Abstract:Most studies on seismic wave attenuation in anisotropic media only focus on transversely isotropic media containing a set of fractures. Since there are often several sets of orthogonal or oblique fractures developed in actual reservoirs, it is necessary to study the seismic wave dispersion and attenuation of reservoirs with multiple sets of fractures. Chapman builds a mesoscale squirt flow model including two sets of fractures but does not discuss the influence of those fractures on the chara-cteristic frequency, dispersion, and attenuation magnitude. Therefore, a method for calculating the P-wave frequency-dependent characteristics of reservoirs with multiple sets of fractures is proposed. Firstly, the Chapman model is numerically simulated, and the effects of fracture parameters on characteristic frequency, dispersion, and attenu-ation amplitude are discussed. Then, the rela-tionship between the Chapman model and the standard linear solid model is analyzed. Finally, a method is developed to calculate the frequency-dependent P-wave modulus of reservoirs with multiple sets of fractures by the generalized standard linear solid model. This means that the low-frequency modulus is obtained by the Chapman model and anisotropic Gassmann equation, and the high-frequency modulus is obtained by the Chapman model. The proposed method employs the low-frequency and high-frequency limit modulus and modu-lus loss to characterize the frequency dispersion and attenuation properties of seismic waves. The modulus loss can represent the contribution of each set of fractures, and the following conclusions are obtained. ① Fracture orientations and seismic wave incident direction only affect the velocity (frequency dispersion) and attenuation magnitude but do not affect the frequency dispersion and attenuation frequency band. ② The P-wave velocity VP (or P-wave inverse quality factor QP-1) curves of different fracture development conditions have some algebraic relationship. Therefore, the VP (or QP-1) curves of a single set of fractures can be utilized to represent the VP (or QP-1) curves of two or more sets of fractures. ③ When the propagation direction of seismic waves is parallel to the fractures, the variation of VP with frequency is slight, and the attenuation of P-wave is the smallest. The proposed method is of practical significance for studying the seismic wave field characteristics and seismic response mechanism of anisotropic media.
BIOT M A. Theory of propagation of elastic waves in fluid-saturated porous solid.Ⅰ.Low-frequency range[J].Journal of the Acoustical Society of America,1956,28(2):168-178.
[2]
BIOT M A. Theory of propagation of elastic waves in a fluid-saturated porous solid.Ⅱ.Higher frequency range[J]. Journal of the Acoustical Society of America,1956,28(2): 179-191.
[3]
CHAPMAN M. Frequency dependent anisotropy due to meso-scale fractures in the presence of equant porosity[J]. Geophysical Prospecting,2003,51(5):369-379.
[4]
凌云,杜向东,曹思远.基于Zener线性体的黏弹孔隙介质衰减频散特征分析[J].地球物理学进展,2017,32(1):205-209.LING Yun,DU Xiangdong,CAO Siyuan.Attenuation and dispersion characteristics analysis in visco-poroelastic medium based on Zener linear solid[J].Progress in Geophysics,2017,32(1):205-209.
[5]
李灿苹, 刘学伟. 随机均匀介质地震波振幅属性研究[J]. 石油物探,2009,48(5):465-469.LI Canping,LIU Xuewei. Study on amplitude attribu-tes of seismic wave in random-uniform medium model[J]. Geophysical Prospecting for Petroleum,2009,48(5):465-469.
[6]
YUAN S,WANG S,MA M,et al. Sparse Bayesian learning-based time-variant deconvolution[J].IEEE Transactions on Geoscience and Remote Sensing,2017,55(11):6182-6194.
[7]
刘建华,胥颐,郝天珧.地震波衰减的物理机制研究[J]. 地球物理学进展,2004,19(1):1-7.LIU Jianhua,XU Yi,HAO Tianyao. Study on physical mechanism of the seismic wave attenuation[J]. Progress in Geophysics,2004,19(1):1-7.
BAIRD A F,KENDALL J M,ANGUS D A. Frequency-dependent seismic anisotropy due to fractures:Fluid flow versus scattering[J]. Geophysics,2013,78(2):WA111-WA122.
[10]
白旭明,张以明,杜启振,等. 黏弹性裂缝诱导各向异性介质地震波场传播特征——以束鹿凹陷沙河街组三段下亚段泥灰岩储层为例[J].石油学报,2015,36(增刊1):50-58.BAI Xuming,ZHANG Yiming,DU Qizhen,et al. Seismic wave field propagation characteristics of viscoelastic fracture-induced anisotropic medium:a case study of calcilutite reservoirs in the lower part of Member 3 of Shahejie Formation,Shulu sag [J]. Acta Petrolei Sinica,2015,36(Z1):50-58.
