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.

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Initial reference models in local earthquake tomography

Geiger's method of locating local earthquakes has been extended to include the effect of P velocity variation along the ray paths in three dimensions. The crustal structure was modeled by rectangular blocks, and a parameter was assigned to each block describing the perturbation of P wave slowness in the block. On the basis of an initial model, a set of linear equations for the observed first P arrival times was formulated in terms of the source and medium parameters. The source parameters for all the earthquakes in the data set and medium parameters for all the blocks penetrated by the seismic rays were then determined simultaneously by the damped least squares method. A computer program has been written for the case of a homogeneous initial medium model with constant P velocity. It has been tested with artificial data and applied to a set of local earthquakes recorded by a dense seismic array in Bear Valley, California. The resultant velocity distribution in the top 5 km shows a narrow low-velocity zone of about 5 km/s in the San Andreas fault zone sandwiched between high-velocity regions of about 6 km/s.

Determination of three‐dimensional velocity anomalies under a seismic array using first P arrival times from local earthquakes: 1. A homogeneous initial model

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HYPOELLIPSE; a computer program for determining local earthquake hypocentral parameters, magnitude, and first-motion pattern

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.

Geotomography with local earthquake data

In seismology, a wealth of data-processing programs are available, and a seismic observatory typically makes use of several. A common problem is the lack of a proper database structure which prevents effective use of the data, particularly with data from different sources. A primary goal of SeisAn is to organize data from all kinds of seismic stations into a simple database and to provide most of the tools needed for routine processing. The SeisAn database is a way of organizing data by using the directory and file structure, and is not a relational data system with general access techniques such as SQL, which usually is meant by the term “database.” In addition, the intention is to facilitate research tasks by integrating additional programs to work directly on the database.

A second goal is that SeisAn must work in an identical manner under Sun (Solaris-1 and -2), Linux, and MS-Windows, and...

SeisAn Earthquake Analysis Software

/pdf/hypo71-revised-a-computer-program-for-determining-hypocenter-18f36u3ny9.pdf

John C. Lahr

Papers

HYPO71 (revised; a computer program for determining hypocenter, magnitude, and first motion pattern of local earthquakes