Prestack amplitude analysis methodology and application to seismic bright spots in the PO Valley, Italy

GEOPHYSICS. VOL. 55. NO. 2 (FEBRUARY 1990); P. 157-166, 14 FIGS Prestack amplitude analysis methodology and application to seismic bright spots in the PO Valley, Italy Alfred0 Mazzotti* ABSTRACT The amplitude-versus-offset (AVO) characteristics of three separate bright spots on the same seismic section are analyzed. One of the bright spots results from a water-bearing gravel layer, and the others correspond to gas-saturated sandy beds. The amplitude analysis includes reflections from the entire range of incidence angles available from the survey: for the shallower amplitude anomaly, these angles reached values up to 66. Extension of the analysis to longer offsets is aimed at detecting possible critical-angle phenomena in order to reduce the uncertainty when the zero-offset reflection s polarity is unknown. The reflection from the gravel layer has this property. Its amplitude exhibits an initial decrease followed by a sudden rise in the AVO trend due to critical reflection and head waves. The gas-related anomalies have a much different AVO characteristic, one in which the amplitude increases with offset distance. Two seismic events located above the bright spots were also investigated to further verify the validity of the seismic amplitude processing. The AVO trends of the three bright spots and of the two reference levels were compared with analogous trends of synthetic seismograms that were computed from models derived from borehole data. INTRODUCTION PROPOSED AND METHODOLOGY The amplitude behavior of reflections with offset (Backus et al., 1982; Ostrander, 1984; Gelfand et al., 1986) has recently been analyzed for use in seismic hydrocarbon exploration. However, whenever this methodology is applied, various problems must be tackled, the most important of which relate to correct amplitude processing (Yu, 1985) and suitable petrophysical conditions (Dey-Sarkar and James, 1986). A further aspect that I believe must be considered, especially in some geologic environments, is the uncertainty of reflection polarity at zero offset, due to interference, processing, or source effects. If the zero-offset polarity is unknown. then the analysis of amplitudes limited to short offsets and consequently to a small range of incidence angles could lead to incorrect interpretations. There are indeed numerous cases that require determining both zero-offset reflection polarity (i.e.. knowing whether compressionalwave velocity is increasing or decreasing, assuming density to be nearly constant) and amplitude trend with offset. One of the most common cases cited in the literature is a gas-bearing sand overlain by shales that gives rise to an increasing amplitude-versus-offset (AVO) trend and a decrease in compressional-wave velocity (VP). However, increasing AVO trends are not limited to situations in which V,, decreases. A common geologic situation that yields a strong increase in amplitude versus offset, but also an increase in VP. is where oyster banks occur in a siltstone sequence (Gassaway et al.. 1986). Other situations related to the presence of gas may also give rise to decreasing AVO trends and reductions in compressional-wave velocity. due to porosity or cementation effects. Moreover, as shown below for bright spot no. 1, even in areas where a decreasing AVO trend is by itself a negative indicator of the presence of gas, the interpreter may feel uneasy if this information is not corroborated by reflection polarity. The analysis of longer offset reflection amplitudes may remove the ambiguity in reflection polarity. The extension to greater offsets and hence to wider incidence angles is necessary because similar amplitude trends in a limited range of incident angles could result from signals of different polarities. Koefoed (1955) stressed that, for a limited range of incidence angles (up to 30 ), the shape of reflection coefficient curves is only slightly affected by the interchange of the Presented at the 58th Annual International Meeting, Society of Exploration Geophysicists. Manuscript received by the Editor November 30, 1988; revised manuscript received July 25, 1989. *AGIP S.P.A.. Geophysical Research and Development Department, P.O. Box 12069. 20120 Milano, Italy. 0 1990 Sociely of Exploration Geophysicists. All rights reserved. 157

