Geomagnetic two parameter orthorectification based on complex physical information neural network

Magnetotelluric Sounding (MT) is an important technique for deep geophysical exploration, and the accuracy of its forward modeling directly impacts the reliability of inversion interpretations. This paper considers the dual parameters of conductivity and magnetic permeability, as well as anisotropy, and proposes a one-dimensional forward modeling approach based on Physics-Informed Neural Networks (PINNs). First, a complex-domain extension framework based on PINNs is introduced. Then, by incorporating the Wirtinger operator, we enable backpropagation of complex-valued operations in the neural network, constructing constraint-based physical information equations that support both conductivity anisotropy and dual magnetic permeability parameters. Innovatively, the balance factor is treated as a learnable parameter for adaptive optimization, combined with an adaptive residual refinement sampling strategy, to establish a joint training model for the MT forward problem using PINNs. Numerical experiments demonstrate that the relative error in electromagnetic field calculations for typical resistivity models is less than 2%, showing high consistency with both finite element solutions and analytical results. This validates the method's effectiveness and its potential for engineering applications in simulating complex anisotropic strata.