Spatial discrete data modeling plays a crucial role in geoscientific data analysis, with accuracy and efficiency being significant factors to consider in the modeling of massive discrete datasets. In this paper, an efficient and regularized modeling method, TIN-MQ, which integrates a triangulated irregular network (TIN) and a multiquadric (MQ) function, is proposed. Initially, a constrained residual MQ function and a damped least squares linear equation are constructed, and the conjugate gradient method is employed to solve this equation to enhance the modeling precision and stability. Subsequently, the divide-and-conquer algorithm is used to build the TIN, and, based on this TIN, the concave hull boundary of the discrete point set is constructed. The connectivity relationships between adjacent triangles in the TIN are then utilized to build modeling subdomains within the concave hull boundary. By integrating the OpenMP multithreading programming technology, the modeling tasks for all subdomains are dynamically distributed to all threads, allowing each thread to independently execute the assigned tasks, thereby rapidly enhancing the modeling efficiency. Finally, the TIN-MQ method is applied to model synthetic Gaussian model data, the submarine terrain of the Norwegian fjords, and elevation data from Hunan Province, demonstrating the method’s good fidelity, stability, and high efficiency.

Topographic undulations often have non-negligible influence on frequency-domain airborne electromagnetic method (FAEM) exploration. To study this effect caused by complex topography, this paper proposed a numerical simulation method based on the boundary element method (BEM) to calculate the 3D topography EM field of frequency-domain magnetic dipole source with arbitrary inclination angle. First, according to the vector integral equations and boundary conditions of the EM field, the boundary integral equations are derived, which describes the coupled electric and magnetic fields that are integrated only for the 3D surface. Then, the 3D surface identified by the area of influence of the magnetic dipole source is used as the integration region (Footprint) with unstructured triangular dissection, and the boundary integral equations are solved in this region using BEM. The EM field at the geometric center of gravity of each element on the surface is obtained by solving the dense linear equations using the conjugate gradients squared (CGS) method, and the influence of the 3D topography on the magnetic field (secondary field) at the receiving coil can be calculated according to the magnetic field boundary integral equation in the upper half space. The algorithm is then tested with synthetical models to validate its feasibility and evaluate its performance, where the response characteristics of the magnetic field with different model conditions are analyzed.