The attenuation process acts as a low-pass filter that attenuates the high frequencies (absorption) of the signal spectrum and also changes the phase of the seismic wavelet (dispersion). Seismic frequency losses are usually recovered according to an appropriate processing technique (such as deterministic or statistical deconvolution methods), while phase distortions are generally disregarded. Therefore, accurate processing of seismic data requires a careful investigation of the relationship between absorption and phase.
In this article, a procedure is presented to accomplish this goal. To account for anelastic losses, a complex power function of frequency for the phase velocity is introduced into the one-way wave-field equation in 1D. The compensation, for both effects (absorption and dispersion) described here, is analyzed in the context of wave-field extrapolation in one dimension 1D, equivalent to that in the f-k domain as phase-shift and/or Stolt migration. The phase-only inverse Q filtering works in the frequency domain. It provides for dispersion according to a constant-Q (frequency-independent) model and is valid for any positive value of Q. The extension of this algorithm for a Q depth-variable model is also shown. The amplitude compensation is accomplished through the use of a standard statistical approach. Synthetic and real data are shown to illustrate both amplitude and phase inverse Q filtering of seismic reflection records.