This paper introduces a new method of using earthquake arrival times to simultaneously determine earthquake hypocenters and station corrections. Progressive multiple event location (PMEL) forms a solution in three major steps: (1) hypocenters are located by conventional single event methods using current station correction estimates; (2) an annulled data set (Pavlis and Booker, 1980) is formed and accumulated using Householder transformations; and (3) station correction perturbations are calculated from a pseudoinverse solution of the annulled data set. In practice, PMEL converges rapidly. We analyze the non-uniqueness of PMEL estimates in terms of resolution and covariance matrices. One of the most important features of PMEL is the computer algorithm that we describe which requires only a modest amount of computer memory that is independent of the number of earthquakes to be processed. Consequently, this algorithm can process a virtually unlimited number of earthquakes.
We apply PMEL to a set of 8049 arrival times from 652 earthquakes and 4 explosions recorded by a network in the Coso Range, Inyo County, California. PMEL converges after four adjustments to the station corrections. The final rms misfit of 0.05 sec is remarkably good, and the station correction estimates correlate strongly with surface geology.