Inverse Q -filter for seismic resolution enhancement

Abstract

A principal limitation on seismic resolution is the earth attenuation, or [Formula: see text]-effect, including the energy dissipation of high-frequency wave components and the velocity dispersion that distorts seismic wavelets. An inverse [Formula: see text]-filtering procedure attempts to remove the [Formula: see text]-effect to produce high-resolution seismic data, but some existing methods either reduce the S/N ratio, which limits spatial resolution, or generate an illusory high-resolution wavelet that contains no more subsurface information than the original low-resolution data. In this paper, seismic inverse [Formula: see text]-filtering is implemented in a stabilized manner to produce high-quality data in terms of resolution and S/N ratio. Stabilization is applied to only the amplitude compensation operator of a full inverse [Formula: see text]-filter because its phase operator is unconditionally stable, but the scheme neither amplifies nor suppresses high frequencies at late times where the data contain mostly ambient noise. The latter property makes the process invertible, differentiating from some conventional stabilized inverse schemes that tend to suppress high frequencies at late times. The stabilized inverse [Formula: see text]-filter works for a general earth [Formula: see text]-model, variable with depth or traveltime, and is more accurate than a layered approach, which involves an approximation to the amplitude operator. Because the earth [Formula: see text]-model can now be defined accurately, instead of a constant-[Formula: see text] layered structure, the accuracy of the inverse [Formula: see text]-filter is much higher than for a layered approach, even when implemented in the Gabor transform domain. For the stabilization factor, an empirical relation is proposed to link it to a user-specified gain limit, as in an explicit gain-controlling scheme. Synthetic and real data exam-ples demonstrate that the stabilized inverse [Formula: see text]-filter corrects the wavelet distortion in terms of shape and timing, compensates for energy loss without boosting ambient noise, and produces desirable seismic images with high resolution and high S/N ratio.