Seismic Travel Time Tomography via Monte Carlo Inversion

Peter Voss and Søren Gregersen

Interpretation of seismic data from explosion studies along a profile contains two connected steps (1) classification of seismic arrivals in important and consistent seismic phases to be compared and interpreted (e.g. Gregersen et al., 1992; and Thybo et al., 1998) and (2) a search for models, in which seismic wave propagation can explain the seismic arrivals, with assumptions on the source as well as the velocity structure. We need to hanbdle the forward computation of the travel time of a seismic wave in a specified model and the inverse computation to find one or more models, for which computed travel times fit the observed ones. In the inverse problem we seek the best possible model within some specifica-tions, and with a definition of what we mean by best possible. When solving such a seismic inverse problem we face the task of searching through a solution/model space of high dimension. A common way of searching for the best model is by trial-and-error. This couples the mentioned steps of classifying the seismic arrivals to belong to particular model interfaces, and of modelling. A supplement to this approach has recently been introduced in the form of systematic inversion, minimizing the sum of squares of deviations between observed and computed travel times (e.g. Zelt and Smith, 1992).This would be perfect, if the inversion proces was linear, but since it is non-linear one introduces an iterative scheme of recomputations to take the non-linearity into account. A weakness of least squares solutions is that the search for a solution to the non-linear problem might be non-unique, i.e. the solution may be dependent on the initial guess of a model. We may never find the global minimum of the sum of squared deviations. Consequently non-linear solution methods are worth testing. Monte Carlo methods lend themselves for testing, when the forward computations can be done fast.

Due to the many dimensions it is impossible to search through the whole space. Consequently several methods have been developed for exploring such a space and for searching for solutions in sensible ways: Simulated annealing, tabu search, genetic algorithms and etc.

In recent years we have taken part in projects with seismic data interpreted in standard procedures of trial-and eror or least-squares inversion. In this context we have experimented with inversion through various Monte-Carlo schemes. This includes inversion of wide-angle reflection, explosion data for crustal structure with the result that resolution, accuracy and uniqueness are better evaluated. And it includes synthetic experiments with teleseismic tomography also with evaluation of those same crucial parameters.

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