Douglas J. Foster

Framework for AVO gradient and intercept interpretation

Amplitude variation with offset (AVO) interpretation may be facilitated by crossplotting the AVO intercept (A) and gradient (B). Under a variety of reasonable petrophysical assumptions, brine‐saturated sandstones and shales follow a well‐defined “background” trend in the A-B plane. Generally, A and B are negatively correlated for “background” rocks, but they may be positively correlated at very high VP/VS ratios, such as may occur in very soft shallow sediments. Thus, even fully brine‐saturated shallow events with large reflection coefficients may exhibit large increases in AVO. Deviations from the background trend may be indicative of hydrocarbons or lithologies with anomalous elastic properties. However, in contrast to the common assumptions that gas‐sand amplitude increases with offset, or that the reflection coefficient becomes more negative with increasing offset, gas sands may exhibit a variety of AVO behaviors. A classification of gas sands based on location in the A-B plane, rather than on normal‐...

Suppression of multiple reflections using the Radon transform

Multiple suppression using a variant of the Radon transform is discussed. This transform differs from the classical Radon transform in that the integration surfaces are hyperbolic rather than planar. This specific hyperbolic surface is equivalent to parabolae in terms of computational expense but more accurately distinguishes multiples from primary reflections. The forward transform separates seismic arrivals by their differences in traveltime moveout. Multiples can be suppressed by an inverse transform of only part of the data. Examples show that multiples are effectively attenuated in prestack and stacked seismograms.

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.

Common Angle Imaging With Offset Plane Waves

Migration is commonly used as a wavefield focussing tool in the study of the variation of reflection amplitude with offset (AVO), or with angle of incidence at reflectors. Migrations are typically applied to common offset or common incident angle sections. In many processing systems, common angle sections are formed by simple l-d transformations from offset to angle of common midpoint (CMP) gathers based on ray tracing. In this paper, we provide a wave-equation framework for migrating common incidence angle sections that have been formed from Radon transforms over offset in CMP gathers. Radon transformation of the scalar wave equation results in an independent wave equation for each offset plane wave. The offset plane wave equation is nearly equivalent to the zero offset wave equation, except for an additional term related to dip in the midpoint direction, and to offset ray parameter (angle of incidence at the surface). Within this framework, finite difference, pseudo-spectral, and Kirchhoff migrations for common angle sections can be easily adapted from existing algorithms. The availability of a wave equation for common angle sections allows rigorous and efficient application of wave equation techniques for AVO studies and complex structural imaging problems.

The impact of migration on AVO

Amplitude variation with offset (AVO) analysis is often limited to areas where multidimensional propagation effects such as reflector dip and diffractions from faults can be ignored. Migration-inversion provides a framework for extending the use of seismic amplitudes to areas where structural or stratigraphic effects are important. In this procedure, sources and receivers are downward continued into the earth using uncollapsed prestack migration. Instead of stacking the data as in normal migration, the prestack migrated data are used in AVO analysis or other inversion techniques to infer local earth properties. The prestack migration can take many forms. In particular, prestack time migration of common-angle sections provides a convenient tool for improving the lateral resolution and spatial positioning of AVO anomalies. In this approach, a plane-wave decomposition is first applied in the offset direction, separating the wavefield into different propagating angles. The data are then gathered into common-angle sections and migrated one angle at a time. The common-angle migrations have a simple form and are shown to adequately preserve amplitude as a function of angle. Normal AVO analysis is then applied to the prestack migrated data. Examples using seismic lines from the Gulf of Mexico show how migration improves AVO analysis. In the first set of examples, migration is shown to improve imaging of subtle spatial variations in bright spots. Subsequent AVO analysis reveals dim spots associated with dry-hole locations that were not resolvable using traditional processing techniques, including both conventional AVO and poststack migration. A second set of examples shows improvements in AVO response after migration is used to reduce interference from coherent noise and diffractions. A final example shows the impact of migration on the spatial location of dipping AVO anomalies. In all cases, migration improves both the signal-to-noise ratio and spatial resolution of AVO anomalies.

