### Nonlinear high-resolution three-dimensional seismic travel time tomography

**J. A. Hole**
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
spatially 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.

1992. Journal of Geophysical Research, **97**, 6553-6562.