A hybrid boundary integral equation method for the computation of source time functions for 3-D rupture propagation

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A hybrid space and spatial transform convolution method is developed for computing source time functions based on numerically solving an integral equation formulation of the mixed boundary value problem for fault displacements and tractions. The space domain method is an adaptation of the method of Das (1980) in which the displacements on the broken region of the crack and the tractions on the unbroken region of the crack are computed by convolving the Green's function for a point source with the tractions from all times back to the onset of faulting. The spatial transform domain method performs the convolutions by obtaining the 2-D Fourier transform of the stresses and Green's functions; multiplying them in the transform domain; and then inverse transforming back to the space domain. The space domain method is more accurate and rapid for small grid sizes; it is used for convolving over the tip of the Green's function cone. The spatial transform method is more rapid, and reproduces the old spatial domain method it replaces within 1 per cent; it is used for convolving over the higher times of the Green's function cone. As a check of the accuracy of the overall method the results are compared against the analytic results of Kostrov (1964) for a circular crack which grows without stopping at a fixed rupture velocity of 0.5α. Good agreement is found for the slip displacements. We also test the grid size dependence of the numerical fracture criterion, and show that it decreases somewhat more rapidly than Δx−1/2 for average rupture velocities above about 0.4α but is not well resolved for lower rupture velocities due to the coarse grid sizes involved. The usable frequency bandwidth of both the slip velocities on the fault and the synthetic seismograms is determined by the granularity of the discretization of the rupture process. The usable spectral bodywaves radiated from this model extend in a band 1.0 decades above the corner frequency.