Frequency-dependent seismic field data anomalies, appearing in association with low-Q targets, have, on occasion, been attributed to the presence of a strong absorptive reflection coefficient. This “absorptive reflectivity” represents a potent, and largely untapped, source of information for determining subsurface target properties. It would most likely be encountered where a predominantly elastic/nonattenuating overburden suddenly is interrupted by a highly attenuative target. Series expansions of absorptive reflection coefficients about small parameter contrasts and incidence angles can expose these anomalies to analysis, either frequency-by-frequency (amplitude variation with frequency [AVF]) or angle-by-angle (amplitude variation with angle of incidence [AVA]). Within this framework, variations in P-wave velocity and Q can be estimated separately through a range of direct formulas, both linear and with nonlinear corrections. The latter come to the fore when a contrast from an incidence medium Q (i.e., acoustic/elastic) to a target medium Q510 is encountered, in which case the linearized estimate can be in error by as much as 50%. Algorithmically, it is a differencing of the reflection coefficient across frequencies that separates Q variations from variations in other parameters. This holds for both two-parameter (P-wave velocity and Q) problems and five-parameter anelastic problems, and would appear to be a general feature of direct absorptive inversion.

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