Automatic Estimation of Very Large Residual Statics
, by Daniel H. Rothman
Conventional approaches to residual statics estimation obtain solutions
by performing linear inversion of observed traveltime deviations.
A crucial component of these procedures is the picking of time delays;
gross errors in these picks are known as "cycle-skips" or "leg-jumps,"
and are the bane of linear traveltime inversion schemes.
This paper is a sequel to an earlier work (Rothman, 1984),
which demonstrated that the estimation of
large statics in noise-contaminated data
is posed better as a nonlinear, rather than as a linear, inverse problem.
Cycle-skips then appear as local (secondary) minima of the resulting
nonlinear optimization problem.
In the earlier paper, a Monte Carlo technique
that originated in statistical mechanics
was adapted to perform global optimization,
and the technique was applied to synthetic data.
This paper presents an application of a similar Monte Carlo
method to field data from the Wyoming Overthrust belt.
Key changes, however, have led to a more efficient and practical algorithm.
The new technique performs explicit crosscorrelation of traces.
Instead of picking the peaks of these crosscorrelation functions,
the method transforms the crosscorrelation functions
to probability distributions,
and then draws random numbers from these distributions.
Estimates of statics are iteratively updated by this procedure until
convergence to the optimal stack is achieved.
This paper also derives several theoretical properties of the algorithm.
The method is expressed as a Markov chain, in which
the equilibrium (steady-state) distribution is the Gibbs distribution
of statistical mechanics.
STANFORD