Two-dimensional Laplace-domain waveform inversion using adaptive meshes: an experience of the 2004 BP velocity-analysis benchmark data set

To delineate the Earth's structure precisely by time- or frequency-domain waveform inversions, an appropriate initial model that contains long-wavelength structures of the true model is essential. A Laplace-domain waveform inversion, which can provide a smooth velocity model that is equivalent to a long-wavelength velocity model from scratch, was recently proposed. The Laplace-domain waveform inversion can be used for obtaining a good initial model for full-waveform inversions. To improve the applicability of the 2-D Laplace-domain waveform inversion to field data, we adopted the adaptive finite element not only to deal with sources and receivers at shallow depths but also to reduce the computational burden using larger elements below the sources and receivers. For the boundary condition on the bounded domain for the Laplace-domain modelling and inversion, the unique property of the Laplace-domain wavefield, which was clamped rapidly from a source, was taken into account. The computational domain was extended further from a source and then the Dirichlet boundary condition was applied to the outer edges of the extended model. With these two adaptations, our Laplace-domain waveform inversion could then be tested on a very large 2004 BP velocity-analysis benchmark data set. Numerical tests of the BP model, which contains three salt domes of high-velocity contrast, were conducted on a self-made synthetic data set by Laplace-domain modelling and a time-domain original data set. For the two data sets, a Laplace-domain waveform inversion using the adaptive mesh successfully provided a smooth velocity model that contained long-wavelength structures of the true velocity model. The smooth velocity model obtained by the Laplace-domain waveform inversion was used as a good initial model for the frequency-domain waveform inversion of the original BP data set. The resulting frequency-domain inversion recovered almost every feature of the salt domes except for some subsalt structures.