagation of seismic waves through the Earth. These studies do not lead to a unique and precise determination of the density profile, especially for the inner core. For example, six distinct "solutions" are tabulated in ref. [29], and many more are mentioned in ref. [30]. In this section, we describe a new method that can determine the density profile of the Earth. Our method depends upon the attenuation of neutrinos by the Earth, and in particular, upon the dependence of the attenuation on neutrino energy. Previous suggestions along these lines required that the absolute flux be known to an impracticable precision [31]. Our method does not. In order to illustrate the required sensitivity, we show in fig. 8.1 two models of the density profile of the Earth [29]. We take as a minimum requirement that our procedure be able to clearly distinguish between these models. A vertically-directed neutrino beam traversing an Earth diameter encounters roughly 10 TM gram/cm 2 of matter. In general, the neutrino beam may be directed at an angle 0 relative to the vertical. In this case, the neutrinos transverse not a diameter, but a foreshortened chord of the Earth. The projected

/

//

-

/// // -

MODEL

//

%//

/

/

/// //

12

//

8

6

4-

I

I

I

1 2 3 DEPTH IN THOUSANDS

1

I

4 5 OF KILOMETERS

I 6

Fig. 8.1. Two models of the density of the Earth as a function of depth.

A. De Rtijula et al., Neutrinoexploration of the Earth

mass density M(O)

M(O) is given

=f

385

by an integration

(8.1)

p(r) dx

where p is the Earth's density at radius r, and x is distance along the chord, as shown at the top of fig. 8.2. Also shown in this figure is M(O) as calculated for each of the two density profiles of fig. 8.1. The measurement of M(O) would provide a unique determination of p(r), with the inversion of eq. (8.1). Because of weak-interaction effects, a small fraction of the neutrinos suffer nuclear collisions on their way through the Earth, and are removed from the beam. The neutrino, flux is thereby attenuated in the fashion

(82)

6(E~)-~ (1 - aEv) 6(E~), where the energy-independent parameter a is given by

M(O)

(8.3)

a = M(O) NA (tr./E~) ~ 0.06/TeV 10 kilotons/cm 2"

J

0.5 I

I

L5

2

2.5

3

3.5

4

4.5

5

5.5

I

l

I

I

I

1

i

I

I

I

MINIMAL DISTANCE TO EARTH'S CENTER (thousands of kilometers)

12

~,\ \ N

t0 ~

\\\

MODEL A

ga-MODEL B

~ ' ~ ,

c

E 4

O*

I

IO*

I

I

20* 50* 40 ° ANGLE OF INCIDENCE

I

50*

I

60*

Fig. 8.2. Top: Neutrino beam traversing the Earth at an angle of incidence 0. Bottom: Mass in kilotron/cm2 that the neutrinos traverse, as a function of & for the models of fig. 8.1.

386

A. De R6jula et al., Neutrino exploration of the Earth

About 7% of the neutrinos of energy one TeV are absorbed in traversing the whole Earth. It is the effect of neutrino attenuation upon the surface muon flux that provides the GEOSCAN signal. For this reason, it is essential that muon flux measurements be performed in the deep seas. In this case, muon flux variations due to underground mineral deposits, which were the basis of the GEMINI Project, need not be considered. Another virtue of performing muon flux measurements at sea is the necessity to employ very large but mobile muon detectors. For this purpose, we envisage the use of retrofitted oil tankers whose muon detectors can have collection areas ~6000 m 2. These detectors must be placed at great distances from the accelerator. It is especially important to perform experiments at the antipodes, since the neutrinos that arrive there suffer the maximum attenuation en route. Indeed, from fig. 8.2, we see that the region in which M(O) is poorly known corresponds to values of 0 within 20° of the vertical. The necessity for vertical deployment of the neutrino beam presents special difficulties for Project GEOSCAN which are not shared by GENIUS or GEMINI. The primary protons must be magnetically deflected from the horizontal plane of the accelerator to a nearly vertical inclination. With present technology, a magnet strength of - 1 0 Tesla is a practical upper limit, corresponding to a radius of curvature of the extracted beam of (8.4)

B(km) ~ (Ep/3 TeV).

