15. Measurement of Sonic Attenuation and Amplitude

239

15. MEASUREMENT OF SONIC ATTENUATION AND AMPLITUDE The amplitude of an acoustic wave decreases as it propagates through a medium. This decrease is known as attenuation (Fig. 15-1). The attenuation as the wave moves through the formation depends on several factors, mainly: (a) The wavelength of the wave and its type (longitudinal or transversal). (b) The texture of the rock (pore and grain size, type of grain contact, sorting), as well as the porosity, permeability and the specific surface of the rock pores. (c) The type of fluid in the pores and in particular its viscosity. (d) Rock fractures or fissures. This means that the measurement of attenuation can be of real use in the analysis of formations. In cased wells the attenuation depends mainly on the quality of the cement around the casing. This can be indirectly measured by recording the sonic amplitude. This application is known as the Cement Bond Log (or CBL). 15.1. THEORETICAL CAUSES OF ATTENUATION These are fundamentally of two types. 15.1.1. Loss of energy through heat loss This loss of energy can have several causes.

4 DISPLACEMEN7

Fig. 15-1. Amplitude attenuation of acoustic wave with distance.

15.1.1.1. Solid-to-solid friction The vibration caused by the passage of a sonic wave causes the grains or crystals of the rock to move minutely one against another. This fractional movement generates heat and so a loss of energy. This phenomenon occurs mainly inside the formation. 15.1.1.2. Solid-to-fluidfriction As the forces acting on the solid grains and on the fluids cause different amounts of movement, frictional forces are generated at fluid to solid boundaries, with energy loss in the form of heat. This occurs in porous formations and also in muds that contain solid particles.

15.1.1.3. Fluid-to-fluidfriction When a formation contains two different non-hiscible fluids the wave forces act to create fluid to fluid friction leading to acoustic energy loss. This occurs in porous formations containing water and hydrocarbons. 15.1.2. Redistribution of energy This may occur in several ways. 15.1.2.1. Transfers along the media limits Consider the cycle of a plane primary longitudinal wave moving in a solid M I (Fig. 15-2) which presents a vertical boundary with a liquid M,, with the speed v2 in M, less than that u 1 in M,. The cycle is bounded by the wave fronts FF’ and BB’. The direction of propagation is given by the arrow H. The region under compression is C and that of rarefaction is R. These two regions are separated by a plan NN’ where M I is neither compressed nor dilated. The compression in region C causes medium M, to bulge out into medium M,, as the liquid is more compressible than the solid. Likewise the rarefaction R allows M, to expand slightly. This undulation of the boundary, shown very exaggerated in Fig. 15-2, moves towards the bottom with the primary wave and generates in the medium M, a compressional wave whose forward and rear fronts are shown by F‘F” and B’BB’’. This secondary wave propagates in the direction P, forming with the original direction H,

240

Solid

*1

I

Fig. 15-3. Variation of the coefficients of reflection and transmission as a function of the angle of incidence (from Gregory, 1965).

Liquid

’ v2

Fig. 15-2. Mecanism of transfer of acoustic energy by radiation along a boundary.

an angle equal to the critical angle of incidence. The energy of the secondary wave comes from the primary wave and so a fraction of the original energy is transferred to the medium M,. A transverse wave moving in the medium M, also transfers part of its energy to M, in the form of a compressional wave. All t h s occurs in open hole along the borehole wall where the mud-formation boundary occurs and also in cased hole where the casing is not well cemented. 15.1.2.2. Transfers across media boundaries When a wave crosses the boundary between two media M I and M, of different acoustic impedance we either have, depending on the angle of incidence, total reflection of the wave or part of the wave refracted into the medium M, and part reflected back into M I . In the second case, there is attenuation of the wave. The ratio of the amplitudes of the incident and transmitted waves is called the coefficient of transmission of amplitude T,.

