起伏地表下基于改进BISQ模型双相介质中曲线网格有限差分法波场模拟

本文以基于改进BISQ模型的二维双相各向同性介质一阶速度-应力方程为基础,推导出了曲线坐标系下对应的方程,然后采用低频散、低耗散的同位网格MacCormack有限差分法来离散方程,并采用紧致的单边MacCormack差分格式结合牵引力镜像法来施加自由地表边界条件,实现了地震波场数值模拟.曲线网格有限差分法采用贴体网格来描述自由表面,地表的网格线紧贴地形,避免了台阶近似造成的数值散射.数值模拟结果表明,在双相介质起伏自由地表和分界面处,各类波型复杂的反射透射规律可以清晰展现,曲线网格有限差分法可以精确地解决地震波在含起伏地表的双相各向同性介质中的传播问题.     

双相介质分界面上弹性波的反射与透射

本文基于Biot理论,推导出Zoeppritz形式的双相介质分界面上弹性波的反射与透射公式,对单相Zoeppritz公式与双相反射系数公式进行了比较,对双相介质含油、水、气不同流体时的反射规律以及孔隙度、渗透率、饱和度等储层参数对纵波反射的影响进行了研究.数值模拟分析表明,双相与单相反射公式的主要差异在于双相介质反射公式中考虑了液相、固液耦合相弹性模量的影响;油砂、水砂、气砂岩的慢P波反射差异明显;快P波反射对孔隙度的变化敏感,饱和度次之,对渗透率和频率的变化不敏感.     

横向各向同性多孔介质中的地震波传播

基于各向异性多孔介质中的广义Ｂｉｏｔ理论，导出了横向各向同性多孔介质中波传播的特征方程．指出在多孔介质中有４种类型的频散和耗散波传播：准纵波ＱＰ１（快纵波）、准纵波ＱＰ２（慢纵波）、准横波ＱＳＶ和横渡ＳＨ．文中给出了４种波速度的解析表达式．数值计算频率曲线和衰减曲线与Ｓｃｈｍｉｔｔ（１９８９）用均值处理得到的结果类似．还给出了波传播过程中３种类型准体波之间的耦合系数（或称转换系数）．     

地震逆散射波场和算子的谱分解

本文对地震逆散射的研究,旨在于为抑制层间多次波和地震波场多重散射对一次反射干扰效应提供理论依据.这对薄互层地层滤波的高频恢复、保幅弹性反演、衍射地震勘探及海洋地震勘探中的干扰消除皆具重要意义.本文基于上下行波分解及弹性波互易定理,导出横向变速介质条件下线性预测算子的表达式和反射数据的广义谱分解方程. 文中先由上覆地层广义反射透射矩阵的元素定义线性预测算子,并将其表示成一系列单程波算子的线性组合,之后将横向变速介质条件下线性预测方程表达为反射数据与线性预测算子及其逆的乘积. 对该方程的求解可获得上覆地层的线性预测算子,从而可借以求出相应的反射透射算子. 本文先将水平层状介质条件下垂直入射的一维线性预测方程推广到斜入射的情况,以此为参照,导出横向非均匀介质条件下反射数据的地震逆散射广义谱分解方程.文中也揭示了单程波地震逆散射算子、反射透射算子的性态.本文还针对水平层状介质条件,给出斜入射的数值结果.     

转换波和非转换波与射线参数p的关系

本文对Aki固体-固体分界面的反射和透射公式进行适当变换,使之成为一组适合不同坐标系下,固体、液体、气体和真空之间所有可能形成的分界面上,入射P、SV和SH波所形成的反射和透射公式,从而把不同边界条件的反射和透射方程统一起来,并且阐明了转换波和非转换波动力学特征的差异.指出:在不同弹性介质分界面上入射平面弹性波,转换波的反射系数和透射系数是射线参数p的奇函数;非转换波的反射系数和透射系数是射线参数p的偶函数.根据奇函数和偶函数的性质可见:垂直入射时不存在转换波.同时也为简化Zoeppricz方程,开展AVO分析打开新思路.     

