ENSEMBLE INFERENCE IN TERMS OF EMPIRICAL ORTHOGONAL FUNCTIONS

Many geophysical problems involve inverting data in order to obtain me aningful descriptions of the Earth's interior. One of the basic charac teristics of these inverse problems is their non-uniqueness. Since com putation power has increased enormously in the last few years, it has become possible to deal with this non-uniqueness by generating and sel ecting a number of models that all fit the data up to a certain tolera nce. In this way a solution space with acceptable models is created. T he remaining task is then to infer the common robust properties of all the models in the ensemble. In this paper these properties are determ ined using empirical orthogonal function (EOF) analysis. This analysis provides a method to search for subspaces in the solution space (ense mble) that correspond to the patterns of minimum variability. In order to show the effectiveness of this method, two synthetic tests are pre sented. To verify the applicability of the analysis in geophysical inv erse problems, the method is applied to an ensemble generated by a Mon te Carlo search technique which inverts group-velocity dispersion data produced by using vertical-component, long-period synthetic seismogra ms of the fundamental Rayleigh mode. The result shows that EOF analysi s successfully determines the well-constrained parts of the models and in effect reduces the variability present in the original ensemble wh ile still recovering the earth model used to generate the synthetic se ismograms. Finally, an application of the method to examine the contra st in upper-mantle S-wave velocity across the Tornquist-Tesseyre Zone is presented, indicating a significant change in S-wave velocity in th e upper mantle beneath this zone bordering the East European Platform and Tectonic Europe, and a significantly thicker crust beneath the Eas t European Platform.