158 Mazzotti incident and underlying media; significant differences occur at larger incidence angles, due to the presence of critical reflections and the different rates of change of reflectioncoefficient amplitudes. This is also illustrated in Figures la and lb where, for two quite different models, the P-wave displacement amplitude reflection coefficients are shown. Note that. in each figure, the reflection coefficient amplitude trends for incidence angles less than 30 are very similar regardless of the medium in which the incident and reflected rays are propagating. These coefficients were computed through the exact solution of the Zoeppritz equations. Similar conclusions can be drawn by examining the approximate expression for reflection coefficients developed by Shuey (1985). For the above reasons the AVO analysis methodology proposed here does not concentrate on the short-offset reflections only; it also uses the longer offsets where critical-angle phenomena cause very high amplitudes due to head waves and total reflection. In theory, such analysis would require the availability of signals for the whole range of incidence angles up to 90. In practice, when examining the offset behavior of reflections due to high-velocity contrasts that produce bright spots on stack sections, the range of incidence angles provided by modern long acquisition spreads is often sufficient. In general, receiver-cable length, target depth, and overlying velocity structure determine the range of incidence angles and, hence, the sensitivity to velocity contrasts. The envelope energy, defined as the sum over the selected time gate of the trace values squared and the quadrature trace values squared, has been chosen as- the reflection-coefficient amplitude measure (Mazzotti. 1984). This parameter appears to be a robust AVO indicator, since it is not affected by the shape of the wavelets. To be precise, we should talk about energy versus offset rather then amplitude versus offset analysis, but they are used synonymously below. The knowledge of the velocity structure and target depth, even if approximate, allows the incidence angle to be estimated for each offset for the reflection being examined. When available, geologic, borehole, and seismic data should z 1.c g 0.5 5 4 YI 4 2 90 Bi 1.4 s-l.8 s Low-cut 12 Hz 24 db/octave be used to develop a set of reasonably representative models from which synthetic seismograms can be computed and compared with actual seismic data. The modeling program used throughout this project is a ray-tracing program that uses the Zoeppritz equations to compute the reflection coefficients of plane compressional waves in elastic and isotropic media and uses Ricker wavelets whose dominant frequencies were derived from estimates of the signal spectra. The synthetic seismograms were computed for models with several interfaces and include transmission and interference etfects~ in- the responses. GEOLOGIC SETTING AND AVAILABLE DATA The seismic line in Figure 2 obliquely crosses the main geologic features of the area, known as the Lombardian Plain, with discoveries of gas-bearing traps in neogenic sediments. The traps are mainly stratigraphic sands enclosed in shaly formations such as the Santerno clays of Pliocene age. The seismic data were acquired with the following parameters: asymmetrical split spread with dynamite source; 72- fold nominal coverage; group interval of 30 m.; minimum offset of I5 m.; maximum offset of 3225 m.; receiver pattern of 24 geophones per group; and pattern length of 30 m. These data have undergone a standard processing sequence based on the minimum-phase assumption and conversion of the migrated stack section to zero-phase, making use of well B data. Time-variant frequency filtering was also carried out with the following parameters: 0.0 s-l.4 s Low-cut 15 Hz 24 db/octave High-cut 60 Hz High-cut 50 Hz 48 db/octave 48 db/octave I.8 s-3.5 s Low-cut 12 Hz 24 db/octave High-cut 40 Hz 48 db/octave 0.0 -r 0-2irk-2 ANGLES OF INCIDENCE 0 0 90 30 60 ANGLES OF INCIDENCE 33 0. ANGLES OF INCIDENCE ANGLE8 OF INCIDENCE Vp/Vs=1.8 Vpz2500 Vs=1390 @=2.2 Vp/Vs=l.8 Vp=28OC Vs=156C @=2.? vp/vs=1.5 vpz2200 vs =1470 e=2.2 vp/vs=2.1 Vp = 2200 vs = 1048 Q q 2.1 FIG. I. P-wave reflection coefficients. Velocities are expressed in m/s and densities in g/cm3. (a) The two media have V,l/V,, ratios of 1.8 and 1.5. (b) The two media have VJV,, ratios of 1.8 and 2.1.

Prestack Amplitude Analysis FIG. 2. Above: migrated stack section (the numbers label the bright spots and the horizons investigated). Below: pseudo-interval velocity section (the three bright spots are evident)..i._...m*.. WtLL A WELL % WELL C 0 VELOCITIES DENSITY 0. f VELOCITIES DENSllY 0. VELOCITIES DENSITY 325 325 500 E z 0 650 0 350 lw0 975 975 1600 DO m/s 4001 300 2ooc, I 1) MS 5ow : \ - 20 g/cm FIG. 3. Depth models from wells A, B. and C.