THE APPLICATION OF PML BOUNDARY CODITIONS IN THE SIMULATION OF SEISMIC WAVE BY THE HIGH-ORDER STAGGERED-GRID FINITE DIFFERENCES AT THE TRANSVERSELY ISOTROPIC MEDIA

In the realm of the numerical simulation, finite difference method and finite element method are more intuitive and effective than other simulation methods. In the process of simulating seismic wave propagation, the finite differences method is widely used because of its high computational efficiency and the advantage of the algorithm is more efficient. With the demand of precision, more and more researchers have proposed more effective methods of finite differences, such as the high-order staggered-grid finite differences method, which can restore the actual process of wave propagation on the premise of ensuring accuracy and improving the efficiency of operation. In the past numerical simulation of seismic wave field, different models of isotropic medium are mostly used, but it is difficult to reflect the true layer situation. With the research demand of natural seismology and seismic exploration, the research on anisotropic media is more and more extensive. Transversely isotropic(TI)media can well simulate the seismic wave propagation in the formation medium, such as gas-bearing sandstone, mudstone, shale et al., the character of TI media is reflected by introducing the Thomsen parameters to reflect its weak anisotropy of vertical direction by using Thomson parameter. Therefore, studying the process of seismic wave propagation in TI media can restore the true information of the formation to the greatest extent, and provide a more reliable simulation basis for the numerical simulation of seismic wave propagation. In the geodynamic simulation and the numerical simulation of the seismic wave field, under the limited influence of the calculation area, if no boundary conditions are added, a strong artificial boundary reflection will be generated, which greatly reduces the validity of the simulation. In order to minimize the influence of model boundaries on the reflection of seismic waves, it is often necessary to introduce absorbing boundary conditions. At present, there are three types of absorption boundary conditions: one-way wave absorption boundary, attenuation absorption boundary, and perfectly matched layer(PML)absorption boundary. In terms of numerical simulation of seismic waves, the boundary absorption effect of PML is stronger than the first two, which is currently the most commonly used method, and it also represents the cutting-edge development direction of absorption boundary technology. The perfectly matched layer absorbing boundary is effectively applied to eliminating the reflective waves from model boundaries, but for transversely isotropic medium, the effect of the absorbing is not very well. For this reason, the elastic dynamic wave equations in transversely isotropic media are derived, and we describe a second-order accurate time, tenth-order accurate space, formulation of the Madariaga-Virieux staggered-grid finite difference methods with the perfectly matched layer(PML)are given. In addition, we have established vertical transversely isotropic(VTI)media and arbitrary inclined tilted transversely isotropic(TTI)media models, using a uniform half-space velocity model and a two-layer velocity model, respectively. By combining the actual geoscience background, we set the corresponding parameters and simulation conditions in order to make our model more research-oriented. When setting model parameters, different PML thickness, incident angle, source frequency and velocity layer models were transformed to verify the inhibition of boundary reflection effect by PML absorption boundary layer. The implementations of this simulation show that the formula is correct and for the transversely isotropic(TI)media of any angular symmetry axis, when the thickness of the PML layer reaches a certain value, the seismic wave reflection effect generated by the artificial boundary can be well suppressed, and the absorption effect of PML is not subject to changes in incident angle and wave frequency. Therefore, the results of our study indicate that our research method can be used to simulate the propagation process of seismic waves in the transversely isotropic(TI)media without being affected by the reflected waves at the model boundary to restore the actual formation information and more valuable geological research.     

直接找油气的地球物理新原理的进展现状

近年来,国际上利用地震反射波勘探技术直接找油气的探索研究受到普遍重视.本文试图针对这一发展历史作一综述. 首先,介绍Knott（1899）和Zoeppritz（1919）分别导出的反射波振幅公式进行的数值计算,从而发现振幅与入射角的变化关系及其受反射面两侧岩层泊松比值的影响.然后,列举了几处油气区地震波勘探直接找油气的实例,以试验此项新原理在实践中所遇到的问题,说明直接找油气的地球物理新方法是可取的,是有前途的,但目前还不够有效,要达到实用还有一段较长的距离,因此,有进一步加强基础性实验研究的必要.     

