A procedure for calculating the focal mechanism of an earthquake from the distribution of the ratio of the amplitudes of SV to P waves has been developed and tested. The input consists of information taken from the hypocenter solution for the earthquake, a factor for each station that corrects for the effect of the free surface on the observed wave amplitudes and the observed values of the ratio of the vertical component of P to the vertical component of SV. The procedure starts with the selection of a slip direction. The program then finds the best fault strike and dip corresponding to that slip direction, with “best” measured by the smallest scatter of the dip for any strike. All three fault parameters are then adjusted by an iterative least-squares adjustment. (SV/P)z is a strongly nonlinear function of the fault parameters, so the solution found by the procedure is inherently nonunique. The acceptable solutions can be quite well constrained if the slip direction can be estimated initially on the basis of independent information.
A variety of tests of the procedure have been carried out on real and synthetic data. Given a set of amplitude data for an earthquake in Bear Valley, California, and told only that the mode of slip was predominantly strike-slip, the program “found” the San Andreas fault, i.e., converged to a fault with strike and dip close to the known values. Further work on a German earthquake served to bring out some of the ambiguities of the solutions. Analysis of data from a brief swarm of earthquakes in southwest Germany showed that the method yields useful mechanisms for small events and revealed a rotation of the focal mechanisms during the swarm. Processing of amplitudes from synthetic seismograms gave a fault plane close to the known input, but marked disagreement between the SV amplitudes on the synthetic seismograms and the amplitudes predicted by simple dislocation theory is unresolved.