160 Mazzotti Three wells were drilled to investigate the seismic bright spots, numbered 1, 2, and 3 on both the migrated stack section and the pseudo-interval velocity section of Figure 2. The borehole data consisted of a complete set of logs (sonic, density, resistivity, etc.) and lithostratigraphic information. Shear-wave velocities V, were not measured but were chosen based on a parallel shear-wave survey carried out for direct hydrocarbon detection purposes (Bilgeri et al., 1988). They were then refined by trial and error in the modeling phase to match the actual data. Well A data showed that the strong shallow seismic amplitude anomaly (horizon 1) was caused by a waterbearing unit of partially cemented gravel at the base of the Asti sands formation, a formation that consists of a sequence of platform-slope sediments of Pleistocene age. Figure 3 (we!1 A ) shows- the values- of Y,,, I/,, and densities used in the model that produced the synthetic seismogram in Figure 4; Figure 4 also shows the lithostratigraphy of well A. The label 1 in Figures 2 and 4 indicates the gravel-layer reflection, and 4 corresponds to an Asti sands unit that represents a sedimentation episode in a platform-slope environment. The main reservoir (horizon 2 in Figure 2) was discovered by drilling well B. The pay zone, an Upper Pliocene pinchout that transgresses on the Miocene unconformity, is also evident on the seismic section. The gas has collected in a sandy bed of about 26% porosity that has been interpreted as a subaqueous turbidite fan derived from the erosion of the Alpine Chain. The depth model, defined in terms of VP, V,s, and densities, at well B is illustrated in Figure 3, and the corresponding synthetic seismogram with the well lithostratigraphy is shown in Figure 5. Event no. 2 (Figures 2 and 5) is the reflection from the top of the gas sands, and event no. 5 again relates to a shallower reference horizon in the Asti sands. Well C also drilled a gas-bearing sandy turbidite unit in the Middle Pliocene layers. Figure 3 shows the depth model with VP, V,, and density for each layer. The resulting synthetic seismogram computed by ray tracing and the well lithostratig- raphy are shown in Figure 6. The label 3 points to the gas sand (Figure 3) and to its reflection (Figures 2 and 6). SEISMIC DATA PROCESSING The variation in reflection coefficient with angle of incidence is directly related to the elastic characteristics of the media on both sides of the interface. However, the variation in amplitude and hence energy of the reflected signal with source-receiver distance also depends on propagation, recording, and processing factors that tend to obscure the reflection-coefficientrend. Before tackling AVO analysis, processing aimed at recovery and control of seismic signal amplitudes is required, so that amplitudes depend mainly on reflection coefficients and hence on the elastic parameters of the media. Figure 7 shows the how of data processing operations, the most important of which are described in more detail in the Appendix. The first step involves computing spatially variant geometrical spreading corrections using smoothed values of stacking velocities. The overall effect is to increase amplitudes of longer offset reflections. The second processing step is the application of surface-consistent corrections to seismic data. These have gained wide application both in terms of residual statics corrections and more recently in terms of time-invariant amplitude corrections (Larner et al., 1979; Taner and Koehler, 1981). The latter were very effective in removing effects related to near-surface conditions that strongly affected this land seismic data set. The next operation to be applied to the data is a minimumphase absorption correction (Bickel and Natarajan, 1985), using quality factors estimated with the spectral-ratio method (Jannsen et al., 1983). In terms of AVO analysis, the overall effect is again an increase in amplitudes at larger offsets, although this does not produce great changes in the previously observed trends. The final stages of processing are aimed mainly at maximizing the signal-to-noise ratio. First, the reflections to be investigated by AVO analysis are moveout corrected by static shifts, to avoid stretching effects. Residual time shifts that maximize the horizontal alignment of the reflections are computed by crosscorrelation techniques and applied to the traces in CDP gathers. Finally, to improve the results and to reduce noise effects, an average CDP gather is computed by summing over common-offset traces for each bright spot. Possible reflector dip effects were also taken into account. No correction for receiver-pattern directivity was performed, since the low-velocity near surface causes the emerging rays to be mainly vertical, even for higher offsets. Furthermore. the receiver pattern causes very little signal attenuation; for an incidence angle of 30 from vertical and a frequency of 60 Hz, the attenuation is about 4 db, and for a 20 Hz signal, the attenuation drops to 0.5 db. Comparison of recorded data with synthetic data showed no interference between multiple and primary reflections; and therefore, multiple-removal operations were not performed. AVO ANALYSIS 25 OFFSET cm, 2425 FIG. 4. Lithostratigraphy and synthetic CDP gather corresponding to well A. Bright spot no. 1 (water-saturated gravel layer) Traces taken from about 30 individual CDP gathers were grouped into common offsets every 50 m and then stacked to give the average CDP gather shown in Figure 8 (upper part).

