CA1256975A - Geophysical exploration by interpretation of variations in seismic amplitudes - Google Patents

Abstract

ABSTRACT OF THE DISCLOSURE
The present invention provides a method of seismic exploration for obtaining a measure of the subter-ranean formation rock properties. Incident angle ordered gathers of seismic signal are processed to obtain a measure of the reflection coefficient as well as attri-butes descriptive of variations in amplitude of the seismic signal as a function of incident angle. Such attributes, when plotted on an angle dependent amplitude diagram, are transformed into a most probable estimate of the subterranean formation rock properties as well as a diagnostic of relative lithology and pore fluid contrast.

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Description

~793 Bodine ~2~6~

GEOPHYSICAL EXPLORATION BY
INTERPRETATION OF VARIATIONS
IN SEISMIC AMPLITUDES

BACKG~OUND OF THE INVENTION

1~ The present invention relates generally to a method of geophysical exploration including processing and displaying seismic data to obtain a measure of subterra-nean formation rock properties. Seismic data including a plurality of seismic signals or traces are obtained with 20 sets of seismic sources and seismic receivers. A set of observed attributes, quantitatively descriptive of varia-tions in the seismic signal amplitude as a function of incident angle, are obtained for selected seismic events.
The observed set of attributes provides a measure of the 25 contrast in formation rock properties across subterranean formation interfaces associated with each selected seismic event. The set of observed attributes can be transformed to provide a most probable estimate of the subterranean formation rock properties. Additionally, a diagnostic 30 technique is provided for interpreting relative formation lithology and pore fluid content.
In the continuing search or hydrocarbons con-tained in the earth's subterranean formations, exploration geophysicists have developed numerous techniques ~or 35 imparting seismic wave energy into the earth's subterra-nean Eormations; recording the returning reflected seismic wave energy and processing the recorded seismic wave energy to produce seismic signals or traces. Such seismic :

-2-signals or traces contain a multiplicity of information, e.g., frequency, amplitude, phase, etc., which can be related to formation structure, lithology, or pore fluid content. More recently, geophysicists' interest have 5 turned to evaluating high intensity seismic amplitude events in the seismic signals or traces, i.e., "bright spots" and variations in the seismic signal amplitude as a function of range for selected seismic events. Exemplary of such focus are Quay, et. al., U.S. Patent 10 No. 3,899,768; Thompson, et. al., U.S. Patent No. ~,375,090, and Ostrander, U.S. Patent Nos. 4,316,267 and 4,316,268.
In particular, Ostrander indicates that progres-sive changes in the seismic signal amplitude of a high 15 intensity seismic event, as a function of range, is more likely than not an indicator of a gas-bearing formation.
Specifically, progressive seismic signal amplitude changes, in an increasing or decreasing manner, with increasing range is the criteria for identifying gas-20 bearing formations. Ostrander discloses a method forsignal enhancement to improve the visual resolution of such progressive changes in seismic signal amplitude as a function of range.
Quay recogni~es that lateral variations in the 25 seismic data can be attributed to variations of the litho-logical character of the subterranean formations. Quay obtained such results by extracting selected seismic par-ameters from a seismic wave and thereafter displaying such seismic parameters upon a seismic trace of such seismic 30 data. The visual correlation of events in such seismic parameters relative to the structural interpretation of the seismic trace yielded a scheme for interpreting seismic recor~ sections.
Thompson discloses that acoustic characteristics 35 associated with hydrocarbon-containing formations can be compared with similar synthetic values.
Although evaluation of bright spots has been used to indicate gas reservoirs throughout the world, such -.

analysis is still a calculated risk, as evidenced by the significant number of such events which are nonproductive when actually drilled.
SUMMARY OF THE INVENTION
In accordance with the present invention, a novel method of geophysical exploration is disclosed including processing and displaying seismic data to obtain a measure of subterranean formation rock properties.
Unlike prior qualitative attempts to utilize variations in 10 the amplitude of a seismic signal or trace, the present invention provides the seismologist with a quantitative method for interpreting variations in the amplitude of the seismic signal o{ trace, so as to determine a most prob-able estimate of formation rock properties as well as pore lS fluid content and lithology.
Seismic data including a plurality of seismic signals are obtained from sets of seismic sources and seismic receivers. A first set of attributes descriptive of variations in the seismic signal amplitude as a func-20 tion of incident angle for selected seismic events areobtained. The first set of attributes are transformed into a measure of the subterranean formation rock proper-ties associated with each selected seismic event.
For each selected seismic event, a first measure 25 of reflection coefficient is obtained from variations in the seismic signal or trace amplitude as a function of incident angle. By assuming a set of the most probable rock properties for an overlying formation associated with the selected seismic event of interest and by allowing the 30 underlying formation to have any other set of rock proper-ties, a second measure of reflection coeficient associ-ated with the selected seismic event can be calculated from the contrast in rock properties across such formation interface as well as a second set of attributes.
An angle dependent amplitude diagram can be formed comprising a lithology diagram having contour rep-resentations of the second set of attributes mapped thereon. The first set of attributes are scaled with an , ,.

4 ~ 3~
inversion scalar from units of seismic signal amplitude to units of reflection coefficient. Plotting the scaled first set of attributes on the contour mappings of the second set of attributes of the angle dependent amplitude 5 diagram transforms the quantitative measure of the inci-dent angle dependent seismic signal amplitude into a most probable estimate of rock properties of the underlying formation.
BRIEF DESCRIPTION OF THE DRAWINGS
FIGURE 1 is a common depth point stack of field seismic data;
FIGURE 2 is a common depth point gather of the field seismic traces at SP 491 within a time selected time window;
FIGURE 3 is a plot of seismic amplitude for the seismic event of Figure 2 as a function of incident angle;
FIGURE 4 is a generalized lithology diagLam dem-onstrating the general relationship between formation lithology and the formation properties Vp and Vs;
FIGURE 5 is a lithology diagram demonstrating the transformation of attributes descriptive of variations in the amplitude of the seismic signal as function of incident angle into formation properties;
FIGURES 6a-d are representative diagrams of the 25 variation of the reflection coefficient as an angular function of range for sectors of Bo and Bl values;
FIGURE 7 is an angle dependent amplitude diagram having contour plots of the theoretical attribute Bo values on a lithology diagram;
FIGURE 8 iS an angle dependent amplitude diagram having contour plots of the theoretical attribute B
values on a lithology diagram;
FIGURE 9 is a process flow diagram of the present invention;
FIGURE 10 is an angle dependent amplitude dia-gram with the relationship of the assumed formation rock properties and the calculated reservoir formation rock properties thereon, for the seismic event at SP 491;

