部分饱和多相介质中Rayleigh面波传播特性研究
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摘要
Rayleigh面波在很多领域都显示着重要的作用,比如地震学、地下水、工程、环境、地质学和材料科学。英国学者Lord Rayleigh于1885年首先在理论上发现并证实了,在各向同性均匀弹性介质中Rayleigh面波的存在。这种波沿着自由界面传播,如地球和空气界面,它是纵波和横波的干涉波,并且总是在地震记录中显示出强振幅信号。
在勘探地震和工程地震中,面波曾经被看成是地滚波,是体波波长信号中一种很难消除的噪声。但是随着面波方法,特别是多道面波分析(MASW),数十年的发展,横波速度可以通过反演Rayleigh面波资料快速地得到,面波被认为成一种有用的工具,可以用它获得地下介质的信息。目前,勘探地震频带内(高至200Hz)的面波技术主要认为面波产生于弹性介质。动态弹性理论是面波勘探资料采集、处理和反演在近地表地球物理中应用的理论基础。
固结和未固结的地球介质总是以含有孔隙的固体存在,孔隙中充填有一种或多种流体。多相介质理论可以描述这种含孔隙的固体。Biot(1941,1956a,1956b,1962a,1962b)建立了一种孔弹性理论,这种理论比单相弹性理论更精确地阐述真实介质中的波动现象。基于这一理论,两种类型的纵波,称之为P1波和P2波,和一种横波被证明存在于孔弹性介质。许多科学家在多方面研究了孔弹性介质中波的传播,而且孔弹性理论也在不断地发展和改进,出现了可以描述更复杂的固流混合物的理论。
由于孔隙中流体相的存在,由此产生不只一种类型的自由表面,像可渗透的“开放孔隙”、不渗透的“封闭孔隙”和部分渗透的“半开孔隙”(Deresiewicz and Skalak,1963)。故此,由纵波和横波干涉产生的Rayleigh面波有着更为复杂的特性,它传播过程中可以反映固体介质更多的信息,比如流体压力、孔隙度、渗透率等。因此,在地震勘探的频率范围内,探寻面波在孔弹性介质中的传播特性是改进面波方法的勘探精度,使其更符合真实野外的情况的重要问题。虽然,很多学者研究了Rayleigh面波的传播特性,但是鉴于描述面波比描述体波更为复杂,面波的传播问题没有体波传播研究得充分。在地震频带内重要的衰减机制——中观耗散也没有引入来描述面波的传播。由此可见,分析面波在孔弹性介质中的传播特性,并建立一种简单的等效模型来近似孔弹性模型,对于研究用可行的办法将孔弹性引入面波勘探方法是十分有意义的。研究主要包括以下几个方面：(1)由于在孔弹性多种自由表面的存在,Rayleigh面波的传播受这种边界条件差异的影响。有必要分析在不同的表面边界条件的影响下,特别是未见详细讨论的部分渗透的表面边界的影响下,面波的传播特性；(2)用一种单行的近似的数学模型来描述孔弹性可以简化表述面波的复杂性,因此引入一种等效的单相介质是合理的；(3)这种近似的等效介质模型需要通过理论和数值的试验来验证。
基于面波在孔弹性介质中传播问题的研究现状以及我们所面临的问题,我们研究了孔弹性介质中Rayleigh面波在不同物理条件下的传播特性,并试图建立一种简单的近似模型来描述在有中观尺度耗散机制的孔弹性介质中Rayleigh面波的传播。在研究过程中,我们专注于以下的问题：
(1).我们研究了Rayleigh面波的速度频散、衰减和动态响应特征,并给出了不同自由表面边界条件下的Rayleigh面波的频散方程和动态格林函数。
(2).我们用数值方法分析了在不同的表面边界条件、粘性衰减条件、弹性物性条件和流体流动条件下Rayleigh面波在勘探地震的频率范围内的频散、衰减曲线、波场和频谱的动态响应,以得到Rayleigh面波的传播特性。
(3).我们建立一种等效的单相粘弹性介质来近似部分饱和情况下的孔弹性介质,并考虑中观尺度的衰减机制。我们获得更为简单数学表达的等效频散方程和动态格林函数,较孔弹性介质有明显的简化。
(4).我们也分析了等效介质中Rayleigh面波的频散、衰减特征和波场、频谱响应,得到的结果与Biot介质模型对比,可以表明这种模型的等效性和可用性。
通过分析Rayleigh面波的传播特性,我得到以下结论：
(1).孔隙流体在自由表面不同的渗透条件使得界面上产生不同模式的Rayleigh面波。一种模式的波,我们称之为R1波,在所有的条件下都存在,它的传播特性类似于经典弹性介质中的Rayleigh面波。另外一种模式的波,我们称之为R2波,在闭合孔隙和部分渗透的表面边界条件下出现。这两种模式的Rayleigh面波的传播特性可以总结为：
ⅰ).R1波
