More absorptive AVF inversion - attenuating incidence media and general dispersion laws

Kristopher A. Innanen

In this paper we review our 2009 discussion of direct inversion of absorptive reflectivity, discuss further the requirements for practical implementation, and extend the results to attenuating incidence media and more general attenuation laws. It is the case that frequencydependent 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 rock mechanical properties, and may be of particular relevance to, e.g., reservoir characterization. It would most likely be encountered where a predominantly elastic/non-attenuating overburden is suddenly 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-byfrequency (AVF) or angle-by-angle (AVA). Within this framework, for instance, variations in P-wave velocity and Q may be separately estimated 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 Q 5 - 10 is encountered, in which case the linearized estimate may 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.