"3~i'5 FIGURE 11 is an unstacked CDP gather of field seismic signals at SP 47~ of Figure l;
F~GURE 12 is an unstacked CDP gather of fiel~
seismic signals at SP 474 of Figure l;
FIGURE 13 is a plot of the field seismic signal amplitude for the selected seismic event of Figure 11 as a function of incident angle and a least squares fit thereto;
FIGURE 14 is a plot of the seismic signal ampli-10 tude for the selected seismic event of Figure 12 as a function of incident angle and a least squares fit thereto;
FIGURE 15 iS an angle dependent amplitude dia-gram showing the relationship between the assumed over-15 lying roof formation rock properties and the calculated underlying reservoir formation properties for the seismic event at 2.6 seconds about SP 474, SP 479 and SP 491.
DESCRIPTION OF THE PREFERRED EMBODIMENT
OF THE INVENTION
Prior to the discussion of the preferred embodi-ment of the present invention, a brief description of the fundamental concepts underlying the discovery may prove beneficial and are presented herewith.
Seismic prospecting has employed the concept of 25 imparting seismic wave energy into the surface of the earth whereby the resulting seismic waves propagate down-wardly into the earth and are partially reflected back towards the surface when compressional impedance changes ; within the earth are encountered. A change from one for-30 mation type to another, if accompanied by a change in com-pressional impedancel can provide a measure of the reflec-tion coefficient Rc(~) for normal incidence (~=0) of the seismic wave upon a formation interface. The normal inci-dent reflection coefficient RC(0) depends upon both the 35 compressional velocity and density changes between the two adjacent formations according to the formula:

~ 3 ~2 P2 ~1 P1 Rc(O ) = Ar/Ai ~2 P2 + ~1 Pl (1) where Ar is the amplitude from the reflected seismic 5 signal and Ai is the amplitude of the normally incident seismic signal; ~1 is the compressional velocit~ of the seismic wave in the overlying formation Fl; ~2 is the compressional velocity of the acoustic wave in formation F2 below the interface; P1 is the density of the over-10 lying formation F1 and P2 is the density of the under-lying formation F2.
The reflection coefficient Rc(~) for non-normal incidence depends upon the shear wave velocities in the adjacent formations as well as the compressional veloci-15 ties and densities of both formations. A theoreticalreflection coefficient Rc(~) can be calculated for an assumed contrast in formation rock properties using the exact plane wave solution as shown by K. Aki and R. G. Richards ("Quantitative Seismolog~ Theory and 20 Method", Freeman and Company, San Francisco, 1980, pages 144-151). An approximation to the exact plane wave sol-ution for the theoretical reflection coefficient Rc(~) for any angle of incidence ~ can be obtained using the following:
Rc(~) = Bo ~ Bl tan ~ ~ B2tan ~ sin ~ (2) Attributes Bo~ Bl and B2 provide a quantitative measure of the variations in the seismic signal amplitude as a function of incident angle. Those skilled in the art 30 recognize that the attribute Bo has substantially the same value as shown in Equation (1) for the normally incident reflection coefficient RC(0). The attribute Bo is strictly related to the compressional impedance change across a formation interface. The attributes B1 and B2 35 are related to both changes in compressional wave velocity and shear wave velocity. Moreover, the attribute Bl is related to the mid-range slope or rate of change of the seismic signal amplitude, while attribute B2 is related to large incident angle amplitude changes.
Equation ~2) can also be employed to provide a 5 measure of an observed reflection coe~ficient Rc(0) obtained from incident angle dependent variations in the seismic signal amplitude for a selected seismic event in an incident angle ordered gather of field seismic signals.
Thus, Equation (2) provides means for relating the assumed 10 contrast in formation rock properties to the incident angle dependent variations in the seismic signal amplitude so as to obtain a most probable estimate of the formation rock properties as well as lithology and pore fluid con-tent. Equation (2) is merely by way of example since 15 other parametric equations can be developed having a ne set of attributes related to different formation proper-ties.
Since a selected seismic event in an incident angle ordered gather of field seismic signals is associ-20 ated with an incident angle ~, a least squares solution ofEquation (2) can provide a measure of the observed reflec-tion coefficient Rc(0) and the observed attributes Bo~
Bi, and B2.
The dip and depth of a given subterranean forma-25 tion, the interval velocities as a function of depth, andthe largest offset in the seismic acquisition system det-ermine the maximum incident angle 0 or aperture for the reflected seismic signals. If the incident angle 0 is generally constrained to angles approximately no more than 30 35, the attribute B2 can be disregarded.

Looking first to Figure 1, a common depth point (CDP) seismic section of seismic data is shown. A time window of a CDP gather of unstacked field seismic signals 35 or traces about SP491 of Figure 1 are shown in Figure 2.
Particular attention is drawn to the seismic event at approximately 2.6 sec. of Figure 2 and indicated with arrows thereon.

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Using ~quation (2) and disregarding the B2 term, a least-squares fit can be made to the incident an~le dependent variations in the seismic signal amplitude for the seismic event indicated at time 2.6 sec of Figure 2 to 5 obtain a measure of the observed reflection coefficient Rc(~) as well as observed attributes Bol and Bl'. To do so, the field seismic signal or trace amplitudes corre-sponding to the seismic event, indicated by the arrows in Figure 2, are first measured across the CDP gather of 10 unstacked field seismic signals and then the amplitude for each field seismic signal is represented as a function of incident angle in Figure 3.
Specifically, as shown in the field seismic signal or trace amplitudes for the selected seismic event 15 in Figure 2 are measured to obtain values of the amplitude of the field seismic signals as a function of incident angle. The measured values of the field seismic signal or trace amplitude are represented on Figure 3 as indicated by the curve 10. A least-squares fit approximation to 20 curve 1~ using Equation (2) is represented by curve 20.
Curve ~0 thus provides a statistically optimi~ed fit of the incident angle-dependent variations in the amplitude of the field seismic signals for the selected seismic event as well as a measure of the observed reflection 25 coefficient Rc,(~). Additionally~ the values obtained from Equation (2) for the observed attributes ~0 and Bl are shown on Figure 3. Since the maximum incident angle a was restrained to less than 32~ the attribute B2 can be disregarded.
LITHOLOGY DIAGRAM
Looking now to Figure 4, a lithological diagram is shown having axes of the ratio of compressional wave velocity to shear wave velocity ~Vp/Vs) and shear wave velocity (Vs3. The lithological blocks outlined in 35 Figure 4, i.e., LS, SS~ and SH, indicate that lithology has a general relationship to the ratio of compressional wave velocity to shear wave velocity (Vp/Vs) and shear wave velocity (Vs). Lithology diagrams similar to ~ 3~
_g~
Figure 4 have been proposed by others which map out somewhat different regions for the same lithologies. And, in fact, although the lithology diagram shown in Figure 4 has axes of selected formation rock properties, those 5 skilled in the art recognize that other formation rock properties can be used as axes, e.g., Poissons ratio versus Vp. The present choice of axes is merely by way of example. Regardless of the axes chosen, those skilled in the art agree that such lithology diagrams demonstrate 10 that a general relationship exists between formation lithology and formation properties (e.g., Vp and Vs) even though no precise correlation has been established between formation lithology and these formation properties. It is sufficient that such lithology diagrams recognize a gen-15 eral correlation between relative changes in formationlithology and formation properties.
Specifically, in Figure 4, it has been generally found that block LS can represent limestone formations, block SS can represent sandstone formations, and block SH
20 can represent shale formations. The lithology diagram can also include constant compressional velocity Vp contours.
As we shall see, the lithology diagram of Figure 4, albeit without the lithology blocks represented thereon~ can be used to transform the observed attributes, Bo~ Bi, and 25 B2, descriptive of incident angle-dependent seismic signal amplitude variations, into a most probable estimate of formation rock properties.
An important seismic formation rock property not represented on the lithology diagram of Figure 4 is den-30 sity. However, one can implicitly include formation den-sity p by use of the following dependent relation:
p = a(V )-25 (3) 35 where "a" is approximately equal to 0.23. Therefore, any point on the lithology diagram in Figure 4 can represent the rock properties Vp, Vs and the density as a function of compressional velocity p(Vp) for a given formation.

