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Downflow amplitude decrease of ground penetrating radar reflections in base surge deposits
Journal of Volcanology and Geothermal Research 105 (2001) 25±34
www.elsevier.nl/locate/jvolgeores
Down¯ow amplitude decrease of ground penetrating radar re¯ections in base surge deposits B. Cagnoli*, T.J. Ulrych Department of Earth and Ocean Sciences, University of British Columbia, 6339 Stores Road, Vancouver, BC, Canada V6T 1Z4 Received 24 January 2000; accepted 24 July 2000
Abstract Ground penetrating radar (GPR) data were collected parallel to a ¯ow direction in the base surge deposits of the Ubehebe hydrovolcanic ®eld (Death Valley, California). These data showed a down¯ow amplitude decrease of the re¯ections that was displayed by computing Fourier transforms and the average square of the sample points of the traces. This trend probably re¯ects some aspects of the lateral facies variation of base surge deposits, and could be explained by the concomitant down¯ow increase in sorting and decrease in grain size with a consequent reduction of the differences between the beds, which, in turn, causes a reduction of the re¯ected energy. These results suggest that, although the GPR pro®les are traditionally used merely as 2-D images of the subsurface stratigraphy, they could be useful in obtaining information about the heterogeneous distribution of subsurface physical properties. The down¯ow decrease of the amplitude of the signal could be used as a ¯ow direction indicator when the position of the vent is unknown, although other geologic information and ®eld constraints are probably necessary. q 2001 Elsevier Science B.V. All rights reserved. Keywords: ground penetrating radar; base surge deposits; Ubehebe Crater; California
1. Introduction A topic of ongoing research in rock physics is the attempt to evaluate properties of unexposed rocks (such as their water content, composition or textural features) directly from ground penetrating radar (GPR) data (Rea and Knight, 1998). This should be possible because re¯ections in GPR pro®les are caused by subsurface dielectric discontinuities, which can be, for example, due to differences in water content, chemical composition or texture of the lithostratigraphic units. Although GPR pro®les are traditionally used as 2-D images of the subsurface stratigraphy, they probably contain more information, * Corresponding author. E-mail address: [email protected] (B. Cagnoli).
but the extraction of this information is not straightforward and constitutes virtually a new research ®eld. Ground penetrating radar is an electromagnetic wave re¯ection technique (Davis and Annan, 1989; Daniels, 1996; Reynolds, 1997) that employs transmitting and receiving antennae, which are moved along survey lines. Transmitting antennae emit electromagnetic waves that propagate through the subsurface and are re¯ected (as well as refracted, diffracted, absorbed, etc.) by interfaces characterized by changes in dielectric properties. The re¯ected waves are then detected by receiving antennae. At each antenna location a trace is collected, which comprises a series of sample points equally spaced in time. These traces are then plotted sequentially, forming a GPR pro®le. The important characteristic of radar surveys is that they are suf®ciently easy and
0377-0273/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0377-027 3(00)00250-X
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B. Cagnoli, T.J. Ulrych / Journal of Volcanology and Geothermal Research 105 (2001) 25±34
quick to implement so that data can be collected continuously from proximal to distal positions supplementing the few available outcrops. The purpose of this paper is to show that GPR data can record subsurface heterogeneities which, even if not obvious in GPR pro®les, can be discerned by comparing numerically the individual radar traces. We assume that quantitative differences in the traces relate to changes in the physical properties of the pyroclastic deposits. The GPR data illustrated in this paper have been collected in the Ubehebe hydrovolcanic ®eld (Death Valley, California). 2. Geological background Base surges are high-velocity, turbulent ¯ows produced by explosive magma±water interactions forming tuff cones and tuff rings (Fisher and Schmincke, 1984; Cas and Wright, 1987). They are highly expanded, low particle concentration ¯ows capable of moving in all directions radial to the volcanic vent. During ¯owage the turbulence diminishes and the grain transport mechanism changes from suspension to surface traction, but a rapid deposition from a highly concentrated suspension without tractional transport is expected near the vent (Sohn and Chough, 1989). Base surge deposits are thick around the vent, becoming thinner with increasing distance from the vent, and usually do not reach distances more than 10 km. The phreatomagmatic juvenile clasts, characteristically, are ®ne-grained because of the high degree of fragmentation caused by the magma± water interaction (Cas and Wright, 1987). The Ubehebe Craters are located in the northern part of the Death Valley National Park, California, on the slope of the Tin Mountains at an elevation of 800 m above sea level (Strand, 1967; Crowe and Fisher, 1973). The associated base surge deposits have an alkali basalt composition and were probably formed during the Holocene (Crowe, 1990). There are about 12 craters within an area of 3 km 2, which are all tuff rings (Crowe and Fisher, 1973). The Ubehebe Crater is the largest center (700±800 m in diameter and 235 m deep) and is a maar surrounded by a tuff ring, whose deposits have a maximum thickness of 50 m at the crater rim, decreasing outward with a dip of 10±158. The base surge deposits rest upon a
thick (,500 m) sequence of sandstones and conglomerates, which outcrops also within the Ubehebe Crater (Crowe and Fisher, 1973). Base surge deposits have characteristics suitable for study by GPR. Typically they are ®ne-grained, which should reduce the extent of electromagnetic scattering. Even more importantly, the beds in these deposits are typically thin, which means that when the depth of penetration of the electromagnetic waves is limited, the radargrams are still representative, because they can image several beds. The average bed thickness is 10 cm, ranging from more than 1 m near the vent to only a few centimeters in the most distal locations (Fisher and Schmincke, 1984). The results of preliminary GPR surveys carried out in the Ubehebe hydrovolcanic ®eld with 50, 100 and 200 MHz antennae are described by Cagnoli and Russell (2000). 3. Data collection Data were collected using the GPR PulseEKKO 1000 (manufactured by Sensors and Software) that makes use of a 200 V transmitter. A ®eld computer Husky FC-486 controlled the radar system. All data presented here were collected with 900 MHz antennae (which are shielded) to obtain high-resolution images of the shallow subsurface. The maximum depth of penetration is about 1.2 m and for this reason only base surge deposits have been imaged since, in this area, they are thicker than 1.2 m (Cagnoli and Russell, 2000). Throughout the GPR survey, the collection parameters were kept constant to allow comparisons between the traces. Survey parameters include: antennae separation equal to 17 cm, step size equal to 2 cm, and 32 stacks. The number of stacks is the number of traces collected at each antenna position, which are averaged to increase the signal to noise ratio. In order to minimize the presence and magnitude of artifacts related to the console position (Sensors and Software, 1999), antennae and console were kept at a constant separation of no less than 20±25 m during the entire data collection. The magnitude of these artifacts has been evaluated in a ®eld experiment described in a later paragraph. GPR pro®les were collected along a ¯ow direction north of the Ubehebe Crater (Fig. 1). The ®rst letter of their names is H or K (Fig. 1). These pro®les are 10 m
B. Cagnoli, T.J. Ulrych / Journal of Volcanology and Geothermal Research 105 (2001) 25±34
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the change in radar response due to the lateral facies variations in the base surge deposits. One common mid-point (CMP) pro®le (Annan et al., 1975; Reynolds, 1997) was collected in the same location as each GPR pro®le to evaluate the subsurface velocity of the electromagnetic waves. Fig. 2 presents one of the most proximal CMP (CMPH2X9 coincident with H2X9) and the most distal (CMPK1X9 coincident with K1X9). It is important to note that easily discernible hyperbolae due to re¯ections from subsurface beds can be identi®ed only in proximal CMP pro®les and not in the distal ones (Fig. 2). In any case, the visible hyperbolae suggest an electromagnetic wave velocity equal to 0.12 m/ns. This velocity was computed using the software Gradix q (Interpex). Finally, four GPR pro®les were collected along a ¯ow-perpendicular direction (Fig. 1). The ®rst letter of their names is X (Fig. 1). Only four ¯ow-perpendicular pro®les were collected because pro®les distributed along a larger distance would have probed deposits from other ¯ows, which traveled along other directions radial to Ubehebe Crater.
