Efficient 2D Modeling of Magnetic Anomalies Using NUFFT in the Fourier Domain

We have investigated different Fourier domain approaches to calculate the magnetic anomaly of an arbitrarily shaped geological body with arbitrary magnetic susceptibility distribution, and compared different Fourier domain solutions of each approach with respect to accuracy and speed for any model. Both standard fast Fourier transform (FFT) and nonuniform fast Fourier transform (NUFFT) were used in the Fourier domain solution technique. The simulation results demonstrated that the standard FFT method with grid expansion has a great advantage in computing performance. However, the influence of aliasing, edge effect, and imposed periodicity limit the accuracy. The NUFFT method with a suitable wavenumber optimization scheme can avoid these problems, especially in minimizing the influence of the edge effect. In addition, a fast algorithm for undulating terrain was proposed, and these results showed that the more the number of grid nodes interpolated between the lowest and highest points of the undulating terrain, the greater the speed advantage of the fast algorithm. Finally, simple, complex, and real undulating topography models were designed to further reveal the reliability and stability of the NUFFT method.