If the beam is to be vertically deflected, the beam transport system must extend to a depth of B km. It is followed by a target, a meson focusing system, and finally by a neutrino decay tunnel of length T, as shown in fig. 8.3. If T is scaled up from existing facilities, the vertical extent of the neutrino beam facility, T+B, will be 11km for a 10TeV machine and over 3km for a 3TeV machine. Practical considerations may lead to a compromise for the length of the decay tunnel, and to a consequent alteration of the neutrino flux. How can M(O) be measured by observations of the surface muon flux? Three possibilities come to mind: (1) Place the detector at the center of the emergent neutrino beam and measure the magnitude of the muon flux. The effect of neutrino attenuation as in eq. (8.2) upon the surface muon flux is readily

Beom Extroction

~

"

Proton ~8endmg

B

...................

Torget

D

Pion

T

///////////////////////////

Decoy

Tube

//////////////

Fig. 8.3. Accelerator and beam deployment at sea, a possibility that suggests itself in a GEOSCAN Project.

A. De Rd/ula et al., Neutrino exploration of the Earth

387

computed from eqs. (7.3) and (7.6). The effect is proportional to (1 - 6a (E~)), or

(8.s)

8N/N = -0.02 (Ep/TeV) (M(O)/(IO kt/cm2)).

This procedure may not be practical unless the accelerator energy is at least 10 TeV. The point is that the initial neutrino flux is unlikely to be measured with great precision. (2) A self-normalizing procedure is to measure not the total muon flux, but the mean muon energy, which is affected by the energy-dependent neutrino attenuation. Appeal to eqs. (7.3) and (7.6) yields the result = -a (E.).

8(E.)I(E.>

(8.6)

While this procedure is possible in principle, it is probably impossible in practice. Even for a 10 TeV accelerator, the total effect is only a few percent. To be useful, the seaborne muon detectors must be capable of measuring muon energies to a precision of parts per thousand. This would be extraordinarily difficult. (3) This is a self-normalizing procedure in which muon energies need not be measured. It is the procedure we believe can be implemented with Project GEOSCAN, and we proceed to consider it in detail. It involves the simultaneous use of two or more seaborne detectors, as shown in fig. 8.4. One of the detectors is placed at the central axis of the neutrino beam where the mean neutrino energy is greatest, and is given by 4 (Ev) in the limit of ideal pion focusing. The second detector is placed at a fixed angle t~ off-axis, where the neutrino flux is both less intense and less energetic. The off-axis flux, being less energetic, is less affected by neutrino attenuation in the Earth, than is the on-axis flux. The ratio of the off-axis flux Non to the on-axis flux No, must be measured as a function of the neutrino-direction 0 at which the neutrino beam traverses the Earth. This ratio is given by

P(O, a) = Non~No. = f(a) [1 + 6p(a) a(O) (E.)] ,

(8.7)

i0 o.-A×,s

~/. r

/

~ /~

>'/I

i / .~

./

/

. .~_~/~ ........

/

/

DETECTOR /

/

oF -A×,s

DETECTOR

NEUTRINO BEAM ~ ......

,~'T'r-~, ~, , .SEA. . B O T T O M

Fig. 8.4. Deployment of GEOSCAN detectors. The angle 0 is that of emergence of the neutrino beam axis. The angle a is that of on-axis to off-axis neutrinos.

A. De Rtljula et al., Neutrino exploration of the Earth

388

where the functions f(a) and p(tz) depend upon the detailed properties of the neutrino beam, and upon the precise muon range--energy relation in seawater. If P(O, a) is measured at large 0, the projected mass density is quite small, and attenuation factor a(O) is negligible. These measurements, performed relatively nearby the accelerator where the overall counting rate is high, provide a precise determination of f(a). Measurements at smaller values of 0 then permit the determination of a(O) up to the fixed scale factor p(a). We imagine that the several detectorships travel in tandem as the neutrino beam is deployed at steeper angles. One remaining at a = 0, the others placing themselves at a predetermined and fixed value of a. With further information about the neutrino beam properties, and the energy-range relation for muons in water, the functions f(a) and p(a) can be computed, and the absolute magnitude of a(O) can then be determined. We calculate these functions under three unrealistic hypotheses: that the pions are perfectly focused as they enter the decay tunnel, that none of the neutrinos arise from kaon decay, and that the energy-loss formula for muons in seawater is energy-independent. Our results will be reliable only in order of magnitude. Nonetheless, they are sufficient to judge the feasability of the GEOSCAN Project. The functions f(a) and p(a) are obtained by repeating the considerations of section 7, but at a fixed angle a with respect to the central axis of the neutrino beam, and in the presence of neutrino attenuation. Thus, the expression for the neutrino flux, eq. (7.1), is to be multiplied by the attenuation factor (1 - aEv) of eq. (8.2). The energy of decay muon of eq. (7.2) is to be evaluated at a fixed, nonzero value of a. The resulting expression for the attenuated off-axis neutrino flux is inserted into eq. (7.10) and integrated over E~, and E~. In this procedure, the energy-loss function R (E) is approximated by a constant. We obtain =

