层状饱和多孔介质中Biot慢波的影响
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摘要
本文基于Biot理论对P波在层状饱和多孔介质中的传播进行数值模拟。首先根据Kennett反射方法建立层状介质中地震波的数值模型,然后利用此模型研究层状饱和介质中Biot慢波对地震波性质的影响。文中分别在孔隙为弹性(考虑了P波扩散、Biot全局流及慢波影响)和黏弹性(可忽略慢波影响)两种情况下定量地分析了频率、孔隙率、层厚、渗透率以及岩石弹性模量对Biot慢波效应的影响。对比两种模型的数值模拟结果发现,在低频范围内,沉积盆地地层间液体压力的平衡作用(Biot慢波)能使P波产生显著的衰减;若这种衰减发生在浅层勘探地震波的频带内(几十到几百赫兹)。则介质层厚必然在几厘米到几十厘米范围内;介质越柔顺,孔隙率越大,渗透性越好,则慢波影响越大;在高频段,只要地层足够薄,介质的柔顺性足够好,界面处产生的慢波对高P波散射也会有很大影响。
Based on Biot theory,the paper conducted numeric modeling for P-wave propagation of in layered saturated porous medium. First , the numeric model of seismic wave in layered medium was built up according to Kennett reflection method, then the affects of Biot slow wave on seismic properties in layered saturated porous medium were studied by using the model. The paper quantitatively ana lyzed the affects of frenquency , porosity , thickness of layers and permeability as well as elastic modulus of rocks on Biot slow wave effects separately in two conditions of elastic pores (effects of P-wave dispersion, Biot global fluid and slow wave being considered) and viscoelastic pores (effects of slow wave being neglected). It is discovered by correlation of numeric modeling results of two models that the equilibration action of liquid pressure be- tween layers of sedimentary basin ( Biot wave) can produce significant attenuation for P-wave in low-frequency scope;the thickness of layers in medium has to vary from several centimeters to tens cen timeters if the attenuation takes place within a fre quency-band of shallow seismic exploration (from tens to hundreds Hz); the more compliance the medium,the larger the porosity and the better the permeability, the bigger the influence of slow wave; in high-frequency band, the effects of slow wave produced on the interfaces on the P-wave dispersion will be bigger if the layers are enough thick and compliance of medium is enough good.
Based on Biot theory,the paper conducted numeric modeling for P-wave propagation of in layered saturated porous medium. First , the numeric model of seismic wave in layered medium was built up according to Kennett reflection method, then the affects of Biot slow wave on seismic properties in layered saturated porous medium were studied by using the model. The paper quantitatively ana lyzed the affects of frenquency , porosity , thickness of layers and permeability as well as elastic modulus of rocks on Biot slow wave effects separately in two conditions of elastic pores (effects of P-wave dispersion, Biot global fluid and slow wave being considered) and viscoelastic pores (effects of slow wave being neglected). It is discovered by correlation of numeric modeling results of two models that the equilibration action of liquid pressure be- tween layers of sedimentary basin ( Biot wave) can produce significant attenuation for P-wave in low-frequency scope;the thickness of layers in medium has to vary from several centimeters to tens cen timeters if the attenuation takes place within a fre quency-band of shallow seismic exploration (from tens to hundreds Hz); the more compliance the medium,the larger the porosity and the better the permeability, the bigger the influence of slow wave; in high-frequency band, the effects of slow wave produced on the interfaces on the P-wave dispersion will be bigger if the layers are enough thick and compliance of medium is enough good.
引文
[1] Biot M A. Theory of propagation of elastic waves in a fluid saturated porous solid. I Low-frequency range i II Higher frequency range. J Acoust Soc Am, 1956, 28:168-178;179-191
[2] Biot M A. Mechanics of deformation and acoustic propagation in porous media. J Appl Phys, 1962, 33: 1482-1498
[3] Johnson D L et al. Theory of dynamic permeability a-nd trotuosity in fluid-saturated porous media. J Flu-id Mech, 1987,176:379-402
[4] Thompson A H et al. The microgeometry and transport properties of sedimentary rock. Advances in physics, 1987,36:625-694
[5] White J E et al. Low-frequency seismic waves in fluid-saturated layered rocks. Izvestija Academy of Sciences USSR,Phys Solid Earth,1975,11 :654-659
[6] Plona T J. Observation of a second bulk compression-al wave in a porous medium at ultrasonic frequencies.Appl Phys Lett, 1980,36:259-261
[7] Norris A N. Low-frequency dispersion and attenuation in partially saturated rocks. J Acoust Soc Am, 1993,94:359-370
[8] Gurevich B and Lopatnikov S L. Velocity and attention of elastic waves in finely layered porous rocks. Geophys J Int, 1995,121:933-947
[9] Gelinsky S and Shapiro S A. Dynamic-equivalent me- dium approach for thinly layered saturated sediments.Int J Solids Struct,1997,35:4739-4751
[10] Gelinsky S et al. Dynamic poroelasticity of thinly layered structures. Int J Solids Struct, 1998,35:4739-4751
[11] Steven R P et al. Biot slow-wave effects in stratified rock. Geophysics,2002,67(1): 271-281
[2] Biot M A. Mechanics of deformation and acoustic propagation in porous media. J Appl Phys, 1962, 33: 1482-1498
[3] Johnson D L et al. Theory of dynamic permeability a-nd trotuosity in fluid-saturated porous media. J Flu-id Mech, 1987,176:379-402
[4] Thompson A H et al. The microgeometry and transport properties of sedimentary rock. Advances in physics, 1987,36:625-694
[5] White J E et al. Low-frequency seismic waves in fluid-saturated layered rocks. Izvestija Academy of Sciences USSR,Phys Solid Earth,1975,11 :654-659
[6] Plona T J. Observation of a second bulk compression-al wave in a porous medium at ultrasonic frequencies.Appl Phys Lett, 1980,36:259-261
[7] Norris A N. Low-frequency dispersion and attenuation in partially saturated rocks. J Acoust Soc Am, 1993,94:359-370
[8] Gurevich B and Lopatnikov S L. Velocity and attention of elastic waves in finely layered porous rocks. Geophys J Int, 1995,121:933-947
[9] Gelinsky S and Shapiro S A. Dynamic-equivalent me- dium approach for thinly layered saturated sediments.Int J Solids Struct,1997,35:4739-4751
[10] Gelinsky S et al. Dynamic poroelasticity of thinly layered structures. Int J Solids Struct, 1998,35:4739-4751
[11] Steven R P et al. Biot slow-wave effects in stratified rock. Geophysics,2002,67(1): 271-281
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