Introducing complex geometries to Yee cells in FDTD for transient electromagnetic forward modeling

ABSTRACT The finite-difference time-domain (FDTD) method is widely used in 3D geophysical forward modeling. Yee cells serve as the basic mesh for discretizing the computational domain. However, when handling models with complex boundaries, this method needs to use staircase-distributed cells to approximate the boundaries. Errors caused by inaccurate modeling can substantially affect the accuracy of forward modeling. To address the staircase error, a new FDTD modeling method based on conformal mesh technology was developed. The conformal mesh technology uses two sets of meshes simultaneously: a Yee cell for computations and a conformal mesh for outlining the boundaries of geometric shapes. Triangular surface elements were used as the conformal mesh, and the nesting information between the two meshes was determined through ray tracing technology. Subsequently, the equivalent electrical parameters of the anomalous body were calculated based on the mesh information. This modeling method was applied in the transient electromagnetic forward simulation. Two theoretical models were used to test and verify the algorithm’s accuracy, including a conductive brick embedded in a half-space model and a spherical body embedded in a half-space model. The numerical results showed that the proposed method can effectively characterize complex structures. Finally, a true terrain model was simulated with complex geologic structures. All source code and examples are freely available, ensuring complete reproducibility.