감쇠 최소자승법을 이용한 지표 탄성파 탐사자료의 전파형 역산

초록

The gradient method has been used for full waveform inversion more often than the least-squares method that requires the huge computational memory in solving matrix equation. However, since misfits of the gradient method show an oscillating tendency and updated velocities converge to true values very slowly, the gradient method requires many iterations. In this study, we have presented an inversion algorithm to find the subsurface velocity structure using the damped least-squares method in the frequency domain. To verify our waveform inversion scheme, we applied the algorithm to the synthetic data, and found that comparatively correct solutions were acquired even with a few iterations. To reduce computer memory requirements and computing time, we utilized inversion blocks consisting of 2×2 elements, which are larger than that of forward modelling, and parallel processing technique based on MPI (Message Passing Interface). For investigating the effects of the initial model on inversion results, we compared and analyzed inversion results for two initial velocity models. One is a gradually increasing velocity model and the other is a smoothed horizontally layered velocity model. The latter was constructed based on the assumption that we have horizontally layered velocity information from zero-offset VSP or well logging data. The inversion result obtained by using the smoothed horizontally layered velocity model shows interfaces of subsurface velocity structures more clearly and provides more accurate velocity values than those using the gradually increasing velocity model. In addition, since the damped least-squares method calculates the sensitivity matrix unlike the steepest-descent method, we can identify the influence of frequency range on inversion results by comparing the sensitivity matrices for a couple of frequencies.

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