MODELING SEISMIC IMPEDANCE BY MARKOV CHAINS -- MODEL PROPERTIES
, by Bob Godfrey, Francis Muir, Fabio Rocca
We model impedance as a special type of Markov chain, one which is constrained to have a purely exponential
correlation function. The stochastic model is parsimoniously described by M parameters, where M is the number
of states or rocks composing an impedance well-log. The probability mass function of the states provides M-1
parameters, and the "blockiness" of the log determines the remaining degree of freedom. Synthetic impedance
and reflectivity logs constructed using the Markov model mimic the blockiness of the original logs. Both
synthetic impedance and reflectivity are shown to be Bussgang, i.e. if the sequence is input into an
instantaneous non-linear device, then the correlation of input and output is proportional to the
autocorrelation of the input. The latter property can be used to show convergence of variable norm
deconvolution.
STANFORD