'5 Pairs of points on Figure 4 can be considered to represent a contrast in ~ormation rock properties between adjacent subterranean formations for which a theoretical reflection coefficient Rc(~) can be calculated as well as theoretical 5 attributes Bo~ Bl and B2 associated therewith.
THEORETICAL ATTRIBUTES
Assuming that the elastic formation rock proper-ties (Vp, Vs and p (Vp)) are generally known or reasonable estimates can be made for an overlying Eormation F1 asso-10 ciated with a selected seismic event, such properties canbe represented by a star on a lithology diagram as in Figure 5. Allowing the adjacent underlying reservoir for-mation F2 associated with the selected seismic event to have any other set of elastic rock properties, within a 15 radius of potential formation rock properties about the star, each pair of potential underlying reservoir forma-tion F2 rock properties and assumed overlying roof forma-tion Fl rock properties defines an elastic interface having a specific contrast in rock properties for which 20 the theoretical reflection coefficient Rc(0) can be obtained.
Selected pairs of underlying formation F2 and overlying formation F1 rock properties can be employed to calculate the exact elastic plane wave reflection coeffi-25 cients Rc(~) as described by Aki and Richards in "Quanti-tative Seismology Theory and Method," supra pages 144-151.
A statistically optimized fit of Equation (2) to the resulting exact solution of the theoretical reflection coefficient Rc(~) can be employed to obtain estimates of 30 the theoretical attributes Bol B1, and B2. In the pre-ferred embodiment the statistically optimized fit is obtained by employing a least-squares fit of Equation (2) to the exact solution the theoretical reflection coeffi-cient Rc(~). Those skilled in the art recognize that 35 other statistical techniques can be employed.
In fact, the zero values for the theoretical attributes Bo~ and Bl, can define quadrants as represented . , .

~ ~ r ~ 3~7~

in Figure 5, corresponding to selected contrasts in formation rock properties. The exact plane wave solutions for the theoretical reflection coefficient Rc~ repre-sented in Figures 6a-d correspond to selected contrasts in 5 formation rock properties wherein the selected underlying Eormations F2 rock properties fall within the respective sectors A, B, C, and D of Figure 5. Each sector of Figure 5 thus defines a different combination of values for theoretical attributes Bo and Bl. As shown in Table 1 10 below, it can be seen that the theoretical attributes Bo and Bl have the same sign in sectors B and D and opposite signs in sectors A and C.

Sector Bo Bl A - +
20 B + +
C +
D - _ In this case, the theoretical reflection coeffi-25 cient Rc(~) and the associated theoretical attributes Bo and Bl were obtained by assuming an aperture or maximum incident angle ~ of approximately 30. The assumed set of rock properties for the overlying formation Fl are indi-cated by the star in Figure 5. Thus, pairs of points on 30 the lithology diagram of Figure 5 can be associated with sets of theoretical attributes Bo and Bl which can encom-; pass a complete spectrum of potential rock properties for the underlying formation F2.
The lithology diagram of Figure 5 can be supple-35 mented to include sets of contour lines of the theoretical attributes Bo and Bl, as shown separately in Figures 7 and 8, respectively. Hereafter, lithology diagrams having sets of theoretical attributes Bo and Bl contour lines ., , ,,

3'75 mapped thereon are designated angle dependent amplitu~e (ADA) diagrams.
OBSERVED ATTRIBUTES
As a first step in relating t~e theoretical 5 attributes Bo and Bl to the actual seismic data acquired, it is necessary to analyze unstacked CDP gathers of the ~ield seismic signals to ascertain tru~ variations in the amplitude of the field seismic signal with incident angle for a selected seismic event. Although unstacked CDP
lO gathers of field seismic signals or traces have been employed, such is merely exemplary since it is understood that other methods can be used for sorting field seismic signals or traces into gathers of ordered incident angle (either increasing or decreasing).
Preprocessing of the field seismic signals includes correcting for true relative amplitude recovery;
correcting for normal moveout; correcting for surface and residual statics; balancing the frequency content from near range to far range; and bandpassing for optimum 20 signal-to-noise ratio. Thereafter, selected seismic events can be aligned across unstacked CDP gathers of the field seismic signals and the amplitudes measured so as to obtain a least-squares fit to Equation (2) to obtain a measure of the observed reflection coefficient Rc(~) and 25 the observed attributes Bo and Bi.
~ ecall that the attribute Bo is a measure of the normal incident reflection coefficient RC(0), and the attribute Bl is a measure of the midrange slope or rate of variation of the seismic signal amplitude. The attribute 30 B2 is generally not used because of its sensitivity to noise, an effect that can be avoided by limiting the max-imum incidence angle or aperture to approximately 35 for which the attribute B2 is not significant. After values for the observed attributes Bo and Bi are obtained from 35 the seismic data, it is necessary to relate the observed attributes Bo and Bl to the theoretical attributes Bo and Bl.

