A fundamental modification to Geiger's method of earthquake location for local earthquakes is described which incorporates nonlinear behavior of travel time as a function of source position. The use of Newton's method rather than the usual Gauss-Newton method allows the inclusion of second-order partial derivatives of travel time with respect to source coordinates in the location algorithm. These second-order derivatives can be calculated quite easily for half-space and layered crustal models. Expected benefits are improved convergence and stability, as demonstrated in a series of examples, and more realistic assessment of solution uncertainty.

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