,

p(a)

= 1-

ao = m,dE,, ~=1.1 × 10-3 TeV/Ep,

(8.8)

~o

j~(x) = (4 + i)! j y"+~ exp[-y] (1+ y:x2) -~-~ dy. 0

The functions f(a), p(tz) and p(a)X/f(a) are shown in fig. 8.5. As a increases from zero, the overall muon signal decreases with f(a). However, the fraction of the signal which is attenuation-dependent increases with p(a). The GEOSCAN protocol for the determination of a(O) is optimized when p2[ is maximized, which occurs at a value of a = al = 0.11ao = 1.2 x 10-4 (TeV/Ep).

(8.9)

We shall adopt ot = o~1 as the canonical angular separation at which GEOSCAN is implemented. This means that the distance between the central detector and the peripheral detectors must be d ~ 1.53 km (TeV/Ep),

(8.10)

when they are located at the antipodes. At the separation ot = al we find

P(O, al) = 0,31 [1 + 2.6 a(O) (Ev)].

(8.11)

A. De Rfijula et al., Neutrino exploration of the Earth

389

0.9 0.8 _ ~ f ( 0.7

a)

-

0.6 0,5 0.4 0.3 0.2 0.1 O0

I

0.5

I

.10 a/a o

I

.15

.20

Fig. 8.5. The functions f(a) and p(a) of eqs. (8.8). Also shown is p(et)[)¢(a)] 1/2, whose maximum determines the optimal angle for detector deployment.

Roughly speaking, the fractional effect of attenuation on p(O) is (Ep/TeV)%. In order to determine whether this effect can be detected and measured, we must now compute the muon flux which is to be expected at the detectors. The muon flux at the antipodes on the central axis of the neutrino beam is calculated from eq. (7.11), into which are inserted the energy-loss parameters for water Ro = 2.5 MeV/cm,

(8.12)

B = 1.42/TeV.

For a shipborne detector of area 6000 m 2, the number of detected muons per neutrino burst is N~, = 120 (Ep/TeV)3 [t - ln(1 + t)],

t = 0.316 (Ep/TeV).

(8.13)

This corresponds to about 102 muons for Ep = 2 TeV, 103 muons at Ep = 3 TeV, and 104 muons at Ep = 5 TeV. However, eq. (8.13) depends upon the use of a canonical neutrino decay tunnel of length given by eq. (3.4). For the GEOSCAN Project, the length of the neutrino decay tunnel is limited by the vertical clearance D at the site of the accelerator, or by the expense of constructing such a vertical facility. Thus, the muon counting rate must be multiplied by the ratio

D-B 7.5 km (Ep/10 TeV)'

(8.14)

where B is given in eq. (8.4). Furthermore, eq. (8.13) is to be divided by cos 0 to obtain the muon flux away from the antipodes.

390

A. De Rtljula et al., Neutrino exploration or the Earth

\\

1 MONT"~

\\ 104 •~X~\\

1 WEEK

,,\ \ \,,

ID-l \,'\\ "-. / \

\

Io

SC tEO

F--

\\~\\ \ "\~x \ \ x

10

1

I

2

P

3

I

5

II

\

~. 10

Ep (TeV)

Fig. 8.6. Time required for a meaningful measurement of the Earth's density projected along its diameter, as a function of proton energy. The continuous line is for a neutrino decay tunnel of length 0.75 km (TeV/Ep). The dashed line is for fixed depth clearances D, as defined in fig. 8.3.

