Physics-based GPS data inversion to estimate three-dimensional elastic and inelastic strain fields

The Earth's crust is macroscopically treated as a linear elastic body, but it includes a number of defects. The occurrence of inelastic deformation such as brittle fracture at the defects brings about elastic deformation in the surrounding regions. The crustal deformation observed through geodetic measurements is the sum of the inelastic deformation as source and the elastic deformation as effect. On such a basic idea, we created a theory of physics-based strain analysis with general source representation by moment tensor, and developed an inversion method to separately estimate 3-D elastic and inelastic strain fields from GPS data. In this method, first, the optimum distribution of moment density tensor is determined from observed GPS data by using Akaike's information criterion. Then, the elastic and inelastic strain fields are obtained from the optimum moment tensor distribution by theoretical computation and direct conversion with elastic compliance tensor, respectively. We applied the inversion method to GPS horizontal velocity data, and succeeded in separately estimating 3-D elastic and inelastic strain rate fields in the Niigata–Kobe transformation zone, central Japan. As for the surface patterns of total strain, the present results of 3-D physics-based inversion analysis accord with the previous results of 2-D geometric inversion analysis. From the 3-D patterns of the inverted elastic and inelastic strain fields, we revealed that the remarkable horizontal contraction in the Niigata–Kobe transformation zone is elastic and restricted near the surface, but the remarkable shear deformation is inelastic and extends over the upper crust.