A HOMOTOPY METHOD FOR WELL-LOG CONSTRAINT WAVEFORM INVERSION

Abstract

The primary difficulty posed by the method of waveform inversion for the acoustic-wave equation is the presence of local minima of the objective function. Waveform inversion fails to converge to the global minimum unless the wavefield contains very low frequencies, or the starting model is very close to the true model. Constraints can improve the convergence of the method; however, if the starting model is far from the correct model, normal iterative methods will still get trapped in local minima. We designed a homotopy method to improve the robustness of waveform inversion; it makes natural use of constraints, such as well logs. In addition, to further condition the inverse problem, we incorporate standard Tikhonov regularization. We demonstrate through a synthetic example that our method is more likely to find a global minimum than normal iterative methods.