We have computed the time required for GEOSCAN to provide an accurate determination of the integrated mass density of the Earth through a diameter. This measurement of M(0) must be precise to 6% in order to unambiguously discriminate between the two models shown in fig. 8.2. We have employed one shipborne detector of area 6000 m 2 at the center of the neutrino beam, and three peripheral detectors located at off-axis angle a, given by eq. (8.9). Thus, the on-axis and off-axis counting rates are comparable. In fig. 8.6 we show the result to this calculation as a function of accelerator energy Ep. The solid curve shows the required time with the use of a canonical neutrino decay tunnel as specified by eq. (3.4). Also shown is the required time when the vertical extension of the neutrino facility is constrained to be 1, 3, or 5 km. From the figure, we observe that the measurement of M(0) can be accomplished with a 1 TeV accelerator and one km of vertical clearance in a dedicated run of one month's duration. A 2 TeV accelerator with the same vertical clearance could do the job in several days. This would make practicable a survey at various angles 0, and a complete determination of M(6) to an accuracy of a few percent in a matter of months. The virtues of larger accelerators with larger vertical clearances are evident from the figure.

9. Directions of future research and development In the preceding sections, we have outlined how a major future proton accelerator can be used for purposes other than elementary-particle research. In Project GENIUS, the neutrino beam is used to

A. De Rdjula et al., Neutrino exploration of the Earth

391

inject a sound source at depth for purposes of geological surveying. In Project GEMINI, the secondary muons detected at the surface provide an alternative method of geological exploration. Finally, Project GEOSCAN can reveal the properties of the inner core of the Earth. Of course, the proposed facility will also be used in the conventional fashion as a probe of the fundamental structure of matter. We have discussed the orders-of-magnitude of the relevant parameters of the machine, of the beam deployment system, and of the required signal detection equipment. Nonetheless, considerable research and development remains to be done before a definite conclusion can be reached on the economic feasibility of this kind of geological research at this time. In what follows, we examine some of the main areas of further research that are required. All of them are of intrinsic interest quite beyond their relevance to neutrino-beam surveying. (1) High-energy physics. We have been glib in our discussion of the physics related to a 10 TeV proton accelerator, with an energy 25 times greater than any existing machine. In large measure, our glibness is justified by recent successes of experimental and theoretical high-energy physics. The ISR at CERN collides protons on protons at center-of-mass energy of 60 GeV. This is the equivalent of colliding a 2 TeV proton against a proton at rest. Moreover, the CERN-COLLIDER studies the collisions of protons on antiprotons at 540 GeV in the center-of-mass. This corresponds to a fixed-target energy of about 100 TeV. The general pattern of physics at these high energies is roughly what had been anticipated. To be sure, there are interesting new effects to be discovered. However, these will be small effects which will affect our conclusions hardly at all. We have extrapolated neutrino cross sections to proton energies 25 times larger than have been studied in the laboratory. We are confident with this extrapolation because of the enormous success of weak-interaction theory at lower energies, and because of the elegance of the theory itself. Nonetheless, further high-energy experimentation can be important for the design of our project. Meson multiplicities and momentum distributions, as measured at colliding beam facilities, are necessary inputs to the design of the target and focusing facility, and they will affect the detailed properties of the neutrino beam. The differential cross section for deep-inelastic neutrino scattering off complex nuclei must be measured at the highest available energies. This is directly relevant to the production of the muon signal in Projects GEMINI and GEOSCAN. Equally important are detailed studies of the muon range/energy relation in water, in soil, and in ore materials. Relevant experiments can be done at existing muon beam and neutrino beam facilities. Further theoretical calculations of the muon range in various materials can also be useful. However, most of the uncertainties in our projects lie outside of the domain of high-energy physics. (2) Sound generation by energetic beams. We have discussed in section 4 the extensive experiments that have been done on the production of sound by particle beams traversing liquid targets [12]. The results are in general agreement with the simple thermoacoustic model of section 4.2, except for the curious vanishing of the signal in water at 6°C rather than 4°C. This anomaly may indicate that sound production by particle beams is essentially different from sound production by a thermally equivalent but nonionizing procedure. An important question is whether the anomaly persists when the water is heated by a pulsed laser beam. Can the anomaly be significant for the production of sound by particle beams traversing solids? After all, there is no supporting evidence for the simple thermoacoustic effect in solids. The field of "photoacoustics" is reviving [32] a century after its discovery by Alexander Graham Bell [33]. Here, an acoustic signal is produced by a pulsed beam of light. The acoustic signals are much larger than may be anticipated from the thermal expansion coefficient of the medium [34]. This is presumably due to the interaction of the surface of the medium with the surrounding gas. Moreover,