Fig. 1. Map showing the locations of the GPR pro®les in the Ubehebe hydrovolcanic ®eld, Death Valley, California.
long and present subparallel, subhorizontal and sometimes wavy re¯ections. The geometry of the re¯ections has been interpreted by Cagnoli and Ulrych (submitted). All surveys were carried out directly in contact with the top of the base surge deposits (Strand, 1967) because there is no soil in the area. These pro®les are situated in the central part of the northern valley, where the deposits are probably thicker and less disturbed by an irregular paleotopography. They are positioned to avoid small hillocks that probably correspond to paleotopographic highs. These highs could have disturbed the regular ¯ow of the turbulent base surges affecting the lateral facies variation of their deposits. Furthermore, in the entire data set, there is no evidence of large ballistic blocks that would have caused diffraction hyperbolae due to point re¯ectors (Reynolds, 1997). There was also no evidence of moisture in the deposits (the data were collected at the end of the summer). Re¯ections from large ballistic blocks and/or water could have masked
4. Data analysis: methods and results Traces from the various ¯ow-parallel pro®les were plotted separately and compared visually and numerically after application of a signal saturation correction ®lter (dewow). The ®rst 8 ns of each trace were clipped to eliminate ground and air waves. These earlier events have much higher amplitudes than the deeper re¯ections and would have strongly biased the results of any numerical comparison of the traces. For this reason, the same time window between 8 and 23 ns has been used for each trace. No gain functions have been applied to avoid possible distortion of the data. All calculations were made using MATLAB w routines. Fig. 3 presents one of these comparisons involving one trace from each pro®le, whereas Fig. 4 shows the amplitude spectra computed by means of the Fourier transform. The average square of the amplitude values the of the sample points xk ; 1 , k , N constituting P traces were also computed (i.e. 1=N N1 xk xk ; where N is the number of sample points). This parameter is equivalent to the zero lag autocorrelation (Stearns and
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CMPH1X9 CMPH2X9 Antennae Separation (m) Antennae Separation (m) 0.17
3.53
0
0
5
5
10
10 Time (ns)
Time (ns)
0.17
15
2.41
15
20
20
Ai
rw av e
d
un
ro
G ve wa
25
25
ed
ct
fle
Re s ve wa
Proximal
Distal
Fig. 2. Proximal (CMPH2X9) and distal (CMPK1X9) CMP pro®les collected using 900 MHz antennae. The hyperbolae in CMPH2X9 suggest a subsurface velocity of the electromagnetic waves equal to 0.12 m/ns. The distal pro®le CMPK1X9 does not present visible hyperbolae.
David, 1996) and was plotted versus the distance of the mid position of each pro®le from the center of the Ubehebe Crater. Fig. 5 shows the average square of the sample points (ASSP) of the traces in Fig. 3, whereas Fig. 6 presents the ASSP values of nine other sets of traces, again one from each ¯ow-parallel pro®le. The different traces from the same pro®le are equally spaced along its length for representativeness reasons. Figs. 7 and 8 show, respectively, amplitude spectra and ASSP values of traces from the ¯ow-perpendicular pro®les (those labeled X in Fig. 1). Figs. 3 and 4 show that the amplitudes of the re¯ections of the traces and of the main peaks of the amplitude spectra decrease down¯ow. Also, the ASSP of the traces (Fig. 5) forms a unidirectional data set as suggested by its decrease in the same direction. A similar trend is visible in the plots of the ASSP of the other traces from the same ¯ow-parallel pro®les (Fig. 6). These trends are irregular, but it is clear that
the most proximal values are larger than the most distal ones. Furthermore, the traces from the ¯owperpendicular pro®les and their amplitude spectra (Fig. 7) show maximum amplitude values similar to those of the traces from the ¯ow-parallel ones located at the same distance from the vent (i.e. H4X9 and H5X9). This can be easily checked comparing the ASSP values in Figs. 5 and 8. 5. Models: method and results Two sets of synthetic pro®les have been computed to interpret the observed trend. These synthetic data have been generated using the PulseEKKO Synthetic Radargram Program (Sensors and Software) and making use of 200 MHz waves, which are vertically incident on ¯at layered earth models. The frequency of the electromagnetic waves is lower than that used in the ®eld but this does not affect the generality of the
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Fig. 3. Comparison of one trace from each ¯ow-parallel pro®le. The names of the pro®les are indicated in the plots. The amplitudes are in microvolts.
