Summary: | Techniques for forward modeling and inversion of head wave traveltimes within the
framework of one and two dimensional earth models are well developed. The first portion
of this thesis extends these methods to encompass three dimensional layered models. Each
critically refracting horizon of the model is approximated by a plane interface with arbitrary
strike and dip. An advantage of this simple representation is that rapid computation of head
wave traveltimes for arbitrary source-receiver geometries can be achieved with a minimum
of ray tracing. Inversion methods are then developed for estimating the parameters defining
single-layer and multilayer earth models. For the single-layer model, an algebraic solution
to the inverse problem exists if refraction traveltimes are observed along two independent
line profiles. For multilayer models and/or nonprofile recording geometries, the inversion is
formulated as a constrained parameter optimization problem and solved via linear programming. Inclusion of constraints, in the form of inequality relations satisfied by the model
parameters, often governs the ability of the algorithm to converge to a realistic solution.
The procedure is tested with traveltimes recorded on broadside profiles in a deep crustal
seismic experiment.
The second part of this thesis provides specific improvements to various two dimensional refraction traveltime inversion techniques. The generalized reciprocal method (GRM)
is reformulated on the basis of an earth model characterized by vertical, rather than normal, layer thicknesses. This allows point values of interface depth to be inferred from the
observed traveltimes. A novel interpretation method (critical offset refraction profiling) is
described that yields point values of interface depth, interface dip, and refractor velocity. A
smooth depth profile of the refracting horizon is then constructed using techniques of linear
inverse theory. Finally, an automated version of the classical wavefront method for interpreting refraction traveltimes is developed. Recorded arrival times are downward continued
through a near surface heterogeneous velocity structure with a finite-difference propagation
algorithm. The locus of a refracting horizon is then obtained by applying a simple imaging
condition involving the reciprocal time (the source-to-source traveltime). The method is tested, apparently successfully, on a shallow refraction dataset recorded at an archeological
site.
The final portion of this thesis develops an iterative tomographic inversion procedure
for reconstructing a two dimensional P-wave velocity field from measured first arrival times.
Two key features of this technique are (i) use of a finite-difference algorithm for rapid and ac
curate forward modeling of traveltimes, and (ii) incorporation of constraint information into
the inversion to restrict the nonuniqueness inherent in large scale, nonlinear tomographic
inverse problems. Analysis of a simulated vertical seismic profile (VSP) plus crosswell experiment indicates that the inversion algorithm can accurately reconstruct a smoothly varying
interwell velocity field. Inclusion of constraints, in the form of horizontal and vertical first-difference
regularization, allows the solution of a traveltime tomography problem that is
otherwise severely underdetermined.
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