Extended reflectivity method for modelling the propagation of diffusive–viscous wave in dip‐layered media

The reflectivity method plays an important role in seismic modelling. It has been used to model different types of waves propagating in elastic and anelastic media. The diffusive–viscous wave equation was proposed to investigate the relationship between frequency dependence of reflections and fluid saturation. It is also used to describe the attenuation property of seismic wave in a fluid‐saturated medium. The attenuation of diffusive–viscous wave is mainly characterised by the effective attenuation parameters in the equation. Thus, it is essential to obtain those parameters and further characterise the features of the diffusive–viscous wave. In this work, we use inversion method to obtain the effective attenuation parameters through quality factor to investigate the characteristics of diffusive–viscous wave by comparing with those of the viscoacoustic wave. Then, the reflection/transmission coefficients in a dip plane‐layered medium are studied through coordinate transform and plane‐wave theory. Consequently, the reflectivity method is extended to compute seismograms of diffusive–viscous wave in a dip plane multi‐layered medium. Finally, we present two models to simulate the propagation of diffusive–viscous wave in a dip plane multi‐layered medium by comparing the results with those in a viscoacoustic medium. The numerical results demonstrate the validity of our extension of reflectivity method to the diffusive–viscous medium. The numerical examples in both time domain and time–frequency domain show that the reflections from a dip plane interface have significant phase shift and amplitude change compared with the results of horizontal plane interface due to the differences in reflection/transmission coefficients. Moreover, the modelling results show strong attenuation and phase shift in the diffusive–viscous wave compared to those of the viscoacoustic wave.     

MSH法直接将地球勘探测线转化为深度,密度剖面

根据运动学中的动量守恒定律、分析地震勘探过程中地震波在地下介质中的传播过程,利用反射能量、透射能量与人射能量的计算公式和检波器转化的电信号与地下密度界面反射地震波波动能量的等效原理,推导出直接求层速度和层密度公式。利用某一反射界面直接测得的波速或依据钻孔资料求得的平均速度,在计算机上就可直接计算出各地震测线物性层的埋深和密度（速度、波阻抗）,由此地质工作人员依据已知地质柱状剖面（钻孔资料）可进一步     

含黏性流体孔隙介质分界面上反透射系数特征研究

地下岩石由岩石骨架和孔隙流体组成,通常流体含黏性.地震波在地下介质中传播时受岩石骨架和黏性流体的影响会呈现出复杂的变化.本文将流、固体位移和应力连续作为边界条件,推导出含黏性流体孔隙介质分界面上反透射系数方程;通过建立上层为饱油、下层为饱盐水的砂岩孔隙介质模型,开展反透射系数特征研究,分别分析不同频率、不同黏滞系数条件下,含黏性流体孔隙介质分界面上反透射系数随入射角的变化.研究表明,孔隙介质分界面上和等效介质分界面上的反透射系数分别随入射角的变化趋势基本一致,说明方程推导和数值计算的正确性;快纵波反透射系数受频率、流体黏性的影响较小,而快横波反透射系数在一定入射角范围内受频率、流体黏性的影响比较大;由于黏性孔隙流体的作用,慢纵波和慢横波的反透射系数受入射角、频率及流体黏性的影响都很大.     

热弹性波在层状介质中传播的一类反射问题的解

本文作为基础理论研究, 从热弹性波方程组出发, 求出了热弹性波在层状介质中传播的解析解, 并给出了热弹性波对于平面夹层的反射波, 透射波及其伴随的具有相同传播速度的温度波。此时, 反射系数、 透射系数均为复数表明, 反射波、 透射波的振幅及相位都受介质的物性参数、 夹层厚度及入射波频率的影响。这些与弹性波不同的结果会在地震勘探、 地震工程等有关问题的研究中得到应用。     

Seismic reflection and transmission coefficients at an air-water interface of saturated porous soil

Based on the modified Biot＇s theory of two-phase porous media, a study was presented on seismic reflection and transmission coefficients at an air-water interface of saturated porous soil media. The major differences between air-saturated soils and water-saturated soils were theoretically discussed, and the theoretical formulas of reflection and transmission coefficients at an air-water interface were derived. The characteristics of propagation and attenuation of elastic waves in air-saturated soils were given and the relations among the frequency, the angle of incidence and the reflection, transmission coefficients were analyzed by using numerical methods. Numerical results show that the propagation characteristic of the wave in air-saturated soils is great different from that in water-saturated soils. The frequency and the angle of incidence can have great influences on the reflection and transmission coefficients at interface. Some new cognition about the wave propagation is obtained and the study suggests that we may carefully pay attention to the influence of air on the dynamic analysis of seismic wave.     

