An Algorithm for 3D Seismic Inversion

Abstract

We present an algorithm to solve an inverse problem originated in seismic exploration.
In order to briefly describe the geophysical techique, we can say that while drilling a borehole, the drill-bit generates a signal asumed as a seismic source.
The wavefront propagates through the earth, and the direct and reflected waves at the different interfaces are recorded at a line of geophones laid out on the ground.
Thus we aim to estimate the wave speeds of the different formations within the earth interior from the measurements at the geophone positions. The forward model is formulated,
assuming cylindrical symmetry, by means of the displacements of an elastic solid, and discretized using the Morley mixed finite elements. For the inverse problem,
casted as a minimum squares one, we use a quasilinearization algorithm, which allows for a late discretization of the problem. A parallel version of the algorithm is used to solve the included numerical example.