T, = W

(15-1)

A X

For a normal wave incidence we have for P and S waves:

( 15-2) with rl and r, equal to the acoustic impedance of the media M, and M, ( r = u p with u=velocity and p = density) and the reflection coefficients of amplitude are:

1 - r,/r2 R‘, = 1 r l / r 2

+

R’

=

1

+- r2/r1 r2’rl

for P waves

( 15-3)

for s waves.

( 15-4)

When the angle of incidence is no longer normal the calculation of the reflection and transmission coefficients is more complex. Figure 15-3 gives in graphical form the variation of the coefficients as a function of the angle of incidence. This phenomenon is produced either at the boundary of formation and mud, or between layers of different lithologies or at fracture planes when the fractures are full of fluid or cemented. In a cased hole it occurs at the boundaries of casing-cement-formation when the cement is good. 15.1.2.3. Dispersion When the sonic wave encounters particles, w6ose dimensions are less than the wavelength, the sonic energy is dispersed in all directions, whatever is the shape of the reflection surface. 15.2. CAUSES OF ATTENUATION IN THE BOREHOLE We must distinguish two cases: 15.2.1. Open-hole From what we have said the principal causes of attenuation are: 15.2.1.1. Attenuation in the mud This is due to acoustic losses by frictional losses, solid to fluid, and to dispersion losses at particles in suspension in the mud. In a pure liquid this attenuation follows an exponential law at least for one unique frequency: 8m = e m x

( 15-5)

in which m is the attenuation factor in the liquid, proportional to the source of the frequency, and x is the distance over which the attenuation is measured. For fresh water and at standard conditions of temperature and pressure, for a frequency of 20 kHz the attenuation factor is of the order of 3 x lo-’

24 1

db/ft. It is higher for salt water and oil. It decreases as the temperature and pressure increase. For normal drilling muds which contain solid particles we have to add the effect of dispersion. It is estimated that the total dispersion is of the order of 0.03 db/ft for a frequency of 20 kHz. In gas cut muds the attenuation caused by dispersion is very large, so making all sonic measurements impossible. 15.2.1.2. Attenuation by transmission of energy across the mud-jormatifn boundary for waves arriving at an angle of incidence less than critical The coefficient of transmission depends on the relative impedances of the rock and the mud. As the impedance of the mud is about constant and there is little variation in rock density, the ratio of impedances is effectively proportional to the speed of sound in the rock. 15.2.1.3. Attenuation in the rock Several factors are important: (a) Frictional energy loss In non-fractured rocks the attenuation of longitudinal and transverse waves is an exponential function of the form:

8,

= ear

( 15-6)

in which a is the total attenuation factor due to different kinds of friction: solid to solid (a’), fluid to solid (a”)and fluid to fluid (a ’”): a = a’

+ a” + a”’

(15-7)

and I is the distance travelled by the wave. It is given by the equation:

I = L - (d, - d,,,,)tgi,

(15-8)

where L is the spacing, d , and dtoo,are the diameters of the hole and the tool, i, is the critical angle of incidence, which goes down as the speed in the formation increases. When the rock is not porous, the factors a” and a”’ are zero. When the rock is water saturated, a”’ = 0. In porous rocks, the attenuation factor u” depends on\ the square of the frequency, whereas the factors a’ and a”‘ are proportional to the frequency. The factor a” depends equally on porosity and permeability. It increases as the porosity and permeability increase. The attenuation factors a’ and a” decrease as the differential pressure AP (geostatic pressure - internal pressure of the interstitial fluids) increases. Figure 15-4 from Gardner et al., (1964), gives the relationship for dry rock- the energy losses are then due to solid to solid friction (a’)-and for a water-saturated

dblft

0

1000

2000

4000

3000

5000

PSI

DIFFERENTIAL PRESSURE

Fig. 15-4. Influence of the differential pressure on attenuation (from Gardner et al., 1964).

rock-the difference in attenuation (gap between the curves) is due to fluid to solid friction (a”). When the rock contains hydrocarbons a greater attenuation of the longitudinal wave is observed in the case of gas than for oil (the factor a”’ non zero). From this we can deduce that the viscosity of the fluid has an effect on the attenuation factor a”’. Hence, if we resume all the different parameters acting on the attenuation, we can write that for a given tool:

.