conclusions, because we are interested in the relative change of re¯ected energy when we change the characteristics of the subsurface and keep constant the antennae frequency. All re¯ections, including multiples, have been computed. All the earth models consist of 10-m-thick successions of two alternate beds (i.e. A±B±A±B±A±B´ ´ ´) with different thicknesses, dielectric constants and attenuation coef®cients. The beds of the four earth models of the ®rst set of synthetic pro®les have the same thickness (1 m) and the same attenuation contrast (beds A with 9.5 dB/m and beds B with 10 dB/m), but different dielectric property contrasts. The dielectric constant of beds A of the ®rst earth model is 7. The dielectric constant of beds A of the second earth model is 7.5. The dielectric constant of beds A of the third earth model is 8. The dielectric constant of beds A of the fourth earth model is 8.5. The dielectric constant of beds B in all earth models is always 9. Summing up, the dielectric property contrast decreases from the ®rst to the fourth
earth model. Figs. 9 and 10 present, respectively, traces and their ASSP values for these four synthetic pro®les. In order to discard the ground waves, we have taken into consideration the time window between 16 and 90 ns. These data show that the maximum amplitude of traces and the ASSP values decrease when the contrast in dielectric properties is reduced. The second set of four earth models has the same contrast of dielectric constants (beds A and beds B have dielectric constants equal to 8.5 and 9, respectively) and the same attenuation contrast (beds A with 9.5 dB/m and beds B with 10 dB/m), but different bed thickness. The beds of the ®rst earth model are 1 m thick; those of the second earth model are 50 cm thick, of the third earth model are 10 cm thick, and of the fourth earth model are 5 cm thick. The bed thickness thus decreases from the ®rst to the fourth earth model. Figs. 11 and 12 show, respectively, traces and ASSP values of the four synthetic pro®les. Again, only the time windows between 16 and 90 ns have been taken
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Fig. 4. Comparison of amplitude spectra of the traces in Fig. 3. The name of the pro®les are indicated in the plots. The Nyquist frequency is 5000 MHz.
into consideration to discard the ground waves. These data show that maximum amplitude of traces and ASSP values do not decrease when the bed thickness decreases. 6. Effects of console and computer position: experiment and results A ®eld experiment was carried out to assess the
Fig. 5. ASSP of the traces shown in Fig. 3 plotted versus the distance from the center of the Ubehebe Crater.
presence and magnitude of artifacts related to console and computer position, because the computer and the cable connecting the computer and console are considered strong sources of radio frequency noise (Sensors and Software, 1999). This experiment consisted of a GPR data collection with the shielded antennae always in the same position and the console and computer located at different distances from the antennae (25, 20, 15, 10, 5 and 0 m). These traces are different as shown in Fig. 13. The larger differences are located in the earlier portions of the time windows (arrows), but the traces also become more affected by noise when the distance between antennae and console is reduced (this is visible in the lower part of the time windows). In order to quantify these differences, the ASSP of the traces has been computed and displayed in Fig. 14. A time window between 8 and 23 ns was used each time to allow a comparison with the data collected along ¯ow-parallel and ¯ow-perpendicular directions.
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Fig. 6. ASSP of nine sets of traces, one from each ¯ow-parallel pro®le, plotted versus the distance from the center of the Ubehebe Crater.
7. Discussion Amplitude spectra and traces of the ¯ow-parallel pro®les (Figs. 3 and 4) show that the re¯ected energy decreases down¯ow. This is con®rmed also by the CMP pro®les, because the hyperbolae (which are due to subsurface re¯ections) are easily identi®able only in proximal pro®les and not in the distal ones where the re¯ections attenuate strongly when the antennae separation is larger than three or four step sizes (Fig. 2). The ASSP of the traces synthesizes well
Fig. 7. Comparison of one trace and their amplitude spectra from each ¯ow-perpendicular pro®le. The names of the pro®les is indicated in the plots. The amplitudes are in microvolts. The Nyquist frequency is 5000 MHz.
Fig. 8. ASSP of the traces in Fig. 7 plotted versus the distance from pro®le X1X9. The vertical axes in Figs. 5 and 8 are the same to allow a comparison between the plots.
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Fig. 9. Traces of four synthetic pro®les obtained from a succession of two alternate beds (A±B±A±B´ ´´) with increasingly smaller dielectric property contrast. The numerator and denominator of the ratios (7/9, 7.5/9, 8/9, 8.5/9) show the dielectric constants of beds A and B, respectively.
this down¯ow decrease of the re¯ected energy (Figs. 5 and 6). It is important to note that the differences between the traces are not obvious in traditional GPR pro®les, because in these plots the traces are overlapping and the re¯ections are clipped. The traces must be plotted separately, and the calculations of Fourier transforms and ASSP values are very useful to detect the differences. We have shown the down¯ow changes of the amplitude spectra to better display the decay of energy. The experiment carried out reducing the distance between the antennae and console (but keeping the antennae always in the same position) shows that differences between traces can be related to the console position alone (Fig. 13), because the computer and the cables connecting the computer and console are sources of radio frequency noise that can also affect shielded antennae (Sensors and Software, 1999). This is the reason why, during the entire data collection, the distance between the antennae and console has been no less than 20±25 m (the cable
Fig. 10. ASSP of the four traces in Fig. 9. The synthetic pro®les have been obtained from a succession of two alternate beds (A±B± A±B´ ´´) with increasingly smaller dielectric property contrast. The numerator and denominator of the ratios (7/9, 7.5/9, 8/9, 8.5/9) show the dielectric constants of beds A and B, respectively.
Fig. 11. Traces of four synthetic pro®les obtained from earth models whose beds have different thickness as indicated in each plot.
connecting the antennae and console is 30 m long) and constant (to affect equally all traces). In any case, the difference between the ASSP of the traces collected when the separation between the antennae and console was a maximum (25 m) and when it was a minimum (0 ) is much smaller (Fig. 14) than most of the differences between the ASSP values of the traces of the ¯ow-parallel pro®les (Fig. 5). For this reason, we believe that the decrease down¯ow of the amplitude of the re¯ections is due to the subsurface geology and not to artifacts related to the console position. The down¯ow decrease of the amplitude of the re¯ections is probably caused by some aspects of the lateral facies variation in base surge deposits. In base surge deposits, grain size and bed thickness decreases whereas sorting increases down¯ow (Sohn and Chough, 1989; Chough and Sohn, 1990; Lajoie and Stix, 1992). One possible suggestion to explain the observed trend is that the increase of sorting and decrease of grain size produce beds that become increasingly more similar down¯ow with the consequence that the contrast between their dielectric properties is reduced. The ®rst set of synthetic pro®les (Figs. 9 and 10) shows that a decrease of the dielectric
Fig. 12. ASSP of the traces in Fig. 11. The synthetic pro®les have been obtained from earth models whose beds have different thickness as indicated in the plot.
