| Summary: | Wavelet estimation, ray tracing, and traveltime inversion are fundamental problems in
seismic exploration. They can be finally reduced to minimizing a highly nonlinear cost
function with respect to a certain set of unknown parameters. I use simulated annealing
(SA) to avoid local minima and inaccurate solutions often arising by the use of linearizing
methods. I illustrate all applications using numerical and/or real data examples.
The first application concerns the 4th-order cumulant matching (CM) method for
wavelet estimation. Here the reliability of the derived wavelets depends strongly on the
amount of data. Tapering the trace cumulant estimate reduces significantly this dependency,
and allows for a trace-by-trace implementation. For this purpose, a hybrid strategy
that combines SA and gradient-based techniques provides efficiency and accuracy.
In the second application I present SART (SA ray tracing), which is a novel method for
solving the two-point ray tracing problem. SART overcomes some well known difficulties
in standard methods, such as the selection of new take-off angles, and the multipathing
problem. SA finds the take-off angles so that the total traveltime between the endpoints
is a global minimum. SART is suitable for tracing direct, reflected, and headwaves,
through complex 2-D and 3-D media. I also develop a versatile model representation in
terms of a number of regions delimited by curved interfaces.
Traveltime tomography is the third SA application. I parameterize the subsurface
geology by using adaptive-grid bicubic B-splines for smooth models, or parametric 2-D
functions for anomaly bodies. The second approach may find application in archaeological
and other near-surface studies. The nonlinear inversion process attempts to minimize the
rms error between observed and predicted traveltimes. === Science, Faculty of === Earth, Ocean and Atmospheric Sciences, Department of === Graduate
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