COMMON DEPTH POINT (CDP) SEISMIC EXPLORATION METHOD

Abstract: In a method for determining and displaying the shear-ve­ locity reflectivities of a geologic formation, a compression-­ wave common-depth-point seismic-data-gathering technique is utilized to produce both normal incidence compressional-ve­ locity reflectivity sections and shear-velocity reflectivity sec­ tions for reflection points in the formation. The common-­ depth-point information is gathered for a plurality of incidence angles, (theta), of less than 20-30° such that assumptions concerning various elastic parameters, density, compression­ al-wave-velocity and shear-wave-velocity can be made which allow the application of linear fitting techniques to the gathered data. Estimates are then made of the coefficients (R pp 0 and R pp 1 ) of a linear function fitted to the amplitudes vs. sin² (the­ ta) measured for each point of reflection. The sum of these co­ efficients corresponds to the shear-velocity reflectivity of the reflection point and may be presented with similar data for other points in appropriate shear-reflectivity sections.

Description: A METHOD FOR DETERMINING AND DISPLAYING THE SHEAR-VELOCITY REFLECTIVITIES OF A GEOLOGIC FORMATION The present invention relates to a method for determining and displaying the shear-velocity reflectivities of a geologic formation. One technique for gathering seismic information which has experienced success in the field of oil and gas exploration is the P-wave Common-Depth-Point (CDP) technique. The COP technique is a method for obtaining multiple coverage of each subsurface point using various surface-detector and shot-point spreads. These spreads are selected so that for each spread the reflection points are common for several shot-receiver pairs. Recordings which have common reflection points are then typically combined, or stacked, after the appropriate travel-time corrections for shot-receiver separations have been applied. These techniques enhance reflections which follow the assumed travel path, while other events are reduced. The enhanced reflections may then be plotted in a seismic section which is a mapping of the reflectivity characteristics of the subsurface lithology. Compressional wave (P-wave) information comprises the predominant portion of these plots, but shear-wave information may also be included therein and may result in anomalies in the display. The COP technique has been developed and refined over at least the past forty years. Multiple paths centered around a common depth point had been suggested by 1938, (see Green, C.H. "Velocity Determination by Means of Reflection Profiles", Geophysics 3:295 (1938)). By 1956, Mayne had proposed that information associated with a given reflection point, but recorded with a multiplicity of shot-point and geophone locations, could be combined algebraically after applying appropriate time corrections, (see "Common Reflection Point Horizontal Data Stacking Techniques" by W. Harry Mayne, Geophysics 28:6, 927-938 (1963). Mayne describes these techniques as adding a "new order of magnitude" to the usable dimensions of multi-path pattern array geometry, and as providing signal-to-noise ratios enhanced well beyond the saturation point of conventional pattern methods. Mayne discloses that the horizontal spacing between source and receiver is restricted only by considerations of (1) the greatest distance which will permit coincidence adjustments of requisite accuracy (since the probable error in postulated step-out increases with distance and must be kept small with respect to the reflection), and (2) the greatest distance over which the reflected signals persist with adequate similarity. The theoretical premise for the CDP technique is that the seismic event will be consistently reflected at various incidence angles from the common point of reflection for several different shot-receiver spacings. Theoretically it is assumed that each reflection point is located at a boundary between different media. By at least as early as 1899, C.G. Knott had published work on reflection, transmission, and conversion coefficients for plane elastic waves incident on a plane boundary between homogenous isotropic media. Knott defined reflection coefficients in terms of ratios of displacement potentials. His was one of the first explicit publications of the principle that satisfying the boundary conditions at an interface required an incident P (compressional) or SV (vertically polarized shear) wave to split into four parts: reflected P and SV wave and transmitted P and SV waves. Knott further disclosed an explicit expression for the energy in each wave, which, if the amplitude is known, must sum to the incident energy, (see Knott, C.G., "Reflection and Refraction