A dual-parameter regularization method for electrical conductivity imaging

This paper presents a dual-parameter regularization method with two parameters by introducing a regularization term with a second order regularization operator. The optimal value of the regularization parameter is determined by applying the L-curve criterion, discrepancy principle, and generalized cross-validation. The validity and superiority of the proposed method is verified by numerical simulations of the theoretical model with Truncated Singular Value Decomposition, Conjugate Gradient, and Standard-form Tikhonov Regularization. The results are of very high precision and confirm the stabHity of the method against random data noises. Finally, we apply the proposed method to geophysical inversion problems in electrical conductivity imaging. The imaging results conclude that the proposed method improves the imaging quality and fidelity. This further validates that, when it is applied to geophysical inversion problems, the proposed method improves the stabHity of inversion, reduces the multiplicity of solutions, and performs faster computations.