-13- ~ 3~
A seismic scalar K is employed by the seismolo-gist to invert the observed attributes Bo and Bl from units of seismic signal amplitude into units of reflection coefficient. The seismic scalar K is generally related to 5 the seismic data acquisition parameters and certain of the preprocessing steps as empirically determined by the seis-mologist.
TRANSFORMATION OF ATTRIBUTES
In order to relate the observed attributes Bo lO and Bi to the theoretical attributes Bo and Bl, it is necessary to find an appropriate seismic scalar K to invert seismic amplitude into units of reflection coeffi-cient. This scalar K is generally unknown. Approxima-tions can be made that bracket a reasonable range of 15 values. When the observed attributes Bo and Bl are scaled to reflection coefficient units, the new scaled observed attributes Bo and Bl can be plotted on the theoretical attributes Bo and Bl contour lines of the A~A
diagrams in Figures 7 and 8. The point of intersection of 20 the corresponding attribute contour lines associated with the scaled observed attributes Bo and Bl provides a most probable estimate of the underlying reservoir formation F2 rock properties (Vs, Vp, p ~Vp)).
Looking at Figure 9, which is a process flow 25 diagram, it can be seen that seismic data is first acquired in block 110. Thereafter, such seismic data is preprocessed to enhance the true seismic signal amplitude variations with range, as indicated in block 120. It is also necessary to enhance the signal-to-noise ratio of the 30 seismic signal since the observed attributes, Bo~ Bl and B2 must provide a measure of incident angle-dependent variations in the amplitude of the seismic signal or trace and not noise. In block 130, the preprocessed field seis-mograms are sorted into gathers of ordered incident angle 35 (either increasing or decreasing) such as the unstacked common depth point gathers of the field seismic signals or traces shown in Figure 2. As a result of the least-squares fit of the field seismic signal or trace ampli--14- ~5~t~5 tudes as a function of incident angle to Equation ~) for a selected seismic event, values of the observed attri-butes Bo and Bi are determined as well as an approxima-tion of the observed reflection coefficient RC(~l, all of 5 which are stored in block 145.
Concurrently, the seismologist inputs the most likely overlying formation rock properties for the over-lying roof formation Fl associated with the seismic event, e.g., Vs, Vp and p (Vp~, in block 150. This information 10 is generally known with some precision for the roof forma-tion Fl. As we shall see later, small variations within this assumption do not significantly alter the end result.
For the underlying formation F2, a plurality of possible values of shear wave velocity Vs and compressional wave 15 velocity Vp are assumed for a fixed density p, as shown in block 160.
In ~lock 170, a solution to exact elastic plane wave theoretical reflection coefficient Rc(~) can be obtained using pairs of the formation Fl rock properties 20 and the formation F2 rock properties associated with the selected seismic event. A least-squares fit of Equa-tion (2) thereto provides a set of theoretical attributes Bo and Bl.
It is germane at this point to note that Equa-25 tion (2) has been used to relate (1) the exact elasticsolutions of the theoretical reflection coefficient Rc(~) derived from pairs of adjacent formation rock properties (2) to the observed amplitude variations in the seismic data with incident angle. This is accomplished by 30 obtaining statistically optimized fits of Equation (2) for both the theoretical and observed reflection coef~icients and thereafter relating their respective attributes.
Contour mappings of a plurality of sets of theoretical attributes Bo and Bl on lithology diagrams can 35 be made to produce ADA diagrams in Block 1~0, such as shown separately in Figures 7 and ~, respectively. This sequence can be reiterated, as shown by line 1~1, by returning to block 160, to recalculate the theoretical 3'~

attributes Bo and Bl, for different assumed formation F2 density p according to Equation (3) by changing the value of "a". Moreover, by line 182 returning to block 150, it is possible to assume different values of compressional 5 wave velocity Vp and shear wave velocity Vs for the forma-tion Fl rock properties and thereafter produce additional sets of the theoretical attributes Bo and Bl contour lines.
Those skilled in the art will recognize that in 10 a computer implemented system, ADA diagrams comprising lithology diagrams having contour mappings of the theoret-ical attributes Bo and Bl represented thereon for a broad range of contrasting formation Fl and F2 rock properties need not actually be obtained as indicated in Block 180.
15 Rather, such ADA diagram having contour mappings of the theoretical attributes Bo and Bl can be stored within a memory retrievable on demand.
Returning now to Block 140 of Figure 9, recall that the observed attributes Bo and Bl, in units of 20 seismic amplitude, were determined for selected seismic events using a least squares fit of Equation (2) to a CDP
gather of unstacked field seismic signals for a selected seismic event and stored in Block 145. In order to relate the observed attributes Bo and Bi to the theoretical 25 attributes Bo and Bl, it is necessary to apply an appro-priate inversion scalar K to invert the observed attri-butes Bo and Bl, which are in units of seismic signal amplitude, into reflection coefficient units of the theor-etical attributes Bo and Bl~
The scaler K used will be described in units of the reflection coefficient Rc(~) it produces. This scalar K is generally unknown. ~owever~ the reasonableness of the range of values assumed can be evaluated in terms of the size of the reflection coefficient Rc(~) produced in 35 light of the actual seismic signal amplitudes. When a selected scalar K i5 applied in block 155, the observed attributes Bo and Bl are inverted to have units commen-surate with the theoretical attributes Bo and Bl. The ~r scaled observed attributes Bo and Bl can then be plotted in block 165 on the ADA diagrams having the theoretical attributes Bo and Bl contour lines produced in Block 180.
As a result o this plotting of the scaled observed attri-5 butes Bo and Bl on the ADA diagrams, a most probableestimate of reservoir formation F2 rock properties can be determined at the intersection of the scaled observed attribute contour lines Bo and Bl in Block 190. And in fact by line 166, iteration of this sequence is provided 10 for varying the scalar ~.
Returning now to the ADA diagrams of Figures 7 and 8, three different seismic scalars K have been speci-fied to produce normal incident reflection coefficients RC(0) of -0.05, -0.10 and -0.20 for the scaled observed 15 attributes Bo and Bl. Recall that the attribute contour lines on the ADA diagrams of Figure 7 and 8 were both der-ived assuming a given set of roof formation Fl rock prop-erties and a wide range of possible sets of reservoir for mation F2 rock properties associated with the selected 20 seismic event. Figures 7 and 8 both indicate that the respective values of the scaled observed attributes Bo and Bl for the different values of the scalar K to pro-duce normal incident reflection coefficients RC(0) of -0.05, -0.10 and -0.20. The point of intersection of the 25 Bo contour line of Figure 7 and the Bl contour line of Figure 8 for the scaled observed attributes Bo and Bl deEines a point which uniquely defines the most probable estimate of the reservoir formation F2 rock properties, Vp, Vs and p(Vp) are shown in Figure lO.
Figure lO also shows the point of intersection of the contour lines for the scaled observed attributes Bo and Bl for variations in the density p of formation F2 according to Equation (4) where "a" is 0.218, 0.230, 0.250 and 0.230 and the scalar R is chosen to produce a 35 normal incident reflection coefficient RC(0) of -0.05, -0.10, and -0.20. For each value of the normal incident reflection coefficient RC(0), the variations in the intersection of the contour lines caused by changes in the .-~ 3t~-17-formation the underlying formation F2 density are represented by a square, a circle, a triangle/ and a dia-mond shape, respectively, in Figure lO~
Allowing the density p of formation F2 to vary 5 within prescribed limits can be seen to have little effect. As such, the user through iterative processing can make determinations of both the observed attributes Bo and Bi, and of the inversion scalars K. The inter-section of the scaled observed attributes Bo and Bl lO plotted on the theoretical attribute Bo and Bl contours defines the most probable estimate of the reservoir forma-tion F2 rock properties (Vpl Vs, p (Vp)) for the under-lying formation F2 in block l90.

