Frequency-domain elastic full waveform inversion using a denoise function

For a robust elastic waveform inversion algorithm, we propose incorporating a denoise function into gradients in the l₁-norm waveform inversion. The denoise function is designed by the ratio of modeled data to field data summed over shots and receivers at each frequency, based on the fact that while field data are noisy, modeled data are noise-free. As a result, the denoise function is inversely proportional to the degree of noises and acts like filters. Using the denoise function, we can keep the noise-contaminated gradients from affecting model parameter updates. The denoise function is applied to synthetic data with three types of noises for the modified version of Marmousi-2 model: discontinuous monochromatic random noises, general random noises and outliers. Numerical examples show that the denoise function effectively filters out the noise-contaminated gradients during the inversion process and thus yields better inversion results than the conventional l₁-norm waveform inversion.