| In this dissertation I describe a procedure for determining earthquake hypocenters and seismic velocity structure from earthquake arrival time data. The heart of the method is an "annulling transformation" of the original data to produce new data independent of the hypocenters {lcub}Pavlis and Booker, 1980{rcub}. These new data are inverted for velocity and hypocenters are then located within the model.; In practice, the problem is non-linear and the actual implementation is an iterative scheme that adjusts a one-dimensional velocity model, station corrections, and hypocenters in separate steps. Numerous experiments with synthetic data demonstrate that the inversion process is quite stable and that convergence to a solution linearly close to the truth is generally possible. The advantages of the procedure developed here are: (1) Velocity can be a continuous function. (2) Velocity structure can be appraised by the Backus-Gilbert method {lcub}Backus and Gilbert, 1968, 1970{rcub}. (3) Uncertainty in the hypocenter and station corrections due to uncertainty in the velocity structure can be bounded. In particular, one can show when standard statistical error estimates are sufficient. (4) Program elements such as estimation of station corrections that formerly required large computer storage have memory requirements attainable even with micro-computers. (5) Information on velocity structure, station corrections, and hypocenters can be accumulated and refined as new earthquakes provide additional information.; Two sets of real data have been successfully inverted by this procedure. The results from the first of these from the Humboldt Bay network were questionable because the one dimensional velocity model assumption appears to be a poor one there. The results from a second data set from the Coso Range were, on the other hand, an unqualified success with arrival time residuals after model convergence attributable entirely to random, measurement errors. |
