Box and Doss Oct08 AVOtrends-GOM

1252 The Leading Edge October 2008

The eff ect of fl uid pressure gradient on AVO response is not easy to discern in the literature and is awkward to

communicate. Most explorationists cannot predict how log responses and AVO signatures will change if the fl uid pressure gradient is diff erent at a prospective area than at known control (even if their depths are the same): An increase in fl uid pressure gradient means a decrease in the hardness values of the acoustic properties (VP, VS, and Rho) for both the shales and the sands, but since AVO varies in a nonlinear way with the contrast in these six variables, it is diffi cult for us to intuit what the overall eff ect on AVO will be. Th e depth may also diff er, making the problem even more complex. In Tertiary basins, the most important driver of acoustic properties is compaction (which is primarily a function of depth, but is also aff ected by fl uid pressure gradient). Most modeling packages provide somewhat automated ways to calculate the eff ect of changes in fl uid content, thickness, and porosity—but not fl uid pressure gradient. Equations and methods exist (Gassmann fl uid substitution, Greenberg-Castagna equations, Gardner equation, Widess diagrams, etc.) to investigate the eff ects of changes in density, compressional velocity, shear velocity, thickness, fl uid content, bandwidth, and many other variables, but fl uid pressure gradient is conspicuously absent.

To help fi ll in this gap, we present a new method of model-ing the eff ects of fl uid pressure gradient on AVO, along with some new types of diagrams to illustrate the results. Th e results of this study suggest that fl uid pressure gradient is as impor-tant as depth in controlling AVO.

ConceptTo understand the eff ects of depth and fl uid pressure gradient on AVO, the range of fl uid pressure gradient values (0.45 to 0.95 psi/ft) may be split into fi ve equal increments, analyzed, and modeled separately. Within each pressure range, fi ve equal depth intervals may be analyzed and modeled. Within each depth interval, the acoustic parameters (VP, VS, and den-sity) may be linearly interpolated from “typical” values at the top and bottom of the interval. Th e typical VP and density values for wet sand and shale may be estimated from “trend curves” (defi ned below); the VS values may be computed using Greenberg-Castagna; the values for oil and gas cases may be computed using fl uid substitution. Values other than “typi-cal” ones are possible, but may be ignored here, because the purpose is to hold all variables except depth and fl uid pres-sure constant. Th e result is a 5 × 5 grid of AVO models which demonstrates the relative changes in AVO caused by changes in depth and fl uid pressure gradient.

Determining the input parameters for each grid cell re-quires:

Knowledge of the “typical” acoustic parameter values for • sand and shale in each cell determined from a well log

Typical AVO response as a function of depth and fl uid pressure gradient: Gulf of Mexico shelf

INTERPRETER’S CORNER Coordinated by REBECCA LATIMER

RICK BOX and ERIC DOSS, Hunt Petroleum, Houston, USA

study of the areaDefi nition of one standard lithological scenario, includ-• ing sand thicknesses, bed boundaries, and fl uid con-tents.

Log trends Our study area contained 13 wells from the Louisiana Gulf of Mexico shelf, from West Cameron to Main Pass, including East Cameron, Vermilion, South Marsh Island, Eugene Is-land, and South Timbalier. Th e wells were selected on the ba-sis of their extensive logged range, nearly complete log suites, relative verticality, and interpreted quality. Th is large area (ap-proximately 270 × 100 miles) illustrates the lateral consisten-cy of rock properties. A smaller area would have less variation, and a correspondingly tighter defi nition of “typical.”

Th e wells were purifi ed (that is, the logs were petrophysi-cally edited using a vendor’s proprietary technique); a lithol-ogy fraction curve has been derived from lithology logs (GR, SP, etc.), a fl uid pressure gradient curve has been derived from the shape of the resistivity, sonic, and density curves; and the sonic and density logs were edited to contain no values that contradict other curves.

Th e 13 wells contain more than 200 000 samples. For each acoustic variable, it is necessary to perform a dual-histogram analysis to separate the eff ect of pressure from the eff ect of depth on compaction. For example, the analysis of the VP acoustic variable for shale is shown in Table 1. Th e upper left bin shows that the average sonic transit time for all points whose fl uid pressure gradient falls between 0.45 and 0.55 psi/ft, and whose depth falls between 1500 and 4500 ft is 142 us/ft. Th e mechanics of this process are illustrated in Figure 1a, where all points whose lithology fraction falls between 0% and 20%, in the fi rst pressure column (0.45 < fl uid pressure gradient < 0.55) have their purifi ed sonic transit time plot-ted against depth. Th e results form a “trend curve,” showing how sonic velocity increases smoothly with depth (because of compaction) when other variables are constant. Th e central values were extracted every 3000 ft to form inputs to Table 1, column 1. Th e fi nal two entries in this column are “none” be-cause no shales of such low pressure exist below about 12 500 ft (arguably, the values could be extrapolated from the trend curve, if there were reason to believe that such rocks existed in some undrilled place). Four more graphs like Figure 1a were required to fi ll in the four remaining columns of Table 1. Not surprisingly, the top two entries in the fi nal column are “none” because no shales of such high pressure exist above 7500 ft.

