EGS, Vienna, April, 1997
A new approach to a cross-well tomography
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.