Robert G. Keys

An approximation for the Xu‐White velocity model

In 1995, S. Xu and R. E. White described a method for estimating compressional and shear-wave velocities of shaley sandstones from porosity and shale content. Their model was able to predict the effect of increasing clay content on compressional-wave velocity observed in laboratory measurements. A key step in the Xu-White method estimates dry rock bulk and shear moduli for the sand/shale mixture. This step is performed numerically by applying the differential effective medium method to the Kuster-Toksoz equations for ellipsoidal pores. This step is computationally intensive. Using reasonable assumptions about dry rock elastic properties, this step can be replaced with a set of approximations for dry rock bulk and shear moduli. Numerical experiments show an extremely close match between velocities obtained with these approximations and velocities computed with the differential effective medium method. These approximations simplify the application of the Xu-White method, and make the method computationally more efficient. They also provide insight into the Xu-White method. For example, these approximations show how the Xu-White model is related to the critical porosity model.

Interpretation of AVO anomalies

We investigate the effects of changes in rock and fluid properties on amplitude-variation-with-offset AVO responses. In the slope-intercept domain, reflections from wet sands and shales fall on or near a trend that we call the fluid line.Reflectionsfromthetopofsandscontaininggasorlight hydrocarbonsfallonatrendapproximatelyparalleltothefluidline;reflectionsfromthebaseofgassandsfallonaparallel trendontheopposingsideofthefluidline.Thepolaritystandard of the seismic data dictates whether these reflections from the top of hydrocarbon-bearing sands are below or above the fluid line. Typically, rock properties of sands and shales differ, and therefore reflections from sand/shale interfaces are also displaced from the fluid line. The distance of these trends from the fluid line depends upon the contrast of the ratio of P-wave velocity VP and S-wave velocity VS. This ratio is a function of pore-fluid compressibility and implies that distance from the fluid line increases with increasing compressibility. Reflections from wet sands are closer to the fluid line than hydrocarbon-related reflections. Porosity changes affect acoustic impedance but do not significantly impacttheVP /VScontrast.Asaresult,porositychangesmove theAVO response along trends approximately parallel to the fluidline.TheseobservationsareusefulforinterpretingAVO anomaliesintermsoffluids,lithology,andporosity.

Comparison of Seismic Inversion Methods on a Single Real Data Set

Papers in this volume explore the potential of a variety of seismic inversion methods applied to the same data set. They cover a wide range of topics, including effects of rock properties on seismic response, preparation of seismic data for AVO analysis, and a variety of AVO and inversion methods. The papers are an extension of a 1994 SEG postconvention workshop.

Polarity reversals in reflections from layered media

A polarity reversal is a 180-degree change in the phase of a seismic reflection as a function of offset. Polarity reversals occur when the P-wave reflection coefficient passes through zero when plotted as a function of the angle of incidence.

Another perspective on AVO crossplotting

“Principles of AVO crossplotting” by Castagna and Swan (TLE, April 1997) raises some very interesting points and we would like to add to the discussion. Crossplotting the AVO attributes is useful for interpreting anomalies in the context of lithology and pore fluids. Also, crossplotting shows that there is a background trend for reflections from nonhydrocarbon related interfaces. This trend, which we call the fluid line, comes from correlations of rock properties. To relate AVO anomalies to rock and pore fluid properties, it is important to calibrate background (nonhydrocarbon‐related) seismic attributes to the background rock property trend. Once the trend is established then a quantitative interpretation of an anomaly can be made.

Detecting Subsurface Hydrocarbons with Elastic Wavefields

For angles of incidence (θ) less than 30°, the compressional wave reflection coefficient is approximately a linear function of sin2 (θ). It is defined by its slope and intercept at normal incidence. These slope and intercept parameters contain useful information about the elastic properties of the subsurface. In particular, they can be used to detect the presence of hydrocarbons, because of the distinct effects that hydrocarbons have on the elastic properties of the subsurface.

Convergence properties of a leading order depth imaging series

The objective of seismic depth imaging is to produce a spatially accurate map of the re ectivity below the Earths surface. Current methods for depth imaging require an accurate velocity model in order to place re ectors at their correct locations. Techniques to derive the velocity model can fail to provide this information with the necessary degree of accuracy, especially in areas that are geologically complex.

High-Fidelity Inverse Estimate of AVO Response

There are numerous geophysical phenomena that impact the apparent AVO response on pre-stack imaged data including: NMO/RMS velocity assumptions Velocity analysis not optimized at every CRP Structure Multiples Overall data quality Overburden lateral velocity variation Anisotropy Under-sampling in the time domain (sample-by-sample AVO extraction processes) NMO stretch & other wavelet frequency effects

Unconventional AVO analysis for lithology prediction in the Britannia field, U K North Sea

Forward modeling using Britannia data shows a characteristic set of subtle reservoir AVO signatures due to the significant Vp:Vs contrast that exists between sands and shales (Figure 1). The same responses can be seen, to a certain degree, in an AVO class volume generated over the full field from nearand far-angle stack seismic volumes. A top sand class-1 AVO response was mapped over Britannia platform west and tied to existing well control. Ten of fifteen wells in the area confirmed the class-1 response was indicative of sand presence in the upper reservoir, while five of fifteen wells contain more upper reservoir sand than is suggested by the class volume. No “false positive” class volume predictions are seen. Work to date provides encouragement that AVO information can discriminate sand from shale at the Britannia reservoir level. Significant potential exists to improve reservoir characterization, optimize location of future development wells and positively impact overall field development. The workflows used in this study may also be applicable to similar high impedance reservoir characterization studies in other basins. Britannia is a Lower Cretaceous, deep water turbidite reservoir located approximately 225km north-east of Aberdeen, Scotland (Hill and Palfrey, 2003). A continuous platform drilling program is in progress, set to continue through 2007, with well targets becoming increasingly higher risk as drilling step-out increases. Optimally locating development wells is critical to the ongoing success of the field. Full stack seismic data, however, is limited in the degree of reservoir information provided. Depth of burial reduces the dominant seismic frequency at the reservoir level to about 25Hz. In addition, a major chalk interval in the overburden acts as a source of multiple energy and limits the degree of usable amplitude at far offsets.

AVO Inversion Via Localized Migrations

We present a one-step 2.5-D inversion method that estimates AVO parameter intercept and slope by minimizing data misfit over a range of CMPs in the least-square sense. Represented by either the 2.5-D Born or the 2.5-D Kirchhoff approximation, the predicted data are parameterized in terms of intercept and slope of the angle-dependent reflection coefficient. Minimization with respect to the intercept and slope leads to two five-fold integral equations. Application of multi-dimensional stationary phase approximation reduces these integral equations to manageable algebraic form. The final algorithm locally migrates and stacks the data with two special weight functions, followed by a 2 2 matrix inversion at each image point. Synthetic example validates the proposed methodology. Field data examples demonstrate the superior performance of our algorithm over conventional approaches.