这种面波模式无论任何表面排水条件下都会出现。在其沿界面的传播过程中,显示出和弹性介质中经典的Rayleigh面波一样的强振幅能量。在低频段内,不同条件产生的这种模式的波都趋近于同一速度,该速度为孔弹性等效Gassmann介质内Rayleigh面波的速度。在自由表面部分渗透条件下,这种波有最明显的频散,比封闭孔隙条件稍明显,而在开放孔隙条件下,频散最小。高粘性流体和低骨架渗透率(高的固流耦合衰减系数)使得主要频散发生的频率范围,和衰减系数出现不同频率响应特征的鞍点向高频移动,这反映松弛频率向高频段移动。坚硬的固体骨架和高孔隙弯曲度下低下的流体流动条件使得在不同表面条件下这种面波的频散效应减弱。在地震频率的高频端,R1波在不同的表面渗透条件趋近不同的某一速度值。由于在高频范围,衰减系数显示出与频率的一次相关性,这种面波模式显示出常Q值渗漏衰减。较其它两种情况,R1波在开放孔隙条件对弹性物性参数的变化最为敏感,但是对孔隙弯曲度的变化最不敏感,这种现象也在波场和频谱的变化中表现出来。部分表面渗透可以在低频内产生负衰减效应的非物理R1波,不同的物理条件可以使改变非物理波的出现频率的范围。然而,在波场和频谱中,这种效应没有明显的反映。松弛频率的移动使得在地震频带内R1波最大的衰减在固流耦合衰减系数并非最大时出现。由于与经典Rayleigh面波的相似性,我们可以用这种面波模式来描述真实的面波资料。值得注意的是在非常低的固流耦合系数下,这种模式的波会在闭合孔隙和部分渗透的表面条件下,对另一种面波模式产生辐射,这种效应伴随着明显的能量衰减。
ⅱ).R2波
这种模式的波只有在封闭孔隙和部分渗透的自由表面条件下产生。这种波在低频端显示出耗散,在地震高频范围内有着一个固定的趋近速度,与慢纵波P2波的传播特性相似,但速度较之略低,衰减较之略强。R2波对孔隙弯曲度的变化所带来的流动条件的变化很敏感,高的弯曲度会减小R2波的速度和衰减。像P2波在体波记录中的特征一样,在大多数条件下,R2波不能被观察到。但是在很低固流耦合衰减系数下,这种面波模式可以在地震记录中出现。在部分渗透的表面条件下,R2波甚至有比R1波更强的能量,这是因为R2波出现非物理波,接收R1波的辐射,这种奇异的现象也在频谱中反映。
(2).部分饱和或者非饱和孔隙流体意味着孔隙中含有多种流体,比如水和气。等效流体混合模型可以兼得描述这种多相流体,就是在均匀饱和的流体压力平衡状态下的Reuss平均,和宏观非均匀的多相流体在没有相互作用的条件下的Voigt平均。这些平均方法反映微观和宏观上多相流体的分布,但是在地震频率范围内,在两者之间中观尺度上不均匀是一种重要的衰减机制。孔隙介质斑块饱和模型可以描述这种衰减机制。在不同的斑块中,饱和着不同的一种流体,当纵波通过这些斑块中时,激发起流体流动,在不同斑块界面上产生压力梯度和P2波,并放生中观尺度上的耗散。White (White,1975; White et al.,1975)考虑一种不同斑块几何尺寸的模型来描述这种中观衰减,称之为White斑块饱和模型,这种模型建立在Biot理论上。由于横波只在固体骨架上传播,斑块饱和模型中纵波和横波的耦合可以在自由表面上产生等效Rayleigh面波。这种粘弹性近似孔弹性的建立充分考虑了中观尺度的衰减。
(3).从频散,衰减,波场以及频谱分析的结果可以看到,在与Biot宏观机制不同的高粘性流体和低固体渗透率下,出现中观尺度衰减频率范围,纵波和横波耦合产生的Rayleigh面波与纵波有着相似的频散和衰减特征,但是中观衰减被不受中观尺度不均匀影响的横波削弱。斑块的尺寸的不同产生松弛频率的移动,影响着面波的频散和衰减。通过与微观和宏观不均匀尺度下,用流体平均的Biot理论得到结果比较,等效的粘弹性近似可以用来反映Rayleigh面波的中观尺度衰减。这种近似给我们一种孔弹性的理论框架内,在地震频率范围内考虑中观尺度衰减的描述孔隙介质的频散和衰减的简单方法。
(4).中观尺度机制是在地震频率范围内影响波传播的一个关键因素,对面波频散和衰减的影响也是显而易见的。将中观尺度衰减引入到面波方法中是面波技术发展的重要前景之一。等效近似的理论结果为我们将来的研究工作：在考虑中观尺度不均匀产生的衰减的条件下,建立一种简单的等效介质方程以便使用在面波模拟和反演中去。为获得对应实际介质的孔隙流体的分布对面波的速度频散和衰减的影响,需要进行更多的精确的数值和物理实验,使我们能够在面波勘探方法上有效地应用孔弹性理论。
The importance of Rayleigh waves can be noted in several fields, as earthquake seismology, ground water, engineering, environmental, geology and material science. Lord Rayleigh (1885) first carried out the theoretical investigations in isotropic half space elastic media. These waves that propagate along a free surface, as the earth and air interface, are generated by couple of P and S wave, with always strong energy in seismograms.
