Ensemble inference in terms of empirical orthogonal functions

Abstract

Many geophysical problems involve inverting data in order to obtain meaningful descriptions of the Earth's interior. One of the basic characteristics of these inverse problems is their non-uniqueness. Since computation power has increased enormously in the last few years, it has become possible to deal with this non-uniqueness by generating and selecting a number of models that all fit the data up to a certain tolerance. In this way a solution space with acceptable models is created. The remaining task is then to infer the common robust properties of all the models in the ensemble. In this paper these properties are determined using empirical orthogonal function (EOF) analysis. This analysis provides a method to search for subspaces in the solution space (ensemble) that correspond to the patterns of minimum variability. In order to show the effectiveness of this method, two synthetic tests are presented. To verify the applicability of the analysis in geophysical inverse problems, the method is applied to an ensemble generated by a Monte Carlo search technique which inverts group-velocity dispersion data produced by using vertical-component, long-period synthetic seismograms of the fundamental Rayleigh mode. The result shows that EOF analysis successfully determines the well-constrained parts of the models and in effect reduces the variability present in the original ensemble while still recovering the earth model used to generate the synthetic seismograms. Finally, an application of the method to examine the contrast in upper-mantle S-wave velocity across the Tornquist - Tesseyre Zone is presented, indicating a significant change in S-wave velocity in the upper mantle beneath this zone bordering the East European Platform and Tectonic Europe, and a significantly thicker crust beneath the East European Platform.