平面P-SV波入射时非均匀饱和土 自由场地的响应

基于Biot多孔介质波动模型,研究了非均匀饱和土层对平面P-SV波入射时的动力响应.考虑饱和土地基的物理力学特性沿厚度方向连续变化,利用亥姆霍兹矢量分解原理和动力刚度法,分析了平面入射P-SV波在非均匀饱和土层中的反射和透射,并给出了基岩表面和自由表面处反射系数和透射系数的计算表达式.基于理论推导结果,数值分析了平面SV波入射下非均匀饱和土自由场地的动力响应,其中假设饱和土地基的物理力学性质沿土层深度按幂律梯度变化.数值结果表明,平面SV波入射所引起的地面位移与基岩位移之比均随土层厚度和土体的非均匀程度、波的入射角和入射频率的增加而减小,且其竖向位移比的减小更为显著,厚土层对地震波的耗散作用尤为明显.      

横向各向同性介质拟声波方程及其在逆时偏移中的应用

地下岩石的速度各向异性影响地震波的传播与成像.横向各向同性(TI)介质为最普遍的等效各向异性模型.引入TI介质拟声波方程可以避免复杂的弹性波方程求解以及各向异性介质波场分离,以满足对纵波成像的实际需要.本文从垂直横向各向同性(VTI)介质弹性波方程出发,推导出正应力表达的拟声波方程以及相应的纵波分量的表达式,进而分析从频散关系得到的拟声波方程的物理意义,而后将拟声波方程扩展到更一般的倾斜横向各向同性(TTI)介质中.波前快照与群速度平面的对比验证了拟声波方程可以很好地近似描述qP波的运动学特征.在此基础上,将拟声波方程应用在逆时偏移中并与其特例声波近似方程进行对比,讨论了计算效率、稳定性等实际问题.数值试验表明VTI介质情况下采用声波近似方程可以提高计算效率,而TTI介质qP-qSV波方程则在效率相当的情况下可以保证稳定性.SEG/HESS模型和逆冲模型逆时偏移试验验证了本文TI介质拟声波方程的实用性.     

气枪激发信号传播的谱元法数值模拟研究

为了研究气枪激发信号的波场,本文利用谱元法对双相介质中波的传播做了数值模拟,分析了波的传播特征.本文主要做了以下工作:(1)研究了使用谱无法(SEM)模拟孔隙弹性介质中波的传播,模拟结果表明,采用谱元法能有效解决双相介质的波场传播模拟问题.(2)验证了Biot理论中慢纵波的存在.双相介质中存在明显的慢纵波,流相波场的慢...     

裂缝介质旋转交错网格正演模拟

油气勘探实践表明, 裂缝是油气的储存空间或运移通道, 裂缝介质地震波场的研究越来越受到关注. 实际地层中裂缝形成受多种因素控制, 物理属性比较复杂, 表现出强烈的各向异性. 由于上覆地层的压力使得水平或低陡倾角裂缝存在较少, 大多数为高陡倾角裂缝, 利用线性滑动裂缝介质的等效理论将高陡倾角裂缝介质等效为横向各向同性介质, 便于实际应用. 本文采用各向异性弹性波旋转交错网格模拟方法对含裂缝介质单炮记录进行模拟与分析. 结果表明: 裂缝的存在相当于人为增加反射界面; 裂缝密度越大, 裂缝纵横比越小, 裂缝充填物与背景介质弹性性质差别越大, 引起的反射波能量变化越大. 本文模拟结果为利用地震数据进行裂缝介质参数反演与储层识别及油气预测提供了依据.      