Surface wave was treated as ground roll of the most troublesome noise making the useful bulk wave fields in exploration and engineering seismology. But as the surface wave method, especial the Multichannel analysis of surface wave (MASW) has been developing these decades, S wave velocities can be estimated quickly from inversion of Rayleigh wave data. Surface wave is regarded as the available tools to obtain the subsurface information. Surface-wave techniques in the exploration seismic frequency band (up to200Hz) primarily regard surface-wave generating in elastic media. Dynamic elastic theory is the fundamental of surface-wave data gathering, processing, and inversion in the near-surface geophysics community.
The earth media, consolidated and unconsolidated, are representative composed of solid with pores, one or multiple fluids are filled in. Multiphase theory can describe this solid of porous media. Biot (1941,1956a,1956b,1962a,1962b) established a poroelastic theory, which can more precisely elucidate the property of wave phenomena in real world media than single-phase elasticity. Two types of P waves, referred as P1waves and P2waves, and one type of S waves were theoretically predicted existing in poroelastic media. Many scientists have widely investigated the wave propagation in poroelastic media, and the poroelastic theory has been progressing and improving to represent the more complex solid and fluid composites.
For the existence of the fluid phases in the pores, it generates more than one type of free surfaces of permeable "open-pore", impermeable "close-pore" and partially permeable interfaces (Deresiewicz and Skalak,1963). As the result, the Rayleigh wave, interfered by P and S wave, in poroelastic media has more complex properties, which carry more information about solid media, such as fluid pressure, porosity, permeability, etc. Therefore, to find the propagation characteristics of surface waves in poroelastic media in the exploration seismic frequency band is a key issue to improve prospecting precision of surface wave methods to face real-world conditions. Although, the propagation of Rayleigh wave has been studied by several researchers, in consideration of the more difficulty to describe the surface wave, the propagation of surface wave is not sufficiently analyzed as bulk waves. Mesoscopic loss, an important attenuation mechanism in seismic frequency band has not introduced into the surface wave propagation. Therefore, analysis propagation of surface wave in poroelastic media and establishing an effective simple model to approximate the poroelastic model is meanful to for us to acquire some applicable method to introduce poroelasticity in surface wave method. The main aspects include:(1) as the different free surface interfaces, Rayleigh wave in poroelastic media are effected by this difference. It is necessary to analysis the propagation characteristics under the different surface conditions, especially the partial surface condition, which is lack in explicit analysis;(2) an approximate mathematical single phase model of the poroelasticity can simplify the complexity of the expressions of the surface wave, so introduce a single phase effective media could be feasible; and (3) the approximate method of effective media should be verified in numerical and theoretical experiments.
Based on the facts of the studies on the surface wave propagation in poroelastic media, and the problems we face, we studied the characteristics of Rayleigh wave in poroelastic media for different physical conditions and tried to construct a simple approximate model to describe the poroelastic media with the important mesoscopic loss mechanism. In analysis of the propagation, we focused on the following subjects.
(1). We investigated velocity dispersion, attenuation and dynamic response characteristics of Rayleigh waves, and gave the dispersion equations and dynamic Green's functions for different free surface conditions.
(2). We numerical analyzed the dispersion, attenuation curves, wave field and spectral dynamic responses under different surface conditions, viscous damping, elastic properties and porous fluid flowing conditions in seismic frequency band to figure out the characteristics of Rayleigh wave propagation.
(3). We established an effective single phase viscoelastic media to approximate poroelstic media of partial saturation case with the mesoscopic loss mechanism considered. We derived the effective dispersion equation and dynamic Green's functions in a simple expression comparing to poroelastic media.
(4). We also analyzed the dispersion, attenuation characteristics and wave field, spectrum responses of Rayleigh waves in the effective media. The results are compared to that of Biot's model to demonstrate the applicable of the effective model.