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A. De R(qula et at~, Neu~no exploration of the Earth

mechanically constrained surfaces yield enhanced thermoacoustic signals, as predicted by White [32] and verified by Santfeld and Melcher [32]. Relevant experiments on sound production can be carried out with laser beams [35] or X-ray beams, or with particle beams produced at existing accelerators. Of greatest relevance to the GENIUS Project would be experiments performed with high-energy particle beams. These experiments, neither very difficult nor expensive, could greatly clarify the question of sound generation by the neutrino beam of GENIUS. One may envisage a scaled-down GENIUS prototype, with a particle beam impinging on a known target of soil or rock material. The target may be permeated with oil, water, or natural gas and maintained at high pressure. Acoustic signals are read out with microphone arrays as in the GENIUS Project. Useful experiments of this kind can be carried out with beams of electrons, muons, or protons. If the thermoacoustic model is correct, the acoustic signals should not depend upon the identity of the projectiles, but only upon the magnitude and spatial distribution of deposited energy. Thus, it is unnecessary to carry out "realistic" tests of the GENIUS procedure with neutrino beams. This is fortunate, since the energies of available neutrino beams are too low to implement such experiments. Below, we consider two feasible studies that can be carried out at existing facilities. Consider the 3 GeV proton beam produced by the SATURN accelerator at Saclay, near Paris. This beam would penetrate 30-50 cm of a solid material with density p = 2-4 g/cm3. Its interactions would widen an initially narrow beam to a diameter of o" - 1 cm towards the end of its path in the target. With a typical sound velocity of c = 4 km/sec, the sound transit time across the beam is - 5 I~S. The duration of the pulse can be made much shorter than this, so that the characteristic frequency of the sonic pulse is f = c/zro"- l0 s Hz.

(9.1)

At these frequencies, thermal noise dominates the background. The rms thermal noise pressure in a frequency window (fl, f2) is p ( f 2, f l) = [(4 7rk Tp/3c ) (f~ - f~)]m .

(9.2)

For the circumstances at hand, in a frequency window extending up to 3 x 105 Hz, the numerical value of the thermal noise background is p --- 0.15 dynes/cm2 .

(9.3)

In the proposed experiment, let N denote the number of protons per pulse. The energy deposition per unit length of the 3 GeV proton beam is d W/dy = 3N GeV/30 cm = 1.6 x 10-'N erg/cm.

(9.4)

The corresponding sound pressure signal from this line source at distance R large compared to o- is given by eq. (4.21) to be p ~ ( d W ] d y ) A tr -3/2 R -v2

(9.5)

where A is the parameter defined in eq. (4.4) and is typically 0.1. The sonic signal, at a distance of 10 cm from the source is given by

A. De R~jula et al., Neutrino exploration of the Earth

p ~ 5x

10 - 6

N dynes/cm2 .

393

(9.6)