[11]
刘芸菲,陈学华,罗鑫,等. 双相不混溶流体饱和裂缝—孔隙岩石依赖频率的地震响应数值分析[J]. 石油地球物理勘探,2020,55(4):821-830.LIU Yunfei,CHEN Xuehua,LUO Xin,et al. Numerical analysis of frequency-dependent seismic responses from fractured-porous rock saturated with two-phase immiscible fluids[J].Oil Geophysical Prospecting,2020,55(4):821-830.
[12]
尹志恒,狄帮让,魏建新,等.裂缝参数对纵波能量衰减影响的物理模型研究[J].石油地球物理勘探,2012,47(5):728-734,753.YIN Zhiheng,DI Bangrang,WEI Jianxin,et al. P-wave attenuation by fracture parameter on physical models[J]. Oil Geophysical Prospecting,2012,47(5):728-734,753.
[13]
李民龙,刘浩杰,杨宏伟,等. 跨频段岩石波速及频散的实验研究[J]. 石油地球物理勘探,2020,55(2):373-378.LI Minlong,LIU Haojie,YANG Hongwei,et al. Experimental study on cross-frequency wave velocity and dispersion in rocks[J]. Oil Geophysical Prospecting,2020,55(2):373-378.
[14]
张繁昌,桑凯恒,路亚威. 硬币型裂缝介质的频散与衰减[J]. 石油地球物理勘探,2019,54(4):836-843.ZHANG Fanchang,SANG Kaiheng,LU Yawei. Frequency dispersion and attenuation of porous rocks with penny shaped fractures[J].Oil Geophysical Prospecting,2019,54(4):836-843.
[15]
GUREVICH B,BRAJANOVSKI M,GALVIN R,et al. P-wave dispersion and attenuation in fractured and porous reservoirs-poroelasticity approach[J].Geophysical Prospecting,2009,57(2):225-237.
[16]
MULLER T M,GUREVICH B,LEBEDEV M. Seismic wave attenuation and dispersion resulting from wave-induced flow in porous rocks-A review[J]. Geo-physics,2010,75(5):75A147-75A164.
[17]
段茜,刘向君,梁利喜,等. 裂缝参数对纵波各向异性影响的数值模拟[J].石油地球物理勘探,2020,55(3):575-583,590.DUAN Xi,LIU Xiangjun,LIANG Lixi,et al. Numeri-cal simulation to the influence of fracture parameters on P-wave anisotropy[J].Oil Geophysical Prospecting,2020,55(3):575-583,590.
[18]
SAROUT J. Impact of pore space topology on permea-bility,cut-off frequencies and validity of wave propagation theories[J].Geophysical Journal International,2012,189(1):481-492.
[19]
SHI P D,YUAN S Y,WANG T Y,et al. Fracture identification in a tight sandstone reservoir:A seismic anisotropy and automatic multisensitive attribute fusion framework[J]. IEEE Geoscience Remote Sensi-ng Letter,2018,15(10):1525-1529.
[20]
CHAPMAN M.Modeling the effect of multiple sets of mesoscale fractures in porous rock on frequency-dependent anisotropy[J].Geophysics,2009,74(6):D97-D103.
[21]
MAULTZSCH S,CHAPMAN M,LIU E,et al. Modelling frequency-dependent seismic anisotropy in fluid-saturated rock with aligned fractures:implication of fracture size estimation from anisotropic measurements[J]. Geophysical Prospecting,2003,51(5):381-392.
[22]
YUAN S Y,LIU Y,ZHANG Z,et al. Prestack stochastic frequency-dependent velocity inversion with rock-physics constraints and statistical associated hydrocarbon attributes[J]. IEEE Geoscience Remote Sensing Letter,2019,16(1):140-144.
[23]
PICOTTI S,CARCIONE J M,RUBINO J G,et al. A viscoelastic representation of wave attenuation in poro-us media[J]. Computer & Geoscience,2010,36(1):44-53.
[24]
PICOTTI S,CARCIONE J M. Numerical simulation of wave-induced fluid flow seismic attenuation based on the Cole-Cole model[J]. Journal of the Acoustical Society of America,2017,142(1):134-145.