Linearized Seismic Waveform Inversion Using Banded Triangular Preconditioners

In linearized inversion methods, the computational cost is dominated by the generation of the sensitivity matrix and by the least-squares solution of linear systems. The multiple re-weighted least square (MRLS) is more robust than to the Gauss-Newton method and explores the model space in an extensive and effective way, since many models can be generated from the same sensitivity matrix. In the present paper we investigate the use of preconditioners associated to triangular matrices formed by L-bands in order to decrease the computational cost of the MRLS method. The preconditioners are generated from a partial orthogonalization of the sensitivity matrix. The original system of linear equations is modified in order that the coefficient matrix, in the normal equation, has a band of L co-diagonals with null elements. We apply the new approach to the inversion of 2D seismic waveform inversion. Numeric examples illustrate the performance of the MRLS approach and the decrease in the total computational cost as a function of the number L of bands in the preconditioners.