of Seismic Waves with Seismological Applications", Phil. Mag. S, 5, Vol. 48, No. 290, 3uly, 1899, pp. 64-96). By 1919, K. Zoeppritz had derived equations for reflection coefficients defined as ratios of displacement amplitudes, (see Zeoppritz, K. "Uber Erdbebuellen VIIb", Gottinger Nachrichten, 1919, pp. 66-84). Unfortunatley, the Zoeppritz equations are extremely complex. In fact, these equations are so complex that various authors have commented that the equations have seldom been published without error, (see Richter, C.F., "Elementary Seismology", W.H. Freidman and Company, 1968; Spencer, T.W. "The Method of Generalized Reflection and Transmission Coefficients", Geophysics, Vol. 25, No. 3, June, 1960, pp. 625-641). Perhaps one of the best papers on this topic written in recent times was authored by Tooley, R.D., Spencer, T.W., and Sagoci, H.F., entitled "Reflection and Transmission of Plane Compressional Waves", Geophysics, Vol. 30, No. 4, August, 1965, pp. 552-570. Tooley et al provide explicit expressions for the energy reflection coefficients of incident waves. Even this paper, however, contains an error at equation 5 where in the calculation of P+, the term "cos" should read "sin" (of alpha). Since it has been recognized in theory that the amplitudes of shear and compressional reflectivities at a given boundary change with the angle of incidence, attention in recent years has been directed to using such changes to determine the physical characteristics at the boundary. Shear-waves are produced in significant amplitudes by conversion at solid-solid boundaries at certain angles of incidence if there is a significant velocity contrast. For example, when a low-velocity layer is disposed over a higher-velocity layer, up to about 90% of the incident P-wave energy may be transmitted or reflected as P-waves for incident angles much smaller than the critical angle (e.g. less than about 250), whereas a much larger fraction of the incident P-wave energy may be converted to shear wave energy for greater non-critical angles of incidence (e.g. about 300 - 500). One of the reasons for interest in shear-wave reflectivities is the insensitivity of the shear-wave velocities to the fluid content of rocks. P-wave velocities may be strongly influenced by fluid content in high porosity rocks. Accordingly, if a data-gathering and display technique can be developed which will permit a convenient comparison between the P-wave and S-wave reflectivities of a given section, it may be possible to distinguish between areas which are more or less likely to contain hydrocarbon deposits. In recent years it has been suggested that the nature of a reservoir fluid associated with a hydrocarbon deposit can be predicted seismically. Experimentally, a shale layer overlaying a gas-saturated sandstone may cause an increase in reflection amplitude with source-receiver offset, while a water-saturated sandstone would show an amplitude decrease with offset. Theoretically, the amplitude vs. offset response for an oil-saturated sandstone response would be intermediate between those for gas and water. A conventional stacked COP seismic section contains information about the vertical and lateral changes in the acoustic impedances of the subsurface. Normally, the correlation between a vertical-incidence P-wave reflection-coefficient series convolved with a time-invariant seismic wavelet and the amplitudes of stacked seismic data is adequate for conventional hydrocarbon analysis. However, COP gathers of seismic traces also contain information about-the dependence of the reflection amplitude on the incidence angle of the wave front. There are some inherent limitations to the detection of amplitude changes associated with oblique-angle reflections. Amplitude dependence on incidence angle exists in the seismic field system itself, in the propagation of the seismic wave, and in the geologic reflection response. In connection with prior COP techniques, practitioners have already developed a number of techniques which are intended to minimize field system and wave front propagation limitations.