Triclinic Half-space Research Articles

Reflection phenomena of plane wave at an initially stressed nonlocal triclinic half-space with stress-free interface

Reflection phenomena of plane wave at an initially stressed nonlocal triclinic half-space with stress-free interface

Tuning effects of a thin layer with triclinic anisotropy

Tuning effects, induced by the interference between scattering waves at the top and bottom interfaces, characterize the dependence of thin-layer seismic responses on wave frequencies, thin-layer thicknesses, and medium elastic properties. The characteristics of tuning effects are frequently used to infer thin-layer properties. We analyze the tuning effects of a thin triclinic layer between two varying triclinic half-spaces. Exact thin-layer reflection and transmission (R/T) coefficients are developed to characterize the prestack thin-layer tuning effects of P, S1, and S2 waves. The thin-layer R/T coefficient approximations are developed to build concise relationships between tuning effect characteristics and medium parameters. The relationships give insights when estimating thin-layer properties from interpreting tuning effect characteristics. As inferred from the approximations, the tuning effect of a thin triclinic layer is composed of two fundamental tuning effects that make sense for two particular thin-layer models wherein one has identical enclosing half-spaces and the other has identical elastic parameter discontinuities at the bottom and top interfaces. The combined influence of wave frequencies, thin-layer thicknesses, and incidence angles on the two fundamental tuning effects can be assessed by a unique factor for each wave mode. For a general thin triclinic layer, this factor characterizes the periodic variations of reflection amplitudes versus wave frequencies. The maximum and minimum thin-layer reflection amplitudes are determined by the reflectivities at the top and bottom interfaces. With wave frequencies or thin-layer thicknesses increasing from zero, thin-layer reflections have smaller or larger amplitudes when the two single-interface reflectivities have equal or opposite polarities, respectively. We develop a method to evaluate the sensitivity of thin-layer reflection amplitudes to thin-layer elastic parameters. The sensitivity is higher when the two single-interface reflectivities have opposite polarities compared with the equal-polarity case. Numerical tests are used to demonstrate our approximation accuracy and the characteristics of tuning effects.

On reflection and transmission of qP waves in initially stressed viscoelastic triclinic layer between distinct triclinic geomedia with sliding interface

The present study dwells with the propagation of quasi seismic qP waves in an initially stressed highly anisotropic viscoelastic triclinic layer which is in sliding contact with the upper initially stressed viscoelastic triclinic half-space. The propagation characteristics of all the reflected/transmitted wave generated by the incident qP wave through initially stressed viscoelastic triclinic substratum have been analysed in detail. Closed-form analytical expressions for reflection/transmission (RT) angles, velocity and coefficients of all the propagating waves have been derived. Effects of incident angle, layer width, initial stress and sliding parameter have been analysed and shown graphically. The energy ratio and slowness diagram have also been calculated and depicted graphically. Particular cases of free and fixed welded interface are analysed and drawn for validating the results of numerical simulation. Present work may be useful in domain with highly anisotropic viscoelastic geomedia equipped with initial stress and imperfect bonding between different interfaces such as transform-fault boundary.

Reflection of three-dimensional plane waves at the free surface of a rotating triclinic half-space under the context of generalized thermoelasticity

Reflection of three-dimensional plane waves at the free surface of a rotating triclinic half-space under the context of generalized thermoelasticity

Reflection and transmission coefficient approximations for P, S1 and S2 waves in triclinic media

SUMMARY The conventional assumptions, in most published approximations of the reflection and transmission (R/T) coefficients of plane waves at a plane interface between two anisotropic half-spaces, confine their applications to weakly anisotropic and/or weak contrast models. We consider the horizontal interface enclosed by two triclinic half-spaces to approximate the R/T coefficients normalized by the vertical energy flux. The homogeneous background medium can be anisotropic with arbitrary symmetry to better simulate the strongly anisotropic media. The second-order approximations are proposed to accommodate the strong contrast interface. We also consider an isotropic background medium under the weak anisotropy assumption. The obtained approximations can be applied to P, S1 and S2 waves, except for the transmission coefficients between the S1 and S2 waves. The S-wave transmission coefficients are insensitive to the model parameter contrasts and predominately rely on the S-wave polarization directions in the half-spaces above and below the interface. The proposed approximations are tested numerically.

Scattering of plane-wave through fluid medium of finite width between self-reinforced and triclinic half spaces

The appearance of scattering (reflection and transmission phenomena) in three-dimensional plane-waves incident at a triclinic half space superimposed by the fluid layer underneath a self- reinforced half space is discussed thoroughly. The techniques of Christoffel equation and Cardon's method are applied to analyze the theoretical and numerical results. Closed form solution for reflection and refraction coefficient of plane waves is accomplished. Reflection and refraction curves are sketched for plane-waves by adjusting some significant values. The concepts of energy ratio, critical angle and conservation of energy are introduced. A closed form solution for velocity profile and reflection/refraction coefficients of all reflected and refracted waves is obtained along with numerical simulation. The effect of incidence angle on reflection/transmission angle is discussed thoroughly. The graphs of energy ratio, velocity profile, reflection and refraction coefficient for a plane-wave is determined.

