Efficient calculation method of derivative of traveltime using SWEET algorithm for refraction tomography

Inversion of traveltime requires an efficient algorithm for computing the traveltime as well as its Frechêt derivative. We compute the traveltime of the head waves using the damped wave solution in the Laplace domain and then present a new algorithm for calculating the Frechêt derivative of the head wave traveltimes by exploiting the numerical structure of the finite element method, the modern sparse matrix technology, and SWEET algorithm developed recently. Then, we use a properly regularized steepest descent method to invert the traveltime of the Marmousi-2 model. Through our numerical tests, we will demonstrate that the refraction tomography with large aperture data can be used to construct the initial velocity model for the prestack depth migration.