- For example, it is known to compensate for differences in amplitude loss and phase distortion as the emergent angle of a wave front increases, (see Hawes et al "Some Effects of Spacial Filters on Signal", Geophysics 39:4, pp. 464-498, 1974). It is also known that the propagation of a seismic wave front introduces a time-variant gain into the field data due to geometrical divergence and attenuation. The amplitude offset dependence for these effects can be related to the normal moveout equation which defines the travel-time to a reflection as a function of offset for conventional spread lengths. The divergence correction compensates the reflection amplitude for geometrical spreading losses, so that the corrected reflection amplitudes simulate the response to a plane-wave source, (see Newman, P., "Divergent Effects in a Layered Earth", Geophysics Vol. 38, No. 3, pp. 481-488, 1973). Similarly, attenuation due to intrabed multiples and absorption is generally accepted to be a constant, independent of frequency in the seismic passband, such that amplitudes of reflections decrease with increasing travel-time, approximately as 1/T. In conducting most COP analyses, a basic assumption about the COP gather is that all traces impinge upon the same subsurface point whose reflection response may be observed at 2-way travel-times defined by a hyperbolic NMO function. Normal moveout functions are generally based on reasonable velocity estimates for the given substrate. Accordingly, in COP gathers, including those processed to determine changes of amplitude with offset, it is known to use conventional demultiplexing, programmed gain control, band-pass filtering, deconvolution, wavelet compression, normal moveout corrections, trace-amplitude equalization and muting. Trace amplitude equalization, and other normalizations, are often conducted using a mean or median trace amplitude as determined from some predetermined, non-event associated time window. In determining amplitude-offset changes, it is further known to use trace muting to eliminate amplitude data collected at the critical angle, which data would otherwise unnecessarily interfere with thety desired amplitude vs. offset determinations. The Zoeppritz equations have now been analyzed to determine a simple analytical estimation for the solution of the Zoeppritz-equation reflection coefficients Rpp (theta) and Rps (theta), where Rpp refers to the reflection coefficient for an incident and reflected compressional waves and Rps refers to the coefficient for an incident compressional wave and a reflected shear wave, when the angle of incidence 8, is a small quantity, i.e., less than about 300. This analysis has shown that the reflection coefficient Rpp (theta) for a reflection at an interface between a medium 1 and a medium 2 can be estimated according to the following formula for such angles of incidence: Rpp (#) # Rpp (#) = Rpp,0 + Rpp,1 sin2# (1) where the coefficient for normal incidence reflection and the first order Taylor expansion are shown in equations- (2) and (3) respectively: : EMI6.1 and Rpp = -2V2 (l-K) (1-Y) (3) -2V2 (1+V-Z) [1- (Z/@)2] where p2 K = and p1, p2 are the densities of media 1 and 2 p1 respectively; V @ = Vp1 and Vp1, Vp2 are the velocities of compressional waves in media 1 and 2 repectively; Vs1 V = V @ and Vsl is the velocity of shear-waves in medium 1; pi Vs2 and Z = and Vs2 is the velocity of shear-waves in medium 2. Vp1 Note that p2 Vp2 Rpp,1 in (3) is expanded in terms of (1-), (1-) and p1 Vp1 EMI6.2 so that EMI7.1 If the elastic parameters are rewritten as: #1 = # #2 = # + ## Vpl = Vp Vp2 = Vp +AVp (5) Vs1p1 = V2p Vs2p2 = Vsp + # Vsp and it is assumed that delta rho, delta Vp and delta V5 are small enough so that second order terms can be ignored and that Vp is approximately equal to 2 Vs, then the reflection coefficient becomes: : EMI7.2 = Rpp,0 + Rpp,1 sin2# It has now been recognized that separate estimates of Rpp,0 and Rpp,1 1 can provide values for normal incidence compressional reflectivity Rpp,0 and shear reflectivity #Vs/Vs, and that this latter shear reflectivity value is approximately equal to (Rpp,0 + Rpp,1). Similarly, the P-SV reflection coefficient is RDC (#) # R@@ (#) (7) ps 4(V-KZ) 2KZ (Y-2Z) = (sin #) { + (1-K) ( ) # 1-KY V+KZ (1+KY) where the first term is proportional to (p1V51 - p2V52) and the 2nd term to Cl- P2/P1)- The present invention provides a method for determining and displaying the compressional- and shear-velocity reflectivities of geologic formations using a P-wave CDP seismic data gathering technique. This method comprises gathering CDP P-wave reflectivity data for a plurality of angles of offset (theta) of less than about 30 ; estimating the values of sin2 (theta) for each of said angles of offset; fitting a function to the amplitudes vs. sin2 (theta) measured and determined for each reflection point; determining the coefficients of said function for each reflection time and location point; and displaying said coefficients or combinations of coefficients in sections configured to generally correspond to said geologic formations, whereby such sections display the nature of the compressional- and shear-velocity reflectivities of the reflection points in said geologic formations. A preferred method takes advantage of the fact that constants Rpp, and Rpp,1 are the linear coefficients for the Taylor expansion of the reflection coefficient Rpp By limiting the angles