Geotomography with local earthquake data

The inversion of local earthquake data (LED) for three‐dimensional velocity structure requires the simultaneous solution of the coupled hypocenter‐model problem. The Aki‐Christoffersson‐Husebye method (ACH) involves the inversion of large matrices, a task that is often performed by approximative solutions when the matrices become too big, as is the case for most LED, considering the coupled inverse problem. Such an approximate method (herein referred to as approximate geotomographic method) is used to perform tests with LED to obtain the best suited inversion parameters, such as velocity damping and number of iteration steps. The ACH method has been proposed for use of teleseismic data. Several adjustments to the original ACH method, which are necessary for use of LED, have been developed and are discussed. Such adjustments are the separation of the unknown hypocentral from the velocity model parameters for the inversion, the use of geometric weighting and step length weighting, the calculation of a minimum one‐dimensional (1D) model as the starting three‐dimensional (3D) model for the model inversion, and the display of an approximate resolution matrix (ray density tensors) before the inversion is performed. The ray density tensors allow the block cutting, e.g., the definition of the 3D velocity grid, to better correspond with the resolution capability of the specific data set. The adjustments to the method are tested by inversion of realistic LED of known variance. Synthetic LED are also used to demonstrate the effects of systematic errors, such as mislocations of seismic stations, on the resulting velocity field. Using the data sets from Long Valley, California, Yellowstone National Park, Wyoming, and Borah Peak, Idaho, the effects of improvements to the ACH method and of the data filtering process are shown. The use of the minimum 1D models for routine earthquake location improves this location procedure, as shown with the relocation of shots for the Long Valley and Yellowstone areas. The three‐dimensional velocity fields obtained by the ACH method for the Long Valley and Yellowstone areas show local anomalies in the p velocity that can be correlated with tectonic and volcanic features. A pronounced anomaly of low p velocity below the Yellowstone caldera can be interpreted as a large magma chamber. However, the bulk of the paper addresses problems of the inversion method. The LED from the areas mentioned above are used to numerically and theoretically tune the inversion method for the defects that all real data contain. It is shown that one of the most important steps for any inversion of LED is the selection of the data for quality and for geometrical distribution.