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 polarization data is proposed that is computationally simpler than the existing methods [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 polarization data, we start with ray perturbation theory and assume that the medium is weakly inhomogeneous. Then the problem formulation for polarization data is approximately expressed as a linear integral of the gradient of the medium slowness perturbation along a reference ray. We call this a quasi-linear approximation which ignores the effect of the perturbation of the ray 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 constraint term. Then a new conjugate gradient type of iterative reconstruction algorithm is developed to solve this minimization problem. This algorithm is also an extension of the conjugate gradient approach for standard least-squares problems. The feasibility and capability of the proposed tomography method is illustrated by conducting both noise-free and noisy synthetic experiments in a cross-hole geometry. The numerical results demonstrate that the additional use of polarization data not only improves the image quality, 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.
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Department of Physics and BernardPrice Institute for Geophysical Research, University of the Witwatersrand, South Africa. lpsong@hrz.uni-kassel.de
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Wright
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