A novel method of hypocentre location

The determination of earthquake locations requires a good velocity model for the region of interest, appropriate statistics for the residuals encountered and an efficient, stable inversion algorithm. A direct nonlinear inversion scheme has been constructed which can use any velocity model for which travel times can be calculated from an arbitrary source position to the receivers in the seismic network. The procedure is based on the minimization of a misfit function depending on the residuals between observed and calculated arrival times. Different statistics, e.g. Gaussian and Jeffreys distributions, can be accommodated by the choice of misfit function. The algorithm is based on a directed grid search which narrows down the range of possible origin times whilst carrying out a spatial search in the neighbourhood of the current minimum of the misfit function. No numerical differentiation of travel times is required, and convergence is rapid, stable and tolerant of occasional large errors in reading observed travel times. A useful product of the method is that the misfit function values are available in the neighbourhood of the minimum, so that a fully nonlinear treatment of the statistical confidence regions for a particular location can be made. A prerequisite for the use of the algorithm is the delineation of bounds on the four hypocentral parameters. Epicentral bounds are constructed using a variant of the ‘arrival order’ technique, and rapid scanning in depth and origin time over this region yields useful bounds on these parameters. The new nonlinear algorithm is illustrated by application to the SE Australian seismic network, for an event in the most active seismic zone. Two different velocity models are used with both Gaussian and Jeffreys statistics and good convergence for the algorithm is achieved despite significant nonlinearity in the behaviour. The Jeffreys statistics are more tolerant of large residuals and are to be preferred when the requisite velocity model is not too well known.