Figure 1b shows a potential pitfall. Plotting purifi ed son-ic log values against depth for the 13 wells for shales of all pressures results in a trend that is less clear. It would be very easy to conclude that there is a poor relationship due to the combination of wells from a wide area which may encompass very diverse geology; but Figure 1a demonstrates that holding

October 2008 The Leading Edge 1253

pressure constant removes this impression. Th is is often the case—what appears to be a lateral variation in rock properties disappears when the log data are purifi ed, and pressure is ac-counted for.

Figure 1c extends this idea. Plotting purifi ed sonic log values against depth for the 13 wells for all rocks (shale and wet sand) for all pressures results in a trend that is marginally less clear than Figure 1b. Analyzing sands and shales together (something most people would instinctively avoid) causes less trend obfuscation than failing to account for pressure. Togeth-

er, Figures 1a, 1b, and 1c illustrate that pressure and depth are fi rst-order controls on sonic velocity, while lithology is sec-ondary, and lateral variations are tertiary. Th is accords with laboratory experiments, physical intuition, and results we have observed in clastic basins around the world.

Th e numbers in Table 1 were contoured, as shown in Fig-ure 2, in order to confi rm that the sonic trends in shales vary smoothly with respect to pressure, as they do with respect to depth (as shown in Figure 1a).

Similar trend curve analysis was done for wet sand transit

INTERPRETER’S CORNER

Figure 1a. Purifi ed sonic logs versus depth for 13 wells, allowing normally pressured (0.45–0.55 psi/ft) shales (0–20% lithology fraction), color coded by well. Th ere is a single trend, as expected. Varia-tions from the trend are mainly due to diff erences in sand quality (grain size, sorting, etc.). Diff erences between wells are small: about the same as diff erences within wells. Five of these 2D trends (for the fi ve fl uid pressure gradient intervals studied) combine to form a coherent 3D whole (compare to Figure 2).

Table 1. Sonic transit times in shales (0.00 to 0.20 lf).


times, wet sand densities, and shale densities. Th e results were also stable, confi rming that the values are representative of the region, and appropriate for use in AVO modeling. Th ere was not enough shear log data, or data in gas and oil sands, to al-low analysis of these cases by the method shown above. Shear-velocity values were computed using the standard Greenberg-Castagna method.

Fluid substitution was used to fi nd the gas-sand traveltime and density due to the insuffi cient log data over productive zones. Parameters used for gas (a standard dry gas) and oil

(a “fl at” oil) were also held con-stant to allow comparison between models.

Standard scenario for modelingAn arbitrary geologic scenario was chosen, consisting of a 3000-ft interval with seven distinct sands separated by shale intervals (Table 2).

Within each interval, the li-thology varies somewhat randomly to simulate the jitter in typical li-

thology logs due to the fi ne-scale layering of the Earth. All other logs in the suite were calculated from this standard li-thology log, parameterized by the rock property results (such as Figure 2).

Th e wet sands (A, C, E, and G) are identical to each oth-er in thickness, lithology, and fl uid content, but since they occur at diff erent depths, they have diff erent acoustic prop-erties. Th is illustrates the eff ect of compaction on the AVO background trend lines. Sands B and D contain gas and have identical sharp bases; but B has a transitional (shaling upward)


Figure 1b. Purifi ed sonic logs versus depth for 13 wells, allowing shales (0–.2 lithology fraction) of all pressures, color coded by well. Th e trend of traveltime versus depth is unclear. We will show that the reason is not because wells from a wide area (270 × 100 miles) were combined; it is because shales of various pressures were combined. Compare to Figure 1a.

Table 2.Standard scenario for modeling.



top, while D is blocky, litho-logically identical to A, C, E, F, and G. Comparisons of B to D allow investigation of whether the crispness of the top has appreciable eff ect on the AVO signature.

Th is model, unlike most published AVO models, ac-counts for the eff ects of com-paction. Each parameter was interpolated at each interme-diate depth. For example, giv-en a shale traveltime of 124 us/ft at a depth of 3000 ft and 114 us/ft at 6000 ft, the trav-eltime at 4500 ft depth will be 119 us/ft.

