A tomographic inversion procedure is described and applied to a synthetic three-dimensional (3-D) seismic refraction data set, demonstrating that tomography is capable of determining a densely sampled velocity model with large velocity contrasts. Forward and inverse modeling procedures are chosen to minimize the computational costs of the inversion. Parameterizing the linearized inversion using functions defined along the ray paths, simple backprojection with zero pixel size is shown to exactly solve the linear problem, producing the smallest model for the slowness perturbation. For small grid cells, simple backprojection closely approximates the exact solution and is a sufficient solution for an iterative nonlinear inversion. This eliminates the need to store or solve a large system of linear.equations. Accurate first arrival travel times are rapidly computed using a finite difference algorithm. Forward modeling between each simple backprojection allows the procedure to correctly account for the locations of the rays. This becomes more important as the spatial resolution of the model is improved. The computational efficiency of the entire nonlinear procedure allows the model to be densely sampled, providing a spatia!ly well-resolved 3-D tomographic image. The synthetic refraction survey is designed to be similar to a published 3-D survey over the East Pacific Rise. Tests based on this example and others show that 3-D tomography is capable of inverting a large travel time data set for detailed earth structure with large lateral velocity variations and is stable in the presence of noisy data. INTRODUCTIONInformation about the three-dimensional seismic velocity structure of the earth can be obtained through the inversion of seismic travel times. Although the word tomograph means "slice picture" and was adopted by the medical community to describe two-dimensional (2-D) image reconstruction from line integrals, geophysicists use "seismic tomography" to describe two-and three-dimensional (3-D) imaging. Aki et al. [1977] divides the earth into a number of constant velocity blocks to invert teleseismic travel times. Thurber [1983] uses velocities interpolated between regularly spaced grid points to invert local earthquake and explosion source travel times. Other 3-D model parameterizations include those of Hawley et al. [1981], Thomson and Gubbins [1982], and Tarantola and Nercessian [1984]. The development of 2-D tomography applied to cross-borehole seismic data has paralleled that of 3-D tomography, and the formulation of the problem is very similar [e.g., Dines and Lytle, 1979; Wong et al., 1983; McMechan, 1983; Peterson et al., 1985; Scales, 1987; Bregman et al., 1989]. Most of the 3-D tomographic interpretations published to date are limited because of two factors. The first limitation lies in the nonlinearity of the seismic travel time problem. Many tomographic inversion techniques avoid the fact that the ray paths depend on the unknown velocity structure by assuming that the velocity variations are small enough t...

S U M M A R YA method has been developed to compute seismic reflection traveltimes in complex 3-D velocity models with complex 3-D reflector geometry. An existing finitedifference algorithm for calculating first-arrival traveltimes was modified t o handle large, sharp velocity contrasts properly. T h e modified algorithm is faster and more accurate than several alternative schemes, and was incorporated in a procedure to compute reflection traveltimes. Snell's law for reflections is used in the vicinity of the reflecting interface. The reflector model is allowed to vary smoothly in depth, increasing the accuracy compared with a discretized reflector model. Reflection traveltimes are computed simultaneously for all revivers, requiring only two applications of the finite-difference algorithm for each shot. This results in a significant saving in computation time in comparison with other algorithms which require one pass of the finite-difference algorithm for each shot and each receiver. T h e reflection traveltime procedure is well suited for incorporation in inversion schemes for 3-D velocity and reflector structure.

