| Summary: | The wavefields generated by monopole and dipole sources in a fluid filled borehole embedded in multilayered transversely isotropic saturated porous formations are studied.
The layers are modeled following Biot theory modified in accordance with homogenization
theory. It allows to take into account a transversely isotropic skeleton and/or
a transversely isotropic complex permeability tensor. Their axes of symmetry are assumed
to coincide, parallel to the vertical axis of the borehole. A general formulation,
valid for any order of multipole source and based on the Thomson Haskell method,
allows to take into account any combimi.tion of elastic and saturated porous layers,
either isotropic or transversely isotropic. The presence of an external fluid layer is also possible. The study focuses on the modes behavior. It is achieved through the computation of dispersion and attenuation curves, sensitivity coefficients with respect to the stiffness constants of the skeleton(s), and full waveform synthetic microseismograms using the discrete wavenumber method.
In the simple hole model with an impermeable borehole wall, whatever the type
of the formation (fast or slow), the behavior of the modes is analogous to that in the
presence of simple elastic formations with body wave attenuations added. The phase
velocity of the Stoneley wave generated by a monopole source is sensitive to the horizontally propagating SH-wave velocity. Such a coupling decreases with increasing
frequency and stiffness of the formation. The low frequency part of the zero-th order
(Le., flexural) mode generated by a multi(di)pole source measures the vertically propagating SV-wave velocity. The shear wave anisotropy may then be evaluated. With
a fast formation, the vertically propagating SV-wave velocity can also be obtained from the low frequency (high velocity) part of the pseudo-Rayleigh mode generated
by the monopole source. The anisotropy of the complex permeability tensor cannot
be detected. Moreover, only the attenuation of the vertically propagating P wave is
sensitive to the only vertical permeability. Any anelastic (anisotropic) attenuation will
supersede the latter.
When the borehole wall is permeable, the fluid flow which takes place at the interface
refers to the horizontal mobility (I.e., horizontal permeability/saturant fluid
viscosity). Assuming greater horizontal velocities, the decrease of the Stoneley wave
phase velocity and the increase of its low frequency attenuation are enhanced. The
shear wave transverse isotropy cannot be anymore detected and any estimation of the
horizontal permeability based on Stoneley wave characteristics may become questionable
with a high anisotropy degree of the skeleton. However, detection of permeability
variation may still be reasonably performed.
In the presence of an invaded zone, whatever the boundary conditions at the borehole
wall, Stoneley wave integrates the properties of the inner layer in the entire frequency
range. This coupling phenomenon increases with increasing thickness and
decreasing body wave velocities of the inner layer. As a result, both estimations of the
shear wave transverse anisotropy and the permeability of the virgin formation from
the Stoneley wave characteristics are ill posed. Of course, such a result hold true in a
cased borehole, whatever the quality of the bonding. In any of the multilayered configuration, the low frequency part of both the flexural mode and the pseudo-Rayleigh
mode, when it exists, measures the characteristics of the vertically propagating SV
wave of the virgin formation. Such an interesting information may be however difficult
to extract.
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