Bounding the rate of moment deficit accumulation along the Tohoku segment using GEONET GPS data

Geodetic estimates of strain accumulation compared to the rate of past moment release provide important input to earthquake hazard forecasts. Prior to the March 2011 Tohoku earthquake a number of studies investigated plate coupling along the Japan Trench in NE Japan using GEONET GPS data. Most of these assumed an elastic back-slip framework, and regularized the underdetermined inverse problem by minimizing some norm of the back-slip rate. All studies apparently smoothed to zero coupling at the trench and therefore infer the highest coupling just offshore. In contrast, we estimate rigorous bounds on the maximum and minimum permissible rates of moment deficit (MDR) accumulation, not a ``favored'' model according to some ad hoc regularization, using methods of Johnson et al [1994] and Murray and Segall [2002]. Given a domain of interest (the Tohoku rupture segment) and Green's functions G relating slip to data, we solve the following optimization problem for back-slip rate m: {minimize}\ || G m - d ||_2² \ {subject to} \ A m = M₀ \ \ {and} \ \ 0 ≤ m_i ≤ v_plate, where A = [1,1, ... 1], such that A m yields the (normalized) moment-rate. on the model domain. Preliminary results find that || G m - d ||_2² exhibits a broad minimum over a factor of 2 in MDR. For the minimum MDR the locked zone is just offshore, while the plate-boundary near the trench slips at the plate rate. At the maximum MDR the locked zone is much larger, including the entire fault near the trench. This clearly demonstrates that the shallow fault is completely in the null-space for onshore data, and that there is at least a factor of two uncertainty in MDR. We will present results employing a bootstrap procedure that is independent of an assumed error distribution in the GPS data. We also extend the method to include viscoelastic earthquake cycle effects, including time-dependence due both to past earthquakes and steady backslip. In these models, fault locking near the trench induces flow which generates on-shore deformation that is not observed in elastic models.