ROBUSTNESS OF LAPLACE DOMAIN WAVEFORM INVERSIONS TO CYCLE SKIPPING

摘要

The local minima problem introduced by cycle skipping is an important barrier for a successful waveform inversion. However, numerical examples of the Laplace-domain full waveform inversions show that we can start from simple initial models to obtain subsurface models, without the local minima problem. Although we can infer that the Laplace-domain inversion is robust to the cycle skipping problem from previous literatures, theoretical examination about the effect of cycle skipping in the Laplace domain is missing. We explain why the Laplace-domain logarithmic objective function is robust to cycle skipping by examining the effect of time shifts of seismic traces on the objective function. A test using a sine wavelet shows that the Laplace transform converts the time shift in the time domain to an amplitude change in the Laplace domain. The amplitude change due to the time shift shows monotonous variations as the amount of time shift increases. Therefore, no cycle skipping effect in the Laplace domain is evident, and the Laplace domain objective function shows a monotonous variation. Numerical examples using 1D and 2D models demonstrate that the Laplace domain objective function is robust to cycle skipping.