Fast 3‐D large‐scale gravity and magnetic modeling using unstructured grids and an adaptive multilevel fast multipole method

Abstract

A novel fast and accurate algorithm is developed for large‐scale 3‐D gravity and magnetic modeling problems. An unstructured grid discretization is used to approximate sources with arbitrary mass and magnetization distributions. A novel adaptive multilevel fast multipole (AMFM) method is developed to reduce the modeling time. An observation octree is constructed on a set of arbitrarily distributed observation sites, while a source octree is constructed on a source tetrahedral grid. A novel characteristic is the independence between the observation octree and the source octree, which simplifies the implementation of different survey configurations such as airborne and ground surveys. Two synthetic models, a cubic model and a half‐space model with mountain‐valley topography, are tested. As compared to analytical solutions of gravity and magnetic signals, excellent agreements of the solutions verify the accuracy of our AMFM algorithm. Finally, our AMFM method is used to calculate the terrain effect on an airborne gravity data set for a realistic topography model represented by a triangular surface retrieved from a digital elevation model. Using 16 threads, more than 5800 billion interactions between 1,002,001 observation points and 5,839,830 tetrahedral elements are computed in 453.6 s. A traditional first‐order Gaussian quadrature approach requires 3.77 days. Hence, our new AMFM algorithm not only can quickly compute the gravity and magnetic signals for complicated problems but also can substantially accelerate the solution of 3‐D inversion problems.

Gravity Gradient Tensor of Arbitrary 3D Polyhedral Bodies with up to Third-Order Polynomial Horizontal and Vertical Mass Contrasts

“…Using recent Delaunay triangulation techniques (e.g., Si 2015), geophysicists can easily set up discretised triangulated grids to represent complicated anomalous targets. Therefore, unstructured grid techniques have been widely used in the geophysical community, not only in gravity exploration (Jahandari and Farquharson 2013;Ren et al 2017c), but also in the electromagnetic induction community (Li and Key 2007;Schwarzbach et al 2011;Ren et al 2013) and the seismic imaging field (Lelièvre et al 2011). Testing a single tetrahedral mass body not only aims to test the performance of our new closed-from solutions for complicated density contrasts (horizontal and vertical density contrasts), but also demonstrates its compatibility with other codes developed for unstructured grids.…”

Large-Scale 3D Modeling and Inversion of Multiphysics Airborne Geophysical Data: A Case Study from the Arabian Shield, Saudi Arabia

“…A detailed analysis of the CPU time performance as a function of the number of processors can be found in [28]. The interested reader can find another example of large-scale gravity and magnetic field modeling in [29,30].…”

Multiple Object Localization in Underwater Wireless Communication Systems using the Theory of Gravitation

“…The 3-D coordinate mass P (x, y, z) causes some gravity potential k at the kth base station . This gravity potential k is produced with a constant density ⇢ with negligible inertial centrifugal force as follows [10]- [12]…”