Aplicación de la aproximación circular en la estimación de estructuras sísmicas bidimensionales

Abstract

The computational procedure reported here estimates seismic wave velocities for two-dimensional heterogeneous media from observations of body-wave travel times. The solution of the forward problem is based on the circular approximation. The structure is discretized in a grid of triangular cells and the velocity gradient is held constant within each triangle. In order to estimate the velocity field, a linearized sheme is applied using a Taylor series expansion around an initial solution. The partial derivatives of the travel times with respect to the model parameters are computed from closed form expressions. The initial model does not necessarily has to be laterally heterogeneous. A double stabilization of the least-squares solution of the inverse problem follows from the application of both, the singular-value decomposition and a simple regularization scheme. The results of several numerical experiments validate the computational procedure. In these experiments, we have modeled a real situation where travel time observations are used from 15 explosions and 12 sensors located at the perimeter of a square (with sides 30 m long) to detect low-velocity regions at maximum depths of 10 to 20 m. The solutions are illustrated with maps of velocity isolines and are evaluated taking into account the smoothness of the solution, the behaviour of the residuals and the resolution matrix, as well as our prior information about the physics of the problem. The procedure is more efficient than those using rectangular homogeneous cells.