Plane-wave Q deconvolution

Often the information content of measured signals from distance sources is hidden, because the signal distorts, weakens, and loses resolution as it propagates. For seismic energy traveling in the earth, these propagation effects can be approximated by the constant (frequency‐independent) Q model for attenuation and dispersion. For a propagating plane wave, this model leads to a spatial attenuation factor that is an unbounded function of frequency. Consequently, the broadband inverse of the constant-Q filter does not exist. For a fixed distance between the source and receiver the effects of the propagation path can be deconvolved (removed) within the seismic band by reversing the propagation of the plane wave. This propagation reversal is done by a time reversal with Q replaced by —Q, thereby changing absorption to gain in the complex wavenumber. Normally, measured seismic traces contain returns from a variety of depths. The interference of waves with different amounts of attenuation complicates the invers...