Highly accurate computations of slip eigenmodes for faults in half space

Starting from a slip dependent friction law on faults in half space,we study loss of stability, called nucleation phase. By linear stability analysis displacements during this phase are solutions to an eigenvalue problem, which we propose to solve with high accuracy. This calculation has been successfully completed in the 2D strike slip case, in free 2D space as well as in half plane. We are investigating extensions to previous results to 3D elasticity in free space as well as in half space. We have already done preliminary computations in free space using a finite element package. The general profile of solutions obtained in this way appears to be largely correct in view of numerical convergence and success of the method when applied to the better known 2D case. However the numerical value of the eigenvalues computed in this way is likely to be at best 1 to 10 percent accurate. This is due on one hand to the space of finite elements, which cannot accurately capture the square root singularities at the boundary and on the other hand to artificial boundary conditions imposed at the edge of the computational domain to simulate decay at infinity. In contrast integral equation methods yield much more accurate results. We have already obtained promising results for a simple practice case where the fault is the square [-1, 1]×[-1, 1] lying in free space. Numerical convergence rates are clearly observed and the first two figures of the computed solutions match those of solutions obtained using finite element packages. Finite element computation for the first eigenmode from our eigenvalue problem derived form slip dependent friction law on faults.