HYPOCENTER: An earthquake location method using centered, scaled, and adaptively damped least squares

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Abstract
We present an earthquake location method, HYPOCENTER, which combines features of the two well-known algorithms HYPO71 and HYPOINVERSE, with a new technique which we term adaptive damping. Each column of the linearized condition matrix T, which relates changes in arrival time to changes in hypocentral position, is centered and scaled to have zero mean and a norm of one. Origin time is defined as the mean arrival time minus the mean travel time. The three least-squares normal equations for hypocentral coordinates, with diagonal terms equal to one, are then solved iteratively by adding a variable damping factor, θ2, to their diagonal terms before inversion. If the residual sum of squares increases, we return to the previous iteration, increase θ2, then try again. This procedure, which we term adaptive damping, always results in residuals which are less than or equal to the HYPO71 or HYPOINVERSE residuals. We demonstrate HYPOCENTER by comparing it to HYPO71 and HYPOINVERSE using synthetic and real arrival time data for four- and eight-station seismic arrays.