(15-9)

a = f ( f , * , + , k , S , c L J P ,P ) with:

frequency; velocity of the sound; + = porosity; k = permeability; s = saturation; c L = viscosity of the fluids; A P = differential pressure; P = density of the formation. (b) Loss of energy through dispersion and diffraction: this appears mainly in vuggy rocks.

f = u

=

~~

0

30”

60”

90”

DIP ANGLE OF ?HE FRACTURE PLANE

Fig. 15-5. Variations of the coefficients of transmission as a function of the apparent dip angle of a fracture plan with regard to the propagation direction (solid lines from Knopoff et al., 1957; dash tines from Moms et al., 1964).

242

15.2.2. Cased hole

DIP ANGLE

Fig. 15-6. Attenuation across a fracture as a function of the apparent dip angle of a fracture plan with regard to the propagation direction (from Morris et al., 1964).

(c) Transmission across the boundaries of a medium. When a formation is made up of laminations of thin beds of different lithology at each boundary some or all of the energy will be reflected according to the angle of incidence. This angle is dependent on the apparent dip of the beds relative to the direction of the sonic waves. In the case of fractured rocks the same kind of effect occurs with the coefficient of transmission as a function of the dip angle of the fracture with regard to the propagation direction. The chart given in Fig. 15-5 is only applicable in the case of thin fractures that are open. It does not include the acoustic losses due to friction in the fracture. Figure 15-6 is derived from Fig. 15-5, but applies to experimental data. From these two figures we can draw the following conclusions: (a) the P waves are only slightly attenuated when they cross a horizontal or vertical fracture. The attenuation is large when the angle of the fracture plane is between 25 and 85 degrees and (b) The S waves are strongly attenuated when they cross a fracture at a slight angle. The attenuation decreases as the dip increases. 15.2.1.4. Transfer of energy along the borehole wall This phenomenon, described previously, leads to a n attenuation of the signal at the receiver. We can generally conclude that the attenuation linked to this is a function of the tool transmitter to receiver spacing, the diameter of the hole, and the frequency and speed of the P and S waves.

The attenuation is affected by the casing, the quality of the cement and the mud. If the casing is free and surrounded by mud, it can vibrate freely. In this case, the transfer factor of energy to the formation is low and the signal at the receiver is high. Remarks: In some cases, even when the casing is free we can see the formation arrivals (on the VDL). This can happen if the distance between the casing and the formation is small (nearer than one or two wavelengths), or when the casing is pushed against one side of the well but free on the other. Transmission to the formation is helped by the use of directional transmitters and receivers of wide frequency response. If the casing is inside a cement sheath that is sufficiently regular and thick (one inch at least) and the cement is well bonded to the formation the casing is n o longer free to vibrate. The amplitude of the casing vibrations is much smaller than when the casing is free and the transfer factor to the formation is much higher. Just how much energy is transferred to the formation depends on the thickness of the cement and the casing. As energy is transferred into the formation the receiver signal is, of course, smaller. Between the two extremes (well bonded casing, free pipe) the amount of energy transferred and hence the receiver signal will vary. 15.3. MEASUREMENT OF ATTENUATION This is not possible directly so an indirect measurement of amplitude is used. 15.3.1. Cement Bond Log

In the case of the Cement Bond Log (CBL), the general method is to measure the amplitude of the first arrival in the compressional wave at the receiver(s) (Fig. 15-7).

e

t

_hz_

P waves

Am

mud Stoneley waves waves

S waves and and Rayleigh waves

Fig. 15-7. Complete theoretical acoustical signal received from the formation showing the arches usually used for the amplitude measurement. A,: amplitude of compressional wave (P). A,: amplitude of shear wave (S). A,: maximum amplitude.

