Shuey s Two-Term Approximation

Transcription

1 INTERPRETER S Principles of AVO crossplotting JOHN P. CASTAGNA, University of Oklahoma, Norman, Oklahoma HERBERT W. SWAN, ARCO Exploration and Production Technology, Plano, Texas Hy d rocarbon related AVO anomalies may show increasing or decreasing amplitude variation with offset. Conversely, brine-saturated background rocks may show increasing or decreasing AVO. A m p l i t u d e - v e r s u s - o fset interpretation is facilitated by crossplotting AVO intercept (A) and gradient (B). Under a variety of reasonable geologic circumstances, As and Bs for brine-saturated sandstones and shales follow a well-defined background trend. AVO anomalies are properly viewed as deviations from this background and may be related to hydrocarbons or lithologic factors. The common three-category classification developed by Rutherford and Williams is incomplete. We propose that an additional category (Class IV) be considered. These Summary are low impedance gas sands for which reflection coefficients decrease with increasing offset; they may occur, for example, when the shear-wave velocity in the gas sand is lower than in the overlying shale. Thus, many classical bright spots exhibit decreasing AVO. If interpreted incorrectly, AVO analysis will often yield false negatives for Class IV sands. Clearly, the conventional association of the term AVO anomaly with an amplitude increase with offset is inappropriate in many instances and has led to much abuse of the AVO method in practice. Similarly, interpretation of partial stacks is not as simple as looking for relatively strong amplitudes at far offsets. We recommend that all AVO analysis be done in the context of looking for deviations from an expected background response. Figure 1. The two-term Shuey approximation to the Zoeppritz equations represents the angular dependence of P-wave reflection coefficients with two parameters: the AVO intercept (A) and the AVO gradient (B). In practice, the AVO intercept is a band-limited measure of the normal incidence amplitude, while the AVO gradient is a measure of amplitude variation with offset. Assuming appropriate amplitude calibration, A is the normal incidence reflection coefficient and B is a measure of offset-dependent reflectivity. Shuey s Two-Term Approximation R( ) = A + B sin 2 ( ) +... R = reflection coefficient = angle of incidence A = AVO intercept B = AVO gradient

2 Figure 2. For brine-saturated clastic rocks over a limited depth range in a particular locality, there may be a well-defined relationship between the AVO intercept (A) and the AVO gradient (B). A variety of reasonable petrophysical assumptions (such as the mudrock trend and Gardner s relationship) result in linear A versus B trends, all of which pass through the origin (B = 0 when A = 0). Thus, in a given time window, nonhydrocarbon-bearing clastic rocks often exhibit a well-defined background trend; deviations from this background are indicative of hydrocarbons or unusual lithologies. Figure 3. This figure shows A versus B trends for various constant ratios of compressional (V p ) to shear wave (V s ) velocity. Notice that the AVO gradient (B) and the AVO intercept (A) are generally negatively correlated, and that the A versus B trends become more positive as V p /V s increases. Also, note that the trend becomes positive at high V p /V s ratios. Thus, the normal response for (nonhydrocarbon-related) reflections at very high background V p /V s (as we would expect for very shallow unconsolidated sediments) is an amplitude increase versus offset. Large reflection coefficients associated with shale over porous brine-sand interfaces will exhibit false positive AVO anomalies in the sense that they will have larger AVO gradients than weaker reflections lying along the same background trend. When interpreted in terms of deviation from the background A versus B trend, such reflections are correctly interpreted as not being anomalous.

3 Figure 4. Deviations from the background petrophysical trends, as would be caused by hydrocarbons or unusual lithologies, cause deviations from the background A versus B trend. This figure shows brine sand-gas sand tie lines for shale over brine-sand reflections falling along a given background trend. In general, the gas sands exhibit more negative As and Bs than the corresponding brine sands (assuming the frame properties of the gas sands and the brine sands are the same). Note that the gas sands form a distinct trend which does not pass through the origin. Figure 5. We propose that the classification of AVO responses should be based on position of the reflection of interest on an A versus B crossplot. First, the background trend within a given time and space window must be defined. This can be done with well control if the seismic data are correctly amplitude calibrated, or with the seismic data itself if care is taken to exclude prospective hidden hydrocarbon-bearing zones. Top of gas sand reflections then should plot below the background trend and bottom of gas sand reflections should plot above the trend. We can classify the gas sand response according to position in the A-B plane of the top of gas sand reflections. Our classification is identical to that of Rutherford and Williams (Geophysics, 1989) for Class I (high impedance) and Class II (small impedance contrast) sands. However, we differ from Rutherford and Williams in that we subdivide their Class III sands (low impedance) into two classes (III and IV). The Class IV sands are highly significant in that they exhibit AVO behavior contrary to established rules of thumb and occur in many basins throughout the world including the Gulf of Mexico. EDGENET DECEMBER 1997

