This paper deals with the problem of nonlinear seismic velocity estimation from first-arrival traveltimes obtained from crosshole and downhole experiments in three dimensions. A standard tomographic procedure is applied, based on the representation of the crosshole area into a number of cells which have an initial slowness assigned. For the forward modeling, the raypath matrix is computed using the revisited ray bending method, supplemented by an approximate computation of the first Fresnel zone at each point of the ray, hence using physical and not only mathematical rays. Since 3-D ray tracing is incorporated, the inversion technique is nonlinear. Velocity images are obtained by a constrained least-squares inversion scheme using both “damping” and “smoothing” factors. The appropriate choice of these factors is defined by the use of appropriate criteria such as the L-curve.
The tomographic approach is improved by incorporating a priori information about the media to be imaged into our inversion scheme. This improvement in imaging is achieved by projecting a desirable solution onto the null space of the inversion, and including this null-space contribution with the standard non–null-space inversion solution. The efficiency of the inversion scheme is tested through a series of tests with synthetic data. Moreover, application in the area of the Ural Mountains using real data demonstrates that the proposed technique produces more realistic velocity models than those obtained by other standard approaches.