Returning to Figures l and 2, the selected seismic event of interest is shown at SP 491 and approxi-mately 2.6 seconds. The results of various trials of res-ervoir formation F2 rock properties (Vs, Vp and p(Vp)) and the seismic inversion scalar K according to the present 20 invention are shown in Tables 2 and 3. In fact, the Fig-ures 7, 8 and lO are demonstrative of the implementation of the present invention as applies to the seismic event at SP 491 and 2.6 seconds and corresponds to the data shown in Table 2.

~5~5 Reservoir Density Reflection Calculated Reservoir Most Relation Coefficient Formation F2 Properties Likely to Vp Rc(~) _Vp Vs Vp/Vs p Result a = 0.218 -0.20 5520 2300 2.40 1.88 -0.10 6510 3100 2.10 1.96 *
-0.05 7020 3600 1.95 2.00 a = 0.230 -0.20 5268 2150 2.45 1.96 *
-0.10 6119 2900 2.11 2.03 *
-0.05 6698 3400 1.97 2.08 a = 0.250 -0.20 4875 1950 2.50 2.09 -0.10 5687 2570 2.13 2.17 *
-0.05 6200 3100 2.00 2.22 a = 0.280 -0.20 4470 1760 2.54 1.29 -0.10 5268 2450 2.15 2.3g *
-0.05 5729 2850 2.01 2.44 Assumed Roof Formation Fl ~ssumed Reservoir Formation F2 Vp = 6777 p = a (Vp) Vs = 3567 Vp/Vs = 1.9 p = 2.276 = .25 (Vp) 25 Within Table 2 the overlying roof formation Fl rock properties are fixed while the potential rock proper-ties of the reservoir formation F2 are allowed to vary to 35 produce sets of theoretical attributes Bo and Bl contour lines as shown in Figures 7 and 8. The density p of the reservoir formation F2 is varied by changing "a" in Equa-tion (3) to values of 0.218, 0.230, 0.250 and 0.280. The q3~7~

scalar K is v~ried to produce normal incident reflection coefficients Rc(O ) from -.05 to -0.20 as seen in Fig~
ures 7, 8 and 10 and is used to invert the observed attri-butes Boi and Bl' derived from a least squares Eit of 5 Equation (23 to the amplitude of the field seismic signals as a function of incident angle as shown in Figure 3.
When higher values of the ratio Vp/Vs are assumed for the roof formation Fl, the same relative dis-tribution of intersection points results, but now is 10 upward and to the right from the formation Fl rock proper-ties shown by the star in in Figure 10. Changes in the density in the roof formation Fl results in a slight rota-tion of the intersection points, but does not otherwise affect the relative overall distribution of intersection 15 points as seen in Table 3, as noted by looking at the det-ermined reservoir formation F2 rock properties.

3'7~

Reservoir Density Reflection Calculated Reservoir Most Relation Coefficient Formation F2 Properties Likely to Vp Rc(~) Vp Vs Vp/Vs __e_ Result a = 0.218 -0.20 5515 2050 2.51 1.85 -0.10 6021 2820 2.14 1.92 *
-0.05 6476 3300 1.96 1.96 a = 0.230 -0.20 4914 1960 2.51 1.93 -0.10 5790 2690 2.15 2.01 *
-0.05 6166 3130 1.97 2.04 a = 0.250 -0.20 4572 1840 2.49 2.06 -0.10 5381 2500 2.15 2.14 *
-0.05 5769 2910 1.9~ 2.18 a = 0.280 -0.20 4161 1630 2.55 2.25 -0.10 4895 2230 2.20 2O34 -0.05 5287 2640 2.00 2.39 Assumed Roof Formation F1 Reservoir Formation F2 Vp = 6777 p = a (Vp) Vs = 3567 Vp/Vs = 1 . 9 p = 2.086 = .23 (vp).25 By examining Tables 2 and 3, a seismologist would agree that certain of the possible calculated reser-voir formation F2 rock properties can be eliminated since 35 only reasonable reservoir formation F2 rock properties are to be considered. In this case, seismologist would con-sider that a normal incident reflection coefficient RC(0) of -0.05 for the large amplitude event indicated at SP 491 ,.....

~ 5~'~'375 and 2.6 seconds of Figures 1 and 2 appears too small, and thus seismologists can eliminate all of those possible rock properties. Likewise, the seismologist can also eli-minate as unlikely all calculated reservoir formation ~2 5 rock properties where the compressional velocity Vp is less than 5000 ft/sec or the density p is less than 1.9 gm/cc. Similarly, all calculated reservoir formation F2 rock properties for reelection coefficient Rc values of -.2 can be eliminated except for a calculated reservoir 10 formation F2 density p is defined by a = 0.23. The remainder of the calculated reservoir ~ormation F2 rock properties are associated with the normal incident reflec-tion coefficient Rc(O ) having a value of about -.10. As such, a range of the most probable estimate of rock pro~
15 erties associated with the seismic event at SP 491 a~d 2.6 seconds are shown in Table 4 derived from the ADA. dia--gram in Figure 10.