By the analysis of the Rayleigh wave, we conclude that:
(1). Different free surfaces of different surface permeabilities for porous fluid at the interface generate the different modes of Rayleigh type surface waves. One mode referred as R1wave exists under all the conditions, as the classical Rayleigh wave in elastic media, the other mode referred as R2wave exists for closed pore and partially permeable surface conditions, the exact propagation characteristics of these two modes of Rayleigh wave are summarized as:
i). R1wave
This surface-wave mode exists for no matter the surface drainage condition changes. The surface-wave mode propagates with strong energy, as the classical Rayleigh wave in elastic media. At the low frequency, the velocities of surface-wave mode are all asymptotic to a same value of the Gassmann effective Rayleigh wave velocity. Velocity dispersion for partially permeable surface is most (slight more than closed pore condition), and for open pore is least. Large fluid viscosity or low permeability (High couple damping coefficient) make the shift to high frequencies of the main dispersion frequency range, and the attenuation coefficient knee points for the different frequency dependence, which represents the relaxation frequency movement to high frequencies. A rigid solid frame skeleton and low fluid flowing condition of large tortuosities weaken the velocity dispersion for all the surface conditions. At high frequencies in seismic frequency band, R1waves propagate with different limited velocity for the three surface cases, respectively. Because the attenuation coefficient is f1dependence at high frequencies, this surface-wave mode shows constant-Q leaky attenuation. R1waves for the open pore condition is most sensitive to the elastic modulus variation, but least sensitive to tortuosoty variation, which also can be represented in the wave fields and spectra changing to other two cases. The partial surface permeability can generates the non-physical R1waves with negative attenuation at low frequency range, which can be effected by the different physical properties. But it has the no distinct reflection in wave fields and spectra. The relaxation frequency shift makes a most attenuation appear at an intermediate couple damping coefficient. For similarity to the classical Rayleigh wave, we can use this surface-wave mode to describe the real world surface wave data. It is noticed that at very low couple damping coefficient, this surface-wave mode radiates with energy loss into the other surface-wave mode for closed pore and partially permeable surface.
ii). R2Wave
This surface-wave mode is only generated by the closed pore and partially permeable free surface. Diffusion at low frequency and a limit velocity at high frequencies in seismic frequency band, this surface-wave mode is similar to the slow P2wave, with slight low velocity and high attenuation. R2wave is sensitive to tortuosity variation as flowing condition changing, high tortuosity diminish the velocity of R2wave velocity with low attenuation. As P2wave in bulk wave seismograms, R2wave is not observed for majority condition. But at very low couple damping coefficient, this surface-wave mode displays. For partially permeable surface, R2wave even bears stronger energy than R1wave, because of radiation of R1wave to the non physical R2wave, the peculiar phenomenon is also reflected in spectra.
(2). Partial saturated or unsaturated porous fluid means the multiphase fluids in the pores, for instance, water and gas. Effective mixture fluid can simply describe these fluids, i.e. Reuss average for uniform isostress condition of homogeneous saturation with equilibrium porous pressure, and Voigt average for macroscopic inhomogeneity with non interactions of the multiphase. These averages reflect the microscopic and macroscopic multiphase fluid distribution, but a mesoscopic scale unhomogeneity between these is very important to the attenuation mechanism in seismic frequency band. Patchy saturation model of porous media can describe this mechanism. In the different patches saturated one type of fluids, when longitudinal wave passes through the different patches, the wave induced flow generates the pressure gradient and P2wave between the interfaces among the different patches saturated with different fluids, and diffusion as a mesoscopic loss mechanism. White (White,1975; White et al.,1975) considered a model of two specific patchy geometry sizes to describe this mesoscopic attenuation, referred as White's patchy saturation model, and built on the Biot's theory. As the S wave propagates in the solid frame skeleton, the combination of P wave and S wave in patchy saturation model generates the effective Rayleigh surface wave at the free surface. The viscoelastic approximation of poroelasticity is established with mesoscopic loss considered
(3). Results of dispersion, attenuation, wave field and spectrum analyses show that, in the dominate frequency of mesoscopic loss of large fluid viscosity or low solid permeability, opposite to the macroscopic mechanism in Biot's theory, Rayleigh wave, couple of P wave and S wave, has the similar dispersion and attenuation characteristics as P wave, but the mesoscopic loss is weakened by the S wave, which is little effected by mesoscopic unhomogeneity. The patch size also effects the dispersion and attenuation by shifting the relaxation frequency. By comparing to fluid average for microscopic and macroscopic unhomogeneity in Biot's theory, the effective viscoelstic approximation is applicable to reflect the mesoscopic loss in Rayleigh wave. The approximation shows us a simple way for poroelasticity to describe dispersion and attenuation for porous media with mesoscopic attenuation in seismic frequency band.
(4). Mesoscopic mechanism is a key factor of effecting the wave propagation in seismic frequency band, which also obviously effects the dispersion and attenuation of surface wave. Introduction the mesoscopic loss into the surface wave method is one of the important perspectives for surface wave technique. The theoretical results of approximation show us a good guide for future work of constructing a simple and applicable guide equation for effective media in seismic modeling and inversion with the mesoscopic unhomogeneity attenuation considered. In order to obtain the velocity dispersion and attenuation of surface wave with the actual fluid distribution scale corresponding the in-situ state of porous media in real world, more exact numerical and physical experiments should be carried on for effectively practical utilizing of poroelasticity in surface wave method.