Migration velocity analysis using common angle image gathers

The common angle imaging (CAI) framework provides an analysis methodology for extracting AVO and velocity information from full wave-field migration algorithms. The common angle imaging condition extracts the zero time wavefield at constant offset ray parameter during downward continuation of source and receiver wavefields in the frequency domain. Images at a number of angles (or offset ray parameter values) can be extracted to provide the equivalent of migrated tau-p gathers for each surface location. The CAI gathers can be inverse transformed or “offset stacked” (the inverse operation of producing angle stacks from offset gathers) to produce familiar image gathers for existing residual velocity analysis programs. Alternatively, residual velocity analysis can be performed directly in the depth offset ray parameter (z-Ph) domain. When the migration velocity differs from the true velocity, the resulting residual moveout on CAI gathers is approximately elliptical in shape. Semblance scans over elliptical trajectories are used to determine residual moveout as a function of depth and surface location. The observed residual moveout can be expressed as a line integral of velocity errors along a ray path. Simple vertical updates or more complicated back-projection schemes can then be used to generate updates to the migration velocities. For migrations of the SEG/EAEG Salt Model C3 Narrow Angle synthetic dataset using phase screen propagators, CAI gathers are flat when the correct velocity is used, and show the expected residual moveout when incorrect velocities are used. Simple 1-D updates based on residual moveout picks from differential semblance analysis provide improved velocity estimates for subsequent iterations.

Common Angle Imaging Conditions For Pre-stack Depth Migration

Summary New classes of wave equation based wavefield extrapolators now allow us to produce accurate depth images of complex structural targets. The most common imaging condition extracts the zero time wavefield at zero offset, yielding a single image at each depth. Migration-inversion theory provides a framework for constructing imaging conditions that exploit redundancy in the extrapolated wavefields to provide more information on subsurface properties. The most important of these are background velocity and amplitude as a function of incidence angle. The common angle imaging condition (CAI) extracts the zero time wavefield at constant offset ray parameter. Images at a number of angles (or offset ray parameter values) can be extracted to provide the equivalent of migrated taup gathers for each surface CMP location. Since offset ray parameter is proportional to angle of incidence at the reflector, CAI gathers provide amplitude versus angle information that automatically incorporates reflector dip. Residual velocity analysis is performed on CAI gathers by scanning for residual elliptical moveout using familiar tau-p formulations. The combination of fast, accurate wavefield extrapolators (for example, the common offset pseudo-screen operators reported by Jin and Wu, 1999) with the common angle imaging condition now provides a complete set of tools for structural imaging, AVO, and velocity analysis with wave equation based techiques.

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.

An inverse‐scattering sub‐series for predicting the spatial location of reflectors without the precise reference medium and wave velocity

The accurate location, resolution and identification of targets beneath complex media (e.g., salt, basalt and karsted sediments) are high priority and essentially unsolved problems today. Imaging methods that are tested and compared using synthetic data with precise model velocity as input are not addressing the real-world problem. At the very least, imaging methods need to be tested using synthetic data and a velocity model that corresponds to what would be estimated from the data using current best velocity analysis techniques. This bit of realism would help focus on the relevant issue: how do we achieve accurate imaging at depth given our current ability to estimate the velocity, especially under complex geologic circumstances? There are two responses to this challenge: (1) to significantly improve velocity estimation capability, and (2) to develop methods that can produce accurate images at depth without precise velocity. We support both approaches and this paper represents an effort in the second category.

A closer look at hydrocarbon indicators

The deficiences of the AVO indicators are explored. Currently, one type of AVO anomaly is being identified as a positive hydrocarbon indicator (HCI). This type of anomaly is the magnitude of a reflected event increasing with offset. This is a common type of AVO anomaly but is by no means the only anomaly associated with hydrocarbons. Using the present HCI other types of anomalies give a negative indication and, therefore, hydrocarbons may be overlooked. Correlations of rock properties (i.e. velocities and densities) imply a more robust way of indicating the presence of hydrocarbons. These correlations observed in the petrophysical properties can be utilized to develop a more general HCI. This new form of HCI can also be less dependent on preprocessing of seismic data. A more robust HCI makes AVO analysis more reliable as well as open new areas of exploration.