Elastic wave propagation along a borehole in an anisotropic medium

Ellefsen, Karl J.

doi:10.1190/1.1890038

Cited by 31 publications

(20 citation statements)

References 71 publications

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“…The finite difference method (FDM) [11][12][13][14][15][16], the finite element method (FEM) [17][18][19], the boundary integral approach [20], the boundary element method (BEM) [21,22] and hybrid methods [23][24][25] are some of the techniques most often used.…”

Section: Introductionmentioning

confidence: 99%

3D elastic wave propagation modelling in the presence of 2D fluid-filled thin inclusions

Tadeu

Amado-Mendes

António

2006

Engineering Analysis with Boundary Elements

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In this paper, the traction boundary element method (TBEM) and the boundary element method (BEM), formulated in the frequency domain, are combined so as to evaluate the 3D scattered wave field generated by 2D fluid-filled thin inclusions. This model overcomes the thin-body difficulty posed when the classical BEM is applied. The inclusion may exhibit arbitrary geometry and orientation, and may have null thickness. The singular and hypersingular integrals that appear during the model's implementation are computed analytically, which overcomes one of the drawbacks of this formulation. Different source types such as plane, cylindrical and spherical sources, may excite the medium. The results provided by the proposed model are verified against responses provided by analytical models derived for a cylindrical circular fluid-filled borehole.The performance of the proposed model is illustrated by solving the cases of a flat fluid-filled fracture with small thickness and a fluid-filled Sshaped inclusion, modelled with both small and null thickness, all of which are buried in an unbounded elastic medium. Time and frequency responses are presented when spherical pulses with a Ricker wavelet time evolution strikes the cracked medium. To avoid the aliasing phenomena in the time domain, complex frequencies are used. The effect of these complex frequencies is removed by rescaling the time responses obtained by first applying an inverse Fourier transformation to the frequency domain computations. The numerical results are analysed and a selection of snapshots from different computer animations is given. This makes it possible to understand the time evolution of the wave propagation around and through the fluid-filled inclusion. q

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Section: Introductionmentioning

confidence: 99%

3D elastic wave propagation modelling in the presence of 2D fluid-filled thin inclusions

Tadeu

Amado-Mendes

António

2006

Engineering Analysis with Boundary Elements

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“…This work examines two different formations (see Table 1), identical to the ones used by Ellefsen [13] in his studies on the determination of the phase and group velocities of a fluid-filled circular borehole.…”

Section: Numerical Applicationsmentioning

confidence: 99%

Influence of the cross-section geometry of a cylindrical solid submerged in an acoustic medium on wave propagation

Pereira¹,

Tadeu²,

António³

2002

Wave Motion

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This paper studies wave propagation in the vicinity of a cylindrical solid formation submerged in an acoustic medium generated by point blast loads placed outside the inclusion. The full 3D solution is obtained first in the frequency domain as a discrete summation of responses for 2D problems defined by a spatial Fourier transform. Each 2D solution is computed using the Boundary Element Method, which makes use of two-and-a-half-dimensional Green's functions. This model is implemented to obtain Fourier spectra responses which make it possible to identify the behavior of both the axisymmetric and non-axisymmetric guided wave modes, when the cross-section of the elastic inclusion changes from circular to smooth oval.When the cylindrical elastic inclusion is submerged in a fluid, thus allowing a dilatational wave velocity greater than the shear wave velocity of the elastic medium (slow formation), our computations show a progressively slower flexural wave and the increased importance of a second flexural mode as the ovality of the inclusion becomes more pronounced. The waves associated with the screw mode become less important as the ovality ratio of the inclusion increases.When the formation is fast (the shear wave velocity of the cylindrical solid inclusion is faster than the pressure wave velocity of the fluid), the responses again indicate a progressively slower flexural wave, as the inclusion becomes more oval. The results computed at the receivers placed on the axis appear to be weakly affected by the ovality ratio of the inclusion.

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“…The examples provided in this work consider fluid-filled boreholes (radius 0.1016 m) placed inside a fast or slow formation, as studied by Ellefsen (1990), with the properties listed in Table 1. Frequency and time results are displayed.…”

Section: Numerical Applicationsmentioning

confidence: 99%

The use of monopole and dipole sources in crosswell surveying

António

Tadeu

2004

Journal of Applied Geophysics

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This paper implements a boundary element method (BEM) solution, formulated in the frequency domain, to simulate the crosswell S wave surveying technique. In this technique, one fluid-filled borehole hosts the source, and the other the receivers. The system is excited by a monopole or a dipole source placed near the first wall of the borehole wall, while the pressure field is recorded in the second borehole. The three-dimensional solution is computed as a summation of 2.5D solutions for different axial wave numbers. This model is used to assess the influence of the distance between boreholes and the material properties of the medium on the pressure field generated in the second borehole. Slow and fast formations are both simulated. It was found that the responses recorded the contribution of the non-dispersive body waves (the dilatational (P) and shear (S) waves) as well as the effect of dispersive waves associated with different wave modes. The final time solutions are thus intricate, exhibiting wave patterns that may make it difficult to interpret the arrival times of the refracted P and S waves. D

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Elastic wave propagation along a borehole in an anisotropic medium

Cited by 31 publications

References 71 publications

3D elastic wave propagation modelling in the presence of 2D fluid-filled thin inclusions

3D elastic wave propagation modelling in the presence of 2D fluid-filled thin inclusions

Influence of the cross-section geometry of a cylindrical solid submerged in an acoustic medium on wave propagation

The use of monopole and dipole sources in crosswell surveying

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