Two-Dimensional inversion of triaxial induction logging data in transversely isotropic formation

2015 ◽  
Author(s):  
Su Yan ◽  
Gong Li Wang ◽  
Aria Abubakar
Keyword(s):  
Transversely Isotropic ◽  
Two Dimensional ◽  
Induction Logging

A weak-anisotropy approximation to multicomponent induction responses in cross-bedded formations

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. F61-F66 ◽  
Author(s):  
Tsili Wang
Keyword(s):  
Apparent Resistivity ◽  
Transversely Isotropic ◽  
Anisotropy Ratio ◽  
Weak Anisotropy ◽  
Bedding Planes ◽  
Geometric Average ◽  
Induction Logging ◽  
Anisotropic Formation ◽  
The Cross

The multicomponent induction logging response to a cross-bedded formation has been modeled under a weak-anisotropy approximation. With the approximation, a cross-bedded formation can be modeled as a transversely isotropic (TI) medium. The validity of the approximation has been tested for the main (coplanar and coaxial) components of the induction response. The conditions for the weak-anisotropy approximation to be valid depend on the component of the response. For the coplanar components, the approximation is valid for an anisotropy ratio up to 2 if the relative dipping angle between the cross-bedded formation and the borehole axis is below [Formula: see text]. For the coaxial component, the approximation reduces to a previously established result that the apparent resistivity for such a component is the geometric average of the resistivities, parallel and perpendicular to the bedding planes of an anisotropic formation, respectively, if the borehole is ignored. Hence, the approximation holds for the coaxial component regardless of the anisotropy ratio.

Plane Electromechanical Fieldes in a Piezoelectric Material with a Crack

2006 ◽  
Vol 324-325 ◽  
pp. 247-250
Author(s):  
Shu Hong Liu ◽  
Meng Wu ◽  
Shu Min Duan ◽  
Hong Jun Wang
Keyword(s):  
Boundary Condition ◽  
General Solution ◽  
Piezoelectric Material ◽  
Mechanical Load ◽  
Electric Displacement ◽  
Transversely Isotropic ◽  
Two Dimensional ◽  
Electric Boundary Condition ◽  
Boundary Collocation Method ◽  
Transversely Isotropic Piezoelectric Material

A two-dimensional electromechanical analysis is performed on a transversely isotropic piezoelectric material containing a crack based on the impermeable electric boundary condition. By introducing stress function, a general solution is provided in terms of triangle series. It is shown that the stress and electric displacement are all of 1/2 order singularity in front of the crack tip. In addition, the electromechanical fields in the vicinity of the crack when subjected to uniform tensile mechanical load are obtained using boundary collocation method.

Transient fundamental solutions for a transversely isotropic elastic half space

1993 ◽  
Vol 442 (1916) ◽  
pp. 505-531 ◽  
Keyword(s):  
Half Space ◽  
Transient Response ◽  
Analytical Solutions ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Integral Transforms ◽  
Fundamental Solutions ◽  
Elastic Half Space ◽  
Kernel Functions ◽  
Two Dimensional

This paper is concerned with the study of transient response of a transversely isotropic elastic half-space under internal loadings and displacement discontinuities. Governing equations corresponding to two-dimensional and three-dimensional transient wave propagation problems are solved by using Laplace–Fourier integral transforms and Laplace−Hankel integral transforms, respectively. Explicit general solutions for displacements and stresses are presented. Thereafter boundary-value problems corresponding to internal transient loadings and transient displacement discontinuities are solved for both two-dimensional and three-dimensional problems. Explicit analytical solutions for displacements and stresses corresponding to internal loadings and displacement discontinuities are presented. Solutions corresponding to arbitrary loadings and displacement discontinuities can be obtained through the application of standard analytical procedures such as integration and Fourier expansion to the fundamental solutions presented in this article. It is shown that the transient response of a medium can be accurately computed by using a combination of numerical quadrature and a numerical Laplace inversion technique for the evaluation of integrals appearing in the analytical solutions. Comparisons with existing transient solutions for isotropic materials are presented to confirm the accuracy of the present solutions. Selected numerical results for displacements and stresses due to a buried circular patch load are presented to portray some features of the response of a transversely isotropic elastic half-space. The fundamental solutions presented in this paper can be used in the analysis of a variety of transient problems encountered in disciplines such as seismology, earthquake engineering, etc. In addition these fundamental solutions appear as the kernel functions in the boundary integral equation method and in the displacement discontinuity method.

Fundamental solution for a two-dimensional problem in transversely isotropic micropolar thermoelastic media

2017 ◽  
Vol 13 (3) ◽  
pp. 409-423 ◽  
Author(s):  
Vijay Chawla ◽  
Sanjeev Ahuja ◽  
Varsha Rani
Keyword(s):  
General Solution ◽  
Fundamental Solution ◽  
Heat Source ◽  
Harmonic Functions ◽  
Transversely Isotropic ◽  
Fundamental Solutions ◽  
Two Dimensional ◽  
Point Heat Source ◽  
Content Type ◽  
Thermoelastic Material

Purpose The purpose of this paper is to study the fundamental solution in transversely isotropic micropolar thermoelastic media. With this objective, the two-dimensional general solution in transversely isotropic thermoelastic media is derived. Design/methodology/approach On the basis of the general solution, the fundamental solution for a steady point heat source on the surface of a semi-infinite transversely isotropic micropolar thermoelastic material is constructed by six newly introduced harmonic functions. Findings The components of displacement, stress, temperature distribution and couple stress are expressed in terms of elementary functions. From the present investigation, a special case of interest is also deduced and compared with the previous results obtained. Practical implications Fundamental solutions can be used to construct many analytical solutions of practical problems when boundary conditions are imposed. They are essential in the boundary element method as well as the study of cracks, defects and inclusions. Originality/value Fundamental solutions for a steady point heat source acting on the surface of a micropolar thermoelastic material is obtained by seven newly introduced harmonic functions. From the present investigation, some special cases of interest are also deduced.

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