Comparison of four optimization methods in elastic full-waveform inversion

Elastic full-waveform inversion (EFWI) is a high-precision imaging method. Since it is a highly nonlinear problem in nature, local optimization algorithms are often used to solve it, but the inversion results of different optimization algorithms are very different. On the basis of the commonly used conjugate gradient (CG) method and limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method, the pseudo-Hessian matrix is adopted as the gradient preconditioning operator to devise a preconditioning CG (P-CG) method and a preconditioning L-BFGS (P-L-BFGS) method. The principles and implementation processes of these four optimization algorithms are expounded. Then, the diffraction model and the Marmousi Ⅱ model are used to test the four algorithms. The following conclusions can be drawn from the results: ①The pseudo-Hessian preconditioning operator can compensate for the deep energy and accelerate the convergence of inversion; ②The CG method and the P-CG method are easy to implement, but they cannot suppress the multi-parameter coupling effect because they only use first-order gradients. However, the P-CG method can deliver inversion results that are slightly inferior to those of the L-BFGS method for the complex Marmousi Ⅱ mo-del. ③The implementation of the L-BFGS method and the P-L-BFGS method is more complicated. Nevertheless, because the pseudo-Hessian matrix is calculated in the inversion process, the multi-parameter coupling effect is suppressed to a certain extent. ④As for the Marmousi Ⅱ model, both the L-BFGS method and the P-L-BFGS method can obtain compressional wave (P-wave) and shear wave (S-wave) velocity models with high inversion accuracy, but density inversion will be subject to the overfitting phenomenon. © 2022, Editorial Department OIL GEOPHYSICAL PROSPECTING. All right reserved.