Gravity inversion using wavelet-based compression on parallel hybrid CPU/GPU systems: application to southwest Ghana

We solve the 3-D gravity inverse problem using a massively parallel voxel (or finite element) implementation on a hybrid multi-CPU/multi-GPU (graphics processing units/GPUs) cluster. This allows us to obtain information on density distributions in heterogeneous media with an efficient computational...

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Published in:	Geophysical journal international Vol. 195; no. 3; pp. 1594 - 1619
Main Authors:	Martin, Roland, Monteiller, Vadim, Komatitsch, Dimitri, Perrouty, Stéphane, Jessell, Mark, Bonvalot, Sylvain, Lindsay, Mark
Format:	Journal Article
Language:	English
Published:	Oxford University Press 01.12.2013 Oxford University Press (OUP)
Subjects:	Analysis of PDEs Mathematics Sciences of the Universe Numerical approximations and analysis Wavelet transform Gravity anomalies and Earth structure Inverse theory Satellite gravity
ISSN:	0956-540X, 1365-246X
Online Access:	Get full text
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Abstract	We solve the 3-D gravity inverse problem using a massively parallel voxel (or finite element) implementation on a hybrid multi-CPU/multi-GPU (graphics processing units/GPUs) cluster. This allows us to obtain information on density distributions in heterogeneous media with an efficient computational time. In a new software package called TOMOFAST3D, the inversion is solved with an iterative least-square or a gradient technique, which minimizes a hybrid L 1-/L 2-norm-based misfit function. It is drastically accelerated using either Haar or fourth-order Daubechies wavelet compression operators, which are applied to the sensitivity matrix kernels involved in the misfit minimization. The compression process behaves like a pre-conditioning of the huge linear system to be solved and a reduction of two or three orders of magnitude of the computational time can be obtained for a given number of CPU processor cores. The memory storage required is also significantly reduced by a similar factor. Finally, we show how this CPU parallel inversion code can be accelerated further by a factor between 3.5 and 10 using GPU computing. Performance levels are given for an application to Ghana, and physical information obtained after 3-D inversion using a sensitivity matrix with around 5.37 trillion elements is discussed. Using compression the whole inversion process can last from a few minutes to less than an hour for a given number of processor cores instead of tens of hours for a similar number of processor cores when compression is not used.
AbstractList	We solve the 3-D gravity inverse problem using a massively parallel voxel (or finite element) implementation on a hybrid multi-CPU/multi-GPU (graphics processing units/GPUs) cluster. This allows us to obtain information on density distributions in heterogeneous media with an efficient computational time. In a new software package called TOMOFAST3D, the inversion is solved with an iterative least-square or a gradient technique, which minimizes a hybrid L 1-/L 2-norm-based misfit function. It is drastically accelerated using either Haar or fourth-order Daubechies wavelet compression operators, which are applied to the sensitivity matrix kernels involved in the misfit minimization. The compression process behaves like a pre-conditioning of the huge linear system to be solved and a reduction of two or three orders of magnitude of the computational time can be obtained for a given number of CPU processor cores. The memory storage required is also significantly reduced by a similar factor. Finally, we show how this CPU parallel inversion code can be accelerated further by a factor between 3.5 and 10 using GPU computing. Performance levels are given for an application to Ghana, and physical information obtained after 3-D inversion using a sensitivity matrix with around 5.37 trillion elements is discussed. Using compression the whole inversion process can last from a few minutes to less than an hour for a given number of processor cores instead of tens of hours for a similar number of processor cores when compression is not used. We solve the 3-D gravity inverse problem using a massively parallel voxel (or finite element) implementation on a hybrid multi-CPU/multi-GPU (graphics processing units/GPUs) cluster. This allows us to obtain information on density distributions in heterogeneous media with an efficient computational time. In a new software package called TOMOFAST3D, the inversion is solved with an iterative least-square or a gradient technique, which minimizes a hybrid L1-/L2-norm–based misfit function. It is drastically accelerated using either Haar or fourth-order Daubechies wavelet compression operators, which are applied to the sensitivity matrix kernels involved in the misfit minimization. The compression process behaves like a pre-conditioning of the huge linear system to be solved and a reduction of two or three orders of magnitude of the computational time can be obtained for a given number of CPU processor cores. The memory storage required is also significantly reduced by a similar factor. Finally, we show how this CPU parallel inversion code can be accelerated further by a factor between 3.5 and 10 using GPU computing. Performance levels are given for an application to Ghana, and physical information obtained after 3-D inversion using a sensitivity matrix with around 5.37 trillion elements is discussed. Using compression the whole inversion process can last from a few minutes to less than an hour for a given number of processor cores instead of tens of hours for a similar number of processor cores when compression is not used.