A modest beam of 10 6 protons per pulse produces a signal well above the noise level of eq. (9.3). Proton or electron accelerator facilities can make extensive measurements of sound production in solids, and especially in such composites as occur underground. Proton experiments are limited by the small range of these particles due to their strong interactions. Experiments with muon beams can more closely mimic the GENIUS configuration. Two muon beams at CERN can be useful for those purposes. The North Area muon beam consists of pulses of - 3 x 10 7 muons with average energy 200 GeV. These muons are dumped about 2 meters underground in a fiat grassy field. The diameter of the beam at the dump is o"- 10 cm, so that the sound transit time across the pulse is typically 50 ~ts, corresponding to a frequency ~104 Hz. The thermal and seismic noise background is again -0.1 dyne/cm2. The energy deposition of the muons in soil is -100ergs/cm corresponding to a sonic signal ~0.02 dyne/cm2. Clearly, this beam is not powerful enough for an efficient study of the thermoacoustic effect in different materials. However, it can be used to test the deployment of microphone arrays for the purpose of signal extraction in a situation of unfavorable S/N ratio, much like the anticipated situation for GENIUS. Another muon beam available at CERN is the beam which inevitably accompanies the neutrino beam. Its diameter is also - 1 0 cm. While its muons are lower in energy than the North Area beam, it consists of - 6 x 1011 muons per pulse. Such a beam produces an acoustic pulse with a very favorable S/N ratio. It is absorbed in a very long shield made of iron and concrete which could readily be instrumented to detect the thermoacoustic signal. Considerable research on sound generation by particle beams in liquids has been conducted. All we are saying in this section is that a similar research effort should be dedicated to solid targets with the characteristics that are likely to be encountered in a GENIUS Project. 3. Analysis of seismic noise and signals. Two great uncertainties beset our calculations of the signal/noise ratios for the GENIUS Project: the size of the signal and the nature of the background noise. We have mentioned some of the experiments that can clarify the nature of the sonic signal to be expected from neutrino interactions underground. The second uncertainty relates to the degree of coherence and directionality of background seismic noise from a few Hz to a few hundred Hz. We simply cannot reliably estimate the background noise that would be received by a microphone array focused in the direction of the sound-generating neutrino beam. A study of these properties of seismic noise could be of interest in itself. Moreover, it is useful to investigate the propagation of the sonic signal from an underground source, and its detection under unfavorable S/N conditions. The effect of neutrino heating underground could be simulated with a radio-frequency source placed at depth which is appropriately coupled to the ambient rock. It should provide a sudden deposit of heat in a long cylinder of rock with a radius - 10 m. The magnitude of the energy deposition should be small, and comparable to what could optimistically be anticipated in GENIUS, namely ~ 1000 ergs per cm, per pulse. An array of surface microphones seeks to detect and measure the sonic signal. The success of this experiment is a necessary condition for the feasibility of the GENIUS Project..

I0. Conclusion

We have shown how the neutrino beam produced at a large proton accelerator may be used for purposes of geological surveying. Perhaps, neutrinos will be for geology what X-rays were for medicine.

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What is needed for "whole Earth tomography" is a form of radiation whose range in matter is neither very much greater nor very much smaller than the size of the Earth. Of all the particles in the elementary-particle zoo, only high-energy neutrinos fit this requirement. For example, energetic muons penetrate only a few kilometers of matter, while low-energy solar or reactor neutrinos penetrate a light-week of matter. Neutrinos with energy of a few TeV are just right, having a range only somewhat larger than the Earth's diameter. Such neutrinos present the only chance for high-energy technology to address the unsolved problems of Earth sciences. We have examined three possible geological applications of a high-energy neutrino beam: the Projects GENIUS, GEMINI and GEOSCAN. The first two projects are motivated by practical or pecuniary considerations: the search for hydrocarbon or heavy metal resources. The third project, GEOSCAN, is a purely scientific endeavor which would "X-ray" the Earth as a whole to determine the density of its inner core. The required size of the proton accelerator varies from project to project, but lies in the broad range, 1 TeV -< Ep <- 20 TeV. We are proposing the construction of a multi-TeV fixed-target proton synchrotron dedicated to geological exploration and of an energy and cost perhaps an order of magnitude larger than any existing facility. The construction of such a machine is now considered to be technically feasible, even without any dramatic breakthrough in accelerator design. Our straightforward extrapolations of the present state of the art constitute an unwarranted and ahistorical pessimism. Giant steps of the past (the cyclotron, the synchrotron, strong focusing, are examples) will certainly be followed by further advances. It is premature to lament the cost and difficulty of construction of future machines. We may not build GENIUS tomorrow, but we will certainly build it the day after. The principal technical challenge for neutrino geology is the development of a neutrino beam which may be precisely directed towards a remote part of the Earth. An ideal solution is to place the accelerator at sea, sufficiently under the surface where the water is tranquil. This solution poses novel technical problems. If one is willing to compromise the solid angle within which the neutrino beam is aimed, less radical solutions come to mind. The accelerator may be placed in a coastal region near which the sea becomes deep. Or, it may be placed on flat land on a mesa, or tangent to a deep canyon. In either case, the bending magnets for the extracted proton beam and the neutrino decay tunnel may be deployed along the natural terrain without prohibitive earth-moving costs. In the GENIUS Project, the neutrino beam is used to implant a sonic signal at arbitrary depth, at any distance from the accelerator within a range of order 10 3 km. The sonic signal can be detected and interpreted with an array of geophones. The data analysis does not involve the inverse scattering problem, so that elaborate computer analysis is not required. It is straightforward to obtain a vertical profile of the local sound velocity in any region accessible to geophone arrays. Additional local data about the underground domain is obtained from the magnitude and spectral form of the observed signal. Depth is not a serious limitation, so that deep deposits of natural gas of nonbiological origin may be sought [36]. Both the quantitative and qualitative nature of the data obtained are quite different from what is deduced from conventional reflective seismology. A careful feasibility study is required to determine whether or not such a facility as we imagine is cost-effective. Our considerations are based on estimates of high frequency incoherent seismic noise that may be wrong by an order of magnitude in amplitude. The signal calculations are based on a minimal thermoacoustic model that has not been tested with solid targets. For complex composite materials, like porous rock permeated with gas or oil under high pressure and unrelieved stress, our estimates of the signal are certainly unduly pessimistic. Research and development is needed to determine what energy proton accelerator is needed to implement the GENIUS Project.

