Wave simulation in double-porosity media based on the Biot-Rayleigh theoryWave simulation in double-porosity media

Abstract

We develop a numerical algorithm for simulation of wave propagation in double-porosity media, where the pore space is saturated with a single fluid. Spherical inclusions embedded in a background medium oscillate to yield attenuation by mode conversion from fast P-wave energy to slow P-wave energy (mesoscopic or wave-induced fluid-flow loss). The theory is based on Biot theory of poroelasticity and the Rayleigh model of bubble oscillations. The differential equation of the BiotRayleigh (BR) variable is approximated with the Zener mechanical model, which results in a memory-variable viscoelastic equation. These approximations are required to model mesoscopic losses arising from conversion of the fast P-wave energy to slow diffusive modes. The model predicts a relaxation peak in the seismic band, depending on the diameter of the patches, to model the attenuation level observed in rocks. The wavefield is obtained with a grid method based on the Fourier differential operator and a second-order time-integration algorithm. Since the presence of 1Istituto Nazionale di Oceanografia e di Geofisica Sperimentale (OGS), Borgo Grotta Gigante 42c, 34010 Sgonico, Trieste, Italy. E-mail: [email protected] 2 School of Earth Science and Engineering, Hohai University, Nanjing, 211100, China. Page 1 of 39 GEOPHYSICS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 This paper presented here as accepted for publication in Geophysics prior to copyediting and composition. © 2019 Society of Exploration Geophysicists. G E O PH Y SI C S D ow nl oa de d fr om li br ar y. se g. or g by U ni ve rs ita t d e B ar ce lo na C R A I on 0 1/ 12 /1 9. F or p er so na l u se o nl y.