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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.
By introducing the regularization term with the second-order regular operator, a two-parameter hybrid regularization method is established. In order to determine the optimal regularization parameter, L-curve method, deviation principle and generalized cross-check criterion The first step is to simulate the theoretical model.Comparing with the results of the truncated singular value decomposition method, the conjugate gradient method and the standard Tikhonov regularization method, the results show that this method not only has high precision, but also has the following advantages Then the method is applied to the calculation of conductivity inversion imaging, and the conductivity inversion imaging obtained is accurate and reliable, which is also in line with the actual situation.This shows that in the inversion of geophysical problems, The stability and reduce the multiplicity of solutions at the same time, but also to further improve the calculation speed of inversion.