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UBC Theses and Dissertations

Analysis and inversion of seismic refraction traveltimes Aldridge, David Franklin


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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