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Fig. 13. Traces collected keeping the antennae always in the same position and the console and computer at different distances from the antennae. These distances are shown in the plots. The arrows indicate the position of the larger differences between the traces. The amplitudes are in microvolts.
property contrast causes a decrease of the amplitude of the re¯ections. It is important to note that the reduction of the bed thickness alone does not produce a decrease of the re¯ected energy, as suggested by the second set of synthetic pro®les (Figs. 11 and 12). But the effect of the dielectric property contrast can compensate that arising from the bed thickness, because it decreases the differences between these beds. Unfortunately, the re¯ections in GPR pro®les are not impulse-like but wavelets comprising more than one peak (Daniels, 1996). This certainly decreases the resolution of the trend, but the general pattern does not appear to be masked. In any case, we assume that the wavelet is the same in all pro®les because the conditions of data collection were the same during the
Fig. 14. ASSP of the traces in Fig. 13. The traces have been collected keeping the antennae always in the same position and the console and computer at different distances from the antennae. These distances are shown in the plot. The vertical axes in Figs. 5, 6 and 14 are the same to allow a comparison between the plots.
entire GPR survey (i.e. the differences between the traces are not due to different wavelets). The destructive interference of overlapping wavelets can explain why the amplitudes of the re¯ections in the earth model with 5-cm-thick beds are smaller than those with 10-cm-thick beds (although both are larger than in the other models with thicker beds). The down¯ow decrease of the amplitude of the signal could be used as a ¯ow direction indicator when the position of the vent is unknown. But this trend is not regular, and traces from pro®les distributed along a large distance must be taken into consideration, because opposite trends can be observed in small portions of the data set (Figs. 5 and 6). For example, the traces of the few ¯ow-perpendicular pro®les (Figs. 7 and 8), although similar to those of the ¯ow-parallel ones which are at the same distance from the crater rim, form a west±east decreasing trend. This suggests that extreme care must be taken in assessing ¯ow directions with this method, and other geologic information and ®eld constraints are probably necessary. The comparisons between traces are also affected by the position of the selected time window, because too shallow a time window can include the strong air and ground waves, whereas too deep a time window is noisier. Other variables affecting the comparison between traces are for example, the presence or lack of water in the deposits (i.e. the season) and local features such as large ballistic blocks or irregularities in the palaeotopography, which can cause strong re¯ections unrelated to the lateral facies variation.
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8. Conclusions Ground penetrating radar data are mainly used to image major underground discontinuities, but they probably contain a larger amount of subsurface information, because characteristics such as grain size, packing and composition of a rock control its dielectric properties. For example, the GPR data collected along a ¯ow direction in the Ubehebe hydrovolcanic ®eld present a down¯ow decrease of the amplitude of the re¯ections. This probably re¯ects some aspects of the lateral facies variation of base surge deposits whose sorting increases and grain size decreases down¯ow. The concomitant increase of sorting and decrease of grain size probably reduce the differences between the beds in more distal positions and consequently also the amplitude of the re¯ections. But a simple visual inspection of GPR pro®les does not allow the recognition of subtle degrees of similarities or dissimilarities between the traces. For this reason a numerical comparison of the traces is recommended, and the evaluation of amplitude spectra and the average square of the sample points is a very useful visual and computational aid. Acknowledgements We gratefully acknowledge the reviewing of the manuscript by the responsible editor Professor Lionel Wilson. We are also indebted to Steve Cosway of Sensors and Software for the use of the PulseEKKO 1000. The ®rst author was awarded a NATO Fellowship. We thank also the rangers of the Death Valley National Park for the research permit. References Annan, A.P., Davis, J.L., Scott, W.J., 1975. Impulse radar wide
angle re¯ection and refraction sounding in permafrost. Geol. Surv. Can. Pap. 75-1C, 335±341. Cagnoli, B., Russell, J.K., 2000. Imaging the subsurface stratigraphy in the Ubehebe hydrovolcanic ®eld (Death Valley California) using ground penetrating radar. J. Volcanol. Geotherm. Res. 96, 45±56. Cagnoli, B., Ulrych, T.J., submitted. Ground penetrating radar images of unexposed climbing dune-forms in the Ubehebe hydrovolcanic ®eld (Death Valley, California). J. Volcanol. Geotherm. Res. Cas, R.A.F., Wright, J.V., 1987. Volcanic Successions, Modern and Ancient. Chapman & Hall, London, 520 pp. Chough, S.K., Sohn, Y.K., 1990. Depositional mechanics and sequences of base surges, Songaksan tuff ring, Cheju Island, Korea. Sedimentology 37, 1115±1135. Crowe, B.M., Fisher, R.V., 1973. Sedimentary structures in base surge deposits with special reference to cross-bedding, Ubehebe Craters, Death Valley, California. Geol. Soc. Am. Bull. 84, 663±682. Crowe, B.M., 1990. Ubehebe, California. In: Wood, C.A., Kienle, J. (Eds.), Volcanoes of North America, United States and Canada. Cambridge University Press, Cambridge, 354 pp. Daniels, D.J. 1996. Surface-penetrating Radar. The Institution of Electrical Engineers, London, 300 pp. Davis, J.L., Annan, A.P., 1989. Ground penetrating radar for highresolution mapping of soil and rock stratigraphy. Geophys. Prospecting 37, 531±551. Fisher, R.V., Schmincke, H.-U., 1984. Pyroclastic Rocks. Springer, Berlin, 472 pp. Lajoie, J., Stix, J. 1992. Volcaniclastic rocks. In: Walker, R.G., James, N.P. (Eds.), Facies Models, Response to Sea Level Change. Geological Association of Canada, pp. 101±118. Rea, J., Knight, R., 1998. Geostatistical analysis of ground-penetrating radar data: a means of describing spatial variation in the subsurface. Water Resour. Res. 34, 329±339. Reynolds, J.M., 1997. An Introduction to Applied and Environmental Geophysics. Wiley, Chichester, UK, 796 pp. Sensors and Software 1999. PulseEKKO 1000 Run. User's guide, version 1.2, 70 pp. Sohn, Y.K., Chough, S.K., 1989. Depositional processes of the Suwolbong tuff ring, Cheju Island (Korea). Sedimentology 36, 837±855. Stearns, S.D., David, R.A., 1996. Signal Processing Algorithms in Matlab. Prentice Hall, Upper Saddle River, 372 pp. Strand, R.G. 1967. Mariposa Sheet, Geologic Map of California in scale 1:250.000, Division of Mines and Geology, Sacramento, CA.