4 Class Relative Impedance Quadrant A B Amplitude vs. Offset I Higher than overlying unit IV + - Decreases II About the same as the II, III, or IV + or - - Increase or decrease; overlying unit may change sign III Lower than overlying unit III - - Increases IV Lower than overlying unit II - + Decreases Figure 6. This chart summarizes the AVO behavior of the various gas sand classes. Note that when we say amplitude versus offset we are referring to the variation of the magnitude of the reflection coefficient. Thus, a negative reflection coefficient that becomes more positive with increasing offset has a decreasing reflection magnitude versus offset. Note that Class IV gas sands are anomalous in that they have a positive AVO gradient and that amplitude decreases with increasing offset. Plane-wave reflection coefficient at top of gas sand Figure 7. We have superimposed an example of a Class IV gas sand on a figure taken from Rutherford and Williams which shows their gas-sand classification based on normal incidence reflection coefficient. The vertical axis is reflection coefficient and the horizontal axis is local angle of incidence. Note that Class III and IV gas sands may have identical normal incidence reflection coefficients, but the magnitude of Class IV sand reflection coefficients decreases with increasing angle of incidence while Class III reflection coefficient magnitudes increase. Figure 8. Here are examples of shale over gas-sand and shale over brine-sand reflections. Both decrease in amplitude versus offset and have about the same AVO gradient, even though the gas sand is a bright spot (it is Class IV). The model parameters are: Lithology Vp (km/sec) Vs (km/sec) p (gm/cc) Shale Brine Sand Gas Sand

5 Figure 9. This figure shows the difference in AVO behavior for a gas sand when overlain by a shale or, alternatively, by a high-velocity tight streak. In both cases, the gas sand is a bright spot. When overlain by a shale, the gas sand is Class III and amplitude increases with increasing angle of incidence. However, when overlain by a tight streak, the gas sand is Class IV and amplitude decreases with increasing angle of incidence. The parameters are: Lithology Vp (km/sec) Vs (km/sec) p (gm/cc) Shale Brine Sand Gas Sand The model parameters for this example were obtained from well log measurements and provided by Jeremy Greene of ARCO Exploration and Production Technology. Figure 10. Consider a bright gas sand reflection with an AVO intercept (A) of -.4 and an AVO gradient (B) of.4. If the frame properties of the brine sand are not identical to that of the gas sand, the reflection coefficient for the shale over brine-sand reflection with an A of, say -.2, could easily have the same B of.4. This cir - cumstance would con - found most interpreters in that the gas sand is a bright spot (A = normal incidence reflection coefficient = -.4) but (1) the reflection magnitude decreases with offset (B is positive so the negative reflection becomes smaller!), and (2) the AVO gradient is not anomalous with respect to the brine sand. Thus, the result would be a false negative for most interpreters. (Commentary: So this perfectly good bright spot may not be drilled because it has not been verified by AVO analysis. Imagine management s disgust when a competitor who (1) hasn t bothered doing AVO, or (2) has interpreted the AVO data correctly comes along and drills a discovery. Is it any wonder that AVO has a bad name in some quarters? Of course, the problem here is not with AVO, it is with interpreters who cling to naive rules of thumb; i.e., gas-sand amplitude increases with offset or use partial stacks rather than more sophisticated analysis techniques even though they may have no idea what to look for on a partial stack until after the well has been drilled and logged. Clearly, one should interpret anomalous AVO behavior in the context of deviation from background gradient AND intercept behavior.)

