Two-Dimensional Magnetotelluric Modeling Based on Stochastic Path Integral: TE Case

In this study, we investigate the application of the stochastic path integral (SPI) for 2-D magnetotelluric (MT) modeling. Our goal is to assess whether electromagnetic (EM) numerical algorithms can mechanistically adapt to parallel heterogeneous computing architectures and maximize the conversion of computational power into efficient EM field simulations. Using the Feynman–Kac formula, we derive a path integral representation of the MT Helmholtz equation in a stochastic framework. We can then investigate the online–offline two-stage MT-SPI algorithm that includes Monte Carlo (MC) random walks, mapping matrix construction, and large-scale matrix–vector multiplication. Numerical experiments verify the correctness and stability of the proposed SPI algorithm. At the relative error of 1.2%, SPI simultaneously achieves over $550\times $ acceleration and approximately 30% memory reduction on GPU under a MATLAB-based implementation, compared with the finite difference method (FDM).