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Down¯ow amplitude decrease of ground penetrating radar re¯ections in base surge deposits B. Cagnoli*, T.J. Ulrych Department of Earth and Ocean Sciences, University of British Columbia, 6339 Stores Road, Vancouver, BC, Canada V6T 1Z4 Received 24 January 2000; accepted 24 July 2000
Abstract Ground penetrating radar (GPR) data were collected parallel to a ¯ow direction in the base surge deposits of the Ubehebe hydrovolcanic ®eld (Death Valley, California). These data showed a down¯ow amplitude decrease of the re¯ections that was displayed by computing Fourier transforms and the average square of the sample points of the traces. This trend probably re¯ects some aspects of the lateral facies variation of base surge deposits, and could be explained by the concomitant down¯ow increase in sorting and decrease in grain size with a consequent reduction of the differences between the beds, which, in turn, causes a reduction of the re¯ected energy. These results suggest that, although the GPR pro®les are traditionally used merely as 2-D images of the subsurface stratigraphy, they could be useful in obtaining information about the heterogeneous distribution of subsurface physical properties. The down¯ow decrease of the amplitude of the signal could be used as a ¯ow direction indicator when the position of the vent is unknown, although other geologic information and ®eld constraints are probably necessary. q 2001 Elsevier Science B.V. All rights reserved. Keywords: ground penetrating radar; base surge deposits; Ubehebe Crater; California
1. Introduction A topic of ongoing research in rock physics is the attempt to evaluate properties of unexposed rocks (such as their water content, composition or textural features) directly from ground penetrating radar (GPR) data (Rea and Knight, 1998). This should be possible because re¯ections in GPR pro®les are caused by subsurface dielectric discontinuities, which can be, for example, due to differences in water content, chemical composition or texture of the lithostratigraphic units. Although GPR pro®les are traditionally used as 2-D images of the subsurface stratigraphy, they probably contain more information, * Corresponding author. E-mail address: [email protected] (B. Cagnoli).
but the extraction of this information is not straightforward and constitutes virtually a new research ®eld. Ground penetrating radar is an electromagnetic wave re¯ection technique (Davis and Annan, 1989; Daniels, 1996; Reynolds, 1997) that employs transmitting and receiving antennae, which are moved along survey lines. Transmitting antennae emit electromagnetic waves that propagate through the subsurface and are re¯ected (as well as refracted, diffracted, absorbed, etc.) by interfaces characterized by changes in dielectric properties. The re¯ected waves are then detected by receiving antennae. At each antenna location a trace is collected, which comprises a series of sample points equally spaced in time. These traces are then plotted sequentially, forming a GPR pro®le. The important characteristic of radar surveys is that they are suf®ciently easy and
0377-0273/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0377-027 3(00)00250-X
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quick to implement so that data can be collected continuously from proximal to distal positions supplementing the few available outcrops. The purpose of this paper is to show that GPR data can record subsurface heterogeneities which, even if not obvious in GPR pro®les, can be discerned by comparing numerically the individual radar traces. We assume that quantitative differences in the traces relate to changes in the physical properties of the pyroclastic deposits. The GPR data illustrated in this paper have been collected in the Ubehebe hydrovolcanic ®eld (Death Valley, California). 2. Geological background Base surges are high-velocity, turbulent ¯ows produced by explosive magma±water interactions forming tuff cones and tuff rings (Fisher and Schmincke, 1984; Cas and Wright, 1987). They are highly expanded, low particle concentration ¯ows capable of moving in all directions radial to the volcanic vent. During ¯owage the turbulence diminishes and the grain transport mechanism changes from suspension to surface traction, but a rapid deposition from a highly concentrated suspension without tractional transport is expected near the vent (Sohn and Chough, 1989). Base surge deposits are thick around the vent, becoming thinner with increasing distance from the vent, and usually do not reach distances more than 10 km. The phreatomagmatic juvenile clasts, characteristically, are ®ne-grained because of the high degree of fragmentation caused by the magma± water interaction (Cas and Wright, 1987). The Ubehebe Craters are located in the northern part of the Death Valley National Park, California, on the slope of the Tin Mountains at an elevation of 800 m above sea level (Strand, 1967; Crowe and Fisher, 1973). The associated base surge deposits have an alkali basalt composition and were probably formed during the Holocene (Crowe, 1990). There are about 12 craters within an area of 3 km 2, which are all tuff rings (Crowe and Fisher, 1973). The Ubehebe Crater is the largest center (700±800 m in diameter and 235 m deep) and is a maar surrounded by a tuff ring, whose deposits have a maximum thickness of 50 m at the crater rim, decreasing outward with a dip of 10±158. The base surge deposits rest upon a
thick (,500 m) sequence of sandstones and conglomerates, which outcrops also within the Ubehebe Crater (Crowe and Fisher, 1973). Base surge deposits have characteristics suitable for study by GPR. Typically they are ®ne-grained, which should reduce the extent of electromagnetic scattering. Even more importantly, the beds in these deposits are typically thin, which means that when the depth of penetration of the electromagnetic waves is limited, the radargrams are still representative, because they can image several beds. The average bed thickness is 10 cm, ranging from more than 1 m near the vent to only a few centimeters in the most distal locations (Fisher and Schmincke, 1984). The results of preliminary GPR surveys carried out in the Ubehebe hydrovolcanic ®eld with 50, 100 and 200 MHz antennae are described by Cagnoli and Russell (2000). 3. Data collection Data were collected using the GPR PulseEKKO 1000 (manufactured by Sensors and Software) that makes use of a 200 V transmitter. A ®eld computer Husky FC-486 controlled the radar system. All data presented here were collected with 900 MHz antennae (which are shielded) to obtain high-resolution images of the shallow subsurface. The maximum depth of penetration is about 1.2 m and for this reason only base surge deposits have been imaged since, in this area, they are thicker than 1.2 m (Cagnoli and Russell, 2000). Throughout the GPR survey, the collection parameters were kept constant to allow comparisons between the traces. Survey parameters include: antennae separation equal to 17 cm, step size equal to 2 cm, and 32 stacks. The number of stacks is the number of traces collected at each antenna position, which are averaged to increase the signal to noise ratio. In order to minimize the presence and magnitude of artifacts related to the console position (Sensors and Software, 1999), antennae and console were kept at a constant separation of no less than 20±25 m during the entire data collection. The magnitude of these artifacts has been evaluated in a ®eld experiment described in a later paragraph. GPR pro®les were collected along a ¯ow direction north of the Ubehebe Crater (Fig. 1). The ®rst letter of their names is H or K (Fig. 1). These pro®les are 10 m
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the change in radar response due to the lateral facies variations in the base surge deposits. One common mid-point (CMP) pro®le (Annan et al., 1975; Reynolds, 1997) was collected in the same location as each GPR pro®le to evaluate the subsurface velocity of the electromagnetic waves. Fig. 2 presents one of the most proximal CMP (CMPH2X9 coincident with H2X9) and the most distal (CMPK1X9 coincident with K1X9). It is important to note that easily discernible hyperbolae due to re¯ections from subsurface beds can be identi®ed only in proximal CMP pro®les and not in the distal ones (Fig. 2). In any case, the visible hyperbolae suggest an electromagnetic wave velocity equal to 0.12 m/ns. This velocity was computed using the software Gradix q (Interpex). Finally, four GPR pro®les were collected along a ¯ow-perpendicular direction (Fig. 1). The ®rst letter of their names is X (Fig. 1). Only four ¯ow-perpendicular pro®les were collected because pro®les distributed along a larger distance would have probed deposits from other ¯ows, which traveled along other directions radial to Ubehebe Crater.