Author	Monteiller, Vadim Martin, Roland Perrouty, Stéphane Jessell, Mark Bonvalot, Sylvain Komatitsch, Dimitri Lindsay, Mark
Author_xml	– sequence: 1 givenname: Roland surname: Martin fullname: Martin, Roland email: roland.martin@get.obs-mip.fr organization: 1Laboratoire GET, Université Toulouse 3 Paul Sabatier, IRD, CNRS UMR 5563, Observatoire Midi-Pyrénées, 31400 Toulouse, France. E-mail: roland.martin@get.obs-mip.fr – sequence: 2 givenname: Vadim surname: Monteiller fullname: Monteiller, Vadim email: roland.martin@get.obs-mip.fr organization: 1Laboratoire GET, Université Toulouse 3 Paul Sabatier, IRD, CNRS UMR 5563, Observatoire Midi-Pyrénées, 31400 Toulouse, France. E-mail: roland.martin@get.obs-mip.fr – sequence: 3 givenname: Dimitri surname: Komatitsch fullname: Komatitsch, Dimitri email: roland.martin@get.obs-mip.fr organization: 1Laboratoire GET, Université Toulouse 3 Paul Sabatier, IRD, CNRS UMR 5563, Observatoire Midi-Pyrénées, 31400 Toulouse, France. E-mail: roland.martin@get.obs-mip.fr – sequence: 4 givenname: Stéphane surname: Perrouty fullname: Perrouty, Stéphane email: roland.martin@get.obs-mip.fr organization: 1Laboratoire GET, Université Toulouse 3 Paul Sabatier, IRD, CNRS UMR 5563, Observatoire Midi-Pyrénées, 31400 Toulouse, France. E-mail: roland.martin@get.obs-mip.fr – sequence: 5 givenname: Mark surname: Jessell fullname: Jessell, Mark email: roland.martin@get.obs-mip.fr organization: 1Laboratoire GET, Université Toulouse 3 Paul Sabatier, IRD, CNRS UMR 5563, Observatoire Midi-Pyrénées, 31400 Toulouse, France. E-mail: roland.martin@get.obs-mip.fr – sequence: 6 givenname: Sylvain surname: Bonvalot fullname: Bonvalot, Sylvain email: roland.martin@get.obs-mip.fr organization: 1Laboratoire GET, Université Toulouse 3 Paul Sabatier, IRD, CNRS UMR 5563, Observatoire Midi-Pyrénées, 31400 Toulouse, France. E-mail: roland.martin@get.obs-mip.fr – sequence: 7 givenname: Mark surname: Lindsay fullname: Lindsay, Mark email: roland.martin@get.obs-mip.fr organization: 1Laboratoire GET, Université Toulouse 3 Paul Sabatier, IRD, CNRS UMR 5563, Observatoire Midi-Pyrénées, 31400 Toulouse, France. E-mail: roland.martin@get.obs-mip.fr
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Copyright	The Authors 2013. Published by Oxford University Press on behalf of The Royal Astronomical Society. 2013 Distributed under a Creative Commons Attribution 4.0 International License
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Keywords	Numerical approximations and analysis Wavelet transform Gravity anomalies and Earth structure Inverse theory Satellite gravity
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