Time Variable Stress Inversion of Centroid Moment Tensor Data Using Gaussian Processes

Abstract

This study presents a new method of centroid moment tensor (CMT) data inversion to estimate time‐dependent regional stress fields. The Gaussian process (GP) is applied to resolve the computational difficulty of the existing basis function expansion method when analyzing high‐dimensional data, including time dependence. A critical step in the formulation is an analytical derivation of the relationship of the covariance function, which is a key ingredient of GP, between CMT data and the model stress field based on an observation equation. The validity and efficiency of the proposed method are verified through applications to CMT data in and around Japan after the 2011 Tohoku earthquake. The estimated stress field exhibits small‐scale heterogeneity in space and long‐term stability in time for most regions. Additionally, significant temporal variations are observed around the margin of the focal region of the 2011 event, with opposite changes on landward and oceanward sides. GP would be particularly effective for geophysical inversions of high‐dimensional data distributed over a broad region.