The auxiliary function method for waveform based earthquake location

Abstract

This paper introduces the auxiliary function method, a novel, fast and simple approach for waveform based earthquake location. From any initial hypocenter and origin time, we can construct the auxiliary function, whose zero set contains the real earthquake hypocenter and the origin time. This translates the earthquake location problem into the problem of searching the common zeros of the auxiliary functions.The computational cost of constructing the auxiliary functions is close to the cost of one single iteration of the traditional iterative method. And the cost of searching the common zeros of the auxiliary functions is almost negligible. Thus, the overall cost of this new method is significantly less than that of the iterative methods. Moreover, there is only one common zero point of the auxiliary functions in most practical situations. This means that the new method only requires one round of calculation to obtain an accurate earthquake hypocenter and origin time from arbitrary initial values. According to our numerical tests, even for large data noise, the method can still achieve good location results.