  This paper introduces the auxiliary function method (AFM), 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. In most of
situations, there are very few elements in this set. The overall computational
cost of the AFM is significantly less than that of the iterative methods.
According to our numerical tests, even for large noise, the method can still
achieve good location results. These allow us to determine the earthquake
hypocenter and the origin time extremely fast and accurate.
