Quasi-Rayleigh Waves in Transversely Isotropic Half-Space with Inclined Axis of Symmetry

A method for determination of characteristics of quasi-Rayleigh (qR) wave in a transversely isotropic homogeneous half-space with inclined axis of symmetry is outlined. The solution is obtained as a superposition of qP, qSV and qSH waves, and surface wave velocity is determined from the boundary conditions at the free surface and at infinity, as in case of Rayleigh wave in an isotropic half-space. Though the theory is simple enough, a numerical procedure for calculation of surface wave velocity presents some difficulties. The difficulty is caused by necessity to calculate complex roots of a non-linear equation, which in turn contains functions determined as roots of non-linear equations with complex coefficients. Numerical analysis shows that roots of the equation corresponding to the boundary conditions do not exist in the whole domain of azimuths and inclinations of the symmetry axis. The domain of existence of qR wave depends on the ratio of the elastic parameters: for some strongly anisotropic models the wave cannot exist at all. For some angles of inclination qR-wave velocities deviate from those calculated on the basis of the perturbation method valid for weak anisotropy, though they have the same tendency of variation with azimuth. The phase of qR wave varies with depth unlike Rayleigh wave in an isotropic half-space. Unlike Rayleigh wave in an isotropic half-space, qR wave has three components - vertical, radial and transverse. Particle motion in horizontal plane is elliptic. Direction of the major axis of the ellipsis coincides with the direction of propagation only in azimuths 0° (180°) and 90° (270°).     

The reflection and transmission of elastic waves at a interface between a transversely isotropic elastic soils and saturated soils

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Amplitude variation with incident angle and azimuth inversion for Young's impedance,Poisson's ratio and fracture weaknesses in shale gas reservoirs

By analogy with P- and S-wave impedances, the product of Young's modulus and density can be termed as Young's impedance, which indicates the rock lithology and brittleness of unconventional hydrocarbon reservoirs. Poisson's ratio is also an effective indicator of rock brittleness and fluid property of unconventional reservoirs, and fracture weaknesses indicate the fracture properties (fracturing intensity and fracture fillings) in fracture-induced unconventional reservoirs. We aim to simultaneously estimate the Young's impedance, Poisson's ratio and fracture weaknesses from wide-azimuth surface seismic data in a fracture-induced shale gas reservoir, and use the horizontal transversely isotropic model to characterize the fractures. First, the linearized PP-wave reflection coefficient in terms of Young's impedance, Poisson's ratio, density and fracture weaknesses is derived for the case of a weak-contrast interface separating two weakly horizontal transversely isotropic media. In addition, an orthorhombic anisotropic case is also discussed in this paper. Then a Bayesian amplitude variation with incident angle and azimuth scheme with a model constraint is used to stably estimate Young's impedance, Poisson's ratio and fracture weaknesses with only PP-wave azimuthal seismic data. The proposed approach is finally demonstrated on both synthetic and real data sets with reasonable results.     

Triaxial behaviour of transversely isotropic materials: application to sedimentary rocks

Failure and long‐term behaviour of oriented solids are studied. Transversely isotropic materials are considered and a mathematical formulation that respect the material symmetry is developed and applied to model the triaxial behaviour of sedimentary rocks. Two failure criteria and a viscoplastic constitutive model that describe, respectively, triaxial failure and triaxial creep tests are presented and discussed. The application of the developed models to describe the mechanical behaviour of Tournemire shale shows that theoretical predictions are in good agreement with the experimental data. In the present paper, the developed approach is applied to sedimentary rock materials, nevertheless, it can be generalized to any material that exhibits transverse isotropy. Copyright © 2007 John Wiley & Sons, Ltd.     

Axisymmetric interaction of a rigid disc with a transversely isotropic half‐space

A theoretical formulation is presented for the determination of the interaction of a vertically loaded disc embedded in a transversely isotropic half‐space. By means of a complete representation using a displacement potential, it is shown that the governing equations of motion for this class of problems can be uncoupled into a fourth‐order partial differential equation. With the aid of Hankel transforms, a relaxed treatment of the mixed‐boundary value problem is formulated as dual integral equations, which, in turn, are reduced to a Fredholm equation of the second kind. In addition to furnishing a unified view of existing solutions for zero and infinite embedments, the present treatment reveals a severe boundary‐layer phenomenon, which is apt to be of interest to this class of problems in general. The present solutions are analytically in exact agreement with the existing solutions for a half‐space with isotropic material properties. To confirm the accuracy of the numerical evaluation of the integrals involved, numerical results are included for cases of different degrees of the material anisotropy and compared with existing solutions. Further numerical examples are also presented to elucidate the influence of the degree of the material anisotropy on the response. Copyright © 2009 John Wiley & Sons, Ltd.     

Static analysis of vertically loaded pile group in multilayered transversely isotropic soils

In this paper, a coupling approach is presented to study the static responses of vertically loaded pile group embedded in multilayered transversely isotropic soils. The individual pile in pile group is modeled by the finite element method, while the analytical layer-element method is applied to represent the soil's behavior. Then, the interaction equation of piles and soils is obtained by considering the force equilibrium and displacement compatibility conditions and solved by a FORTRAN program. The results computed by the proposed approach compare favorably with those from some existing solutions and field test. Some typical parametric analysis cases are investigated to study the effect of soil anisotropy, pile stiffness ratio, and pile spacing on the behavior of vertically loaded pile group.     

煤体中直立裂隙的多波地震响应及预测

裂隙探测是煤层气勘探开发与煤矿安全生产的重要研究内容。规则发育的直立裂隙在理论上可等效为具有水平对称轴的横向各向同性（HTI）介质,本文通过正演记录研究了HTI介质的多波地震响应,分析了裂隙发育方位对横波偏振特性的影响规律,在此基础上分析了利用横波记录的方位角道集获取地下裂隙参数的可行性与基本原理,为便于工业应用,文中研究了一种基于两个水平分量叠加剖面的角度扫描法求取地下目标煤层的裂隙发育方位。实际资料处理证明了该方法的准确性与可靠性。