Depth scaling strategy for the noise-included inverse problem

We propose a depth scaling method to mitigate the sensitivity of the elastic full waveform inversion (FWI) to random noise, which is designed introducing flexible damping factor in the Levenberg-Marquardt method. When the damping factor is constant over iterations, FWI can be severely affected by noise distributions over depths. In our depth scaling strategy, inversion starts with large damping factors, and then semi-automatically decreases according to the tendency of errors as the iteration goes on. With the flexible damping factors we can control the parameter-update regions so that shallow parts can be mainly updated in the early iterations and the parameter-update regions can move to deeper parts at the later iterations. Numerical examples for a simple graben model show that our depth scaling strategy yields more robust inversion results for noisy data than the conventional FWI using a constant damping factor.