Spectral-infinite-element simulations of magnetic anomalies

SUMMARY We implement a spectral-infinite-element method (SIEM) to compute magnetic anomalies by solving a discretized form of the Poisson/Laplace equation. The SIEM combines the highly accurate spectral-element method with the mapped-infinite element method, which reproduces an unbounded domain accurately and efficiently. This combination is made possible by coupling Gauss–Legendre–Lobatto quadrature in spectral elements with Gauss–Radau quadrature in infinite elements along the infinite directions. Our method has two distinct advantages over traditional methods. First, the higher-order discretization accurately renders complex magnetized heterogeneities. Second, since the computation time is independent of the number of observation points, the method is efficient for very large models. We illustrate the accuracy and efficiency of our method by comparing calculated magnetic anomalies for various magnetized heterogeneities with corresponding analytical and commonly used computational solutions. We conclude with a practical example involving a complex 3-D model of an ore mine.