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The purpose of the GEMINI Project is to detect and map deposits of heavy metals at vertical depths of a few hundred meters, at sites thousands of kilometers from the accelerator. In this case, we understand quite well the physics underlying signal production, and our estimate of signal strength are reliable. An accelerator of energy Ep = 1-3 TeV is sufficient to reveal underground deposits of order one ton/meter 2 in vertical projection. What we cannot judge is the usefulness of the data to the mining industry, and the cost-effectiveness of its acquisition. The GEOSCAN Project requires an accelerator of the same energy as GEMINI. The information it would yield is complementary to what is deduced from seismic studies. The project we imagine is one of the most ambitious ever conceived by our species. We are thinking of a mobile circular submarine accelerator with a circumference of 100 miles. It rivals the construction of the pyramids, the cathedrals, and the manned space program. Unlike the other projects, ours is of direct and down-to-Earth significance: it is a carefully honed tool for the purpose of studying our own planet. It will detect and survey conventional deposits of oil, gas and other commercially important minerals. Not limited in depth as are present techniques, it can also search for unconventional resources, like very deep deposits of natural gas. The development of this new technology may enable us to mine all those minerals lying on the sea bottom or below. In the summer of 1983, the U.S. High Energy Physics community has chosen as its highest priority the construction of a 20-40 TeV proton-proton collider for purposes of basic research. Fitted with a fast extracted beam, such a machine becomes an ideal Geotron prototype. In circumstances of limited funding, this kind of cooperation between basic and directed research is mandatory. Earth "tomography" studies will become possible that will enable the measurement of the shape and size of the Earth's core. Our project represents a magnificent fusion of pure and applied research that will forever remain a landmark of scientific endeavor:

Acknowledgement For encouragement, generous assistance, and/or valuable discussions technical and otherwise, we are deeply grateful to the following persons: Paula C. Constantine, Arthur H. Dubow, Richard Garwin, Walter Gilbert, John Hopfield, Carl Kaysen, Arshag Mazmanian, Peter Mclntyre, Lev B. Okun, Carl Romney, Larry Sulak, and Samuel C.C. Ting. One of us (S.L.G.) thanks the Aspen Center for Physics, for its hospitality when part of this work was completed.

References [1] [2] [3] [4] [5]

R.R. Wilson, Physics Today 30 (1977) 23; Rev. Mod. Phys, 51 (1979) 259. Proc. DPF Summer Study on the Physics of Future Accelerators (Snowmass, Co. tO be published). H. Hirabayashi et al,, K.E.K. (1980), private communication. See, for instance, K. Kleinknccht, in: Proc. 1978 CERN School of Physics, CERN 78-10. See, for instance, Proc. Second ICFA Workshop on Possibilities and Limitations of Detectors, ed. Ugo Amaldi (CERN R/D/450-1500 June 1980). [6] Proc. DUMAND Workshop, DUMAND 76, ed. A. Roberts (Fermilab Office of Publications, 1977); DUMAND 78, ed. A. Roberts (Dumand Scripps Institute of Oceanography, Code A-010, La Jolla, CA 92093); DUMAND 79, ed. J.G. Learned (Hawaii Dumand Center, University of Hawaii, 2505 Correa Road, Honolulu, HI 96822). [7] G.A. Askarian and B.A. Dolgoshein, Preprint No. 160, Lebedev Physics Institute, Moscow (1976); V.D. Volovik et al., Proc. 9th U.S.S.R. Acoustics Conference, Moscow (1977) VDK 534.2:108:530.1.076. [8] Laser beam experiments that may have detected microbubhle-induced signals in water near 4"C temperature are reported by S.D. Hunter et al., in: DUMAND 79, ref. [6] p. 140.