Vp = 5900 + 600 ft/sec Vs = 2780 ~ 330 ft/sec Vp/Vs = 2.12 + 0.03 p = 2O14 + 0.20 gm/cm Seismologists would generally expect that a decrease in both the compressional velocity Vp and density p for the reservoir formation F2, i.e., change of forma-tion rock properties of up and to the right from the assumed reservoir formation rock properties indicated by 30 the star on the ADA diagram of Figure 10, is consistent with a change to more poorly consolidated rock. Poor con-solidation at depths on the order of 8,000 to 10,000 ft (generally corresponding to a two way travel time of 2.6 sec) and deeper is characteristic mainly of rocks that 35 are undercompacted. Undercompaction can be associated with overpressurized zones. Thus, one would expect that the seismic event at SP 491 is indicative of the contrast between a consolidated rock and an overpressurized, under-l~ ~`b ~ 9 ~5 compacted rock. Moreover, such a conclusion would indicate that this particular seismic event would be a poor candidate for gaseous hydrocarbons because o~ its high Vp/Vs ratio.
EXAMPLES 3 and 4 However, if we now look at additional field seismic signals or traces progressively to the left on Figure 1, we see in Figures 11 and 12 that the character of the seismic event at approximately 2.6 seconds at 10 SP 479 and SP 474 is changing.
In Figure 11 an unstacked CDP gather of field seismic signals is shown. The field seismic signal ampli-tude for the seismic event indicated by arrows is large and negative at small incident angles (on the left of 15 Figure 11) and decreases with increasing incident angles (to the right). Looking at Figure 12~ an unstacked gather of field seismic signals at SP 474, the field seismic amplitudes for the seismic event indicated by arrows, while still negative, are smaller than previously, and the 20 field seismic signal amplitude increases with increasing incident angle (to the right). The change in character of the seismic event at 2.6 seconds between SP 474 and 479 is clearly shown in Figures 13 and 14 wherein the field seismic signal amplitudes for the selected seismic event 25 of Figures 11 and 12 are plotted as a function of incident angle in curves 60 and 7~, respectively, and a least squares fit of such seismic data to Equation (2) is plotted in curves 80 and 90 to obtain values for the observed attributes Bo and Bl. The values of the 30 observed attributes Bo and Bi have changed from SP 479 to SP 474 such that the observed attributes Bo and Bi both have the same sign at SP ~74. Since the maximum incident angle ~ is less than 35, the attribute B2 can be disregarded.
The most probable estimate of reservoir forma-tion F2 rock properties for the three different locations (i.e., SP 491, SP~479 and SP 474) are shown on the ADA
diagram in Figure 15. ~ere the seismic scalar K has been ~C~75 selected so as to produce a normal incident reflection coefficient RC(0) of -0.10. It is concluded that the change from roof formation Fl to reservoir formation F2 at SP 474 in Figure 12 is toward a more consolidated, yet low 5 velocity formation. The most probable calculated reser-voir formation F2 rock properties at this location are shown in Table 5.

Vp = 6450 + 600 ft/sec, Vs = 4260 + 360 ft/sec, Vp/Vs = 1.51 + 0.01, 2 and p = 2.19 ~ 0.20 gm/cm .
For this set of reservoir formation F2 rock properties, there is a substantial increase in the shear velocity Vs and possibly density p with little change in compressional velocity Vp. This, in addition to the low 20 Vp/Vs ratio which is normally associated with accumulated gas~ suggests a reservoir formation of harder matrix rock, which is gas saturated. ~hereas the seismic data associ-ated with SP 479 appears similar in nature to that of SP 491 previously discussed. The results illustrated in 25 Figure 15 also reveal that the subtle change in the seismic signal amplitude of Figure 1 is dramatically dem onstrated.
Recalling that the lithology diagram, as shown in Figure 5, was subdivided into quadrants depending on 30 the signs of the theoretical attributes Bo and Bl, a high probability of evaluating a seismic event as a gas-bearing formation exists in the quadrants in which the values of the scaled observed attributes Bo and Bl are of the same sign. In fact, a superposition of the theoretical attri-35 butes Bo and Bl zero contour lines on Figure 15 indicatesthat only the scaled attributes Bo and Bl intersections for SP 474 meet this criteria.

., 9~5 An additional attribute BL derived from Bo and ~1 indicates when the seismic signal amplitude is changing with range and the relative values of the attributes Bo and Bl where:
BL = arc tan ~Bl/Bo).
In effect, the attribute ~L indicates the ~uad-rant in which the underlying formation F2 rock properties are located as well as providing an immediate and simple correlation of the underlying formation. F2 to a gas 10 bearing formation.
Although only a single selected seismic even~
has been analyzed to obtain a most probable estimate of the underlying formation rock properties associated with the selected seismic event, those skilled in the art can 15 appreciate that an entire seismic trace can be interpreted sequentially whereby the most probable estimate of under-lying formation rock properties become the assumed over~
lying formation rock properties for the next selected seismic event. Additionally, by so handling adjacent 20 seismic traces, lateral variations in formation rock prop-erties, lithology and pore fluid content can be deter-mined.
Changes may be made in combination and arrange-ment of steps as heretofore set forth in the specification 25 and shown in the drawings; it being understood that changes may be made in the embodiment disclosed without departing from the spirit and scope of the invention as defined in the following claims.

Claims (52)

WHAT IS CLAIMED IS:

1. A method of geophysical exploration for processing seismic data, including the steps of:
(a) obtaining a representation of a reflection coefficient for selected seismic events from the seismic signal amplitude variations as a function of incident angle, and obtaining a first set of attributes descriptive of seismic signal amplitude variations, as a function of incident angle, for selected seismic events; and (b) transforming the first set of attri-butes into a measure of the subterranean formation rock properties associated with each selected seismic event.

2. The method of Claim 1 wherein Step (a) includes:
obtaining a representation of a first reflection coefficient from an optimized statistical fit of the variations in the seismic signal ampli-tude, as a function of incident angle, for each selected seismic event, according to:

R?(.theta.) = B'0 + B? tan2.theta. + B? sin2.theta. tan2.theta.

where R?(.theta.) is the first reflection coefficient as a function of incident angle;
.theta. is the incident angle; and B?, B? and B? comprise the first set of attri-butes.

3. The method of Claim 1 wherein step (a) includes:
obtaining a representation of a first reflection coefficient from an optimized statistical fit of the variations and seismic signal amplitude, as a function of incident angle, for each selected seismic event, according to:
R?(.theta.) = Bo' + B? tan2.theta. where R?(.theta.) is the first reflection coefficient as a function of inci-dent angle;
.theta. is the incident angle;
B? and B? comprise the first set of attri-butes.

4. The method of Claim 1 wherein step (b) includes:
inverting the first set of attributes into units of reflection coefficient; and mapping the inverted first set of attri-butes on an angle dependent amplitude diagram.

5. The method of Claim 4 wherein the angle dependent amplitude diagram comprises:
a lithology diagram relating relative changes in formation rock properties to relative changes in formation lithology; and contour lines mapped on the lithology dia-gram representative of an assumed contrast in forma-tion rock properties associated with each selected seismic event.

6. The method of Claim 5 wherein:
the contour lines are representative of a second reflection coefficient for the assumed con-trast in formation rock properties associated with each selected seismic event.

7. The method of Claim 5 wherein:
the contour lines are representative of a second set of attributes descriptive of the assumed contrast in formation rock properties associated with each selected seismic event.

8. The method of Claim 7 wherein:
the contour lines are representative of an optimized statistical fit to an exact reflection coefficient obtained from the assumed contrast in formation rock properties associated with each selected seismic event according to:

RC(.theta.) = B0 + B1 tan2.theta. + B2 sin2.theta. tan2.theta.
where Rc(.theta.) is the second reflection coefficient as a function of incident angle;
.theta. is the incident angle; and B0, B1 and B2 comprise the second set of attri-butes.