Prestack Amplitude Analysis 161 The reflection at abotir4q ms is caused by the gravel bed and corresponds to the amplitude anomaly on the seismic sections in Figure 2. Offset distances range from 2.5 m to 2375 m and correspond to incidence angles from 1 to 66 for rays striking the shale-gravel interface at a depth of 823 m. The total envelope energy was computed within the indicated time gate for each trace, and the resulting energy versus offset trend is shown in the lower part of Figure 8. The vertical axis represents the normalized envelope energy, and, on the horizontal axis, trace numbers, source-receiver offsets, and estimated incidence angles are indicated. The solid line depicts the energy trend for the actual data. Note that after a decrease at short and middle offsets, a sharp~inereasetakesplace at an offset d&me&about 1900 m. This energy increase has been interpreted as a consequence of critical reflections and head waves for the compressional waves, thus indicating an increase in VP, which with our display convention would produce a trough in a perfect zero-phase seismic section. The band-limited actual data of the seismic sections of Figure 2 cannot resolve the thin gravel layer (10 m), and interference effect make the reflection polarity ambiguous. The synthetic data shown in Figure 8 (central part) represent a close-up of the reflections labeled no. 1 (after NM0 correction) in the synthetic seismogram of Figure 4. The characteristics of the depth model are illustrated in Figure 3 (well A ), and the parameters of the layers being examined are also listed in the following table: v, v, Density (m/s) (m/s) (g/cm31 --~ Overlying sandy shales 2310 1255 2.13 Gravel bed 2730 1539 2.30 Depth of the gravel layer: 823 m Thickness of the gravel layer: 10 m FIG. 5. Lithostratigraphy and synthetic CDP gather corresponding to well B. FIG. 6. Lithostratigraphy and synthetic CDP gather corresponding to well C.

162 Mazzotti Although the synthetic data have different wavelet shapes than do the actual data, the validity of AVO analysis is not affected. The dashed line in Figure 8 represents the energy trend of the synthetic reflections. This curve decreases at the low and middle offsets and increases sharply at long offsets, as does the actual data trend. The greatest discrepancy appears at the low offsets, where the actual data have higher energy than do the synthetic data. In addition, the sharp rises in energy at long offsets do not coincide exactly. The correspondence was not improved by simple modifications, such as using different wavelets, reinterpreting borehole logs, checking the processing sequence, etc. The discrepancy at low offsets could have several causes: interference, focusing, spherical wavefront effects, and mode conversions. The first possibility has been thoroughly analyzed with limited results: the robustness of the energy versus offset trend makes the changes in wavelet shape irrelevant. The overburden could indeed act as a focusing lens especially for the low offsets, but the sections shown in Figure 2 make this second hypothesis improbable. The third cause appears to be the most interesting one. Rendleman and Levin (1988) deal with a liquid earth and show that indeed the spherical nature of the wavefront causes smoothing of the reflection coefficient curve with angle of incidence. However, since we are dealing with a decreasing energy trend before the critical angle, smoothing cannot increase the energy at lower offsets. The opposite can be deduced from Krail and Brysk s (1983) work, where they show that mode conversions in a solid earth can generate relative maxima in the reflection coefficient curve at low incidence angles, despite a decreasing trend before the critical angle. However, their