243

:t

100

2

1

/

/

80

5 60. z

W

’

5

40.

r

8

I

.

/*

/

I

/-

/-

t

20-

/

, /

0-

,

‘
60

*I. CIRCUMFERENCE

CEMENT OR CEMENT NOT BONDED

80

100

BONDED

Fig. 15-8. Per cent attenuation vs per cent circumference bonded (courtesy of Schlumberger).

t

I

Amplilvdr

E3

Fig. 15-9. Schematic receiver output signal wi!h unbonded casing and with bonded casing (courtesy of Schlumberger).

t

Ampliludi

Fig. 15-10. Gating systems (courtesy of Schlumberger).

These arrivals have a frequency between 20 and 25 kHz. The amplitude of the first arrival is a function partly of the type of tool (particularly the tool spacing) and of the quality of the cementation: the nature of the cement and the percentage of the circumference of the tubing correctly bound to the formation (Fig. 15-8). As we have seen the amplitude is a minimum, and hence the attenuation a maximum, when the tool is in a zone where the casing is held in a sufficiently thick annulus of cement (one inch at least). The amplitude is largest when the casing is free (Fig. 15-9). The amplitude is measured using an electronic gate (or window) that opens for a short time and

measures the maximum value obtained during that time. In the Schlumberger CBL (Fig. 15-10) there is a choice of two systems for opening the gate: (a) Floating gate: the gate opens at the same point in the wave as the At detection occurs and remains open for a time set by the operator, normally sufficient to cover the first half cycle. The maximum amplitude during the open time is taken as the received amplitude measurement. (b) Fixed gate: the time at which the gate opens is chosen by the operator and the amplitude is measured as the maximum signal during the gate period. The fixed gate measurement is therefore independent of A t . In the case of the fixed gate care must be taken to follow the position of the E, arrival if for any reason true At varies, as, for example, when the fluid inside the casing changes. Normally however, when At is properly detected at E l the two systems give the same result. If E , is too small then A t detection will cycle skip to E, (the case where the casing is very well cemented). The two systems then give: (a) fixed gate: E l is still measured and is small; and (b) floating gate: E l is measured and is usually large (Fig. 15-11). The measurement and recording of transit time at the same time as amplitude allows cycle skippihg to be detected (Fig. 15-12). Excentralization of the tool may cause a drop in the transit time (Figs. 15-13 and 15-14): the wave that has the shorter path through the mud arrives before the theoretical wave coming from a centred sonde, and triggers the measurement of A t , even if its amplitude is attenuated (Fig. 15-13b). The transformation to attenuation from the amplitude measured in a CBL tool in millivolts depends mainly on the transmitter receiver spacing (Fig. 1515). We can establish that smaller spacings (3 feet) always give better resolution than a large spacing. Figure 15-16 is an example of a CBL log. The interpretation of the CBL consists of the determination of the bond index whch is defined as the ratio of the attenuation in the zones of interest to the maximum attenuation in a well cemented zone. A bond index of 1 therefore, indicates a perfect bond of casing to cement to formation. Where the bond index is less than 1, this indicates a less than perfect cementation of the casing. However, the bonding may still be sufficient to isolate zones from one another and so still be acceptable. Generally some lower limit is set on the bond index, above which the cementation is considered acceptable (Fig. 15-17). The interpretation of the bond index is helped by the use of the Variable Density Log or VDL. Attenuation can be calculated from the amplitude by using the chart shown in Fig. 15-18, which also

244

FIXED

GATE

FLOATING

GATE

Fig. 15-11. Example of logs recorded with fixed gate and floating gate showing the influence of the gate system on the measurement (courtesy of Schlumberger).

allows determination of the compressional strength of the cement. Some companies offer this computation directly from their well-site equipment (e.g. the Schlumberger CSU). 15.3.2. Attenuation index

at

Amplitude

at

In its use in open hole Lebreton et al. (1977) proposed a calculation of an index I, defined by the relation: 1, = (V2 +

K P ,

TOOL CENTERED DETECTION LEVEL

TOOL ECCENTEREO

Time TRANSIT

--

TIME A t

(15-1 1)

EFFECT on A t

where V,, V2 and V3 are the amplitude of the three first half-cycles of the compressional wave. According

Amplitude

POOR BONO

E3

I+

M

a

I"l

J

\

Skipping

Fig. 15-12. Cycle skipping with floating gate system recording in the case of good bond (courtesy of Schlumberger).