6 Reasonable petrophysical assumptions for clastic stratigraphic intervals result in linear background trends for limited depth ranges on AVO intercept (A) versus gradient (B) crossplots. In general, background B/Abecomes more positive with increasing V p /V s. Thus, if too large a depth range is selected for A versus B crossplotting, and background V p /V s varies significantly, a variety of background trends may be superimposed, resulting in a less well-defined background relationship. For very high V p /V s, as may occur in very soft, shallow, brine-saturated sediments, the background trend B/A becomes positive; n o n h y d ro c a r b o n - related re f l e c t i o n s may exhibit increasing AVO and show false positive anomalies (especially for l a rge reflection coefficients). Partial stacks, Atimes B pro d- uct indicators, and improperly calibrated fluid-factor sections are all susceptible to such false positives. Deviations from the background trend may be indicative of hydrocarbons. This is the basis for the fluid factor of Smith and Gidlow (1987), the NI versus Poisson reflectivity of Verm and Hilterman (1995), and related indicators. Inspection of the A versus B plane reveals that gas sands may exhibit AVO behavior which differs dramatically from conventional rules of thumb. S u re l y, the idea that gas-sand amplitude increases versus offset should finally be put to rest for all time. We suggest that hydrocarbon-bearing sands should be classified according to their location in the A-B plane, rather than by their normal-incidence reflection coeff i c i e n t alone. Class I sands are higher impedance than the overlying unit. They occur in quadrant IV of the A-B plane. The normal incidence reflection coefficient is positive while the AVO gradient is negative. The result is that the reflection coefficient decreases with increasing offset. Class II sands have about the same impedance as the overlying unit. They exhibit highly variable AVO behavior and may occur in quadrants II, III, or IV of the A-B plane. The normal incidence reflection coefficient (A) may be positive or negative and B is negative. The reflection coefficient becomes increasingly negative versus offset, but the reflection amplitude may increase or decrease depending on the sign of the reflection coefficient. When the reflection coefficient is positive at near offset, amplitude will initially decrease and may reverse polarity and then increase with offset (the Class IIp of Ross and Kinman, where p indicates phase reversal). Class II sands often exhibit poor ties between conventional synthetic seismograms and the stacked seismic data. Our Class III sands differ from Rutherford and Williams Class III sands in that we include only those reflections which occur in quadrant III. These sands are lower impedance than the overlying unit and are frequently bright. They have negative A and B and the reflection coefficient becomes increasingly negative with offset. These are the quintessential gas sands for which amplitude increases versus offset. Our Class IV sands are those low impedance sands which occur in quadrant II. These sands have negative A but a positive B. The reflec - tion coefficient becomes less negative with increasing offset and amplitude decreases versus offset, even though these sands may be bright spots. Bear in mind that the two-term Shuey approximation may not be appropriate for AVO analysis of long-offset data. Analysis of such data should include (1) corrections for various effects of anisotropy and (2) utilization of the full Zoeppritz equations. AVO analysis techniques that rely on AVO product indicators (such as Atimes B) or inspection of partial stacks (for weak amplitude at near offsets associated with strong amplitudes at far offsets) are designed for Class III sands. Clearl y, these approaches can easily lead to misinterpretation for other gas-sand classes. A l t e r n a t i v e l y, the fluid factor and related indicators will theoretically work for any gas-sand class. Unfortunately, some algorithms for extraction of A s and Bs are not robust, particularly in the presence of small NMO errors, so partial stacks are often resorted to. Sometimes, for logistical or economic reasons, the interpreter only has access to partial stack data. In these situations, the data should still be interpreted in the context of the A-B plane and deviation from some background behavior should still be the means of defining anomalies. LE Conclusions and Discussion Suggestions for further study. The Shuey approximation is described in his 1985 paper in GEOPHYSICS. The fluid factor was introduced by Smith and Gidlow in a 1987 article in Geophysical Prospecting. This paper should be required reading for anyone doing AVO analysis. The Rutherford and Williams classification can be found in their classic 1989 paper in GE O P H Y S I C S. This paper gives real world examples of Class I, Class II, and Class III reservoirs. The Rutherford and Williams classification is further discussed in GEOPHYSICS by Castagna and Smith (1994) and Ross and Kinman (1995). AVO crossplotting is described in some versions of Hilterman s SEG Contin - uing Education Course Notes, beginning in the mid-tolate 1980s. Some superb examples were shown by Foster, Smith, Dey-Sarkar, and Swan at SEG s 1993 Annual Meeting. TLE readers were introduced to the subject by Castagna in 1993 and Verm and Hilterman in N o t a b l y, two papers co-authored by Herb Swan are still awaiting publication in GEOPHYSICS. One of these was submitted in Jim DiSiena received a best presentation award at AAPG s 1996 convention for application of AVO crossplotting techniques to 3-D seismic data. Would you like to learn more? John Castagna is currently performing and compiling case studies on datasets with Class IV sands and studying AVO responses at long offsets. He can be reached at or [email protected] for the digitally inclined, if you are interested in collaborating, cofunding, or otherwise participating. Acknowledgments: This tutorial is based on a more extensive paper (complete with mathematics) co-authored by Doug Foster and Carolyn Peddy which was submitted to GEOPHYSICS some months ago and may be published some day in the distant future. This work was partially supported by GRI under contract , by ARCO Explo - ration and Production Te c h n o l o g y, and by The University of Oklahoma Institute for Exploration and Production Geosciences.