Weighted multifrequency seismic full‐waveform data inversion

Abstract

We present a simultaneous multifrequency inversion method for processing of full waveform seismic data. The forward simulator used in the inversion is based on a finitedifference frequency domain (FDFD) method that employs the perfectly matched layer (PML)-absorbing boundary condition, which effectively eliminates artificial reflections caused by the truncation of the computational domain. The frequency domain forward model enables us to obtain the fields simultaneously by solving a linear system. We employ an LU decomposition method in solving this linear system. Hence, the computational cost is almost independent of the number of sources. This feature makes this FDFD method very efficient for acoustic inversion where a great number of sources are used. The inversion is done in the frequency domain and a limited portion of the frequency domain data is inverted simultaneously. We propose a novel multifrequency data weighting scheme that balances the contributions from different frequency components effectively, to realize this multifrequency data simultaneous inversion. We employ an inverse algorithm based on the Gauss-Newton method to solve this nonlinear optimization problem. By introducing a modified adjoint formulation, we are able to calculate the Jacobian matrix efficiently, while the properties of the PML layers vary automatically and adaptively during inversion processes, which ensures the correct direction of the inversion and implies that this algorithm is appropriate for realistic applications where no priori information is available around the inversion domain. Because of the ill-posed nature of this problem, regularization is necessary. Two different regularization schemes, an L2 norm and a weighted L2 norm, are used in this algorithm. The latter has an advantage over the former in reconstructing images with sharp boundaries. The regularization parameter is chosen automatically using the so-called multiplicative regularization. In addition, a line search procedure is incorporated in the algorithm for the purpose of the monotonic decrease enforcement. A nonlinear transform is applied on the unknown parameters to constrain them within their physical bounds.