A method is presented for the computation of near-field particle displacements and particle velocities resulting from a dynamic propagating, stress relaxation occurring on a finite fault plane embedded within a three-dimensional semiinfinite medium. To check our numerical procedure we compare our results for a circular fault in a full space with Kostrov's (1964) analytic solution for a self-similar propagating stress relaxation.
We have simulated two bilateral strike-slip earthquakes differing only in hypocentral location and examined the particle motion on the traction-free surface and on the rupture surface. Focusing of energy is evident in both ruptures. The static displacement on the rupture surface overshoots the theoretical static value by approximately 25 per cent. For the rupture that nucleated at depth the free surface almost doubled the particle velocities along the fault trace as compared with the rupture that nucleated at the free surface.
Our numerical results indicate that for an earthquake occurring on a semi-circular fault with radius of 10 km, an effective stress of 100 bars and a rupture velocity of 0.9β in a medium characterized by β = 3 km/sec, α = and a density of 2.7 gm/cm3 particle velocities can reach 400 cm/sec and displacements 250 cm.
We also compare our numerical results with the observations made by Archuleta and Brune (1975) for a spontaneous stress relaxation on a semi-circular crack in a prestressed foam rubber block.