I

I

I

2"

I

I I"

, , I , , 0

1 I"

1

I

2"

DI STA N C E ECC E N TE RE D

Fig. 15-13. a. Phenomenon of Ar decrease due to eccentralization of the tool (courtesy of Schlumberger). b. Compressional arrival amplitude vs the distance by which a tool is eccentered in open hole (from Morns et al., 1963).

245

SINGLE RECEIVER MICROSECONDS

I

SNW RECEIVER GAMMA RAY MILLIVOLTS

Do

MCROSKOlDS

In

Fig. 15- 16. Example of a CBL recorded with a VDL. Case of a well bonded casing (courtesy of Schlumberger). Fig. 15-14. Example of eccentering effects on Ar and amplitude recorded with the CBL (courtesy of Schlumberger).

h

Care of a 7” casing

to these authors this index should be a function of the permeability: (15-12) 1, = a log(k,/C1) + P where: k , = permeability measured along the axis of the core; FOR Born) INDEX.0.8

SOUND A TTENUA TION (dblft)

Fig. 15-15. Relationship between amplitude and attenuation for different spacings (from Brown et al., 1971).

Fig. 15-17. Length of cemented interval required for zone isolation (for Bond Index = 0.8).

246 dblft

COMP~IESSIVE STRENGTH psi

70

4ooo xxx)

1ooo

lo00

Fig. 15-20. Photograph of the signal received o n the oscilloscope.

yx)

2 50 I00

50

Fig. 15-18. CBL interpretation chart for centered tool only and 3 foot-spacing (courtesy of Schlumberger).

p, =viscosity of the wetting fluids in the rock; a and p are constants for a given tool and well.

However, we have to take into account the fact that it is not possible to record the whole wave using the

CBL, except if we use the long-spacing sonic. In that case, we can record the entire signal as shown by Fig. 15-19 and of course process it. In the other cases, it is necessary to use a photographic system on the screen of an oscilloscope (Fig. 15-20) or to use a digitization of the wave train that can later be played back on film. We can equally, as proposed by Welex, measure the amplitude of the same half-wave of the signal at two different receivers, and calculate the ratio, which should be only a function of the acoustic transmission factor of the formation. The ratio is converte$ to attenuation by using a chart (Fig. 15-21). We have to remember, however, that the transmission coefficients in open hole are very sensitive to the hole size and rugosity of the wall which in effect implies that attenuation as measured in open hole cannot normally be used. 15.4. AN EXPRESSION FOR THE LAW OF ATTENUATION IN OPEN HOLE By using experimental laboratory measurements Morlier and Sarda (1 97 1) proposed the following

A TTENUA TION (db/ft)

Fig. 15-19. Digital recording of the wave train: (a) amplitude-time mode or wiggle-trace; (b) intensity modulated-time mode (VDL).

Fig. 15-21. Chart to convert amplitude ratio to attenuation (from Anderson and Riddle, 1963).

247

equations for the attenuation of the longitudinal and transverse waves in a saturated porous rock: (15-13) S, = 2.3 Sp

(15-14)

where: S = specific surface (surface area of the pores per unit volume); = porosity; k = permeability; pr = fluid density; p = fluid viscosity; f = signal frequency.

+

Fig. 15-23. Schematic explaining the conversion of amplitude in white and black (from Guyod and Shane, 1969).

