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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Bibliographic Details
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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Summary: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.
ISSN:0956-540X
1365-246X
DOI:10.1093/gji/ggt334