A stable and efficient approach of inverse <i>Q</i> filtering

TLDR

Inverse Q filtering is generally challenged by stability and efficiency issues. The study proposes a stable, efficient inverse Q filtering method grounded in wavefield downward continuation theory. The method layers a depth‑dependent Q model, extrapolates the surface wavefield to each layer top, applies a constant‑Q inverse filter, uses a reversed upward continuation for overburden, approximates the amplitude‑compensation operator as a product of time‑ and frequency‑dependent 1‑D functions, and implements the combined phase‑amplitude filter efficiently in the Fourier domain.

Abstract

Stability and efficiency are two issues of general concern in inverse Q filtering. This paper presents a stable, efficient approach to inverse Q filtering, based on the theory of wavefield downward continuation. It is implemented in a layered manner, assuming a depth‐dependent, layered‐earth Q model. For each individual constant Q layer, the seismic wavefield recorded at the surface is first extrapolated down to the top of the current layer and a constant Q inverse filter is then applied to the current layer. When extrapolating within the overburden, instead of applying wavefield downward continuation directly, a reversed, upward continuation system is solved to obtain a stabilized solution. Within the current constant Q layer, the amplitude compensation operator, which is a 2‐D function of traveltime and frequency, is approximated optimally as the product of two 1‐D functions depending, respectively, on time and frequency. The constant Q inverse filter that compensates simultaneously for phase and amplitude effects is then implemented efficiently in the Fourier domain.