在勘探地震和工程地震中,面波曾经被看成是地滚波,是体波波长信号中一种很难消除的噪声。但是随着面波方法,特别是多道面波分析(MASW),数十年的发展,横波速度可以通过反演Rayleigh面波资料快速地得到,面波被认为成一种有用的工具,可以用它获得地下介质的信息。目前,勘探地震频带内(高至200Hz)的面波技术主要认为面波产生于弹性介质。动态弹性理论是面波勘探资料采集、处理和反演在近地表地球物理中应用的理论基础。
固结和未固结的地球介质总是以含有孔隙的固体存在,孔隙中充填有一种或多种流体。多相介质理论可以描述这种含孔隙的固体。Biot(1941,1956a,1956b,1962a,1962b)建立了一种孔弹性理论,这种理论比单相弹性理论更精确地阐述真实介质中的波动现象。基于这一理论,两种类型的纵波,称之为P1波和P2波,和一种横波被证明存在于孔弹性介质。许多科学家在多方面研究了孔弹性介质中波的传播,而且孔弹性理论也在不断地发展和改进,出现了可以描述更复杂的固流混合物的理论。
由于孔隙中流体相的存在,由此产生不只一种类型的自由表面,像可渗透的“开放孔隙”、不渗透的“封闭孔隙”和部分渗透的“半开孔隙”(Deresiewicz and Skalak,1963)。故此,由纵波和横波干涉产生的Rayleigh面波有着更为复杂的特性,它传播过程中可以反映固体介质更多的信息,比如流体压力、孔隙度、渗透率等。因此,在地震勘探的频率范围内,探寻面波在孔弹性介质中的传播特性是改进面波方法的勘探精度,使其更符合真实野外的情况的重要问题。虽然,很多学者研究了Rayleigh面波的传播特性,但是鉴于描述面波比描述体波更为复杂,面波的传播问题没有体波传播研究得充分。在地震频带内重要的衰减机制——中观耗散也没有引入来描述面波的传播。由此可见,分析面波在孔弹性介质中的传播特性,并建立一种简单的等效模型来近似孔弹性模型,对于研究用可行的办法将孔弹性引入面波勘探方法是十分有意义的。研究主要包括以下几个方面：(1)由于在孔弹性多种自由表面的存在,Rayleigh面波的传播受这种边界条件差异的影响。有必要分析在不同的表面边界条件的影响下,特别是未见详细讨论的部分渗透的表面边界的影响下,面波的传播特性；(2)用一种单行的近似的数学模型来描述孔弹性可以简化表述面波的复杂性,因此引入一种等效的单相介质是合理的；(3)这种近似的等效介质模型需要通过理论和数值的试验来验证。
基于面波在孔弹性介质中传播问题的研究现状以及我们所面临的问题,我们研究了孔弹性介质中Rayleigh面波在不同物理条件下的传播特性,并试图建立一种简单的近似模型来描述在有中观尺度耗散机制的孔弹性介质中Rayleigh面波的传播。在研究过程中,我们专注于以下的问题：
(1).我们研究了Rayleigh面波的速度频散、衰减和动态响应特征,并给出了不同自由表面边界条件下的Rayleigh面波的频散方程和动态格林函数。
(2).我们用数值方法分析了在不同的表面边界条件、粘性衰减条件、弹性物性条件和流体流动条件下Rayleigh面波在勘探地震的频率范围内的频散、衰减曲线、波场和频谱的动态响应,以得到Rayleigh面波的传播特性。
(3).我们建立一种等效的单相粘弹性介质来近似部分饱和情况下的孔弹性介质,并考虑中观尺度的衰减机制。我们获得更为简单数学表达的等效频散方程和动态格林函数,较孔弹性介质有明显的简化。
(4).我们也分析了等效介质中Rayleigh面波的频散、衰减特征和波场、频谱响应,得到的结果与Biot介质模型对比,可以表明这种模型的等效性和可用性。
通过分析Rayleigh面波的传播特性,我得到以下结论：
(1).孔隙流体在自由表面不同的渗透条件使得界面上产生不同模式的Rayleigh面波。一种模式的波,我们称之为R1波,在所有的条件下都存在,它的传播特性类似于经典弹性介质中的Rayleigh面波。另外一种模式的波,我们称之为R2波,在闭合孔隙和部分渗透的表面边界条件下出现。这两种模式的Rayleigh面波的传播特性可以总结为：
ⅰ).R1波
这种面波模式无论任何表面排水条件下都会出现。在其沿界面的传播过程中,显示出和弹性介质中经典的Rayleigh面波一样的强振幅能量。在低频段内,不同条件产生的这种模式的波都趋近于同一速度,该速度为孔弹性等效Gassmann介质内Rayleigh面波的速度。在自由表面部分渗透条件下,这种波有最明显的频散,比封闭孔隙条件稍明显,而在开放孔隙条件下,频散最小。高粘性流体和低骨架渗透率(高的固流耦合衰减系数)使得主要频散发生的频率范围,和衰减系数出现不同频率响应特征的鞍点向高频移动,这反映松弛频率向高频段移动。坚硬的固体骨架和高孔隙弯曲度下低下的流体流动条件使得在不同表面条件下这种面波的频散效应减弱。