Errors due to the anisotropic-common-ray approximation of the coupling ray theory

The common-ray approximation eliminates problems with ray tracing through S-wave singularities and also considerably simplifies the numerical algorithm of the coupling ray theory for S waves, but may introduce errors in travel times due to the perturbation from the common reference ray. These travel-time errors can deteriorate the coupling-ray-theory solution at high frequencies. It is thus of principal importance for numerical applications to estimate the errors due to the common-ray approximation applied. The anisotropic-common-ray approximation of the coupling ray theory is more accurate than the isotropic-common-ray approximation. We derive the equations for estimating the travel-time errors due to the anisotropic-common-ray (and also isotropic-common-ray) approximation of the coupling ray theory. The errors of the common-ray approximations are calculated along the anisotropic common rays in smooth velocity models without interfaces. The derivation is based on the general equations for the second-order perturbations of travel time.     

线性粘弹介质中地震波场数值模拟

本文将以往两种粘弹介质中地震波模拟方法的优点结合起来，以模型理论和积分本构方程为基础，从理论上分析了模型对地震波场的影响；采用交错网格有限差分法对粘弹介质中的地震波进行数值模拟.数值计算结果表明该方法不仅便于计算，同时也便于从力学的角度来分析地震波的传播.数值计算结果与理论分析一致，说明这种方法可以更为有效地模拟粘弹介质中地震波的传播.     

TTI介质的相速度研究

推导了二维TTI介质的相速度表达式,并且依据推导出来的相速度表达式,模拟并分析了二维TTI介质相速度的传播快照以及TI介质相速度的传播快照;对比并分析了TTI介质和TI介质模型的相速度理论计算值的X分量特征的差异。TTI介质的相速度研究具有较高的理论研究价值和实际应用价值．     

A computational method for approximating a Darcy–Stokes system governing a vuggy porous medium

We develop and analyze a mixed finite element method for the solution of an elliptic system modeling a porous medium with large cavities, called vugs. It consists of a second-order elliptic (i.e., Darcy) equation on part of the domain coupled to a Stokes equation on the rest of the domain, and a slip boundary condition (due to Beavers–Joseph–Saffman) on the interface between them. The tangential velocity is not continuous on the interface. We consider a 2-D vuggy porous medium with many small cavities throughout its extent, so the interface is not isolated. We use a certain conforming Stokes element on rectangles, slightly modified near the interface to account for the tangential discontinuity. This gives a mixed finite element method for the entire Darcy–Stokes system with a regular sparsity pattern that is easy to implement, independent of the vug geometry, as long as it aligns with the grid. We prove optimal global first-order L ² convergence of the velocity and pressure, as well as the velocity gradient in the Stokes domain. Numerical results verify these rates of convergence and even suggest somewhat better convergence in certain situations. Finally, we present a lower dimensional space that uses Raviart–Thomas elements in the Darcy domain and uses our new modified elements near the interface in transition to the Stokes elements.     

采用复合单元法模拟裂隙多孔介质变饱和流动

采用复合单元法建立了模拟裂隙多孔介质变饱和流动的数值模型。该模型具有以下特点：裂隙不需要离散成特定单元，而是根据几何位置插入到孔隙基质单元中形成复合单元；在复合单元中，分别建立裂隙流和孔隙基质流的计算方程，二者通过裂隙?基质界面产生联系并整合成复合单元方程；复合单元方程具有和常规有限单元方程相同的格式，因此，可以使用常规有限单元方程的求解技术。采用欠松弛迭代、集中质量矩阵以及自适应时步调节等技术，开发了裂隙多孔介质变饱和流动计算程序。通过模拟一维干土入渗和复杂裂隙含水层内的流动问题，验证了该模型的合理性和适用性。模拟结果为进一步认识非饱和裂隙含水层地下水流动特性提供了理论依据。     

Comparison of Galerkin-type discretization techniques for two-phase flow in heterogeneous porous media

A comparison of Standard Galerkin, Petrov-Galerkin, and Fully-Upwind Galerkin methods for the simulation of two-phase flow in heterogeneous porous media is presented. On the basis of the coupled pressure-saturation equations, a generalized formulation for all three finite element methods is derived and analysed. For flow in homogeneous media, the Petrov-Galerkin method gives excellent results. But this method fails miserably for problems with heterogeneous media. This is because it is not able to capture correctly processes that take place at interfaces when, for instance, the capillary pressure-saturation relationship after Brooks and Corey is assumed. The Fully-Upwind Galerkin method is superior to the Petrov-Galerkin approach because it is able to give correct results for flow in homogeneous and heterogeneous media for the two models of van Genuchten and Brooks-Corey. The widely used formulation which is correct for the homogeneous case cannot be used for heterogeneous media. Instead the straightforward approach of gradp_c in combination with a chord-slope technique must be utilized.     

General absorbing boundary conditions for dynamic analysis of fluid-saturated porous media

General absorbing boundary conditions based on Biot's two-phase mixture theory and paraxial approximation is presented for the dynamic analysis of fluid-saturated porous media with isotropic, transverse isotropic, and anisotropic properties. For the last two cases, the equivalent Lame's constants, under conditions of uniqueness, are introduced to facilitate the analytical solutions. The numerical results show that the proposed absorbing boundary can greatly suppress spuriously reflected waves and efficiently model the far field of the system with sufficient accuracy.     

Adaptive hierarchical upscaling of flow in heterogeneous reservoirs based on an a posteriori error estimate

This paper treats the upscaling of the absolute permeability in a heterogeneous reservoir. By replacing the fine scale permeability tensor with an upscaled, or effective permeability tensor, a modelling error is introduced. An a posteriori error estimate on this modelling error is formulated and tested. An implementation of the theory, based on domain decomposition coupled with a hierarchical representation of the absolute permeability field, is given. As hierarchical basis functions we have chosen the Haar system, which leads to a wavelet representation of the permeability. The wavelet representation offers a natural upscaling technique which resembles the highcut filters commonly used in signal analysis. This procedure represents an adaptive upscaling method. The numerical results show that this method conserves both the dissipation and the mean velocity in the problem fairly well. The a posteriori error estimate on the modelling error coupled with domain decomposition methods constitutes a powerful modelling tool.     

Velocities of elastic waves andv P/v S ratios in dry and water-saturated rock samples at high pressure

Elastic wave velocities and the ratiov _P/v _S were studied for dry and initially saturated samples of carbonate and crystalline rocks at pressures to 2 kbar. In initially saturated samplesv _P increases in crystalline rock, whereas in sedimentary rock it may either increase or decrease with increasing pressure. Under the same conditionsv _S remains approximately constant in crystalline rocks and decreases in sedimentary samples. The ratiov _P/v _S as a function of pressure increases in dry rocks and decreases in saturated ones. Saturated samples always have higherv _P/v _S ratios than dry ones. It appears that the geometry of the pore space influences the acoustic properties of saturated crystalline rocks.