Tomography of joint P-wave traveltime and polarization data: A simple approach for media with low to moderate velocity gradients

An elastic wave tomography method utilizing joint traveltime and polarizati on data is proposed that is computationally simpler than the existing metho ds [Hu and Menke, Geophys. J. Int. 110, 63 (1992); Farra and Begat, Geophys . J. Int. 121, 371 (1995)], In the linearization problem for the use of pol arization data, we start with ray perturbation theory and assume that the m edium is weakly inhomogeneous, Then the problem formulation for polarizatio n data is approximately expressed as a linear integral of the gradient of t he medium slowness perturbation along a reference ray, We call this a quasi -linear approximation which ignores the effect of the perturbation of the r ay position on the first-order perturbation of the ray slowness vector. To efficiently obtain the solution for multi-data sets. a quadratic objective functional is constructed by including the data misfit terms and a model co nstraint term. Then a new conjugate gradient type of iterative reconstructi on algorithm is developed to solve this minimization problem. This algorith m is also an extension of the conjugate gradient approach for standard leas t-squares problems. The feasibility and capability of the proposed tomograp hy method is illustrated by conducting both noise-free and noisy synthetic experiments in a cross-holt geometry. The numerical results demonstrate tha t the additional use of polarization data not only improves the image quali ty, but also has a stabilizing effect on the iterative tomography solution. However, the limitation of the method is that it becomes inaccurate if the velocity variations in the medium change rapidly with position. (C) 2001 A coustical Society of America.