Fig. 1. Map showing the locations of the GPR pro®les in the Ubehebe hydrovolcanic ®eld, Death Valley, California.
long and present subparallel, subhorizontal and sometimes wavy re¯ections. The geometry of the re¯ections has been interpreted by Cagnoli and Ulrych (submitted). All surveys were carried out directly in contact with the top of the base surge deposits (Strand, 1967) because there is no soil in the area. These pro®les are situated in the central part of the northern valley, where the deposits are probably thicker and less disturbed by an irregular paleotopography. They are positioned to avoid small hillocks that probably correspond to paleotopographic highs. These highs could have disturbed the regular ¯ow of the turbulent base surges affecting the lateral facies variation of their deposits. Furthermore, in the entire data set, there is no evidence of large ballistic blocks that would have caused diffraction hyperbolae due to point re¯ectors (Reynolds, 1997). There was also no evidence of moisture in the deposits (the data were collected at the end of the summer). Re¯ections from large ballistic blocks and/or water could have masked
4. Data analysis: methods and results Traces from the various ¯ow-parallel pro®les were plotted separately and compared visually and numerically after application of a signal saturation correction ®lter (dewow). The ®rst 8 ns of each trace were clipped to eliminate ground and air waves. These earlier events have much higher amplitudes than the deeper re¯ections and would have strongly biased the results of any numerical comparison of the traces. For this reason, the same time window between 8 and 23 ns has been used for each trace. No gain functions have been applied to avoid possible distortion of the data. All calculations were made using MATLAB w routines. Fig. 3 presents one of these comparisons involving one trace from each pro®le, whereas Fig. 4 shows the amplitude spectra computed by means of the Fourier transform. The average square of the amplitude values the of the sample points xk ; 1 , k , N constituting P traces were also computed (i.e. 1=N N1 xk xk ; where N is the number of sample points). This parameter is equivalent to the zero lag autocorrelation (Stearns and
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CMPH1X9 CMPH2X9 Antennae Separation (m) Antennae Separation (m) 0.17
3.53
0
0
5
5
10
10 Time (ns)
Time (ns)
0.17
15
2.41
15
20
20
Ai
rw av e
d
un
ro
G ve wa
25
25
ed
ct
fle
Re s ve wa
Proximal
Distal
Fig. 2. Proximal (CMPH2X9) and distal (CMPK1X9) CMP pro®les collected using 900 MHz antennae. The hyperbolae in CMPH2X9 suggest a subsurface velocity of the electromagnetic waves equal to 0.12 m/ns. The distal pro®le CMPK1X9 does not present visible hyperbolae.
David, 1996) and was plotted versus the distance of the mid position of each pro®le from the center of the Ubehebe Crater. Fig. 5 shows the average square of the sample points (ASSP) of the traces in Fig. 3, whereas Fig. 6 presents the ASSP values of nine other sets of traces, again one from each ¯ow-parallel pro®le. The different traces from the same pro®le are equally spaced along its length for representativeness reasons. Figs. 7 and 8 show, respectively, amplitude spectra and ASSP values of traces from the ¯ow-perpendicular pro®les (those labeled X in Fig. 1). Figs. 3 and 4 show that the amplitudes of the re¯ections of the traces and of the main peaks of the amplitude spectra decrease down¯ow. Also, the ASSP of the traces (Fig. 5) forms a unidirectional data set as suggested by its decrease in the same direction. A similar trend is visible in the plots of the ASSP of the other traces from the same ¯ow-parallel pro®les (Fig. 6). These trends are irregular, but it is clear that
the most proximal values are larger than the most distal ones. Furthermore, the traces from the ¯owperpendicular pro®les and their amplitude spectra (Fig. 7) show maximum amplitude values similar to those of the traces from the ¯ow-parallel ones located at the same distance from the vent (i.e. H4X9 and H5X9). This can be easily checked comparing the ASSP values in Figs. 5 and 8. 5. Models: method and results Two sets of synthetic pro®les have been computed to interpret the observed trend. These synthetic data have been generated using the PulseEKKO Synthetic Radargram Program (Sensors and Software) and making use of 200 MHz waves, which are vertically incident on ¯at layered earth models. The frequency of the electromagnetic waves is lower than that used in the ®eld but this does not affect the generality of the
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Fig. 3. Comparison of one trace from each ¯ow-parallel pro®le. The names of the pro®les are indicated in the plots. The amplitudes are in microvolts.