ratio of wavefront radius to wavelength is rather high (about SO), so this elastic explanation, despite its appeal, can be accepted only if some focusing is also present. Bright spot no. 2 (gas-saturated sand layer) The upper part of Figure 9 shows the average CDP gather computed from the actual data. The trace interval is again 50 m. Irregular coverage has resulted in only a few traces at some offsets; these offsets are excluded from the average CDP gather, causing a gap of 600 m between offsets of 525 m and 1125 m. The reflection at about 1. I s comes from the top of the gas sand at a depth of 1143 m with a porosity of about 26%. Shot-to-group offsets range from 25 m to 2375 m corresponding to incidence angles on the target from lo to 59. The energy trend of the actual data was filtered by a three-point smoothing operator and is represented by the solid line in Figure 9; it clearly increases with angle of incidence, as 19 48 SW 66 475 1475 1975 2375 I QEOMETRICAL SpREADINGcorrect I SURFACE CM AMPl..FActoRs w. i corr.ctlo ~ NM0 STATIC corroctlon remldurl l tatlcs corroctlon I COMMON OFFSET GATHERINQ PARTIAL STACK I PRESTACK AMPLITUDE ANALYSIS FIG. 7. Seismic data processing. Flow diagram for amplitudes. FIB;. 8. Horizon no. 1 (gravel layer): (top) actual data, $;$lje) synthetic data, and (bottom) energy versus offset

Overlying shales 2670 1480 2.3 Gas sand 2290 1530 2.1 Depth of the sand layer: 1143 m Thickness of the sand layer: 73 m Prestack Amplitude Analysis 163 is peculiar to reflections from horizons with low Poisson s 2 and IO is caused by the low velocity of the gas sand. Rays ratio, such as sedimentary unjts with trapped gas. strike the shale-sand interface with angles ranging from I to Figure 9 (central part) shows the synthetic seismograms 49 and are recorded at offsets from 25 m to 2475 m. The from the top of the gas sand: the depth model and the energy behavior of the actual reflections is shown by the complete synthetic seismogram are illustrated in Figures 3 solid line, smoothed with a three-point operator, in Figure (well B ) and 5, and the characteristics of the specific IO; this clearly increasing trend is again indicative of a low target are listed below: value of Poisson s ratio in the layer being examined. The corresponding synthetic reflections illustrated in the VP VA Density central part of Figure 10 result from an interface with the (m/s) - (m/s) - (g/cm3) following characteristics: The reflection response, in terms of energy values of the synthetic CDP gather, is represented by the dashed line in Figure 9. The increasing energy trend for the synthetic data corresponds well with that for the actual data (solid line) for the whole range of incidence angles. Bright spot no. 3 (gas-saturated sand layer) The average CDP gather is shown in the upper part of Figure 10 and, for the reasons mentioned previously. a gap of 300 m occurs between offsets of 1675 m and 1975 m. The bright spot at about I.5 s on the seismic sections of Figures VP V, Density (mis) (m/s) (g/cm3) - - Overlying shales 2800 155.5 2.3 Gas sand 2.545 1697 2.2 Depth of the gas-sand layer: 1640 m Thickness of the gas-sand layer: 20 m The complete depth model and the resulting synthetic seismogram are ihustrated in Figures 3 (we!1 C ) and 6. The energy trend for the synthetic data (dashed line in Figure 10) shows a good match with the actual data trend. Rel Er?nce horizons nos. 4 and 5 The reference horizons were considered mainly for checking the accuracy of the amplitude processing at points on the 9. Horizon no. 2 (gas sand): (top) actual data, (middle) synthetic data, and (bottom) energy versus offset trends. FIG. FIG. IO. Horizon no. 3 (gas sand): (top) actual data, (middle) synthetic data. and (bottom) energy versus offset trends.

