We employ an inversion algorithm based on the constrained Gauss-Newton method (Habashy and Abubakar, 2004) to solve the nonlinear optimization problem. The forward model is based on a finitedifference frequency domain (FDFD) method combined with the perfectly matched layer (PML) absorbing boundary condition (Bérenger, 1994). Two different regularization schemes, the L2-norm and the weighted L2-norm (van den Berg and Abubakar, 2001), are used to overcome the ill-posed nature of this problem. The regularization parameter is chosen automatically using the so-called multiplicative regularization technique (van den Berg et al., 1999; van den Berg and Abubakar, 2001; van den Berg et al., 2003). By introducing a modified adjoint formulation, we are able to calculate the Jacobian matrix efficiently while the properties of the PML layers vary automatically during the inversion processes, which ensures the correct direction of the inversion and implies that this algorithm is appropriate for realistic and challenging applications. We propose a novel multi-frequency data-weighting scheme, which enables our algorithm to invert the multi-frequency data simultaneously. This multi-frequency simultaneous inversion method is shown to be more robust and effective than the traditional multi-frequency sequential inversion.
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机译：我们采用基于约束高斯-牛顿法的反演算法（Habashy和Abubakar，2004）来解决非线性优化问题。正向模型基于有限差分频域（FDFD）方法和完美匹配层（PML）吸收边界条件（Bérenger，1994）。两种不同的正则化方案L2范数和加权L2范数（van den Berg和Abubakar，2001）用于克服该问题的不适定性。使用所谓的乘法正则化技术自动选择正则化参数（van den Berg等，1999; van den Berg和Abubakar，2001; van den Berg等，2003）。通过引入改进的伴随公式，我们能够有效地计算雅可比矩阵，而PML层的属性在反演过程中会自动变化，这确保了反演的正确方向，这意味着该算法适用于现实而具有挑战性的应用。我们提出了一种新颖的多频数据加权方案，该方案使我们的算法能够同时反转多频数据。事实证明，这种多频同时反演方法比传统的多频顺序反演方法更加健壮和有效。
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