9. The method of Claim 7 wherein the contour lines are representative of an optimized statistical fit to an exact reflection coefficient obtained from the assumed contrast in formation rock properties associated with each selected seismic event according to:

Rc(.theta.) = B0 + B1 tan2.theta.

where Rc(.theta.) is the second reflection coefficient as a function of incident angle;
.theta. is the incident angle; and B0, B1 comprise the second set of attributes.

10. The method of Claim 9 wherein the maximum incident angle .theta. is less than 35°.

11. The method of Claim 1 further including the step of:
determining the most probable estimate of the underlying formation rock properties associated with the selected seismic event.

12. The method of Claim 1 wherein step (b) includes the steps of:
assuming a set of formation rock properties for an overlying formation associated with each selected seismic event;
assuming any other set of formation rock properties for an underlying formation associated with each selected seismic event;
the assumed formation rock properties define a contrast in the formation rock properties across a subterranean formation interface associated with each selected seismic event, obtaining second sets of attributes from a plurality of assumed contrasts in rock properties for each selected seismic event;
mapping contour lines of the second sets of attributes onto a lithology diagram; and plotting the first set of attributes onto the respective contour lines of the second sets of attributes to obtain a most probable estimate of the underlying formation rock properties.

13. The method of Claim 12 further including the step of:
developing an angle dependent amplitude diagram from a plurality of assumed contrasts in the formation rock properties associated with each selected seismic event.

14. The method of Claim 13 further including the step of:
mapping the first set of attributes on the angle dependent diagram to determine a most probable estimate of the underlying formation rock properties associated with each selected seismic event.

15. A method of geophysical exploration for displaying seismic data including the steps of:
(a) preparing a lithology diagram having axes of selected formation rock properties for relat-ing contrasts in formation lithology to contrasts in formation rock properties;

(b) plotting contour lines on the lithology diagram representative of contrasts in assumed forma-tion rock properties across a subterranean formation interface; and (c) mapping a first set of attributes descriptive of variations in amplitude of a seismic signal, as a function of incident angle, for a selected seismic event associated with the subterra-nean formation interface.

16. The method of Claim 15 wherein step (a) includes:
selecting formation rock properties from the group comprising Poisson's ratio, compressional velocity, shear velocity, the ratio of the compres-sional velocity to shear velocity and density.

17. The method of Claim 15 wherein step (b) includes:
plotting contour lines of a second set of attributes obtained from an optimized statistical fit of an exact reflection coefficient for the assumed contrast in formation rock properties according to:
Rc(.theta.) = B0 + B1 tan2.theta. + B2 sin2.theta. tan2.theta.

where Rc(.theta.) is the reflection coefficient as a function of incident angle;
.theta. is the incident angle; and B0, B1 and B2 comprise attributes of the second set of attributes.

18. The method of Claim 17 wherein the maximum incident angle .theta. is less than 35° and Rc(.theta.) = B0 + B1 tan2.theta..

19. The method of Claim 15 wherein the step (c) includes:
obtaining the first set of attributes by performing an optimized statistical fit of the vari-ations in the amplitude seismic signal according to Rc(.theta.) = B0 + B1 tan2.theta. + B2 sin2.theta. tan2.theta.

where Rc(.theta.) is the reflection coefficient as a function of incident angle;
.theta. is the incident angle; and B0, B1 and B2 comprise attributes of the first set of attributes.

20. The method of Claim 19 wherein the maximum incident angle is less than 35° and Rc(.theta.) = B0 + B1 tan2.theta..

21. A method of geophysical exploration for displaying seismic data including the steps of:
preparing a lithology diagram having axes of selected formation rock properties for relating contrast in formation lithology to contrasts in for-mation rock properties;
plotting contour lines on the lithology diagram representative of zero values for theoretical attributes obtained from an assumed contrast in the formation rock properties across a subterranean for-mation interface; and mapping sets of observed attributes descriptive of variations in amplitude of a seismic signal, as a function of incident angle, for a selected seismic event associated with the formation interface.

22. An angle dependent amplitude diagram for interpreting seismic data comprising:
a lithology diagram having axes of selected formation rock properties for relating observed attributes descriptive of amplitude variations of seismic events as a function of incident angle to contrasts in formation rock properties, and contour lines representative of an assumed contrast in formation rock properties across subter-ranean formation interface or mapped onto the lithol-ogy diagram.

23. The angle dependent amplitude diagrams of Claim 22 wherein:
only the zero values of the contour lines representative of an assumed contrast in formation rock properties across a subterranean formation interface are mapped onto the lithology diagram.

24. An angle dependent amplitude diagram for interpreting seismic data comprising:
a lithology diagram having axes of selected formation rock properties for relating observed attributes descriptive of amplitude variations of seismic events as a function of incident angle to contrasts in formation rock properties; and contour lines representative of assumed reflection coefficients across formation interface are mapped onto the lithology diagram.

25. The angle dependent amplitude diagram of Claim 24 wherein:
only the zero values of the contour lines representative of the assumed reflection coefficient across the formation interface are mapped onto the lithology diagram.

26. A method of geophysical exploration for obtaining a measure of subterranean formation rock proper-ties including the steps of:
obtaining a set of observed attributes descriptive of amplitude variations as a function of incident angle for seismic events in the seismic sig-nals;
obtaining a set of theoretical attributes descriptive of contrasts in assumed formation rock properties across a subterranean formation interface associated with the selected seismic event;
plotting a plurality of theoretical attri-bute contour lines on a lithology diagram having axes of selected formation rock properties for relating contrasts in formation lithology to contrasts in for-mation rock properties;

scaling the observed set of attributes to units of reflection coefficient; and plotting a scaled observed attribute onto the contour lines of the theoretical set of attri-butes to obtain a measure of the underlying formation rock properties associated with the seismic event.

27. The method of Claim 26 wherein:
only the zero values of the theoretical attribute contour lines are plotted on the lithology diagram.

28. The method of Claim 27 wherein:
the zero values of the theoretical attri-butes subdivide the lithology diagram into quadrants, selected quadrants being correlated to gas bearing formations.

29. The method of Claim 28 wherein:
the quadrants in which the scaled observed attributes having the same sign correlate with gas bearing formations.

30. The method of Claim 28 wherein:
locating the quadrant for the observed attributes according to:
BL = arc tan where B0 and B1 comprise the observed attri-butes.