All sands are thinner than a quarter of the wavelength of the wavelet, so tuning is a fac-tor in the amplitudes (as it is in most gas fi elds in the Gulf

Figure 1c. Purifi ed sonic logs versus depth for 13 wells, allowing all lithologies and all pressures, color coded by well. Th e trend of traveltime versus depth is unclear. Compare to Figure 1b.: Plotting sands and shales together obscures the trend, but not as severely as disregarding pressure did.

Figure 2. Shale transit time versus depth and pressure. Binned pressures vary from 0.45 to 0.85 psi/ft on the horizontal axis and depths vary from 3000 to 18 000 ft on the vertical axis; together they form a 6 × 5 grid, with 22 of the 30 cells populated. Acoustic transit times for shale (μs/ft) are posted and contoured. Lowest ve-locities are towards the top right, where high fl uid pressure and shallow burial combine to produce the least compaction. Each column of values was extracted from a trend curve, such as the one in Figure 1a. Th e composite of fi ve 2D trends forms a 3D trend with good consistency, as confi rmed by the smooth contours. Th is “map” contours shale transit time; similar maps of sand transit time, shale density, and sand density were done and also observed to be smooth.


of Mexico). It would be instructive to repeat the modeling for a thicker-than-tuning case.

AVO modelingFor each scenario, an AVO model was computed using an identical workfl ow. Figure 3 shows the model for the high-est fl uid pressure gradient category (0.85–0.95 psi/ft) and fairly deep depths (12 000–15 000 ft). Shale fraction, fl uid pressure, sonic, density, and resistivity logs were generated by the interpolation method described in the previous section, using parameters derived from trend curve analyses (such as the example shown in Figure 2). Shear logs were generated via Greenberg-Castagna methods (there was insuffi cient mea-sured shear data to grid and contour them similarly to the density and compressional velocity). Seismic angle gathers (red and blue color-density displays in Figure 3) were modeled using a full Zoeppritz solution and a constant 20-Hz zero-phase Ricker wavelet. A two-term Aki-Richards fi t through

the gathers produced the intercept and gradient traces (blue).A crossplot of the intercept and gradient was made for each

model. Th e four wet sands clustered more or less together, and a regression was fi t through these points. Th e angle, chi, of this regression line was used to rotate the axes. After coordinate transformation, the “max-fl uid” and “max-lith” traces emerge. Th e objective of the transformation is to make the response on the max-fl uid trace in wet zones be near zero. Th e hydrocar-bon zones remain bright and therefore stand out.

Assembling the piecesTh e completed models were assembled into a poster (not shown) that is tremendously valuable for understanding the eff ects of compaction on AVO. Th e details of such a large dis-play are not visible at page size, therefore, summary displays were made. Figure 4 reduces the clouds of points on the cross-plots to their centroids: a shale-over-wet-sand point (blue), a shale-over-oil-sand point (green), and a shale-over-gas-sand

Figure 3. An AVO model (depths from 12 000 to 15 000 ft; fl uid pressure gradient fi xed at 0.85 psi/ft). Log suites (inferred from trend curve results) were put into a Zoeppritz AVO model, to generate angle gathers for traces from 0 to 50° incrementing by 5° degrees, using a 20-Hz zero-phase Ricker wavelet. A standard set of AVO displays were generated from the gathers. Th e 0–10° traces were summed to produce the near trace (fi rst black trace). Th e 30–45° traces were summed to produce the far trace (second black trace). A standard two-term Aki-Richards curve-fi t was performed on the gather to compute the intercept (fi rst blue trace) and gradient (second blue trace). Th ese were crossplotted to defi ne a chi angle, and coordinates were rotated by the Chi angle to produce the fl uid (red) trace and the lith (gray) trace. Th e rotation was chosen to make the fl uid trace zero for wet sands. But, due to compaction, the four wet sands diff er somewhat. In this case, none of the sands were completely zeroed, although sand A was closest. Diff erent depth and pressure scenarios were run through identical AVO modeling. Th e results are compared in Figure 4.


October 2008 The Leading Edge 1259

point (red). Th e “clock-hands” display illustrates how AVO changes as a function of depth and fl uid pressure gradient. A grid cell is empty if the rock properties are un-known at the beginning or ending depth.

Figure 5a shows the ra-tio of the shale-over-gas-sand amplitude to the shale-over-wet-sand amplitude (i.e., the ratio of the length of the red clock hand in Figure 4 to the length of the blue hand). It demon-strates that rules of thumb, such as, “I never drill a gas prospect unless the amplitude is fi ve times the background,” should not be used unless calibrated to depth and fl uid pressure gradient.

