This paper presents an overview and a detailed description of the key logic steps and mathematical-physics framework behind the development of practical algorithms for seismic exploration derived from the inverse scattering series. There are both significant symmetries and critical subtle differences between the forward scattering series construction and the inverse scattering series processing of seismic events. These similarities and differences help explain the efficiency and effectiveness of different inversion objectives. The inverse series performs all of the tasks associated with inversion using the entire wavefield recorded on the measurement surface as input. However, certain terms in the series act as though only one specific task,and no other task, existed. When isolated, these terms constitute a task-specific subseries. We present both the rationale for seeking and methods of identifying uncoupled task-specific subseries that accomplish: (1) free-surface multiple removal; (2) internal multiple attenuation; (3) imaging primaries at depth; and (4) inverting for earth material properties. A combination of forward series analogues and physical intuition is employed to locate those subseries. We show that the sum of the four taskspecific subseries does not correspond to the original inverse series since terms with coupled tasks are never considered or computed. Isolated tasks are accomplished sequentially and, after each is achieved, the problem is restarted as though that isolated task had never existed. This strategy avoids choosing portions of the series, at any stage, that correspond to a combination of tasks,i.e.,

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 [Formula: see text] 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‐incidence reflection coefficient, is proposed. According to this classification, bright‐spot gas sands fall in quadrant III and have negative AVO intercept and gradient. These sands exhibit the amplitude increase versus offset which has commonly been used as a gas indicator. High‐impedance gas sands fall in quadrant IV and have positive AVO intercept and negative gradient. Consequently, these sands initially exhibit decreasing AVO and may reverse polarity. These behaviors have been previously reported and are addressed adequately by existing classification schemes. However, quadrant II gas sands have negative intercept and positive gradient. Certain “classical” bright spots fall in quadrant II and exhibit decreasing AVO. Examples show that this may occur when the gas‐sand shear‐wave velocity is lower than that of the overlying formation. Common AVO analysis methods such as partial stacks and product (A × B) indicators are complicated by this nonuniform gas‐sand behavior and require prior knowledge of the expected gas‐sand AVO response. However, Smith and Gidlow’s (1987) fluid factor, and related indicators, will theoretically work for gas sands in any quadrant of the A-B plane.

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.

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. Reflections from the top of sands containing gas or light hydrocarbons fall on a trend approximately parallel to the fluid line; reflections from the base of gas sands fall on a parallel trend on the opposing side of the fluid line. The polarity standard 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 [Formula: see text] and S-wave velocity [Formula: see text]. 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 impact the [Formula: see text] contrast. As a result, porosity changes move the AVO response along trends approximately parallel to the fluid line. These observations are useful for interpreting AVO anomalies in terms of fluids, lithology, and porosity.

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