Initial reference models in local earthquake tomography
The inverse problem of three-dimensional (3-D) local earthquake tomography is formulated as a linear approximation to a nonlinear function. Thus the solutions obtained and the reliability estimates depend on the initial reference model. Inappropriate models may result in artifacts of significant amplitude. Here, we advocate the application of the same inversion formalism to determine hypocenters and one-dimensional (1-D) velocity model parameters, including station corrections, as the first step in the 3-D modeling process. We call the resulting velocity model the minimum 1-D model. For test purposes, a synthetic data set based on the velocity structure of the San Andreas fault zone in central California was constructed. Two sets of 3-D tomographic P velocity results were calculated with identical travel time data and identical inversion parameters. One used an initial 1-D model selected from a priori knowledge of average crustal velocities, and the other used the minimum 1-D model. Where the data well resolve the structure, the 3-D image obtained with the minimum 1-D model is much closer to the true model than the one obtained with the a priori reference model. In zones of poor resolution, there are fewer artifacts in the 3-D image based on the minimum 1-D model. Although major characteristics of the 3-D velocity structure are present in both images, proper interpretation of the results obtained with the a priori 1-D model is seriously compromised by artifacts that distort the image and that go undetected by either resolution or covariance diagnostics.