Figure 5b shows how the angular diff erence (i.e., the dif-ference between the gas angle and the wet angle in Figure 4) varies according to depth and fl uid pressure gradient. Below 5000 ft, this is a reliable gas indicator; above 5000 ft, the am-plitude ratio (Figure 5a) is preferred. No single AVO indicator is best everywhere—the entire pattern of AVO is important.

Table 3 shows data extracted from three key points in Fig-ure 5b. Interestingly, these angular diff erences were about the same, causing the 30° contour in Figure 5b to pass near all

three points. Locally, for the angular diff erence between wet and gas vectors, a 3000-ft change in depth is off set by a 0.10-psi/ft (1.9 ppg) diff erence in fl uid pressure gradient. In some portions of Figure 5b, the eff ect of fl uid pressure gradient is even more severe, and in some portions it is less, but in any case it is enough to warn us not to ignore pressure when in-terpreting AVO.

ConclusionsTh e diffi cult and nonintuitive questions surrounding • how changes in fl uid pressure gradient alter the AVO response of reservoir rocks in clastic basins were illumi-nated by separately analyzing fi ve diff erent pressure re-gimes.Within each pressure range, velocity and density of wet •

Figure 4. Grid of AVO clouds. Th is is a “clock hands” display. Within each cell, intercept is plotted on the horizontal axis, and gradient on the vertical. Th e cases are shale-over-gas-sand (red), shale-over-wet-sand (blue), and shale-over-oil-sand (green). Th e eff ect of fl uid pressure gradient (independent of depth) on AVO is visible by comparing columns within a row.


Table 3. AVO eff ects of pressure and depth.


Figure 5. (a) Grid of amplitude ratios. In Figure 4, the length of the gas sand vector (red) is typically greater than that of the wet sand vector (blue). Th e ratio of these lengths is a better gas indicator in softer rocks (top right) than in harder rocks (bottom left). (b) Angular diff erences versus depth and pressure. In Figure 4, the angle of the gas sand vector (red) is typically diff erent from that of the wet sand vector (blue). Th e angular diff erence is a gas indicator that works except around a depth of 5000 ft, where the sign of the diff erence is changing.



sand and of shale may be estimated from multiwell em-pirical trend results of purifi ed log data. A fl uid pressure gradient increase of 0.1 psi/ft (1.9 ppg) • had an eff ect on AVO angular diff erence similar to that of a reduction in depth of 3000 ft (more or less at dif-ferent depths and pressures). Th erefore, it is perilous to interpret AVO without considering the eff ect of fl uid pressure gradient. Rules of thumb, such as, “I never drill a gas prospect unless the amplitude is fi ve times the back-ground,” should not be used unless calibrated to depth and fl uid pressure gradient. Discriminating gas sands from wet sands is easier at shal-• lower depths and higher pressures. Th e lower the eff ec-tive stress, the higher the water content, and the more distinct the AVO signature.No single AVO attribute (such as angular diff erence or • amplitude ratio) distinguished hydrocarbons from brine at all depths and pressures.Even over a signifi cant (270 • × 100 miles) portion of the Louisiana shelf, lateral changes in rock properties were small compared to changes caused by lithology and fl uid pressure gradient.Prospect-level AVO studies, especially comparison • to analogous situations may be locally superior to the method shown here because they include locally im-portant variables such as atypical shales (with varying calcite content), atypical sands (varying cementation, etc), variations in fl uid content (low saturation gas, dry

versus wet gas, diff erent types of oils, etc), atypical shear velocity situations, anisotropy, and so on. However, the method used here (regional analysis of typical sands and shales) allows interpreters to develop better physical in-tuition about how AVO generally depends on depth and fl uid pressure gradient over a wide area of study.

Suggested reading. “Excellent synthetic seismograms through the use of edited logs: Lake Borgne Area, Louisiana, US” by Box (TLE, 2004). “AVO inversion: Isolating rock property contrasts” by Kelly et al. (TLE, 2001). “Nonbright-spot AVO: Two exam-ples” by Ross and Kinman (Geophysics, 1995). “Pressure and porosity infl uences on VP/VS ratio of unconsolidated sands” by Zimmer et al. (TLE, 2002).

Acknowledgments: Th e authors thank everyone who helped us com-plete this work: Denny Loren for pioneering the concept of log trend curves; Rosa Ethridge and Paul Lowrey at Loren and Associates for doing the well log purifi cation; Rob Mayer at CGGVeritas for as-sistance with using the Hampson-Russell software; Lee Ethetton for assistance with porting data between diff erent hardware platforms and software systems; Laura Kay Ethetton for assembling the log data base; Pete Harth and Jeremy Greene for proofreading and advice on making the fi gures logical; and Tony Curtis for making the fi gures clear.

Corresponding author: [email protected]


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