EGS,  Vienna,  April, 1997

G.A. Ryzhikov,  M.S. Biryulina ( University of Bergen, Norway),  K.S.Osypov and  J.A.Scales
(Department of Geophysics and Center for Wave Phenomena, Colorado School of Mines, Golden, US)
 

Conventional approachs such as travel-time tomography or full-waveform inversion often fail when applied to cross-well seismic data: the first one because of waveguides, near-field zones  and corresponding nongeometrical waves which lead to problems of first arrival picking and interpretation in terms of Fermat's extremals, and the second one because of multipal minima of L₂-norm on waveform residuals.
A new approach is suggested which is based on:
1. a  proper parametrization of seismic wavefields in terms of so called energetic envelopes;
2. applying of the Kullback-Leibler (KL) measure  to fitting of observed and synthetic envelopes.
The parametrization of wavefields is tied to an a priori representation of a cross-well space as a medium  stratified vertically and perturbed by random, transversally oriented inhomogeneities. It allows us to treat every seismic record statistically which in its turn is implied by a time-domain diffusion of  energetic  wavelets. This procedure provides us with a space-time distributions of energy and makes it much easier to fit the latters with synthetic ones while the main kinematical parameters of unknown medium  are fairly saved.
A new objective function, that we suggest for dynamic inversion, as an alternative to L₂-norm, is the KL-measure, or the relative entropy, on pseudo-probabilistic density functions constructed from energetic envelopes.
The approach is illustrated by applying to real cross-well 3C-data with/without additional well log data.