在地震频率的高频端,R1波在不同的表面渗透条件趋近不同的某一速度值。由于在高频范围,衰减系数显示出与频率的一次相关性,这种面波模式显示出常Q值渗漏衰减。较其它两种情况,R1波在开放孔隙条件对弹性物性参数的变化最为敏感,但是对孔隙弯曲度的变化最不敏感,这种现象也在波场和频谱的变化中表现出来。部分表面渗透可以在低频内产生负衰减效应的非物理R1波,不同的物理条件可以使改变非物理波的出现频率的范围。然而,在波场和频谱中,这种效应没有明显的反映。松弛频率的移动使得在地震频带内R1波最大的衰减在固流耦合衰减系数并非最大时出现。由于与经典Rayleigh面波的相似性,我们可以用这种面波模式来描述真实的面波资料。值得注意的是在非常低的固流耦合系数下,这种模式的波会在闭合孔隙和部分渗透的表面条件下,对另一种面波模式产生辐射,这种效应伴随着明显的能量衰减。
ⅱ).R2波
这种模式的波只有在封闭孔隙和部分渗透的自由表面条件下产生。这种波在低频端显示出耗散,在地震高频范围内有着一个固定的趋近速度,与慢纵波P2波的传播特性相似,但速度较之略低,衰减较之略强。R2波对孔隙弯曲度的变化所带来的流动条件的变化很敏感,高的弯曲度会减小R2波的速度和衰减。像P2波在体波记录中的特征一样,在大多数条件下,R2波不能被观察到。但是在很低固流耦合衰减系数下,这种面波模式可以在地震记录中出现。在部分渗透的表面条件下,R2波甚至有比R1波更强的能量,这是因为R2波出现非物理波,接收R1波的辐射,这种奇异的现象也在频谱中反映。
(2).部分饱和或者非饱和孔隙流体意味着孔隙中含有多种流体,比如水和气。等效流体混合模型可以兼得描述这种多相流体,就是在均匀饱和的流体压力平衡状态下的Reuss平均,和宏观非均匀的多相流体在没有相互作用的条件下的Voigt平均。这些平均方法反映微观和宏观上多相流体的分布,但是在地震频率范围内,在两者之间中观尺度上不均匀是一种重要的衰减机制。孔隙介质斑块饱和模型可以描述这种衰减机制。在不同的斑块中,饱和着不同的一种流体,当纵波通过这些斑块中时,激发起流体流动,在不同斑块界面上产生压力梯度和P2波,并放生中观尺度上的耗散。White (White,1975; White et al.,1975)考虑一种不同斑块几何尺寸的模型来描述这种中观衰减,称之为White斑块饱和模型,这种模型建立在Biot理论上。由于横波只在固体骨架上传播,斑块饱和模型中纵波和横波的耦合可以在自由表面上产生等效Rayleigh面波。这种粘弹性近似孔弹性的建立充分考虑了中观尺度的衰减。
(3).从频散,衰减,波场以及频谱分析的结果可以看到,在与Biot宏观机制不同的高粘性流体和低固体渗透率下,出现中观尺度衰减频率范围,纵波和横波耦合产生的Rayleigh面波与纵波有着相似的频散和衰减特征,但是中观衰减被不受中观尺度不均匀影响的横波削弱。斑块的尺寸的不同产生松弛频率的移动,影响着面波的频散和衰减。通过与微观和宏观不均匀尺度下,用流体平均的Biot理论得到结果比较,等效的粘弹性近似可以用来反映Rayleigh面波的中观尺度衰减。这种近似给我们一种孔弹性的理论框架内,在地震频率范围内考虑中观尺度衰减的描述孔隙介质的频散和衰减的简单方法。
(4).中观尺度机制是在地震频率范围内影响波传播的一个关键因素,对面波频散和衰减的影响也是显而易见的。将中观尺度衰减引入到面波方法中是面波技术发展的重要前景之一。等效近似的理论结果为我们将来的研究工作：在考虑中观尺度不均匀产生的衰减的条件下,建立一种简单的等效介质方程以便使用在面波模拟和反演中去。为获得对应实际介质的孔隙流体的分布对面波的速度频散和衰减的影响,需要进行更多的精确的数值和物理实验,使我们能够在面波勘探方法上有效地应用孔弹性理论。
The importance of Rayleigh waves can be noted in several fields, as earthquake seismology, ground water, engineering, environmental, geology and material science. Lord Rayleigh (1885) first carried out the theoretical investigations in isotropic half space elastic media. These waves that propagate along a free surface, as the earth and air interface, are generated by couple of P and S wave, with always strong energy in seismograms.
