A chaos-based objective function and gradient preconditioned method for elastic full waveform inversion under nonstationary amplitude

Abstract

Elastic full waveform inversion (FWI) is highly sensitive to the nonstationary amplitude distribution of seismic data, which is mainly caused by wave propagation effects such as reflection, transmission, and attenuation. This amplitude imbalance leads to unstable inversion and poor reconstruction in deep regions. Conventional least-squares objective functions rely strongly on amplitude information and are therefore prone to cycle-skipping and degradation under such conditions. To address this issue, we propose a chaos-based objective function for FWI by introducing a nonlinear mapping derived from the Duffing oscillator system. The proposed objective function reduces the dependence on absolute amplitude and enhances robustness against nonstationary amplitude variations. In addition, a depth- and frequency-dependent compensation factor is incorporated to balance gradient magnitudes and further improve deep imaging. Numerical experiments show that the proposed method significantly enhances inversion stability and deep velocity reconstruction without increasing computational cost.