Geodetic inversion for space–time distribution of fault slip with time-varying smoothing regularization |
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Authors: | Jun'ichi Fukuda Shin'ichi Miyazaki Tomoyuki Higuchi Teruyuki Kato |
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Institution: | Earthquake Research Institute, University of Tokyo, Yayoi 1-1-1,;Bunkyo-ku, Tokyo 113-0032, Japan. E-mail: The Institute of Statistical Mathematics, 4-6-7;Minami-Azabu, Minato-ku, Tokyo 106-8569, Japan |
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Abstract: | We have developed a new geodetic inversion method for space–time distribution of fault slip velocity with time-varying smoothing regularization in order to reconstruct accurate time histories of aseismic fault slip transients. We introduce a temporal smoothing regularization on slip and slip velocity through a Bayesian state space approach in which the strength of regularization (temporal smoothness of slip velocity) is controlled by a hyperparameter. The time-varying smoothing regularization is realized by treating the hyperparameter as a time-dependent stochastic variable and adopting a hierarchical Bayesian state space model, in which a prior distribution on the hyperparameter is introduced in addition to a conventional Bayesian state space model. We have tested this inversion method on two synthetic data sets generated by simulated aseismic slip transients. Results show that our method reproduces well both rapid changes of slip velocity and steady-state velocity without significant oversmoothing and undersmoothing, which has been hard to overcome by the conventional Bayesian approach with time-independent smoothing regularization. Application of this method to transient deformation in 2002 caused by a silent earthquake off the Boso peninsula, Japan, also shows similar advantages of this method over the conventional approach. |
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Keywords: | Time series analysis Inverse theory Probability distributions Transient deformation |
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