conclusions, because we are interested in the relative change of re¯ected energy when we change the characteristics of the subsurface and keep constant the antennae frequency. All re¯ections, including multiples, have been computed. All the earth models consist of 10-m-thick successions of two alternate beds (i.e. A±B±A±B±A±B´ ´ ´) with different thicknesses, dielectric constants and attenuation coef®cients. The beds of the four earth models of the ®rst set of synthetic pro®les have the same thickness (1 m) and the same attenuation contrast (beds A with 9.5 dB/m and beds B with 10 dB/m), but different dielectric property contrasts. The dielectric constant of beds A of the ®rst earth model is 7. The dielectric constant of beds A of the second earth model is 7.5. The dielectric constant of beds A of the third earth model is 8. The dielectric constant of beds A of the fourth earth model is 8.5. The dielectric constant of beds B in all earth models is always 9. Summing up, the dielectric property contrast decreases from the ®rst to the fourth
earth model. Figs. 9 and 10 present, respectively, traces and their ASSP values for these four synthetic pro®les. In order to discard the ground waves, we have taken into consideration the time window between 16 and 90 ns. These data show that the maximum amplitude of traces and the ASSP values decrease when the contrast in dielectric properties is reduced. The second set of four earth models has the same contrast of dielectric constants (beds A and beds B have dielectric constants equal to 8.5 and 9, respectively) and the same attenuation contrast (beds A with 9.5 dB/m and beds B with 10 dB/m), but different bed thickness. The beds of the ®rst earth model are 1 m thick; those of the second earth model are 50 cm thick, of the third earth model are 10 cm thick, and of the fourth earth model are 5 cm thick. The bed thickness thus decreases from the ®rst to the fourth earth model. Figs. 11 and 12 show, respectively, traces and ASSP values of the four synthetic pro®les. Again, only the time windows between 16 and 90 ns have been taken
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Fig. 4. Comparison of amplitude spectra of the traces in Fig. 3. The name of the pro®les are indicated in the plots. The Nyquist frequency is 5000 MHz.
into consideration to discard the ground waves. These data show that maximum amplitude of traces and ASSP values do not decrease when the bed thickness decreases. 6. Effects of console and computer position: experiment and results A ®eld experiment was carried out to assess the
Fig. 5. ASSP of the traces shown in Fig. 3 plotted versus the distance from the center of the Ubehebe Crater.
presence and magnitude of artifacts related to console and computer position, because the computer and the cable connecting the computer and console are considered strong sources of radio frequency noise (Sensors and Software, 1999). This experiment consisted of a GPR data collection with the shielded antennae always in the same position and the console and computer located at different distances from the antennae (25, 20, 15, 10, 5 and 0 m). These traces are different as shown in Fig. 13. The larger differences are located in the earlier portions of the time windows (arrows), but the traces also become more affected by noise when the distance between antennae and console is reduced (this is visible in the lower part of the time windows). In order to quantify these differences, the ASSP of the traces has been computed and displayed in Fig. 14. A time window between 8 and 23 ns was used each time to allow a comparison with the data collected along ¯ow-parallel and ¯ow-perpendicular directions.
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Fig. 6. ASSP of nine sets of traces, one from each ¯ow-parallel pro®le, plotted versus the distance from the center of the Ubehebe Crater.
7. Discussion Amplitude spectra and traces of the ¯ow-parallel pro®les (Figs. 3 and 4) show that the re¯ected energy decreases down¯ow. This is con®rmed also by the CMP pro®les, because the hyperbolae (which are due to subsurface re¯ections) are easily identi®able only in proximal pro®les and not in the distal ones where the re¯ections attenuate strongly when the antennae separation is larger than three or four step sizes (Fig. 2). The ASSP of the traces synthesizes well
Fig. 7. Comparison of one trace and their amplitude spectra from each ¯ow-perpendicular pro®le. The names of the pro®les is indicated in the plots. The amplitudes are in microvolts. The Nyquist frequency is 5000 MHz.
Fig. 8. ASSP of the traces in Fig. 7 plotted versus the distance from pro®le X1X9. The vertical axes in Figs. 5 and 8 are the same to allow a comparison between the plots.
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Fig. 9. Traces of four synthetic pro®les obtained from a succession of two alternate beds (A±B±A±B´ ´´) with increasingly smaller dielectric property contrast. The numerator and denominator of the ratios (7/9, 7.5/9, 8/9, 8.5/9) show the dielectric constants of beds A and B, respectively.
this down¯ow decrease of the re¯ected energy (Figs. 5 and 6). It is important to note that the differences between the traces are not obvious in traditional GPR pro®les, because in these plots the traces are overlapping and the re¯ections are clipped. The traces must be plotted separately, and the calculations of Fourier transforms and ASSP values are very useful to detect the differences. We have shown the down¯ow changes of the amplitude spectra to better display the decay of energy. The experiment carried out reducing the distance between the antennae and console (but keeping the antennae always in the same position) shows that differences between traces can be related to the console position alone (Fig. 13), because the computer and the cables connecting the computer and console are sources of radio frequency noise that can also affect shielded antennae (Sensors and Software, 1999). This is the reason why, during the entire data collection, the distance between the antennae and console has been no less than 20±25 m (the cable
Fig. 10. ASSP of the four traces in Fig. 9. The synthetic pro®les have been obtained from a succession of two alternate beds (A±B± A±B´ ´´) with increasingly smaller dielectric property contrast. The numerator and denominator of the ratios (7/9, 7.5/9, 8/9, 8.5/9) show the dielectric constants of beds A and B, respectively.
Fig. 11. Traces of four synthetic pro®les obtained from earth models whose beds have different thickness as indicated in each plot.
connecting the antennae and console is 30 m long) and constant (to affect equally all traces). In any case, the difference between the ASSP of the traces collected when the separation between the antennae and console was a maximum (25 m) and when it was a minimum (0 ) is much smaller (Fig. 14) than most of the differences between the ASSP values of the traces of the ¯ow-parallel pro®les (Fig. 5). For this reason, we believe that the decrease down¯ow of the amplitude of the re¯ections is due to the subsurface geology and not to artifacts related to the console position. The down¯ow decrease of the amplitude of the re¯ections is probably caused by some aspects of the lateral facies variation in base surge deposits. In base surge deposits, grain size and bed thickness decreases whereas sorting increases down¯ow (Sohn and Chough, 1989; Chough and Sohn, 1990; Lajoie and Stix, 1992). One possible suggestion to explain the observed trend is that the increase of sorting and decrease of grain size produce beds that become increasingly more similar down¯ow with the consequence that the contrast between their dielectric properties is reduced. The ®rst set of synthetic pro®les (Figs. 9 and 10) shows that a decrease of the dielectric
Fig. 12. ASSP of the traces in Fig. 11. The synthetic pro®les have been obtained from earth models whose beds have different thickness as indicated in the plot.
