TY - JOUR

T1 - Spectral-infinite-element simulations of gravity anomalies

AU - Gharti, Hom Nath

AU - Tromp, Jeroen

AU - Zampini, Stefano

N1 - KAUST Repository Item: Exported on 2021-02-19
Acknowledgements: We thank Volker Oye, Katja Sahala, and ISS for access to the mine model. We thank Frederik J. Simons for helpful discussions. Parallel programs were run on computers provided by the Princeton Institute for Computational Science and Engineering (PICSciE). 3D data were visualized using the open-source parallel visualization software ParaView/VTK (www.paraview.org). This research was partially supported by NSF grants 1644826 and 1550901. Our software is open source and freely available via the Computational Infrastructure for Geodynamics (CIG; geodynamics.org). We thank the editor Prof. Bert Vermeersen, Bernhard Steinberger, David Al-Attar, and an anonymous reviewer for their insightful comments which helped to improve the manuscript..

PY - 2018/8/7

Y1 - 2018/8/7

N2 - Gravity anomalies induced by density heterogeneities are governed by Poisson's equation. Most existing methods for modelling such anomalies rely on its integral solution. In this approach, for each observation point, an integral over the entire density distribution needs to be carried out, and the computational cost is proportional to the number of observation points. Frequently, such methods are sensitive to high density contrasts due to inaccurate resolution of the volume integral. We introduce a new approach which directly solves a discretized form of the Poisson/Laplace equation. The main challenge in our approach involves the unbounded nature of the problem, because the potential exists in all of space. To circumvent this challenge, we combine a mapped infinite-element approach with a spectral-element method. Spectral elements represent the domain of interest, and a single layer of infinite elements captures outer space. To solve the weak form of the Poisson/Laplace equation, we use Gauss-Legendre- Lobatto (GLL) quadrature in spectral elements inside the domain of interest. Outside the domain, we use Gauss-Radau quadrature in the infinite direction, and GLL quadrature in the other directions. We illustrate the efficiency and accuracy of our method by comparing calculated gravity anomalies for various density heterogeneities with corresponding analytical solutions. Finally, we consider a complex 3-D model of an ore mine, which consists of both positive and negative density anomalies.

AB - Gravity anomalies induced by density heterogeneities are governed by Poisson's equation. Most existing methods for modelling such anomalies rely on its integral solution. In this approach, for each observation point, an integral over the entire density distribution needs to be carried out, and the computational cost is proportional to the number of observation points. Frequently, such methods are sensitive to high density contrasts due to inaccurate resolution of the volume integral. We introduce a new approach which directly solves a discretized form of the Poisson/Laplace equation. The main challenge in our approach involves the unbounded nature of the problem, because the potential exists in all of space. To circumvent this challenge, we combine a mapped infinite-element approach with a spectral-element method. Spectral elements represent the domain of interest, and a single layer of infinite elements captures outer space. To solve the weak form of the Poisson/Laplace equation, we use Gauss-Legendre- Lobatto (GLL) quadrature in spectral elements inside the domain of interest. Outside the domain, we use Gauss-Radau quadrature in the infinite direction, and GLL quadrature in the other directions. We illustrate the efficiency and accuracy of our method by comparing calculated gravity anomalies for various density heterogeneities with corresponding analytical solutions. Finally, we consider a complex 3-D model of an ore mine, which consists of both positive and negative density anomalies.

UR - http://hdl.handle.net/10754/629951

UR - https://academic.oup.com/gji/article/215/2/1098/5067876

UR - http://www.scopus.com/inward/record.url?scp=85055329417&partnerID=8YFLogxK

U2 - 10.1093/GJI/GGY324

DO - 10.1093/GJI/GGY324

M3 - Article

AN - SCOPUS:85055329417

VL - 215

SP - 1098

EP - 1117

JO - Geophysical Journal International

JF - Geophysical Journal International

SN - 0956-540X

IS - 2

ER -