Surface wave was treated as ground roll of the most troublesome noise making the useful bulk wave fields in exploration and engineering seismology. But as the surface wave method, especial the Multichannel analysis of surface wave (MASW) has been developing these decades, S wave velocities can be estimated quickly from inversion of Rayleigh wave data. Surface wave is regarded as the available tools to obtain the subsurface information. Surface-wave techniques in the exploration seismic frequency band (up to200Hz) primarily regard surface-wave generating in elastic media. Dynamic elastic theory is the fundamental of surface-wave data gathering, processing, and inversion in the near-surface geophysics community.
The earth media, consolidated and unconsolidated, are representative composed of solid with pores, one or multiple fluids are filled in. Multiphase theory can describe this solid of porous media. Biot (1941,1956a,1956b,1962a,1962b) established a poroelastic theory, which can more precisely elucidate the property of wave phenomena in real world media than single-phase elasticity. Two types of P waves, referred as P1waves and P2waves, and one type of S waves were theoretically predicted existing in poroelastic media. Many scientists have widely investigated the wave propagation in poroelastic media, and the poroelastic theory has been progressing and improving to represent the more complex solid and fluid composites.
For the existence of the fluid phases in the pores, it generates more than one type of free surfaces of permeable "open-pore", impermeable "close-pore" and partially permeable interfaces (Deresiewicz and Skalak,1963). As the result, the Rayleigh wave, interfered by P and S wave, in poroelastic media has more complex properties, which carry more information about solid media, such as fluid pressure, porosity, permeability, etc. Therefore, to find the propagation characteristics of surface waves in poroelastic media in the exploration seismic frequency band is a key issue to improve prospecting precision of surface wave methods to face real-world conditions. Although, the propagation of Rayleigh wave has been studied by several researchers, in consideration of the more difficulty to describe the surface wave, the propagation of surface wave is not sufficiently analyzed as bulk waves. Mesoscopic loss, an important attenuation mechanism in seismic frequency band has not introduced into the surface wave propagation. Therefore, analysis propagation of surface wave in poroelastic media and establishing an effective simple model to approximate the poroelastic model is meanful to for us to acquire some applicable method to introduce poroelasticity in surface wave method. The main aspects include:(1) as the different free surface interfaces, Rayleigh wave in poroelastic media are effected by this difference. It is necessary to analysis the propagation characteristics under the different surface conditions, especially the partial surface condition, which is lack in explicit analysis;(2) an approximate mathematical single phase model of the poroelasticity can simplify the complexity of the expressions of the surface wave, so introduce a single phase effective media could be feasible; and (3) the approximate method of effective media should be verified in numerical and theoretical experiments.
Based on the facts of the studies on the surface wave propagation in poroelastic media, and the problems we face, we studied the characteristics of Rayleigh wave in poroelastic media for different physical conditions and tried to construct a simple approximate model to describe the poroelastic media with the important mesoscopic loss mechanism. In analysis of the propagation, we focused on the following subjects.
(1). We investigated velocity dispersion, attenuation and dynamic response characteristics of Rayleigh waves, and gave the dispersion equations and dynamic Green's functions for different free surface conditions.
(2). We numerical analyzed the dispersion, attenuation curves, wave field and spectral dynamic responses under different surface conditions, viscous damping, elastic properties and porous fluid flowing conditions in seismic frequency band to figure out the characteristics of Rayleigh wave propagation.
(3). We established an effective single phase viscoelastic media to approximate poroelstic media of partial saturation case with the mesoscopic loss mechanism considered. We derived the effective dispersion equation and dynamic Green's functions in a simple expression comparing to poroelastic media.
(4). We also analyzed the dispersion, attenuation characteristics and wave field, spectrum responses of Rayleigh waves in the effective media. The results are compared to that of Biot's model to demonstrate the applicable of the effective model.
