A stable and efficient approach of inverse Q filtering

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.