A practical regularization for seismic tomography

Regularization is usually necessary in solving seismic tomographic inversion problems. In general the equation system of seismic tomography is very large, often making a suitable choice of the regularization parameter difficult. In this paper, we propose an algorithm for the practical choice of the regularization parameter in linear tomographic inversion. The algorithm is based on the types of statistical assumptions most commonly used in seismic tomography. We first transfer the system of equations into a Krylov subspace by using Lanczos bidiagonalization. In the transformed subspace, the system of equations is then changed into the form of a standard damped least squares normal equation. The solution to this normal equation can be written as an explicit function of the regularization parameter, which makes the choice of the regularization computationally convenient. Two criteria for the choice of the regularization parameter are investigated with the numerical simulations. If the dimensions of the transformed space are much less than that of the original model space, the algorithm can be very computationally efficient, which is practically useful in large seismic tomography problems.