The deconvolution of phase‐shifted wavelets

Abstract

The assumption that a seismogram can be represented as a convolution of a source wavelet with a set of real impulses breaks down when the wavelet is phase shifted upon reflection from a boundary. For plane waves and plane layers, this effect occurs only for wide‐angle supercritical reflections, but it may also occur in normal incidence seismograms when either the impinging wavefront or the reflective boundary is curved. We show that seismograms containing time‐displaced, phase‐shifted replications of the source wavelet can be deconvolved to recover both the amplitude and phase of the reflectivity coefficients. The method begins by writing the analytic seismogram as the convolution of a complex reflectivity function with an analytic source wavelet; linear inverse theory is then used to carry out the deconvolution.