To test alternate analysis techniques and verify principal structural results of earlier work, we computed the three-dimensional compressional-wave velocity structure of the upper crust beneath Medicine Lake volcano and surrounding parts of northern California, using damped least squares ''local earthquake'' inversions. Our data are travel times from high-resolution (''NeHT,'' after Nercessian, Hirn, and Tarantola (Nercessian, et al., 1994) tomography experiments plus seismic refraction studies. This data set is inhomogeneous in ray density and ray orientation, though it is of nearly optimal homogeneity beneath the volcano itself. We used the damped least squares methods of Thurber and of Prothero, which differ in the way they trace rays. Both methods allow us to loosen the a priori constraints on raypaths implicit to a previous study done with the ''ACH'' (after Aki, Christofferson, and Husebye (Aki et al., 1977)) ''telesismic'' inversion, and only the NeHT data set. We attempt to calculate the absolute value of the velocity, which is lost in the ACH approach, and to obtain more realistic raypaths. These grains are at the cost of solving a nonlinear problem with increased risk of missing the most realistic or the global-minimum solution.

We first performed inversions of the densely sampled region beneath the volcano, using a heterogeneous starting model taken from refraction and gravity data. These starting models include the primary velocity anomaly beneath the volcano, a large shallow high-velocity lens. We also calculated a ''graded'' series of inversion models, progressing from a coarse grid of velocity nodes to a fine grid. The result at each ''graded'' inversion step becomes the starting model for the next finer step. This graded technique is sometimes recommended to assist discovery of the global-minimum solution, but it may not have succeeded in finding the most realistic model for our inhomogeneous data set. The results of inversions computed with the heterogeneous starting model are very similar to the published ACH results, but results of the graded inversion differ significantly. Though the graded model did reproduce first-order results of the ACH inversion, it differed in many important details and was sensitive to the method of raytracing. We are gratified by the first-order similarities between all models and the excellent agreement between the ACH and the results with the heterogeneous starting model, but doubt that the graded inversion method reliably recovers the best solution from inhomogeneous data sets. ¿ American Geophysical Union 1995