Optimal, scalable forward models for computing gravity anomalies

Abstract

We describe three approaches for computing a gravity signal from a density anomaly. The first approach consists of the classical "summation" technique, whilst the remaining two methods solve the Poisson problem for the gravitational potential using either a Finite Element (FE) discretization employing a multilevel preconditioner, or a Green's function evaluated with the Fast Multipole Method (FMM). The methods utilizing the PDE formulation described here differ from previously published approaches used in gravity modeling in that they are optimal, implying that both the memory and computational time required scale linearly with respect to the number of unknowns in the potential field. Additionally, all of the implementations presented here are developed such that the computations can be performed in a massively parallel, distributed memory computing environment. Through numerical experiments, we compare the methods on the basis of their discretization error, CPU time and parallel scalability. We demonstrate the parallel scalability of all these techniques by running forward models with up to $10^8$ voxels on 1000's of cores.Comment: 38 pages, 13 figures; accepted by Geophysical Journal Internationa

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

“…Although showing an accuracy 2 orders lower than that of the G2 approach, the AMFM‐based algorithm gained a speedup in the range of 2.3 to 3.8 over the G2 approach. The above tests imply that with 1.0 million source elements and 10 thousand observation points, the G2 approach could be the method of choice, which agrees with previous conclusions [ May and Knepley , ].…”

“…With 1 thread, the run time of the AMFM‐based modeling algorithm was 412.5 s, which was reduced to 54.2 s with an efficiency of κ = 0.48 for 16 threads. It is worth mentioning that a very good efficiency of 0.66 to 0.95 was achieved using MPI acceleration techniques for 512 CPUs and 64 CPUs by May and Knepley []. The low parallel efficiency of our AMFM code may arise from the preliminary OpenMP implementation and internal data structure design.…”

“…Its concept has only been sparsely used by the geophysical community with applications reported for the 3‐D direct current resistivity problem [ Blome et al ., ], the seismic wave propagation problem [ Çakir , ; Çakır , ], and the 3‐D electromagnetic induction problem [ Ren et al ., , ]. As for gravity modeling problems, only geometrically simple Earth models with 3‐D structured grids were considered [ May and Knepley , ]. However, the AMFM technique itself imposes no limitations on either the geometrical shapes of source elements or spatial distributions of the observation sites [ Epton and Dembart , ; Gumerov and Duraiswami , ].…”

Incorporating 3‐D parent nuclide zonation for apatite 4He/3He thermochronometry: An example from the Appalachian Mountains

“…We use a multigrid method to solve equation . Multigrid methods have been used previously in geosciences, in particular in the field of geodynamics [e.g., Tackley , ; Tackley and Xie , ; Gerya and Yuen , ], geophysics [ Schinnerl et al ., ; May and Knepley , ], and glacial flow [ J. Brown et al ., ]; see [ Brandt , ] for a review of multigrid methods.…”

On the approximation of the potential fields when using right rectangular prisms

“…Nowadays, finite elements, finite volume methods, and unstructured grids are achieving increasing importance in modelling the subsurface for potential field data (May and Knepley 2011;Jahandari and Farquharson 2013). Also, analytical expressions have been derived for the field produced by polyhedral sources (Tsoulis 2012).…”