Finite-source Green's function with arbitrary elastic heterogeneity derived semianalytically

Sato & Moore (2022) proved for a finite-sized fault or volume element that the homogeneous-medium Green's function can construct those of arbitrary velocity and mass density structures.

The method essential is the use of virtual faults adjoined to velocity contrasts, plus the ordinary fault subdivision. Period. The solution for distributed slips in inhomogeneous volumes is then available as in a homogeneous volume using superposed homogeneous closed forms (the semianalytic scheme) with the piecewise-constant interpolation of the velocity structure. The solution in each homogeneous subdomain is expressed by the associated homogeneous Green's function, and the solutions in the subdomains are matched with each other by the deformation (displacement and stress) continuity boundary condition across the velocity contrasts. Our proposal skips the use of the single force Green's functions that were necessary for previous methods.

The figure below is a result of our 3D application, which evaluates the coseismic surface deformation affected by the elastic compliant domain (green in the left fig.) near the ruptured fault (orange). The interference bands in InSAR are synthesized by the proposal (left) and by the homogeneous half-space closed form (the Okada model; center). The effect of the elastic heterogeneity is shown significant.

We supplemented code examples in the paper. We feel happy if you use them with interest.