The application of a novel perfectly matched layer in magnetotelluric simulations

Abstract

Truncation boundaries are needed when simulating a region in magnetotelluric (MT) modeling. As an efficient alternative truncation boundary, perfectly matched layers (PMLs) have been widely applied in many high-frequency wavefield simulations. However, the governing equation of most electromagnetic exploration methods is for the diffusion field, in which the conduction current is significantly greater than the displacement current. Because the wave and diffusion fields have completely different relations for the frequency and constitutive parameters, conventional PMLs, which are mainly designed for the wavefield, are not a good choice for the diffusion field. For this reason, we propose a formula for a PML that covers the entire frequency band, including the wave and the diffusion fields. It is based on a uniaxial PML. Moreover, we derive a simplified form for the diffusion field. To check the feasibility and application potential of the proposed formula for a PML in MT simulations, we have implemented PMLs using a finite-element method and compared our results with those for a conventional long-distance extended grid. The results of the 1D simulation demonstrate that PMLs can achieve high accuracy and stable performance and have a broad application range. In 2D and 3D models, the air layer is an obstacle in the application of a PML. By selecting appropriate parameters for the PML, 2D and 3D models can achieve satisfactory performance. Therefore, the proposed PML is useful for MT simulations and can achieve satisfactory truncation performance.