15.5. VARIABLE DENSITY LOG (VDL) The principle is shown in Figs. 15-22 and 15-23. A record is made of the signal transmitted along the logging cable during a 1000-ps period using a special camera. We can then either reproduce the trace (Fig. 15-19a) by using an amplitude-time mode in which the wave train is shown as a wiggle trace or translate it into a variable surface by darkening the area depending on the height of the positive half-waves of the sonic signal (Fig. 15-19b). Thls last method is known as the intensity modulated-time mode. The different arrivals can be identified on the VDL. Casing arrivals appear as regular bands whereas the formation amvals are usually irregular. It is sometimes possible to distinguish amongst the arrivals between those linked with compressional waves and those with shear waves, by the fact that the latter arrive later and that they are at a sharper angle (Fig.

Fig. 15-22. Principle of operation of the Variable Density Log (courtesy of Schlumberger).

15-24). They are often of higher energy (higher amplitude and therefore a darker trace). In the case of the Schlumberger VDL the five foot receiver is used in order to improve the separation between waves.

Fig. 15-24. VDL recording showing how the P-waves can be separated from the S-waves by using time and angle (courtesy of Schlumberger).

248 TIME 1

TIME 2

TIME 4

TIME 3

TIME5

1-

"E'

, d

5

.

---- Route of the firstarrival of the refracted compressional wave

-

Route of the firstarrival of the compressional wave reflected a t a bed boundary

Fig. 15-25. Schematic explaining the formation of chevrons (courtesy of Schlumberger).

VDL-recording often has distinguishable chevron patterns. These are related to secondary arrivals caused by reflections and conversion of the primary waves at the boundaries of media with different acoustic characteristics, perhaps corresponding to: (a) bed boundaries; (b) fractures; (c) hole size variations; and (d) casing joints. Chevrons appear on longitudinal as well as transverse waves. The appearance of this phenomenon is explained by the schemes in Fig. 15-25. At time 1, when the wave leaves the transmitter E, part of the wave is refracted downwards as far as the receiver R. Its travel time is Tp. Another part of the wave is re-

fracted upwards, is reflected at a bed boundary and goes down to the receiver. Its transit time is: TI

= (rP>A+2d,(Afp)A

At time 2, the tool has moved up, d decreases (d2) and T, as well. * At time 3, d, is zero and T3 = (Tp)A,. As soon as the transmitter is above the bed boundary (time 4), the wave is reflected upwards and so does not arrive at the receiver. This carries on happening as long as the transmitter and the receiver are on different sides of the boundary. When the receiver itself passes to the other side of

rlME IN PSECS

low transit time zone

I

P S Fig. 15-26. Example of VDL showing chevron patterns on P- and S-waves (courtesy of Schlumberger).

249

MWSIlred chevron angle

TIME IN pSECS

0

Computed At b3clft)

2000

I

( a t s - 1 3 0 - 1.85) Atp 70

P

S

chevron slope = A. tg (chewon angle) =2At

=

A

VDL scale ratio : A ( 1 ) A=-- wseclinch _ -l=W O 100 feethnch 10

t

Fig. 15-27. Computation of A I from ~ the slope of the chevron pattern.

the boundary (time 5) it detects once again an arrival reflected from the boundary and at a transit time equal to:

This can be done if there are S-chevrons. In this case, At, is given by the gradient (Fig. 15-27). We have in fact: At, = id/t

An example of chevron patterns is given in Fig. 15-26. The main applications of a study of chevron patterns are: (A) Fracture detection Depending on the angle that the fracture planes make with the hole we have to consider three different cases: (a) Fractures whose inclination is less than 35". The amplitude of the compression wave is hardly reduced. We can expect only a small amount of reflection. The VDL will have the following characteristics: (1) Strong amplitude of the compressional wave (E, or E2); (2) weak or no P-chevron pattern; (3) low amplitude of the shear waves; and (4) well defined S-chevron pattern. (b) Fractures with an inclination between 35" and 85". The amplitude of the P-wave is reduced. The amplitude of the S-wave goes up and the VDL has the following characteristics: (1) low-amplitude P wave (E, and E2); (2) little or no S-chevron patterns; and (3) some P-chevron patterns. (c) Fractures with an inclination of over 85". These are very difficult to detect by acoustic methods. (B) The calculation of At,

