Abstract The subsurface of the earth comprises rock layers that have different physical properties and are in contact with one another (i.e., are stratified). The boundaries separating the individual layers are referred to as interfaces. Those interfaces may represent contacts between, for example, a sand layer and a shale layer (i.e., a sand-shale interface), or between a shale layer and a limestone layer (a shale-limestone interface), or they may be an interface between gas-filled and water-bearing layers of sandstone. It is helpful to understand the propagation of sound waves through such subsurface interfaces. A simple way to model the partitioning of energy at an interface is to consider a basic model of the subsurface, in which the interface is perfectly planar and separates two infinitely homogeneous, isotropic, elastic media. We refer to such an interface as an ideal reflector .

Abstract A direct correlation of lithology to stacked and migrated seismic data, although an attractive goal, is usually an elusive one. In extreme cases, such as hard limestone formations encased in clastics, lithologic information may be obvious in the seismic amplitudes. For subsurface formations characterized by small velocity changes between different lithologies, however, such a correlation may not be possible. Similarly, acoustic logs themselves are poor indicators or differentiators of lithology, unless they are combined with other logs such as density or porosity logs. One main reason for this is that reservoir rocks such as sandstone, limestone, and shale each exhibit large acoustic-velocity ranges that may overlap significantly. In addition, this limited information is available only at the location of a well, and seismic data are looked upon to provide it elsewhere. Although the goal of direct correlation from seismic to lithology seems simple, serious thought suggests that it could be a complicated exercise. The seismic response of subsurface rocks depends on the contrasts in compressional- and shear-wave velocities and densities. Those contrasts in turn depend on the rock’s lithology, porosity, pore-fluid content, and pressure, all of which affect seismic-wave propagation (e.g., Gregory, 1977; Castagna et al., 1993). That dependence requires knowledge about variations in the elastic properties of rock frames, their mineral constituents, and pore fluids, as well as a model for the interactions among them. Rock physics provides the link between the physical properties of rocks and their seismic response, and that link establishes the P-wave velocity (VP), S-wave velocity (VS), and density (ρ) of the subsurface rocks, along with their relationships to the rocks’ elastic moduli (bulk modulus κ and shear modulus μ ), porosity, pore fluid, temperature, pressure, and the like.

Abstract Amplitude-variation-with-offset (AVO) analysis attempts to use the offset-dependent variation of P-wave reflection coefficients to detect and/or estimate anomalous contrasts in shear-wave velocities and densities across an interface. Although the conventional P-wave reflection coefficient at normal incidence is, in itself, a hydrocarbon indicator, AVO goes beyond the P-wave normal incidence by producing a second attribute (of one kind or another) that is related to the contrast in Poisson's ratio. A crossplot of those two attributes allows interpreters to look for anomalous fluids. Thus, hydrocarbon detection using AVO is based fundamentally on the anomalous relationships between compressional-wave and shear-wave velocities and densities for hydrocarbon-bearing rocks, relative to those relationships for equivalent fully brine-saturated rocks or other background references.

Abstract When an incident P-wave strikes the boundary (or interface) between two media obliquely, the wave is split into reflected and refracted P-wave components and reflected and refracted S-wave components. The reflection and transmission coefficients vary as a function of the angle of incidence (hence, of source-receiver offset) and of the media’s elastic properties, which comprise densities and bulk and shear moduli. The Zoeppritz equations (Chapter 1) give the reflection and transmission coefficients for plane waves, as a function of the angle of incidence and as a function of the three independent elastic parameters on each side of the reflecting interface. If the reflection amplitude is observed as a function of the angle of incidence, the variation of that parameter can be used to make inferences about the elastic parameters.

Abstract Seismic processing is usually conducted to achieve objectives such as structural imaging or stratigraphic resolution, rather than amplitude-variation-with-offset (AVO) analysis. Although the ultimate goal of processing surface seismic data is to obtain a migrated stack section, interpretation objectives have changed over the years. In the 1960s and early 1970s, structural interpretation and reservoir delineation required well-balanced amplitudes and clear, sharp interfaces. Thus, final migrated sections usually had an automatic gain control (AGC) applied. By the middle 1970s, stratigraphic interpretation had caught up, and along with that advance came the awareness that amplitude information on migrated sections is important. At that time, seismic processors began to retain relative amplitudes during processing. That information also helped with detection of bright spots (anomalous reflectors corresponding to gas-charged sands) and flat spots (anomalous subhorizontal reflectors associated with fluid contacts, usually gas on water) on relative-amplitude-processed (RAP) sections. Ostrander's introduction of AVO analysis in 1984 led to the confirmation of bright spots and other anomalous reflections on RAP sections ( Ostrander, 1984 ). Since then, geophysicists have persisted in trying to extract more information from seismic amplitudes, during both prestack and poststack processing. Along with AVO analysis, a plethora of seismic attributes has been studied and is known to add value to the interpretation carried out on such data ( Chopra and Marfurt, 2007 ). The crucial point in amplitude analysis has been the realization that the reliability of the results depends on the nature of the data acquisition and the quality of the processing that generated the amplitudes.

Abstract The ultimate goal of conventional seismic data processing is to derive a response that one can assume is similar to the zero-offset compressional-wave reflection response of the earth. Using recorded multifold seismic data, traces that have different source-receiver offsets and that illuminate the same source-receiver midpoint (or reflecting point) are summed. That is done by applying NMO correction to different offset traces and then stacking them. The mean reflection amplitudes are displayed at their zero-offset time, and the display is assumed to be similar to the zero-offset section. Such an approach works when the reflection amplitudes across different offsets do not change. However, we know that is usually not the case, and in fact reflection amplitudes do change with offset. The change occurs because energy partitioning between reflected and transmitted wave modes is angle-dependent. The P-wave reflected and transmitted amplitudes depend on the compressional-wave velocities and the shear-wave velocities, as well as on the density of the incident and reflecting media.

Abstract The AVO studies that we discussed in the preceding chapters assume that subsurface rock formations are isotropic. Often that assumption is not strictly true, because subsurface formations can exhibit various kinds of anisotropy. In such cases, serious errors can creep into AVO analysis and lead to erroneous interpretations. On the other hand, anisotropic behavior can be used beneficially to characterize fractured reservoirs. Thus, it is important to study the different types of anisotropy encountered in subsurface formations, along with their effect on seismic data, and then to determine their ultimate effect on AVO analysis. We will explore all of these considerations in this chapter.