1. 兰州大学和西部灾害与环境力学教育部重点实验室，兰州 730000
2. 兰州大学和地质科学与矿产学院，兰州 730000
3. 桂林理工大学地球科学学院，桂林 541004
4. Physics of the Earth, Sciences B, University of Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain
5. 中国地震局兰州地震研究所，兰州 730000
6. 东方地球物理公司国际勘探事业部，涿州 072751
Numerical analysis of seismic wave propagation in fluid-saturated porous multifractured media
Guo Gui-Hong1, Yan Jian-Ping2, Zhang Zhi3, José Badal4, Cheng Jian-Wu5, Shi Shuang-Hu6, and Ma Ya-Wei1
1. Lanzhou University & The Key Laboratory of Mechanics on Disaster and Environmental in Western China, Lanzhou 730000, China.
2. Lanzhou University & School of Earth Sciences, Lanzhou 730000, China.
3. School of Earth Science, Guilin university of science and technology, Guilin 541004, China.
4. Physics of the Earth, Sciences B, University of Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain.
5. Lanzhou Institute of Seismology, China Earthquake Administration, Lanzhou 730000, China.
6. BGP International, CNPC, Zhuozhou 072751, China.
Abstract：
Elastic wave propagation and attenuation in porous rock layers with oriented sets of fractures, especially in carbonate reservoirs, are anisotropic owing to fracture sealing, fracture size, fracture density, filling fluid, and fracture strike orientation. To address this problem, we adopt the Chapman effective medium model and carry out numerical experiments to assess the variation in P-wave velocity and attenuation, and the shear-wave splitting anisotropy with the frequency and azimuth of the incident wave. The results suggest that velocity, attenuation, and anisotropy vary as function of azimuth and frequency. The azimuths of the minimum attenuation and maximum P-wave velocity are nearly coincident with the average strike of the two sets of open fractures. P-wave velocity is greater in sealed fractures than open fractures, whereas the attenuation of energy and anisotropy is stronger in open fractures than sealed fractures. For fractures of different sizes, the maximum velocity together with the minimum attenuation correspond to the average orientation of the fracture sets. Small fractures affect the wave propagation less. Azimuth-dependent anisotropy is low and varies more than the other attributes. Fracture density strongly affects the P-wave velocity, attenuation, and shear-wave anisotropy. The attenuation is more sensitive to the variation of fracture size than that of velocity and anisotropy. In the seismic frequency band, the effect of oil and gas saturation on attenuation is very different from that for brine saturation and varies weakly over azimuth. It is demonstrated that for two sets of fractures with the same density, the fast shear-wave polarization angle is almost linearly related with the orientation of one of the fracture sets.
. Numerical analysis of seismic wave propagation in fluid-saturated porous multifractured media[J]. APPLIED GEOPHYSICS, 2018, 15(2): 311-317.
[1]
Agersborg, R., Johansen, T. A., and Jakobsen, M., 2009, Velocity variations in carbonate rocks due to dual porosity and wave-induced fluid flow, Geophys. Prospect., 57(1), 81-98.
[2]
Aki, K., and Richards, P. G., 1980, Quantitative seismology: Thoery and Method, W.H. Freeman and Company, volume 1.
[3]
Batzle, M., Han, D. H., and Hoffmann, R., 2006, Fluid mobility and frequency-dependent seismic velocity - direct measurements: Geophysics, 71(1), N1-N9.
[4]
Borcherdt, R. D., 2009, Viscoelastic waves in layered media: Cambridge University Press.
[5]
Cerveny, V., and Psencik, I., 2009, Perturbation Hamiltonians in heterogeneous anisotropic weakly dissipative media: Geophysical Journal International, 178, 939-949.
[6]
Chapman, M., 2003, Frequency dependent anisotropy due to meso-scale fractures in the presence of equant porosity. Geophys. Prospect., 51(5), 369-379.
[7]
Chapman, M., 2009, Modeling the effect of multiple sets of mesoscale fractures in porous on frequency-dependent anisotropy: Geophysics, 74(6), D97-D103.
[8]
Chapman, M., Maultzsch, S., Liu, E., et al., 2003, The effect of fluid saturation in an anisotropic, multi-scale equant porosity model. J. Appl. Geophy., 54, 191-202.
[9]
Carcione, J. M., 2015, Wave fields in real media: Theory and numerical simulation of wave propagation in anisotropic, anelastic, porous and electromagnetic media: Handbook of Geophysical exploration (3rd ed.), Elsevier.
[10]
Chen, Z. Q., Zeng, L. B., Huang, P., et al., 2016, The application study of the multi-scales integrated prediction method to fractured reservoir description. Applied Geophysics, 13(1), 80-92.
[11]
Crampin, S., 1978, Seismic wave propagation through a cracked solid: polarization as a possible dilatancy diagnostic. Geophs. J. R. astr. Soc., 53(3), 457-496.
