Seismic wavelets and earth’s impulse response amplitude and phase recovery using second order statistics or deterministic methods

In this paper we approach the problem of recovering the earth’s impulse response and the seismic wavelets used to probe the earth by the use of techniques inspired in blind equalization methods developed for digital communication systems. We present a recently proposed class of algorithms to recover, by seismogram observation only, both amplitude and phase of the seismic wavelets and the earth’s impulse response, assuming a single-input multiple-output (SIMO) finite impulse response (FIR) model. In this class of algorithms no assumptions regarding minimum phase of the seismic wavelets are necessary and the earth’s impulse response can be assumed both white or colored (using second order statistics) or even deterministic (using deterministic methods). The only assumption on the seismic wavelets used is that there should be no common zeros on their Z-transforms. With just this assumption we have shown that the recovery of both amplitude and phase of the earth’s impulse response and the seismic wavelets themselves can be accomplished using only second order statistics or direct algebraic manipulations of the seismograms. The only minor drawback is a mild scalar ambiguity intrinsic to the problem. Tests are presented confirming the validity of these algorithms. The results obtained are promising, indicating that this class of algorithms has the potential of opening avenues for a large number of new applications.