By the analysis of the Rayleigh wave, we conclude that:
(1). Different free surfaces of different surface permeabilities for porous fluid at the interface generate the different modes of Rayleigh type surface waves. One mode referred as R1wave exists under all the conditions, as the classical Rayleigh wave in elastic media, the other mode referred as R2wave exists for closed pore and partially permeable surface conditions, the exact propagation characteristics of these two modes of Rayleigh wave are summarized as:
i). R1wave
This surface-wave mode exists for no matter the surface drainage condition changes. The surface-wave mode propagates with strong energy, as the classical Rayleigh wave in elastic media. At the low frequency, the velocities of surface-wave mode are all asymptotic to a same value of the Gassmann effective Rayleigh wave velocity. Velocity dispersion for partially permeable surface is most (slight more than closed pore condition), and for open pore is least. Large fluid viscosity or low permeability (High couple damping coefficient) make the shift to high frequencies of the main dispersion frequency range, and the attenuation coefficient knee points for the different frequency dependence, which represents the relaxation frequency movement to high frequencies. A rigid solid frame skeleton and low fluid flowing condition of large tortuosities weaken the velocity dispersion for all the surface conditions. At high frequencies in seismic frequency band, R1waves propagate with different limited velocity for the three surface cases, respectively. Because the attenuation coefficient is f1dependence at high frequencies, this surface-wave mode shows constant-Q leaky attenuation. R1waves for the open pore condition is most sensitive to the elastic modulus variation, but least sensitive to tortuosoty variation, which also can be represented in the wave fields and spectra changing to other two cases. The partial surface permeability can generates the non-physical R1waves with negative attenuation at low frequency range, which can be effected by the different physical properties. But it has the no distinct reflection in wave fields and spectra. The relaxation frequency shift makes a most attenuation appear at an intermediate couple damping coefficient. For similarity to the classical Rayleigh wave, we can use this surface-wave mode to describe the real world surface wave data. It is noticed that at very low couple damping coefficient, this surface-wave mode radiates with energy loss into the other surface-wave mode for closed pore and partially permeable surface.
ii). R2Wave
This surface-wave mode is only generated by the closed pore and partially permeable free surface. Diffusion at low frequency and a limit velocity at high frequencies in seismic frequency band, this surface-wave mode is similar to the slow P2wave, with slight low velocity and high attenuation. R2wave is sensitive to tortuosity variation as flowing condition changing, high tortuosity diminish the velocity of R2wave velocity with low attenuation. As P2wave in bulk wave seismograms, R2wave is not observed for majority condition. But at very low couple damping coefficient, this surface-wave mode displays. For partially permeable surface, R2wave even bears stronger energy than R1wave, because of radiation of R1wave to the non physical R2wave, the peculiar phenomenon is also reflected in spectra.
(2). Partial saturated or unsaturated porous fluid means the multiphase fluids in the pores, for instance, water and gas. Effective mixture fluid can simply describe these fluids, i.e. Reuss average for uniform isostress condition of homogeneous saturation with equilibrium porous pressure, and Voigt average for macroscopic inhomogeneity with non interactions of the multiphase. These averages reflect the microscopic and macroscopic multiphase fluid distribution, but a mesoscopic scale unhomogeneity between these is very important to the attenuation mechanism in seismic frequency band. Patchy saturation model of porous media can describe this mechanism. In the different patches saturated one type of fluids, when longitudinal wave passes through the different patches, the wave induced flow generates the pressure gradient and P2wave between the interfaces among the different patches saturated with different fluids, and diffusion as a mesoscopic loss mechanism. White (White,1975; White et al.,1975) considered a model of two specific patchy geometry sizes to describe this mesoscopic attenuation, referred as White's patchy saturation model, and built on the Biot's theory. As the S wave propagates in the solid frame skeleton, the combination of P wave and S wave in patchy saturation model generates the effective Rayleigh surface wave at the free surface. The viscoelastic approximation of poroelasticity is established with mesoscopic loss considered
(3). Results of dispersion, attenuation, wave field and spectrum analyses show that, in the dominate frequency of mesoscopic loss of large fluid viscosity or low solid permeability, opposite to the macroscopic mechanism in Biot's theory, Rayleigh wave, couple of P wave and S wave, has the similar dispersion and attenuation characteristics as P wave, but the mesoscopic loss is weakened by the S wave, which is little effected by mesoscopic unhomogeneity. The patch size also effects the dispersion and attenuation by shifting the relaxation frequency. By comparing to fluid average for microscopic and macroscopic unhomogeneity in Biot's theory, the effective viscoelstic approximation is applicable to reflect the mesoscopic loss in Rayleigh wave. The approximation shows us a simple way for poroelasticity to describe dispersion and attenuation for porous media with mesoscopic attenuation in seismic frequency band.
(4). Mesoscopic mechanism is a key factor of effecting the wave propagation in seismic frequency band, which also obviously effects the dispersion and attenuation of surface wave. Introduction the mesoscopic loss into the surface wave method is one of the important perspectives for surface wave technique. The theoretical results of approximation show us a good guide for future work of constructing a simple and applicable guide equation for effective media in seismic modeling and inversion with the mesoscopic unhomogeneity attenuation considered. In order to obtain the velocity dispersion and attenuation of surface wave with the actual fluid distribution scale corresponding the in-situ state of porous media in real world, more exact numerical and physical experiments should be carried on for effectively practical utilizing of poroelasticity in surface wave method.
引文
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