The three-dimensional P and S wave structure of Redoubt Volcano, Alaska, and the underlying crust to depths of 7-8 km is determined from 6219 P wave and 4008 S wave first-arrival times recorded by a 30-station seismograph network deployed on and around the volcano. First-arrival times are calculated using a finite-difference technique, which allows for flexible parameterization of the slowness model and easy inclusion of topography and source-receiver geometry. The three-dimensional P wave velocity structure and hypocenters are determined simultaneously, while the three-dimensional S wave velocity model is determined using the relocated seismicity and an initial S wave velocity model derived from the P wave velocity model assuming an average Vp/Vs ratio of 1.78. Convergence is steady with approximately 73% and 52% reduction in P and S wavearrival time RMS, respectively, after 10 iterations. The most prominent feature observed in the three-dimensional velocity models derived for both P and S waves is a relative lowvelocity, near-vertical, pipelike structure approximately 1 km in diameter that extends from 1 to 6 km beneath sea level. This feature aligns axially with the bulk of seismicity and is interpreted as a highly fractured and altered zone encompassing a magma conduit. The velocity structure beneath the north flank of the volcano between depths of 1 and 6 km is characterized by large lateral velocity variations. High velocities within this region are interpreted as remnant dikes and sills and low velocities as regions along which magma migrates. No large low-velocity body suggestive of a magma chamber is resolved inthe upper 7-8 km of the crust. Introduction Redoubt Volcano, Alaska, one of several active Quaternary volcanoes lying in south-central Alaska at the eastern end of the Aleutian volcanic arc (Figure la), erupted more than 20 times between December 13, 1989, and April 21, 1990. As part of its investigation of this eruption sequence the United States Geological Survey (USGS) deployed a network of 21 portable three-component seismographs in the vicinity of Redoubt Volcano for 3 weeks during July 1991 (Figure lb). The portable seismic network, complemented by a nine-station regional seismic network operated by the Alaskan Volcano Observatory (AVO), recorded thousands of volcano-tectonic (VT) earthquakes that are used to determine the three-dimensional P and S wave velocity structure of Redoubt Volcano and to gain a better understanding of the dynamics of magma migration, emplacement, and eruption.

A seismic reflection and refraction survey across the San Andreas Fault (SAF) near Parkfield provides a detailed characterization of crustal structure across the location of the San Andreas Fault Observatory at Depth (SAFOD). Steep‐dip prestack migration and frequency domain acoustic waveform tomography were applied to obtain highly resolved images of the upper 5 km of the crust for 15 km on either side of the SAF. The resulting velocity model constrains the top of the Salinian granite with great detail. Steep‐dip reflection seismic images show several strong‐amplitude vertical reflectors in the uppermost crust near SAFOD that define an ∼2‐km‐wide zone comprising the main SAF and two or more local faults. Another prominent subvertical reflector at 2–4 km depth ∼9 km to the northeast of the SAF marks the boundary between the Franciscan terrane and the Great Valley Sequence. A deep seismic section of low resolution shows several reflectors in the Salinian crust west of the SAF. Two horizontal reflectors around 10 km depth correlate with strains of seismicity observed along‐strike of the SAF. They represent midcrustal shear zones partially decoupling the ductile lower crust from the brittle upper crust. The deepest reflections from ∼25 km depth are interpreted as crust‐mantle boundary.

The San Andreas fault (SAF) is one of the most studied strike-slip faults in the world; yet its subsurface geometry is still uncertain in most locations. The Salton Seismic Imaging Project (SSIP) was undertaken to image the structure surrounding the SAF and also its subsurface geometry. We present SSIP studies at two locations in the Coachella Valley of the northern Salton trough. On our line 4, a fault-crossing profile just north of the Salton Sea, sedimentary basin depth reaches 4 km southwest of the SAF. On our line 6, a fault-crossing profile at the north end of the Coachella Valley, sedimentary basin depth is ∼2-3 km and centered on the central, most active trace of the SAF. Subsurface geometry of the SAF and nearby faults along these two lines is determined using a new method of seismic-reflection imaging, combined with potential-field studies and earthquakes. Below a 6-9 km depth range, the SAF dips ∼50°-60°NE, and above this depth range it dips more steeply. Nearby faults are also imaged in the upper 10 km, many of which dip steeply and project to mapped surface fault traces. These secondary faults may join the SAF at depths below about 10 km to form a flower-like structure. In Appendix D, we show that rupture on a northeast-dipping SAF, using a single plane that approximates the two dips seen in our study, produces shaking that differs from shaking calculated for the Great California ShakeOut, for which the southern SAF was modeled as vertical in most places: shorter-period (T < 1 s) shaking is increased locally by up to a factor of 2 on the hanging wall and is decreased locally by up to a factor of 2 on the footwall, compared to shaking calculated for a vertical fault.