of incidence at which data from a CDP gather is utilized, by estimating the values of sin2 (theta) for each such angle in the gather, and by fitting a linear function to the measured amplitudes vs. sin2 (theta) for each reflection point, the estimated values of Rpp,0 and Rpp,1 are easily determined. By recognizing that the sum of the linear coefficients (Rpp,1 and Rpp,0) is a value representative of the shear-velocity reflectivities (AV5/V5) of the reflection points, the present method provides a simple technique for determining and plotting such reflectivities. Since one of the coefficients (Rpp O) is representative of the compressional wave reflectivity of each reflection point, a normal incidence P-wave plot is also easily produced. A useful method is thus provided for plotting sections of geologic formations to determine the possible presence of hydrocarbons therein. In accordance with the preferred method described above, estimation of the value of sin2 (theta) for any given angle theta is conducted by estimating the depth of the reflection point using the measured time for each sample and the normal moveout (NMO) velocity. Shot-receiver distances are then used to achieve a sin2 (theta) estimation for each incidence angle. Using the sin2 (theta) estimations thus determined, a linear function regression is performed, which is preferably a least-square regression of Rpp,0 + Rpp 1 sin2 (theta) given the observed amplitudes. Repeating this step for each time (reflection) point of the COP gather (and each COP in the line), values of the normal incidence P section (Rpp,0) and of the normal incidence shear section (Rpp ,0 + Rpp 1) can then be readily displayed for all the points in the gather. In the accompanying drawings, Figure 1 is a normal incidence P-section plot of the compressional reflectivity behavior of a given geologic formation generated in accordance with a method according to one example of the present invention; and Figure 2 is an equivalent shear section display of the geologic formation which was the subject of Figure 1, displaying shear-velocity reflectivities of that formation. Referring to the drawings, in the method of said one example, compressional- and shear-wave reflectivities of a geologic formation are determined and displayed using a COP seismic data gathering technique comprising normal processing up to the point of stacking the COP gathers. Such processing normally includes demultiplexing, programmed gain control, band-pass filtering, deconvolution, wavelet compression, normal moveout correction, trace amplitude equalization, and muting. The trace amplitude equalization is generally based on the mean or median trace amplitude as determined from a preselected time window which does not necessarily correspond to a signal arrival. Since the result may be very sensitive to muting, the method of the present invention should be used only for near vertical-incidence reflections, that is, for incidence angles less than 300, and preferably less than 200, to thereby avoid the necessity of including higher order terms. Similarly, when velocity increases at a boundary, there will be a critical-angle reflection that is always a highamplitude reflection. Accordingly, muting should be used to eliminate such phenomena from the COP gathers. Similarly, visual examination of traces suggests that far traces are often distorted by the presence of non-compressional wave primary reflections and multiple reflections and should preferably be removed by an appropriate muting. COP gathers are gathers of compressional seismic information containing the reflectivities of points in a geologic formation which are disposed along a usually vertical axis which bisects the distance between shot and receiver locations. In such COP gathers, the depth along this vertical axis is typically indicated in terms of time rather than actual physical depth below ground surface. Thus, in Figures 1 and 2, the vertical axis of the sections represents time, while the horizontal axis corresponds to actual physical location. In the present method, it is desired to estimate the actual physical depth of each reflection point along the above-mentioned vertical axis. One of the easiest methods for making such an estimation is to use the velocity assumption used in the normal-moveout function which when multiplied by the reference time and divided by two provides a reasonable estimation of the depth (d) of the point of reflection. Assuming the distance between shot and receiver to be X, and theta to be the angle of incidence between the receiver and the aforementioned vertical axis, an estimate of sin2 (theta) can be calculated using the formula: sin2 (theta) = X2/(X2 + 4d2) (8) This method for estimating the value of sin2 (theta) assumes a homogenous lithology above the point of reflection. Moreover other approximations can be made for propagation velocities and sin2 (theta), particularly if it is desired to utilize information concerning the geologic layers which may be disposed above the point of reflection. Having thus estimated the value of sin2 (theta) for each time sample of the normal-moveout corrected traces, these values are then used to perform a least-squares regression of Rpp, + Rpp 1 sin2 (theta) to the measured amplitudes. This regression technique may be visualized as being equivalent to plotting the measured amplitudes against sin2 (theta), and then fitting a line to the plotted points, whereupon Rpp, is defined by the point wherein the line intersects the amplitude axis (theta =-0), and Rpp, represents the slope of the line. By repeating this step for each time of the COP gather and each CDP gather in the line, values for Rpp,0 and Rpp,1 can be obtained for each reflection point in the section. This information is then assembled for presentation into a display as a normal-incidence P-reflectivity section (Rpp, points) and as a shear-reflectivity section (Rpp,0 + Rpp,l points). Figure 1 represents such a normal incidence P section which is a display of the compressional reflectivity behavior of a particular geologic formation. Figure 2 is an equivalent display of the shearvelocity reflectivities of that geologic formation. It will be seen that substantial differences in such reflectivities are present between such sections which will substantially aid an interpreter of this data in determining the likelihood that a given location in this section contains a possible hydrocarbon deposit. While those of ordinary skill in this art will further recognize that the above-described technique is theoretically less accurate than a technique wherein the Zoeppritz formulas are used in their entireties to represent and display collected data, the large volume of data to be processed, the complexity of the Zoeppritz formulas and the difficulties otherwise encountered in applying the Zoeppritz formulas make the present technique superior to any data gathering, interpretation, presentation and plotting method heretofore known to the art. It will also be recognized that techniques other than the above-mentioned least-squares regression technique may be used to fit a linear function to the measured amplitudes. For most applications, however, the ease and simplicity of performing a least-squares regression makes this the method of choice.

Claims: CLAIMS: 1. A method for determining and displaying at least the shear-velocity reflectivities of a geologic formation using a compressional common-depth-point seismic data gathering technique, comprising: (a) collecting a common-depth-point gather for a plurality of angles of incidence (theta) of less than 50 ; (b) estimating the values of sin2 (theta) for each of said angles of incidence; (c) fitting linear functions to the amplitudes vs. sin2 (theta) for a plurality of points of reflection within said gather; (d) determining the coefficients of said linear function; (e) estimating at least the values of shear-velocity reflectivity of said points of reflection by summing said coefficients; and (f) displaying said values in a display configured to generally correspond to a section of said geologic formation, whereby the nature of shear-velocity reflectivity of said geologic formation is represented by said display. 2. The method of claim 1 wherein said angles of incidence are less than about 200. 3. The method of claim 1 or claim 2 wherein said values of sin2 (theta) are estimated by estimating the depth (d) of each point of reflection at a given time. 4. The method of claim 3 wherein said sin2 (theta) values are estimated by using the formula sin2 (theta) = X2/(X2 + 4d2) where X equals the distance between the shot and receiver positions at said time. 5. The method of any preceding claim wherein said shearvelocity reflectivities are determined using the least squares regression of Rpp,0 + Rpp,1 sin2 (theta) on the measured amplitudes, and wherein each such shear-velocity reflectivity value is determined by summing Rpp,0 and Rpp,1' 6. The method of any preceding claim wherein said method further comprises determining and displaying the compressional (P wave) reflectivities of said formation, said reflectivity values being represented by the intercept coefficients of said functions, whereby the values of said intercept coefficients correspond to the values of the compressional reflectivities (Rpp,o) of said formations.

Inventors: KENNY, GEORGE SCOTT, MCCLURE, CARROLL DEAN, WIGGINS, RALPHE
Applicants: MOBIL OIL CORPORATION
Application year: 1983
Main classification: G01V1
IPC codes: G01V1