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A simulation method for the computation of the effective P-wave velocity in heterogeneous rocks

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Abstract

We propose a set of numerical methods for the computation of the frequency-dependent effective primary wave velocity of heterogeneous rocks. We assume the rocks’ internal microstructure is given by micro-computed tomography images. In the low/medium frequency regime, we propose to solve the acoustic equation in the frequency domain by a finite element method (FEM). We employ a perfectly matched layer to truncate the computational domain and we show the need to repeat the domain a sufficient number of times to obtain accurate results. To make this problem computationally tractable, we equip the FEM with non-fitting meshes and we precompute multiple blocks of the stiffness matrix. In the high-frequency range, we solve the eikonal equation with a fast marching method. Numerical results confirm the validity of the proposed methods and illustrate the effect of density, porosity, and the size and distribution of the pores on the effective compressional wave velocity.

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Acknowledgements

This research was supported by Repsol, the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 777778 (MATHROCKS), the European POCTEFA 2014-2020 Project PIXIL (EFA362/19) by the European Regional Development Fund (ERDF) through the Interreg V-A Spain-France-Andorra programme, the Project of the Spanish Ministry of Economy and Competitiveness with reference MTM-2016-76329-R (AEI/FEDER, EU), the BCAM “Severo Ochoa” accreditation of excellence (SEV-2017-0718), and the Basque Government through the BERC 2018-2021 program, the two Elkartek projects ArgIA (KK-2019-00068) and MATHEO (KK-2019-00085), the grant “Artificial Intelligence in BCAM number EXP. 2019/00432”, and the Consolidated Research Group MATHMODE (IT1294-19) given by the Department of Education.

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Omella, Á.J., Alvarez-Aramberri, J., Strugaru, M. et al. A simulation method for the computation of the effective P-wave velocity in heterogeneous rocks. Comput Mech 67, 845–865 (2021). https://doi.org/10.1007/s00466-020-01966-3

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