164 Mazzotti seismic section other than the bright spots and hence do not correspond to any formations of exploration interest. These data have not been subjected to common-offset gathering and partial stacking; therefore, they have a lower signalto-noise ratio and less statistical significance than do the bright-spot data. Nevertheless, analysis of this type of data may give the interpreter confidence in the processing sequence. The models for which the synthetic reflections were computed and the complete synthetic seismograms are again shown in Figures 3 and 4 for horizon no. 4, and in Figures 3 and 5 for horizon no. 5; the precise positions of the layers and the corresponding reflections are labeled accordingly. Event no. 4 (Figure 11) corresponds to a decrease in compressional-wave velocity from 2260 m/s to 2140 m/s at a depth of 563 m and yields a decreasing energy-versus-offset trend. The reflection labeled no. 5 corresponds to an interface at 781 m depth that separates an upper medium with VP = 2225 m/s from a lower medium with VP = 2350 m/s. The actual and synthetic data are displayed in Figure 12 together with their energy trends. The energy trends of the actual data in Figures 11 and 12 have been filtered with a smoothing operator. In general, the correspondence between actual and synthetic energy trends is not as good as that achieved for the bright-spot units. However, considering the lack of preparation of the actual data, the match is acceptable and confirms the validity of the processing. These energy trends also make us cautious in applying residual amplitude corrections for the bright-spot AVO trends, assuming that the amplitude for time gates situated above the bright spots does not vary with offset. Residual amplitude correction can only be effective when the reference time gates are free of offset-dependent effects; to the contrary, when reflections above the bright spot occur with their peculiar AVO trends, as in the examples considered, residual correction may cause severe distortion of the correct AVO trend. CONCLUSIONS From this study, we conclude the following: (1) In the area examined, AVO analysis may be used effectively to distinguish dry bright spots associated with high-velocity layers, such as bright spot no. 1, from gas-related bright spots, such as bright spots nos. 2 and 3. (2) AVO information should be used with a precise knowledge of the normal-incidence polarity, and when uncertainties exist, reflection analysis must be extended to the longer offsets to be definitive. For bright spots associated with high-velocity layers, such as bright spot no. 1, the most distinctive feature of the amplitude-versus-offset trend is the sharp energy increase at longer offsets due to criticalangle phenomena. This energy increase is detectable provided that the spread length, target depth, velocity structure, and the velocity contrast satisfy specific conditions. (3) Prestack amplitude responses from low-velocity gas sands with particularly low values of Poisson s ratio show an increasing energy trend with shot-to-detector distance, as observed for bright spots nos. 2 and 3. (4) Suitable amplitude processing should produce correct AVO trends for any seismic horizon in the 81 1 26 OFFSET (m) 25 475 94785 TRACE 1 10 20 o.oot-_j TRACE, 10 20 OFFSETi?) : 417i5 jl,5 D 0 FIG. 11. Horizon no. 4 (reference layer): (top) actual data, @ii::) synthetic data, and (bottom) energy versus offset FIG. 12. Horizon no. 5 (reference layer): (top) actual data, (middle) synthetic data, and (bottom) energy versus offset trends.

Prestack Amplitude Analysis 165 seismic section. To test the procedure, reference horizons nos. 4 and 5 located above the bright spots were also analyzed. (5) Comparisons should be made with AVO trends from synthetic seismograms computed for appropriate models to be confident of the amplitude processing and of the actual results. ACKNOWLEDGMENTS This paper has been published with the permission of AGIP S.pA. Italy. REFERENCES Backus, M. M._, Nepomuceno, F., and Cao, J., 1982, The reflection seismogram m a solid layered earth: 52nd Ann. Internat. Mtg., Sot. Expl. Geophys., Expanded Abstracts, 416-417. Bickel, S. H., and Natarajan, R. R., 1985, Plane-wave Q deconvolution: Geophysicq, 50, 14261439. Bilgeri, D., Mazzott~, A., Ferber, R. G., and Marschall, R., 1988. Separation of P-SV waves using 2-D convolution filters to improve the resolution of stratigraphic targets: Presented at the ASEGiSEG Internat. Geophys. Conference. Adelaide. Dey-Sarkar, S. K., and