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Fig. 13. Traces collected keeping the antennae always in the same position and the console and computer at different distances from the antennae. These distances are shown in the plots. The arrows indicate the position of the larger differences between the traces. The amplitudes are in microvolts.
property contrast causes a decrease of the amplitude of the re¯ections. It is important to note that the reduction of the bed thickness alone does not produce a decrease of the re¯ected energy, as suggested by the second set of synthetic pro®les (Figs. 11 and 12). But the effect of the dielectric property contrast can compensate that arising from the bed thickness, because it decreases the differences between these beds. Unfortunately, the re¯ections in GPR pro®les are not impulse-like but wavelets comprising more than one peak (Daniels, 1996). This certainly decreases the resolution of the trend, but the general pattern does not appear to be masked. In any case, we assume that the wavelet is the same in all pro®les because the conditions of data collection were the same during the
Fig. 14. ASSP of the traces in Fig. 13. The traces have been collected keeping the antennae always in the same position and the console and computer at different distances from the antennae. These distances are shown in the plot. The vertical axes in Figs. 5, 6 and 14 are the same to allow a comparison between the plots.
entire GPR survey (i.e. the differences between the traces are not due to different wavelets). The destructive interference of overlapping wavelets can explain why the amplitudes of the re¯ections in the earth model with 5-cm-thick beds are smaller than those with 10-cm-thick beds (although both are larger than in the other models with thicker beds). The down¯ow decrease of the amplitude of the signal could be used as a ¯ow direction indicator when the position of the vent is unknown. But this trend is not regular, and traces from pro®les distributed along a large distance must be taken into consideration, because opposite trends can be observed in small portions of the data set (Figs. 5 and 6). For example, the traces of the few ¯ow-perpendicular pro®les (Figs. 7 and 8), although similar to those of the ¯ow-parallel ones which are at the same distance from the crater rim, form a west±east decreasing trend. This suggests that extreme care must be taken in assessing ¯ow directions with this method, and other geologic information and ®eld constraints are probably necessary. The comparisons between traces are also affected by the position of the selected time window, because too shallow a time window can include the strong air and ground waves, whereas too deep a time window is noisier. Other variables affecting the comparison between traces are for example, the presence or lack of water in the deposits (i.e. the season) and local features such as large ballistic blocks or irregularities in the palaeotopography, which can cause strong re¯ections unrelated to the lateral facies variation.
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8. Conclusions Ground penetrating radar data are mainly used to image major underground discontinuities, but they probably contain a larger amount of subsurface information, because characteristics such as grain size, packing and composition of a rock control its dielectric properties. For example, the GPR data collected along a ¯ow direction in the Ubehebe hydrovolcanic ®eld present a down¯ow decrease of the amplitude of the re¯ections. This probably re¯ects some aspects of the lateral facies variation of base surge deposits whose sorting increases and grain size decreases down¯ow. The concomitant increase of sorting and decrease of grain size probably reduce the differences between the beds in more distal positions and consequently also the amplitude of the re¯ections. But a simple visual inspection of GPR pro®les does not allow the recognition of subtle degrees of similarities or dissimilarities between the traces. For this reason a numerical comparison of the traces is recommended, and the evaluation of amplitude spectra and the average square of the sample points is a very useful visual and computational aid. Acknowledgements We gratefully acknowledge the reviewing of the manuscript by the responsible editor Professor Lionel Wilson. We are also indebted to Steve Cosway of Sensors and Software for the use of the PulseEKKO 1000. The ®rst author was awarded a NATO Fellowship. We thank also the rangers of the Death Valley National Park for the research permit. References Annan, A.P., Davis, J.L., Scott, W.J., 1975. Impulse radar wide
angle re¯ection and refraction sounding in permafrost. Geol. Surv. Can. Pap. 75-1C, 335±341. Cagnoli, B., Russell, J.K., 2000. Imaging the subsurface stratigraphy in the Ubehebe hydrovolcanic ®eld (Death Valley California) using ground penetrating radar. J. Volcanol. Geotherm. Res. 96, 45±56. Cagnoli, B., Ulrych, T.J., submitted. Ground penetrating radar images of unexposed climbing dune-forms in the Ubehebe hydrovolcanic ®eld (Death Valley, California). J. Volcanol. Geotherm. Res. Cas, R.A.F., Wright, J.V., 1987. Volcanic Successions, Modern and Ancient. Chapman & Hall, London, 520 pp. Chough, S.K., Sohn, Y.K., 1990. Depositional mechanics and sequences of base surges, Songaksan tuff ring, Cheju Island, Korea. Sedimentology 37, 1115±1135. Crowe, B.M., Fisher, R.V., 1973. Sedimentary structures in base surge deposits with special reference to cross-bedding, Ubehebe Craters, Death Valley, California. Geol. Soc. Am. Bull. 84, 663±682. Crowe, B.M., 1990. Ubehebe, California. In: Wood, C.A., Kienle, J. (Eds.), Volcanoes of North America, United States and Canada. Cambridge University Press, Cambridge, 354 pp. Daniels, D.J. 1996. Surface-penetrating Radar. The Institution of Electrical Engineers, London, 300 pp. Davis, J.L., Annan, A.P., 1989. Ground penetrating radar for highresolution mapping of soil and rock stratigraphy. Geophys. Prospecting 37, 531±551. Fisher, R.V., Schmincke, H.-U., 1984. Pyroclastic Rocks. Springer, Berlin, 472 pp. Lajoie, J., Stix, J. 1992. Volcaniclastic rocks. In: Walker, R.G., James, N.P. (Eds.), Facies Models, Response to Sea Level Change. Geological Association of Canada, pp. 101±118. Rea, J., Knight, R., 1998. Geostatistical analysis of ground-penetrating radar data: a means of describing spatial variation in the subsurface. Water Resour. Res. 34, 329±339. Reynolds, J.M., 1997. An Introduction to Applied and Environmental Geophysics. Wiley, Chichester, UK, 796 pp. Sensors and Software 1999. PulseEKKO 1000 Run. User's guide, version 1.2, 70 pp. Sohn, Y.K., Chough, S.K., 1989. Depositional processes of the Suwolbong tuff ring, Cheju Island (Korea). Sedimentology 36, 837±855. Stearns, S.D., David, R.A., 1996. Signal Processing Algorithms in Matlab. Prentice Hall, Upper Saddle River, 372 pp. Strand, R.G. 1967. Mariposa Sheet, Geologic Map of California in scale 1:250.000, Division of Mines and Geology, Sacramento, CA.