[12]
Crampin, S., 1985, Evaluation of anisotropy by shear-wave splitting. Geophysics, 50, 142-152.
[13]
Crampin S., 1994, The fracture criticality of crustal rocks. Geophys. J. Int., 118, 428-438.
[14]
Crampin, S., and Gao, Y., 2014, Two species of microcrack. Applied Geophysics, 11(1), 1-8.
[15]
Fedorov, F. I., 1968. Theory of elastic waves in crystals, Springer.
[16]
Guo, G. H., Zhang, Z., Jin, S. X., et al., 2013, Multi-scale fracture and fluid response characteristic in seismic data: Numerical simulation analysis. Chinese J. Geophys., 56(6), 2002-2011 (in Chinese).
[17]
Hao, Q., and He, Q., 2013, A standard linear solid model representation of Chapman’s frequency-dependent anisotropy induced by two sets of aligned mesoscale fractures: Journal of Seismic Exploration, 22, 169-182.
[18]
Hao, Q., and Alkhalifah T., 2017, An acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis: Geophysics, 82, No.1, C9-C20.
[19]
Hao, Q., and Alkhalifah T., 2017, An acoustic eikonal equation for attenuating orthorhombic media: Geophysics, 82(4), WA67-WA81.
[20]
Hudson, J. A., Liu, E., and Crampin, S., 1996, The mechanical properties of materials with interconnected cracks and pores. Geophys. J. Int., 124, 105-112.
[21]
Jakobsen, M., 2004, The interacting inclusion model of wave induced fluid flow. Geophys. J. Int., 158, 1168-1176.
[22]
Kraut, E. A., 1963, Advances in the theory of aniosotropic elastic wave propagation. Rev. Geophys., 1, 401-408.
[23]
Liu, E., Crampin, S., Queen, J. H., et al., 1993, Behaviour of shear-waves in rocks with two sets of parallel cracks. Geophys. J. Int., 113, 509-517.
[24]
Liu, E., Hudson, J. A., Pointer T., 2000, Equivalent medium representation of fractured rock. J. Geophys. Res., 105(B2), 2981-3000.
[25]
Liu, K., Zhang, Z. J., Hu, J. F., et al., 2001, Frequency band dependence of S-wave splitting in China mainland and its implications. Science in China (Series D), 31(2), 155-162.
[26]
Liu, E. R., Yue, J. H., and Pan, D. M., 2006, Frequency-dependent anisotropy: Effects of multiple fracture sets on shear-wave polarizations. Chinese J. Geophys., 49(5), 1401-1409 (in Chinese).
[27]
Liu, E. R., Chapman, M., Zhang, Z. J., and Queen, J. H., 2006, Frequency-dependent anisotropy: Effects of multiple fracture sets on shear polarizations. Wave Motion, 44, 44-57.
[28]
Liu, Y. Y., 2012, Studying on the response of seismic waves in medium with multiple sets of multi-scale fractures. MSc Thesis, China University of Geosciences, Beijing.
[29]
Maultzsch, S., Chapman, M., Liu, E., et al., 2003, Modelling frequency-dependent seismic anisotropy in fluid-saturated rock with aligned fractures: implication of fracture size estimation from anisotropic measurements. Geophys. Prospect., 51(5), 381-392.
[30]
Maultzsch, S., Chapman, M., Liu, E., and Li, X. Y., 2007a, Observation of anisotropic attenuation in VSP data. Journal of Seismic Exploration, 16, 2-4, 145-158.
[31]
Maultzsch, S., Chapman, M., Liu, E., and Li, X. Y., 2007b, Modeling and analysis of attenuation in multiazimuth VSP data from the Clair field. Geophys. Prospect., 55, 627-642.
[32]
Park-Nolte, L. J., and Nolte, D. D., 1992, Frequency dependence of fracture stiffness. Geophys. Res. Lett., 19(3), 325-328.
[33]
Pointer, T., Liu, E., and Hudson, J. A., 2000, Seismic wave propagation in cracked porous media. Geophys. J. Int., 142, 199-231.
[34]
Schoenberg, M., Dean, S., and Sayers, C. M., 1999, Azimuthal-dependent turning of seismic waves reflected from fractured reservoirs. Geophysics, 64(4), 1160-1171.
[35]
Shi, S. H., 2007, Dependency relationship of fracture size, anisotropy and frequency in HTI media based on developing equivalent media model. PhD. Thesis, Jilin University, China.
[36]
Wei, X. C., Lu, M. H., Ba, J., et al., 2008, Dispersion and attenuation of elastic waves in a viscous fluid-saturated anisotropic porous solid. Chinese Journal of Geophysics, 51(1), 213-220.
2018, Vol. 15 
