Douglas R. Toomey

Estimating hypocentral uncertainties for marine microearthquake surveys: A comparison of the generalized inverse and grid search methods

For microearthquake surveys conducted with small networks in regions where the seismic velocity structure has large vertical gradients, the formal errors accompanying hypocentral solutions obtained by a generalized inverse method may be misleading since they do not incorporate the effects of nonlinearity in travel times. An alternative method for estimating uncertainties involves calculating travel time residuals over a regular grid and using the F statistic to contour confidence volumes. We present a statistical expression for the latter confidence limits that is applicable when an independent estimate of arrival time errors is available from observations accumulated for a number of earthquakes. Synthetic experiments comparing the results of the grid search and generalized inverse methods show that in cases where solutions are obtained either without S wave information or for epicenters which lie well outside the network, the effects of nonlinearity on the shape of the confidence regions may be significant. However, for the well-observed events both methods yield comparable confidence volumes in good agreement with the distribution of hypocenters obtained from repeated locations incorporating random errors. The generalized inverse method has the advantage that it requires fewer calculations, so the examination of systematic errors in hypocentral parameters produced by uncertainties in the seismic velocity structure can be studied in a more computationally efficient manner. Except in the cases of poorly resolved earthquakes, the effects of nonlinearity on uncertainties in hypocentral parameters can be observed by the application of the F statistic to the variation of the generalized inverse travel time residuals with focal depth.