Inverse attenuation filtering

Abstract

Inverse-[Formula: see text] filtering is an important seismic-processing operation often used to correct for attenuation and dispersion effects and increase the resolution of reflection records. However, it is important to realize that the [Formula: see text] is an apparent (phenomenological) attribute of the propagating wavefield and not guaranteed to be a material property. By recognizing the apparent character of the [Formula: see text], the attenuation-correction procedure can be significantly extended and generalized. Our approach consists of forward modeling the propagating source waveform by using multiple physical laws followed by multiple types of inverse filtering. The modeling and inverse-filtering algorithms are selectable according to the geology of the study area, data, and goals of processing, which may include reduction of attenuation effects or more general enhancements of reflectivity images. Apparent [Formula: see text] models are inherently smooth in space, which facilitates efficient use of time-variant deconvolution implemented by using overlapping tapered time windows. When using conventional [Formula: see text] models and frequency-domain deconvolution, this procedure contains all existing types of inverse-[Formula: see text] filtering. However, many more realistic forward modeling approaches can (and should) be used depending on the specific subsurface environments, such as wavefront focusing and defocusing, scattering, solid viscosity, or internal friction caused by pore-fluid flows. In general, velocity-dispersion relations cannot be inferred from the frequency-dependent [Formula: see text] and need to be considered separately. It is more precise to view frequency-dependent velocity dispersion and [Formula: see text] as concomitant and arising from a common physical mechanism of wave propagation. Time-domain deconvolution, such as an iterative method well-known in earthquake seismology, offers significant improvements in attenuation-corrected images. The approaches are illustrated on a real reflection data set by using several attenuation laws and types of deconvolution.