Fast and accurate numerical modeling of gravity and magnetic anomalies is the basis of field-data inversion and quantitative interpretation. In gravity and magnetic prospecting, the computation and memory requirements of practical modeling is still a significant issue, which leads to the difficulty of using efficient and detailed inversions for large-scale complex models. A new 3D numerical modeling method for gravity and magnetic anomaly in a mixed space-wavenumber domain is proposed to mitigate the difficulties. By performing a 2D Fourier transform along two horizontal directions, 3D partial differential equations governing gravity and magnetic potentials in the spatial domain are transformed into a group of independent 1D differential equations wrapped with different wavenumbers. Importantly, the computation and memory requirements of modeling are greatly reduced by this method. A modeling example with 4,040,100 observations can be finished in approximately 28 s on a desktop using a single core, and the independent differential equations are highly parallel among different wavenumbers. The method preserves the vertical component in the space domain, and thus a mesh for modeling can be finer at a shallower depth and coarser at a deeper depth. In general, the new method takes into account the calculation accuracy and the efficiency. The finite-element algorithm combined with a chasing method is used to solve the transformed differential equations with different wavenumbers. In a synthetic test, a model with prism-shaped anomalies is used to verify the accuracy and efficiency of the proposed algorithm by comparing the analytical solution, our numerical solution, and a well-known numerical solution. Furthermore, we have studied the balance between computational accuracy and efficiency using a standard fast Fourier transform (FFT) method with grid expansion and the Gauss-FFT method. A model with topography is also used to explore the ability of modeling topography with our method. The results indicate that the proposed method using the Gauss-FFT method has characteristics of fast calculation speed and high accuracy.

With the help of the horizontal 2D Fourier transform, 3D convolutions can be transformed into vertical 1D integrations of different wavenumbers. It has already been proven that the Fourier ...

This study presents an innovative 3D numerical simulation approach tailored for the direct current resistivity method under undulating terrain conditions. The method utilizes 2D Fourier transform technology to convert complex 3D problems into 1D problems in the space-wavenumber mixed domain, thereby simplifying the computational process. We assume a layered background medium and utilize the weighted residual method to solve this simplified 1D problem. Additionally, to precisely handle terrain boundary nodes, we introduce an isogeometric gradient method applied in the logarithmic domain of conductivity. By constructing 3D trapezoidal ridge and valley models, we have validated the effectiveness and accuracy of the proposed algorithm. Further experiments involving a spherical low-resistivity body and a prismatic high-resistivity body beneath ridge terrain demonstrate the significant impact of undulating terrain on the observed results. This highlights the importance of considering terrain undulations in field observations and emphasizes the necessity of making appropriate corrections when interpreting data to prevent erroneous interpretations or significant deviations in results.

The marine controlled-source electromagnetic (MCSEM) method is widely used in offshore oil and gas exploration. In this letter, we present a space-wavenumber domain integral equation (IE) algorithm for simulating marine CSEM responses in 3-D arbitrarily anisotropic media. The algorithm employs a space-wavenumber domain method and a contraction operator in 3-D IEs. The space-wavenumber domain method accelerates simulation speed and reduces memory requirements, while the contraction operator ensures solution convergence. Synthetic models are used to verify the accuracy and efficiency of the newly proposed method by comparing it with an edge-based finite element (FE) method, a space-wavenumber domain differential equation method, and a biconjugate gradient FFT (BCGS-FFT) method. The numerical results of the disk model demonstrate that the marine electromagnetic (EM) fields are significantly influenced by the anisotropic conductivity tensor.