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ABSTRACT: It is useful to extract all components, including compressional, shear, and guided waves, from the full waveforms when we
investigate the acoustic log data. The component waves can be simulated by calculating the contributions from poles and branch
points of the borehole acoustic function according to Cauchy’s theorem. For such an algorithm to be implemented, the multi-valued
function for the borehole wave field in the frequency-axial-wavenumber domain has to be rendered single-valued first. Assuming
that the borehole axis is parallel to the symmetry axis of transverse isotropy, this paper derives the branch points of the
borehole acoustic function. We discover that the number and the locations of those branch points are determined by the relation
among the formation parameters c
33, c
44, ɛ, and δ. Thus the single-valued definitions in the acoustic-wave computation are sorted into two different cases. After building
the Riemann surface related to each radial wavenumber, we give the single-valued definition of the borehole acoustic function
inside and on the integration contour based on the radiation condition. In a formation with δ > ɛ + c
44/2c
33, if we choose the integration contour and the single-valued definition of the acoustic function in the way used in isotropic
cases, the simulation results of component waves will be wrong.
Keywordsanisotropy-acoustic logging-elastic wave-Riemann sheet
Science China: Physics, Mechanics and Astronomy 04/2012; 53(8):1419-1426. · 0.78 Impact Factor
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ABSTRACT: Dipole acoustic fields in an arbitrarily deviated well penetrating a homogeneous as well as a stratified transversely isotropic formation are simulated using a 3-D finite-difference time-domain algorithm in cylindrical coordinates. The modelling results show that a dipole source can excite a fast- and a slow-flexural mode due to the shear wave anisotropy when the borehole is inclined with respect to the symmetry axis of transverse isotropy. Both flexural slownesses change with the wellbore deviation angle. The splitting of flexural modes is prominent in full wave arrays when the shear anisotropy is strong enough. It is revealed that the dipole orientation influences the relative amplitudes of the fast- and slow-flexural waves but it has no effect on their slownesses or phases. In a vertical well parallel to the symmetry axis, the two flexural waves degenerate and propagate at the same speed. The degenerated flexural wave travels approximately at the shear speed along the borehole wall except in a few formations. Our study shows, for example, that it is about 10 per cent slower than the shear wave in Mesaverde clayshale 5501. Even in that kind of formations, however, extraction of the fast- and slow-shear velocities from the flexural modes is still possible if the borehole deviation is large enough. To examine the effect of layering, we modelled the full waves in a formation with a sandwich. When the well is perpendicular to the layer interfaces, reflection is obvious and can be recognized. It becomes weaker or even invisible as the deviation angle increases, so it is difficult to detect a thin layer embedded in a formation directly from reflected waves. The sandwich can, instead, be recognized from the irregularity in the spectra of the full waveforms displayed versus depth.
Geophysical Journal International 02/2010; 181(1):417 - 426. · 2.42 Impact Factor
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ABSTRACT: Monopole acoustic logs in a homogeneous fluid-saturated porous formation can be simulated by the real-axis integration (RAI) method to analytically solve Biot's equations [(1956a) J. Acoust. Soc. Am. 28, 168-178; (1956b) J. Acoust. Soc. Am. 28, 179-191; (1962) J. Appl. Phys. 33, 1482-1498], which govern the wave propagation in poro-elastic media. Such analytical solution generally is impossible for horizontally stratified formations which are common in reality. In this paper, a velocity-stress finite-difference time-domain (FDTD) algorithm is proposed to solve the problem. This algorithm considers both the low-frequency viscous force and the high-frequency inertial force in poro-elastic media, extending its application to a wider frequency range compared to existing algorithms which are only valid in the low-frequency limit. The perfectly matched layer (PML) is applied as an absorbing boundary condition to truncate the computational region. A PML technique without splitting the fields is extended to the poro-elastic wave problem. The FDTD algorithm is validated by comparisons against the RAI method in a variety of formations with different velocities and permeabilities. The acoustic logs in a horizontally stratified porous formation are simulated with the proposed FDTD algorithm.
The Journal of the Acoustical Society of America 05/2009; 125(4):1942-50. · 1.55 Impact Factor
