Fast multidimensional NMR inversion based on randomized singular value decomposition

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Multidimensional NMR inversion has been proposed to improve the capacity of qualitative and quantitative fluids evaluation contained in porous media. However, one reason that restrict the development and application of downhole multidimensional NMR techniques is about the inversion efficiency. Fast and robust inversion algorithm can greatly reduce the downhole NMR logging cost. Taking into consideration the computational efficiency, it is critical to compress the NMR data. Singular value decomposition (SVD) has been recognized as an efficient algorithm for one dimensional (1D) NMR data compression. It is also applicable under certain circumstance for multidimensional NMR inversion, for example, when the NMR kernel matrices are separable. However, in the highly resolution inversion of two dimensional (2D) NMR and three dimensional (3D) NMR, large – scale of kernel matrices would be generated which greatly restrict the application of SVD. In such cases, SVD consumes considerable computational time and memory. We introduce an algorithm, named randomized singular value decomposition (RSVD), as an alternate of SVD. RSVD could produce results that are comparable to the ones produced by SVD. Furthermore, compared with SVD, it requires far less computation time and memory in the large –scale matrix factorization. Sometimes, it is possible to reduce more than 100 times of computation time and memory. Numerous of numerical simulations have been done to demonstrate the robustness and efficiency of multidimensional NMR inversion based on RSVD. We also analyze its anti-noise ability. Because of the highly computational efficiency of RSVD, it deserves widely application promotion in the multidimensional NMR inversion. • RSVD, i.e. randomized singular value decomposition, has been introduced in this paper. It could produce results that are comparable to the ones produced by SVD. • It requires far less computation time and memory in the large –scale matrix factorization. • Two echo trains are used to illustrate the anti-noise ability.