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

Roland Martin 1 Vadim Monteiller 2, 3 Dimitri Komatitsch 4, 3 Stéphane Perrouty 1 Mark Jessell 1 Sylvain Bonvalot 1 Mark Lindsay 1, 5
2 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
3 Sons
LMA - Laboratoire de Mécanique et d'Acoustique [Marseille] : UPR7051
4 O&I - Ondes et Imagerie
LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
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 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.
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Submitted on : Tuesday, February 4, 2014 - 1:11:58 PM
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Roland Martin, Vadim Monteiller, Dimitri Komatitsch, Stéphane Perrouty, Mark Jessell, et al.. Gravity inversion using wavelet-based compression on parallel hybrid CPU/GPU systems: application to southwest Ghana. Geophysical Journal International, Oxford University Press (OUP), 2013, 195 (3), pp.1594-1619. ⟨10.1093/gji/ggt334⟩. ⟨hal-00941851⟩



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