Non-linear methods for event location in a global context

Directed search methods in four-dimensional hypocentre space do not require the differentiation of travel times and are particularly suitable for the use of information from multiple seismic phases including joint use of primary and depth phases (e.g. pP) for a reference model such as a k135. These approaches can be used with a wide range of measures of misfit between observed and estimated times. A very effective method of this class is the use of the neighbourhood algorithm that allows all previous hypocentre estimates to be employed to estimate the shape of the misfit surface. When used with a robust measure of misfit such as the sum of the absolute values of the residuals (L1 norm), the neighbourhood algorithm provides rapid convergence, and a measure of the uncertainty in the hypocentral estimate from the concentration of the points with low misfit in four-space. Such a procedure is well suited to the first pass analysis of observations since it is not distracted by occasional readings associated with other events. Phase association can then be improved and a more conventional procedure used to provide error ellipsoids around a well-defined depth.