31. A method of geophysical exploration for processing seismic data, including the steps of:
(a) fitting seismic signal amplitude vari-ations, as a function of incident angle for selected seismic events to:

R?(.theta.) = B? + B? tan2.theta. + B? sin2.theta. tan2.theta.
where R?(.theta.) is a first reflection coefficient as a function of incident angle;
.theta. is the incident angle; and obtaining a first set of attributes B0', B1' and B2' descriptive of the seismic signal amplitude variation; and (b) mapping the first set of attributes onto an angle-dependent amplitude diagram and trans-forming the first set of attributes into a measure of the subterranean formation rock properties associated with each selected seismic event.

32. A method of geophysical exploration for processing seismic data, including the steps of:
(a) fitting seismic signal amplitude, as a function of incident angle for selected seismic events, to:
R?(.theta.) = B? + B? tan2.theta.
where R?(.theta.) is the first reflection coefficient as a function of incident angle;
.theta. is the incident angle; and obtaining a first set of attributes B0' and B1' descriptive of the seismic signal amplitude variation; and (b) mapping the first set of attributes onto an angle-dependent amplitude diagram and trans-forming the first set of attributes into a measure of the subterranean formation rock properties associated with each selected seismic event.

33. The method of Claim 31 wherein the angle dependent amplitude diagram comprises:
a lithology diagram relating relative changes in formation rock properties to relative changes in formation lithology; and contour lines mapped on the lithology dia-gram representative of an assumed contrast in forma-tion rock properties associated with each selected seismic event.

34. The method of Claim 33 wherein:
the contour lines are representative of a second reflection coefficient for the assumed con-trast in formation rock properties associated with each selected seismic event.

35. The method of Claim 33 wherein:
the contour lines are representative of a second set of attributes descriptive of the assumed contrast in formation rock properties associated with each selected seismic event.

36. The method of Claim 35 wherein:

the contour lines are representative of an optimized statistical fit to an exact reflection coefficient obtained from the assumed contrast in formation rock properties associated with each selected seismic event according to:
Rc(.theta.) = B0 + B1 tan2.theta. + B2 sin2.theta. tan2.theta.

where Rc(.theta.) is the second reflection coef-ficient as a function of incident angle;
.theta. is the incident angle; and B0, B1 and B2 comprise the second set of attributes.

37. The method of Claim 35 wherein the contour lines are representative of an optimized statistical fit to an exact reflection coefficient obtained from the assumed contrast in formation rock properties associated with each selected seismic event according to:
Rc(.theta.) = B0 + B1 tan2.theta.
where Rc(.theta.) is the second reflection coef-ficient as a function of incident angle;
.theta. is the incident angle; and B0, B1 comprise the second set of attri-butes.

38. The method of Claim 37 wherein the maximum incident angle .theta. is less than 35°.

39. The method of Claim 31 or 32 further including the step of:

determining the most probable estimate of the formation rock properties associated with the selected seismic event, wherein the formation rock properties are selected from the group of shear wave velocity, compressional wave velocity and density.

40. A method of geophysical exploration for interpreting seismic data, including the steps of:
(a) obtaining a first set of attributes descriptive of seismic signal amplitude variations as a function of incident angle for selected seismic events in incident angle ordered gathers of seismic signals;
(b) assuming a set of formation rock prop-erties for an overlying formation associated with each selected seismic event;
(c) assuming any other set of formation rock properties for an underlying formation associ-ated with each selected seismic event;
(d) wherein the assumed formation rock pro-perties define a plurality of assumed contrasts in the formation rock properties across the subterranean formation interface associated with each selected seismic event;
(e) obtaining second sets of attributes from the plurality of assumed contrasts in formation rock properties for each selected seismic event;
(f) mapping contour lines of the second sets of attributes onto a lithology diagram; and (g) plotting the first set of attributes onto the respective contour lines of the second set of attributes to obtain a more probable estimate of the underlying formation rock properties.

41. The method of Claim 40 further including the step of:
developing an angle dependent amplitude diagram from a plurality of assumed contrasts in the formation rock properties associated with each selected seismic event.

42. The method of Claim 38 further including the step of:
mapping the first set of attributes on the angle dependent diagram to determine a most probable estimate of the underlying formation rock properties associated with each selected seismic event.

43. A method of geophysical exploration for processing seismic data, including the steps of:
(a) statistically fitting seismic signal amplitude variations, as a function of incident angle, for selected seismic events to a parametric equation relating contrasts in formation rock proper-ties to seismic signal amplitude variations, as a function of incident angle, and obtaining a set of attributes descriptive of such amplitude variations;
and (b) mapping the set of attributes onto an angle-dependent amplitude diagram and transforming the set of attributes into a measure of the contrast in subterranean formation rock properties associated with each selected seismic event.

44. The method of Claim 43 wherein the angle-dependent amplitude diagram comprises:
a lithology diagram having axes of selected formation rock properties for relating contrasts in formation lithology to contrast in formation rock property; and contour lines representative of assumed contrasts and formation rock properties across sub-terranean formation interfaces mapped onto the lithology diagram.

45. The method of Claim 44 wherein:
only the zero values of the contour lines representative of an assumed contrast in formation rock properties across subterranean formation inter-faces are mapped onto the lithology diagram.

TDS:go/ts

46. The method of claim 32 wherein the angle dependent amplitude diagram comprises:
a lithology diagram relating relative changes in formation rock properties to relative changes in formation lithology; and contour lines mapped on the lithology dia-gram representative of an assumed contrast in forma-tion rock properties associated with each selected seismic event.

47. The method of claim 46 wherein:
the contour lines are representative of a second reflection coefficient for the assumed con-trast in formation rock properties associated with each selected seismic event.

48. The method of claim 46 wherein:
the contour lines are representative of a second set of attributes descriptive of the assumed contrast in formation rock properties associated with each selected seismic event.

49. The method of claim 48 wherein:
the contour lines are representative of an optimized statistical fit to an exact reflection coefficient obtained from the assumed contrast in formation rock properties associated with each selected seismic event according to:

Rc(.theta.) = B0 + B1 tan2.theta. + B2 sin2.theta. tan2.theta.

where Rc(.theta.) is the second reflection coef-ficient as a function of incident angle;
.theta. is the incident angle; and B0, B1 and B2 comprise the second set of attributes.

50. The method of claim 48 wherein the contour lines are representative of an optimized statistical fit to an exact reflection coefficient obtained from the assumed contrast in formation rock properties associated with each selected seismic event according to:

Rc(.theta.) = B0 + B1 tan2.theta.

where Rc(.theta.) is the second reflection coef-ficient as a function of incident angle;
.theta. is the incident angle; and B0, B1 comprise the second set of attri-butes.

51. The method of claim 50 wherein the maximum incident angle .theta. is less than 35°.

52. The method of claim 50 or 51 further including the step of:
determining the most probable estimate of the formation rock properties associated with the selected seismic event, wherein the formation rock properties are selected from the group of shear wave velocity, compressional wave velocity and density.