Travel-time inversion for simultaneous earthquake location and velocity structure determination in laterally varying media

Travel times are observed at a network of seismometers from a number of earthquakes. The seismic velocity of the medium through which the waves pass is allowed to vary in all three dimensions and is represented in terms of a finite number (P)</it> of parameters. The travel-time data is inverted for the velocity parameters and the hypocentre coordinates of the earthquakes. A linearized least squares inversion technique is used and both the stochastic and generalized inverses are considered. The method is computationally efficient and requires inversion (or decomposition) of only P</it> × P</it> and 4 × 4 matrices. The method is applied to a dataset of travel times reported to the I. S. C. from 56 earthquakes recorded at stations on the North Island of New Zealand. The velocity structure is characterized by only five parameters, so that only 5 × 5 matrices need be inverted. The inversion gives a 30 per cent reduction in residuals. The resulting velocity model is substantially different from that obtained when the hypocentres are kept fixed and only the velocity parameters are inverted for. A parallel study of synthetic data gives insight into the interpretation of results. In particular, the depth and origin time of some of the earthquakes, together with two of the five velocity parameters, are very poorly determined.