A REGULARIZED CONJUGATE GRADIENT METHOD FOR WAVE FIELD TRANSFORMATION OF TRANSIENT ELECTROMAGNETIC FIELD

The wave field transformation is a useful way of achieving pseudo-seismic interpretation for transient electromagnetic (TEM) method. But the equation in the wave field transformation belongs to the first-class Fredholm integration equation, which is a very ill-posed inverse problem. Considering that the conjugate gradient (CG) method is quite efficient for solving a symmetric positive definite (SPD) system of linear equations whose coefficient matrix has tightly clustered spectrum, in this paper, a new pre-conditioned regularized conjugate gradient (PRCG) method is proposed to realize the full-domain wave field transformation from diffusion equation to wave equation. The SSOR pre-conditioned process significantly reduces the condition number of the coefficient matrix, and regularization improves the spectral properties of the coefficient matrix, while the CG iteration helps run the transformation of wave field in full time-domain. The comparison between the transform results and the known wave field functions shows that the algorithm is stable and reliable. Comparison of the results with the results of the regularized conjugate gradient method and pre-existing PRCG method show that the algorithm proposed in this paper converges faster, and more stable.