James, C. F., 1986, Prestack analysis: relevance of petrophysical properties: 56th Ann. Internat. Mtg.. Sot. Expl. Geophys., Expanded Abstracts, 337-339. Gassawa= J, c -. U., C Brown, R. A.. and Bennett, L. E., 1984, Pitfalls~in seismic amplitude versus offset analysis: case histories: 56th Ann. internat. Mtg., Sot. Expl. Geophys., Expanded Abstracts, 332-334. Gelfand, V.. Ng. P., Nguyen, H., and Larner. K., 1986, Seismic lithologic modeling of amplitude versus offset data: 56th Ann. Internat. Mtg.. Sot. Expl. Geophys., Expanded Abstracts, 334-337. Jannsen, D., Voss, J., and Theilen, F., 1983, Comparison of methods to determine Q in shallow marine sediments from vertical reflection seismograms: Geophys. Prosp., 33, 479-497. Koefoed, 0.. 1955, On the effect of Poisson s ratios of rock strata on the reflection coefficients of plane waves: Geophys. Prosp., 3, 381-387. Krail, P. M.. and Brysk. H., 1983, Reflection of spherical seismic waves in elastic layered media: Geophysics, 48, 655-664. Larner, K. L., Gibson, 9. R., Chambers, R., and Wiggins, R. A., 1979. Simultaneous estimation of residual static and crossdip corrections: Geophysics, 44, 1175-t 192. Mazzotti, A.. 1984, Prestack analysis of seismic amplitude anomalies: 54th Ann. Internat. Mtg., Sot. Expl. Geophys.. Expanded Abstracts, 659-661. Ostrander, W. J., 1984, Plane-wave reflection coefficients for gas sands at nonnormal angles of incidence: Geophysics, 49. 1637-1648. Rendleman, C. A., and Levin, F. K., 1988, Reflection maxima for reflections from single interfaces: Geophysics, 53: 271-275. Shuey. R. T., 1985, A simplification of the Zoeppritz equations: Geophysics. 50, 609-614. Taner. M. T., and Koehler, F., 1981. Surface-consistent corrections: Geophysics, 46, 17-22. Yu, G., 1985, Offset-amplitude variation and controlled amplitude processing: Geaphyksics, 50, 2597-2708. APPENDIX MAIN PROCESSING STEPS Geometrical spreading corrections Geometrical spreading corrections were computed from the smoothed values of stacking velocities. The hyperbolic approximation with Vstack = V,,, gives traveltimes nearly coincident with those calculated by ray tracing depth models derived from well data; for example, for the reflection from the top of the well A gas sands (horizon 2) at an offset of 2500 m, the hyperbolic traveltime approximation is delayed less than 15 ms from the time obtained by ray tracing. For our applications, the corrected reflections generally lie within the time window used to analyze the variation of energy with offset.?y 4 1.7 I Surface-consistent amplitude corrections Sources and receiver ground-coupling variations are clearly seen along the seismic line (Figure A-l, upper part). A regular decay with source-receiver distance is also evident. This estimation was carried out on a single time window from 0.0 s to 3.5 s. Following the application of appropriate time-invariant amplitude corrections, the source and receiver amplitude effects are removed (Figure A-l, lower part). Only the terms related to the subsurface characteristics (indicated with CDP in Figure A-l) assume nonzero values. Absorption corrections Absorption corrections require an estimate of the quality factors for the formations being investigated. Average spectra were estimated for a large number of CDP gathers, and to avoid residual noise effects, Q factors were determined over FIG. A- I. Surface-consistent amplitude factors: (above) before the surface-consistent corrections (below) after amplitude factors have been applied.

166 Mazzotti the signal frequency band determined by coherency measures. The time windows for Q estimation follow zones of uniform lithostratigraphy in the seismic section. The first zone from 0 to 800 ms includes mainly sandy and shaly formations and gives an effective quality factor of 200; the second window from 800 to 2000 ms includes the seismic bright spots and the n~akrunconfo~mity and has an effective Q of 260. The whole set of CDP gathers was then inverse Q filtered over the same time windows and frequency bands used in the Q estimation. By comparing frequency spectra before and after inverse-q filtering (Figure A-2), the effect of the absorption correction can be clearly seen in the increased amplitude at higher frequencies, and in the approximate alignment of slopes in frequencies between 10 and 60 Hz for the spectra in the two time gates. 0 50 100 150 FREQUENCY (Hz) FIG. A-2. Average signal spectra (A) before and (B) after inverse Q filtering. time gates are (top) @0.8 s and (bottom) 0.x-2.0 s.