Poroelastic finite-difference modeling for ultrasonic waves in digital porous cores
Li-Yun Fu1, Yan Zhang1, Zhenglin Pei1,2, Wei Wei1, Luxin Zhang1,3
1 Key Laboratory of Petroleum Resource Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China 2 Beijing North NewTech PetroTech Ltd, Beijing 100192, China 3 Schlumberger WesternGeco, Houston, TX, USA
Poroelastic finite-difference modeling for ultrasonic waves in digital porous cores
Li-Yun Fu1, Yan Zhang1, Zhenglin Pei1,2, Wei Wei1, Luxin Zhang1,3
1 Key Laboratory of Petroleum Resource Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China 2 Beijing North NewTech PetroTech Ltd, Beijing 100192, China 3 Schlumberger WesternGeco, Houston, TX, USA
摘要Scattering attenuation in short wavelengths has long been interesting to geophysicists. Ultrasonic coda waves, observed as the tail portion of ultrasonic wavetrains in laboratory ultrasonic measurements, are important for such studies where ultrasonic waves interact with smallscale random heterogeneities on a scale of micrometers, but often ignored as noises because of the contamination of boundary reflections from the side ends of a sample core. Numerical simulations with accurate absorbing boundary can provide insight into the effect of boundary reflections on coda waves in laboratory experiments. The simulation of wave propagation in digital and heterogeneous porous cores really challenges numerical techniques by digital image of poroelastic properties, numerical dispersion at high frequency and strong heterogeneity, and accurate absorbing boundary schemes at grazing incidence. To overcome these difficulties, we present a staggered-grid high-order finite-difference (FD) method of Biot’s poroelastic equations, with an arbitrary even-order (2L) accuracy to simulate ultrasonic wave propagation in digital porous cores with strong heterogeneity. An unsplit convolutional perfectly matched layer (CPML) absorbing boundary, which improves conventional PML methods at grazing incidence with less memory and better computational efficiency, is employed in the simulation to investigate the influence of boundary reflections on ultrasonic coda waves. Numerical experiments with saturated poroelastic media demonstrate that the 2L FD scheme with the CPML for ultrasonic wave propagation significantly improves stability conditions at strong heterogeneity and absorbing performance at grazing incidence. The boundary reflections from the artificial boundary surrounding the digital core decay fast with the increase of CPML thicknesses, almost disappearing at the CPML thickness of 15 grids. Comparisons of the resulting ultrasonic coda Qsc values between the numerical and experimental ultrasonic S waveforms for a cylindrical rock sample demonstrate that the boundary reflection may contribute around one-third of the ultrasonic coda attenuation observed in laboratory experiments.
Abstract：Scattering attenuation in short wavelengths has long been interesting to geophysicists. Ultrasonic coda waves, observed as the tail portion of ultrasonic wavetrains in laboratory ultrasonic measurements, are important for such studies where ultrasonic waves interact with smallscale random heterogeneities on a scale of micrometers, but often ignored as noises because of the contamination of boundary reflections from the side ends of a sample core. Numerical simulations with accurate absorbing boundary can provide insight into the effect of boundary reflections on coda waves in laboratory experiments. The simulation of wave propagation in digital and heterogeneous porous cores really challenges numerical techniques by digital image of poroelastic properties, numerical dispersion at high frequency and strong heterogeneity, and accurate absorbing boundary schemes at grazing incidence. To overcome these difficulties, we present a staggered-grid high-order finite-difference (FD) method of Biot’s poroelastic equations, with an arbitrary even-order (2L) accuracy to simulate ultrasonic wave propagation in digital porous cores with strong heterogeneity. An unsplit convolutional perfectly matched layer (CPML) absorbing boundary, which improves conventional PML methods at grazing incidence with less memory and better computational efficiency, is employed in the simulation to investigate the influence of boundary reflections on ultrasonic coda waves. Numerical experiments with saturated poroelastic media demonstrate that the 2L FD scheme with the CPML for ultrasonic wave propagation significantly improves stability conditions at strong heterogeneity and absorbing performance at grazing incidence. The boundary reflections from the artificial boundary surrounding the digital core decay fast with the increase of CPML thicknesses, almost disappearing at the CPML thickness of 15 grids. Comparisons of the resulting ultrasonic coda Qsc values between the numerical and experimental ultrasonic S waveforms for a cylindrical rock sample demonstrate that the boundary reflection may contribute around one-third of the ultrasonic coda attenuation observed in laboratory experiments.
基金资助:the National Natural Science Foundation of China (40925013), the Strategic Leading Science and Technology Programme (Class B) of the Chinese Academy of Sciences (Grant No. XDB10010400), and the China National Major Science and Technology Project (2011ZX05023-005-004)
通讯作者:
Li-Yun Fu
E-mail: lfu@mail.iggcas.ac.cn
引用本文:
Li-Yun Fu, Yan Zhang, Zhenglin Pei, Wei Wei, Luxin Zhang. Poroelastic finite-difference modeling for ultrasonic waves in digital porous cores[J]. 《地震学报》英文版, 2014, 27(3): 285-299.
Li-Yun Fu, Yan Zhang, Zhenglin Pei, Wei Wei, Luxin Zhang. Poroelastic finite-difference modeling for ultrasonic waves in digital porous cores. Earthquake Science, 2014, 27(3): 285-299.
