A gradient scaling method for Laplace domain full waveform inversion in acoustic-elastic coupled media

Abstract

In 2D full waveform inversions of acoustic-elastic coupled media, wave propagation is described by the acoustic and isotropic elastic wave equations. To consider the irregular topography of the seafloor in full waveform inversions, the interface between the acoustic and elastic media in wave propagation modeling by the finite element method is represented using both square and isosceles triangular elements. However, numerical artifacts are generated near the seafloor, and widespread abnormal gradient directions are generated in the high velocity area in the target model, when the gradient direction is calculated during full waveform inversion in the Laplace domain. This issue generates unsuitable inversion results near the seafloor. We propose a scaling function that minimizes numerical artifacts in the gradient direction for Laplace domain full waveform inversion of acoustic-elastic coupled media. Based on a heuristic approach, we describe a gradient scaling method of Laplace-domain waveform inversion in acoustic-elastic coupled media that can be used to construct more accurate P- and S-wave velocity models of geological targets beneath the seafloor than previous methods. The technique scales the gradient direction using an accumulated gradient that is generated from the accumulated sum of the squares of the conventional gradient with respect to depth. This approach is designed to improve the imaging of large anomalies with high-velocity structures and to attenuate artifacts that are related to an irregular seafloor. We perform numerical tests using the synthetic SEG/EAGE salt model and field data. The numerical results demonstrate the validity of Laplace-domain waveform inversions that are calculated with the new scaling method for acoustic-elastic coupled media. The proposed gradient scaling method reduces artifacts more with field data than in the synthetic case. In particular, the abnormal high velocity areas near the seafloor in the inverted P- and S-wave velocity models are effectively removed by the gradient scaling method. We also conduct frequency-domain waveform inversion using the Laplace-domain inversion results as an initial model to confirm the accuracy of the inverted model of field data from our proposed inversion algorithm. The reverse time migration images and synthetic seismograms that were obtained from the field data indicate that this gradient scaling method is a useful tool for building accurate long-wavelength inverted P-and S-wave velocity models of field data from the Laplace domain full waveform inversion.