Auto-adjoint elastic FWI: a time domain elastic full waveform inversion accelerated by CUDA with automatic adjoint-source calculation using various kinds of objective functions

Tianze Zhang, Daniel O. Trad, Kristopher A. Innanen

We propose the Auto-adjoint time domain elastic full waveform inversion in this report, which is a FWI framework accelerated with CUDA using adjoint sources calculated with automatic differential method. In this FWI framework, the forward modeling and the adjoint modeling are accelerated by CUDA, and the adjoint sources are calculated by the automatic differential method. These two features allows us to perform time domain FWI with GPU acceleration and explore how different kinds of objective functions can influence the inversion results effectively. We study the objective function behavior for the l-2 norm. l1-norm, Global-correlation based, Envelope based, objective function, and l-1 norm between the real and imaginary part of the synthetic data and the observed data (l-1 RI objective function). According to the numerical test we did in this paper, the l1 RI objective function has better ability to tolerate the noise when poor initial model is used for inversion, compared with all the other objective functions we considered.