Geodetic data inversion using ABIC to estimate slip history during one earthquake cycle with viscoelastic slip‐response functions

SUMMARY We developed a new method of geodetic data inversion to estimate slip history at a plate interface by using Akaike's Bayesian Information Criterion (ABIC). In this method we considered the effects of viscoelastic stress relaxation in the asthenosphere, which cannot be neglected to estimate slip history at a plate interface during one earthquake cycle. We also introduced a proper formulation to incorporate two sorts of partially dependent prior information into observed data by Bayes' rule. By applying the new inversion method to levelling data for 1893–1983 in Shikoku, southwestern Japan, we reconstructed the pattern of space–time variation in slip motion during one earthquake cycle, including the 1946 Nankai earthquake, at the interface between the Eurasian and the Philippine Sea plates. The result shows that a steady slip motion at a plate convergence rate (40 mm yr −1 ) proceeds in the shallow and the deep regions through the entire earthquake cycle. In the intermediate depth range (10–30 km), on the other hand, an instantaneous slip of approximately 4 m occurs at the time of the Nankai earthquake. After that, this portion keeps in stationary contact until the occurrence of the next Nankai earthquake. If we neglect the effects of viscoelastic stress relaxation, the inversion analysis gives geophysically unrealistic results.