Mesh size effect on finite source inversion with 3-D finite-element modelling

Three-dimensional finite-element models, which can handle the stress perturbations caused by subsurface mechanical heterogeneities and fault interactions, have been combined with the finite source inversion to estimate the coseismic slip distribution over the fault plane. However, the mesh grid for discretizing the governing equations in the finite-element model significantly affects the numerical accuracy. In this study, we performed kinematic finite source inversion with idealized (regular observation point array; M1A-M1D) and regional (GEONET, GPS Earthquake Observation Network System stations in Japan; M2A-M2H) models with different mesh sizes to quantitatively analyse the effect of the mesh grid size around the fault plane on the inverted fault slip distribution. Synthetic observation data vectors obtained from the finest models (M1A and M2A) are compared with those from the coarser models (M1B-M1D and M2B-M2H), which were adopted to construct Green's function matrix. We found that the coarser mesh models derived a smaller surface displacement, leading to a decrease in the norm of Green's function matrix, which in turn influences the fault slip magnitude from the finite source inversion. Finally, we performed the source inversion for the fault slip distribution of the 2011 M-w 9.0 Tohoku-Oki earthquake using the coseismic surface displacements recorded at the GEONET and seafloor stations and finite-element modelling. By reducing the mesh size on the fault, we confirmed that the estimated magnitude of fault slip converged to approximately 80 m, which is consistent with the range of fault slip amounts from previous studies based on the Okada model. At least 0.88 million total domain elements and a 6.7 km(2) mesh size on the fault plane with an area of 240 x 720 km(2) are required for the convergence of the fault slip. Furthermore, we found that the location of the maximum fault slip is less sensitive to the mesh size, implying that source inversion based on a coarse mesh model (i.e. less than 0.5 million elements and > similar to 60 km(2 )mesh size) can quickly provide the rough fault slip distribution.