Dynamics of seismic waves in highly anisotropic triclinic media with intermediate monoclinic layer

• Seismic waves in the monoclinic layer between triclinic half spaces are studied. • Analytical expressions for the velocity profile of all scattered waves are derived. • Critical angles for incident quasi P/SV waves are found to be different. • Reflection/transmission coefficients for all quasi P/SV/SH waves are obtained. • Four published results are deduced as particular cases to present study. The propagation patterns of an incident quasi-longitudinal/transverse seismic wave in an intermediate monoclinic layer between highly anisotropic distinct triclinic half – spaces are analysed. Velocity profile of the incident/scattered seismic wave has been found analytically along with closed-form solutions for reflection/transmission coefficients. Velocity profiles for both the unconstrained and constrained geometries are plotted against propagation direction. The critical angle for both the incident quasi P/SV waves is computed and simulations are then performed to further study the effect of relevant parameters on phase velocities and coefficients for lithium niobate monoclinic material between triclinic media. Four published results on reflection/transmission phenomena of quasi P/SV waves are derived as particular cases to present study.

Scattering of three-dimensional plane waves in a self-reinforced half-space lying over a triclinic half-space

Scattering of three-dimensional plane waves in a self-reinforced half-space lying over a triclinic half-space

Plane wave propagation in a 3D anisotropic half-space under Green-Naghdi theory II

In this paper, the theory of coupled thermoelasticity in three dimension is employed for triclinic half-space, subjected to time dependent heat source on the boundary of the space which is traction free and is considered in the context of Green-Naghdi model of type II (thermoelasticity without energy dissipation) of generalized thermoelasticity. Normal mode analysis is used to the non-dimensional coupled equations. Finally, the resulting equations are written in the form of a vector-matrix differential equation which is then solved by eigenvalue approach. Numerical results for the temperature, thermal stresses, and displacements are presented graphically and analyzed. Mathematical results shown in thermoelastic curves were supplemented by tectonic movements of elastic lithospheric plates.

Reflection and Transmission of a Three-Dimensional Plane qP Wave through a Layered Fluid Medium between Two Distinct Triclinic Half-Spaces

AbstractThis paper discusses reflection and transmission phenomena of a three-dimensional (3D) plane quasi-P (qP) wave incident at a triclinic half-space superimposed by a fluid layer underneath another distinct triclinic half-space. The closed-form expressions are obtained for reflection and transmission coefficients of corresponding reflected and transmitted waves. These reflection and transmission coefficients are computed numerically and shown graphically for fixed values of relevant parameters. Certain problems have been discussed as special cases to the present problem. The findings of the current study can be used to analyze problems with similar geometry in different elastic mediums, such as monoclinic, transversely isotropic, and isotropic.

Reflection and refraction of plane quasi-P waves at a corrugated interface between distinct triclinic elastic half spaces

The reflection and refraction pattern of elastic waves at a corrugated interface between two triclinic half-spaces is discussed. The incident wave is taken to be the cause of the interface disturbance and the reflected and refracted waves are effects. This leads to the causality requirement that the reflected and refracted waves must propagate away from the interface. Closed form expressions of reflection and transmission coefficients are derived using Rayleigh’s method of approximation. The formulae of reflection and transmission coefficients are derived in closed form for the first-order approximation of the corrugation. The analytical expressions of all the three phase velocities of qP, qSV and qSH waves have been derived. The variation of reflection and refraction coefficients with the angle of incidence and also with the corrugation parameter is shown. In this paper we have developed Graphical User Interface (GUI) Software in MATLAB which shows the variation of reflection and refraction coefficients with respect to incident angle and corrugation parameter. This software can be generalized to show the variation of reflection and refraction coefficients. Numerical computations are performed for a scientific model and the results obtained are shown graphically.

Calculation of reflection and transmission coefficients for qP waves incident on a planar interface between isotropic and triclinic media

In the paper by Chattopadhyay and Rajneesh (2006, “Reflection and refraction of waves at the interface of an isotropic medium over a highly anisotropic medium’, Acta Geophysica, vol. 54, no. 3, pp. 239–249), the authors proposed a process to calculate R/T (reflection and transmission) coefficients at the interface between isotropic and triclinic half-spaces, with incident qP waves in triclinic media. Unfortunately, besides several misprints, the authors made a fatal assumption that there is no transmitted SH wave generated in isotropic media, which led the successive analytical derivations and numerical calculations thoroughly wrong. In this paper, the errors are analyzed at length and corrections are given. Then an alternative approach to solve the problem is proposed and numerical results are shown and discussed.

Direct 3D BEM for scattering of elastic waves in a homogeneous anisotropic half-space

A direct 3D time-harmonic boundary element method is applied to determine the elastic response of a cavity of arbitrary shape embedded within a 3D homogeneous triclinic half-space. The boundary integral equations for scattered wave field are used in the boundary element method (BEM). Because of the full-space fundamental solutions in the formulation, the traction-free conditions on the half-space surface must be imposed separately. Numerical testing is performed for a 3D isotropic case in order to obtain the size of the half-space discretization surface that ensures the accuracy of the results. Applications are discussed for scattering of elastic waves by a semispherical canyon. The results show that the anisotropic response strongly depends on the incident wave, the material anisotropy and the location of the observation points.