Waveform Inversion of Reflection Seismic Data for Kinematic Parameters by Local Optimization

Abstract

A reformulation of the usual least-squares waveform inversion problem is proposed to retrieve, from seismic data, the kinematic parameters (the two-dimensional (2D) background velocity and the source and cable depth) by local optimization. These last parameters are of paramount importance for a successful inversion of very high resolution (VHR) seismic data which we are interested in. In our inversion the source and cable depth parameters are treated in the same way as the background velocity. To avoid the problem of local minima, a change of unknowns is performed: the depth reflectivity is replaced by its dual variable, called the time reflectivity. In this way, the current value of the reflectivity is stored in the time domain and is strongly decoupled from the current value of the velocity field and cable depth. The increase in modeling complexity (an additional prestackmigration is required for each function evaluation) is compensated by the enlargement of the attraction domain of the global minimum which allows the use of a local optimization technique. A numerical implementation with Born approximation and ray tracing is detailed, in which the derivatives of the travel time are computed via an adjoint state technique for more efficiency. Numerical results illustrate the behavior of the new objective function, and inversion of synthetic and real VHR data for kinematic parameters is performed.