We can also calculate it by a method analyzing the whole wave train. The changes in At, are larger than those of At,, which explains why the S-wave arrivals are not parallel to the P-wave arrivals. The difference in time between P- and S-wave arrivals can be approximated by the equation:

T, - Tp= (spacing) (At, - At,) from which we solve for At,: At , = At p

r,- Tp + ___ spacing

Thus, in the example of Fig, 15-23 between 4277 and 4281 the VDL, whose spacing is five feet, gives:

T, - T, = 200 ps

(approx.)

The At p read by the uncompensated tool is around 45 ps/ft from which we have: At , = 40

+ 45 = 85 ps/ft

Remarks: Another method to find At, is to record two VDL's, one with a 3-ft, the other a 5-ft spacing, and to determine the S-wave arrivals on each one. Then, the respective arrival times are measured and the difference divided by 2 ft.

250

15.6. REFERENCES 1 . CBL Brown, H.D., Grijalva, V.E. and Raymer, L.L., 1971. New developments in sonic wave train display and analysis in cased holes. Log Analyst, 12 (1). Grosmangin, M. et al., 1960. The Cement Bond Log. Soc.Pet, Eng. AIME, Pasadena Meeting, Paper no. 1512 G. Grosmanging, M., Kokesh, F.P. and Majani, P., 1961. A sonic method for analyzing the quality of cementation of borehole casings. J. Pet. Technol., 165-171; Trans., AIME, 222. Muir, D.M. and Latson, B.F., 1962. Oscillographs of acoustic energy and their application to log interpretation. Document P.G.A.C., Houston, 1962. Pardue, G.H., Moms, R.L., Gollwitzer, L.H., and Moran, J.H., 1963. Cement Bond Log. A study of cement and casing variables. Soc. Pet. Eng. AIME, Los Angeles Meeting, Paper No. 453. Poupon, A., 1964. Interpretation of Cement Bond Logs. Document Schlumberger, Paris. Putman, L., 1964. A progress Report on Cement Bond Logging. J. Petr. Technol. Riddle, G.A., 1962. Acoustic Propagation in Bonded and Unbonded Oil Well Casing. Soc. Pet. Eng. AIME, Los Angeles Meeting, Paper no. 454. Thurber, C.H. and Latson, B.F., 1960. SATA Log Checks Casing Cement Jobs. Petrol. Eng., Dec. 1960. Schlumberger, 1976. The essentials of cement evaluation.

2. Attenuation and VDL, VSP Anderson, W.L. and Riddle, G.A., 1963. Acoustic amplitude ratio logging. Soc. Petr. Eng. AIME, 38th Annu. Fall Meeting, New Orleans, Paper 722. Anderson, W.L. and Walker, T., 1961. Application of open hole acoustic Amplitude Measurements. Soc. Petr. Eng. AIME, 36th Annu. Fall Meeting, Dallas, Paper 122. Fons, L.H., 1%3. Use of acoustic signal parameters to locate hydrocarbons and fractured zones. P.G.A.C. Service report, Houston. Fons, L.H., 1963. Acoustic scope pictures. Soc. Pet. Eng. AIME, 38th Annu. Fall Meeting, New Orleans, Paper 724. Fons, L.H., 1964. Utilisation des paramktres du signal acoustique pour la localisation directe des hydrocarbures et la determination des zones fracturh. Bull. Assoc. FranG. Techn. PC., 167 (in English: P.G.A.C., no. 64.5). Gardner, G.H.F., Wyllie, M.R.J. and Droschak, D.M., 1964. Effect of pressure and fluid saturation on the attenuation of the elastic waves in sands.J. Pet. Technol., 16 (2). Gregory, A.R., 1965. Ultrasonic pulsed-beam transmission and reflection methods for measuring rock properties. Some theo-

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