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[9] B.A. Dologoshein, in: DUMAND 76, ref. [6]. [10] T. Bowen, in: DUMAND 76, ref. [6]. [11] J. Learned, Phys. Rev. D 19 (1976) 3293. [12] L. Sulak et al., Nuclear Instruments and Methods 161 (1979) 203. For more recent progress, see S.D. Hunter et al., DUMAND 79, ref. [6] p. 128. [13] P. Morse and K. Ingard, Theoretical Acoustics (McGraw-Hill, N.Y., 1968). [14] B. Gutenberg, Physics of the Earth's Interior (Academic Press, 1959) p. 29. [15] R.M. White, Journal of Applied Physics 34 (1963) 3559; R.J. von Gutfeld and R.L. Melcher, Applied Phys. Lett. 33 (1977) 257. [16] We are indebted to Prof. John Hopfield for discussions on this point. An alternative to the explanation given in the main text has been proposed: the non-excitation of Debye-like modes, see P. Westervelt, in: Conf. Proc. Neutrino 1978 Meeting, ed. E. Fowler (Purdue, West Lafayette, Indiana, 1978). Yet other explanations involve mierobubble formation and/or space-charge effects, see S.D. Hunter et al., T. Bowen et al. and B.W. Jones, in: DUMAND 79, ref. [6]. [17] V.D. Volovik and G.F. Popov, Soviet Phys. JETP 1 (1975) 13. See also ref. [7]. [18] B.L. Beron and R. Hofstadter, Phys. Rev. Lett. 23 (1%9) 184. [19] B.W. Jones, in: DUMAND 78, ref. [6]; L. Sulak, private communication. [20] Jack Capon, in: Methods of Computational Physics Vol. 13, Geophysics, ed. Bruce A. Bolt (Academic Press, New York, 1973). [21] G.E. Frantti, Geophysics 28 (1%3) 547. [22] K. Akamatu, Bull. of the Earthquake Research Inst. (Tokio) 39 (1961) 23; C.D.W. Wilson, Proc. Royal Society A217 (1953) 188. [23] J.E. Fix, Bull. Seismological Society of America 62 (1972) 1753. [24] J,N. Bruce and J. Oliver, Bull. Seismological Society of America 49 (1959) 349. [25] G.M. Wenz, J. Acoustical Society of America 34 (1962) 1936. [26] M. Lomask and R. Frasetto, J. Acoustical Society of America 32 (1960) 1028. [27] P.N.S. O'Brien, Geoexploration 12 (1974) 75; Sci. Prog. Oxf. 64 (1977) 487. [28] See, for instance, N. Mori, in: ref. [5] and Yu.D. Kotov and V.M. Logunov, Acta Physica Academiae Scientarum Hungaricas 29 (1970) 73. [29] Gordon J.F. MacDonald, Mechanical Properties of the Earth, in: Advances of Earth Science, ed. P.M. Hurley (the MIT Press, 1965). [30] Frank Press, in: Nature of the Solid Earth, ed. E.C. Robertson (McGraw-Hill, 1972) pp. t47-171. [31] See, for instance, A. Placci and E. Zavattini, On the Possibility of Using High-Energy Neutrinos to Study the Earth's Interior; A. Placci and E. Zavattini, CERN report, October 1973; L.V. Volkova and G.T. Zatsepin, Izvestia Akademii Nauk 38 (1974) 1060; I.P. Nedelkov, A Method for Model-Independent Determination of the Earth's Density Distribution, Preprint of the Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, January 1981. [32] For recent review, see A. Rosenweig, Photoacoustics and Photoacoustic Spectroscopy (Wiley, New York, 1980) and Science 218 (1982) 233. [33] A.G. Bell, Philos. Mag. 11 (1881) 510. [34] A. Rosenweig and A. Gersho, Journal of Applied Physics 47 (1976) 64. [35] L.S. Gournay, J. Acoustical Society of America 40 (1966) 1332; S.D. Hunter et al. and P.I. Golubnichy et al., in: DUMAND 79, ref. [6]. [36] T. Gold and S. Soter, Scientific American (June 1980) p. 154.