双参数混合正则化方法及在电导率反演成像中的应用

A dual-parameter regularization method for electrical conductivity imaging

通过引入带有二阶正则算子的正则化项,建立了一种双参数混合正则化方法.为确定最佳正则化参数,这里主要应用L-曲线法、偏差原理和广义交叉校验准则的优化组合来确定.首先对理论模型进行了数值模拟,通过与截断奇异值分解法、共轭梯度法及标准Tikhonov正则化法的结果比较,表明该方法不仅精度高,而且对于数据的随机扰动具有稳定性.然后将此方法应用于对电导率反演成像的计算中,得到的电导率反演成像精确细致可靠,也符合实际情况.这表明该方法求解地球物理反问题时,在增强反演的稳定性及减少多解性的同时,还能进一步提高反演计算速度.

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 stability of the method against random data noises. Finally, we apply the proposed method conductivity imaging. The imaging results imaging quality and fidelity. This further inversion problems, the proposed method multiplicity of solutions, and performs faster to geophysical inversion problems in electrical conclude that the proposed method improves the validates that, when it is applied to geophysical improves the stability of inversion, reduces the computations.