Seismic wavefield modeling in media with fluid-filled fractures and surface topography

We present a finite difference (FD) method for the simulation of seismic wave fields in fractured medium with an irregular (non-flat) free surface which is beneficial for interpreting exploration data acquired in mountainous regions. Fractures are introduced through the Coates-Schoenberg approach into the FD scheme which leads to local anisotropic properties of the media where fractures are embedded. To implement surface topography, we take advantage of the boundary-conforming grid and map a rectangular grid onto a curved one. We use a stable and explicit second-order accurate finite difference scheme to discretize the elastic wave equations (in a curvilinear coordinate system) in a 2D heterogeneous transversely isotropic medium with a horizontal axis of symmetry (HTI). Efficiency tests performed by different numerical experiments clearly illustrate the influence of an irregular free surface on seismic wave propagation in fractured media which may be significant to mountain seismic exploration. The tests also illustrate that the scattered waves induced by the tips of the fracture are re-scattered by the features of the free surface topography. The scattered waves provoked by the topography are re-scattered by the fractures, especially Rayleigh wave scattering whose amplitudes are much larger than others and making it very difficult to identify effective information from the fractures.     

2D finite-difference viscoelastic wave modelling including surface topography

We have pursued two-dimensional (2D) finite-difference (FD) modelling of seismic scattering from free-surface topography. Exact free-surface boundary conditions for the particle velocities have been derived for arbitrary 2D topographies. The boundary conditions are combined with a velocity–stress formulation of the full viscoelastic wave equations. A curved grid represents the physical medium and its upper boundary represents the free-surface topography. The wave equations are numerically discretized by an eighth-order FD method on a staggered grid in space, and a leap-frog technique and the Crank–Nicholson method in time.
In order to demonstrate the capabilities of the surface topography modelling technique, we simulate incident point sources with a sinusoidal topography in seismic media of increasing complexities. We present results using parameters typical of exploration surveys with topography and heterogeneous media. Topography on homogeneous media is shown to generate significant scattering. We show additional effects of layering in the medium, with and without randomization, using a von Kármán realization of apparent anisotropy. Synthetic snapshots and seismograms indicate that prominent surface topography can cause back-scattering, wave conversions and complex wave patterns which are usually discussed in terms of inter-crust heterogeneities.     

三维层状孔隙介质中弹性波的一种积分表达式I：理论

孔隙介质弹性波传播理论在地球物理勘探、地震工程和岩土动力学等领域有着广泛的应用.而孔隙介质中的弹性波受孔隙度、渗透率、流体黏滞系数等参数的影响,因此研究波场的传播特征将有助于分析和提取这些信息.本文在Biot理论的基础上,针对三维层状孔隙介质模型,利用在合成理论地震图的研究中已经被证实具有稳定、高效且适用范围较广的Luco-Apsel-Chen（LAC）广义反透射方法,给出了弹性波场的一种积分形式的半解析解,可通过数值方法高效、准确地计算层状孔隙介质中的理论波场,所以该积分形式的半解析解可为三维层状孔隙介质波场传播特征的理论数值模拟研究提供一种新的途径和手段.     

Wavefield simulation in porous media saturated with two immiscible fluids

Wavefields in porous media saturated by two immiscible fluids are simulated in this paper. Based on the sealed system theory, the medium model considers both the relative motion between the fluids and the solid skeleton and the relaxation mechanisms of porosity and saturation (capillary pressure). So it accurately simulates the numerical attenuation property of the wavefields and is much closer to actual earth media in exploration than the equivalent liquid model and the unsaturated porous medium model on the basis of open system theory. The velocity and attenuation for different wave modes in this medium have been discussed in previous literature but studies of the complete wave-field have not been reported. In our work, wave equations with the relaxation mechanisms of capillary pressure and the porosity are derived. Furthermore, the wavefield and its characteristics are studied using the numerical finite element method. The results show that the slow P3-wave in the non-wetting phase can be observed clearly in the seismic band. The relaxation of capillary pressure and the porosity greatly affect the displacement of the non-wetting phase. More specifically, the displacement decreases with increasing relaxation coefficient.