Acoustic multipole logging in transversely isotropic poroelastic formations

The properties of the modes generated by multipole sources in a fluid-filled borehole embedded in (radially layered) formations that include transversely isotropic poroelastic layers are investigated. These layers are modeled following Biot’s and homogenization theories, under the assumption that the principal axes of symmetry of both the transversely isotropic skeleton and the complex permeability tensor are parallel to the vertical axis of the borehole. A general formulation based on the Thomson–Haskell method accounts for any combination of fluid, elastic, and poroelastic layers, either isotropic or transversely isotropic. The investigation is achieved through the computation of dispersion and attenuation curves, and frequency-dependent sensitivity coefficients with respect to the parameters. In the presence of a fast or slow radially semi-infinite transversely isotropic poroelastic formation with an impermeable borehole wall, the shear-wave transverse isotropy of the skeleton can be determined using the low-frequency parts of the fundamental modes generated by a monopole source and one of higher order. With a permeable interface, the fluid flow effects refer to the horizontal mobility (horizontal permeability/saturant fluid viscosity) and disables the determination of the shear-wave transverse isotropy. Without this information, any horizontal mobility determination is incorrect. Whatever the nature of any fluid–poroelastic interface, the presence of radial layering decreases the reliability of any estimation of parameter related to the virgin formation except for the velocity and attenuation of the vertically propagating SV wave. Whatever the configuration, the transverse isotropy of the compressional wave velocity cannot be determined nor can that of the complex permeability tensor or the anelastic attenuation due to the polarization of the (quasi) body waves involved. The results of this work also show that, in contrast to the pure elastic situation, a transverse isotropy of the complex permeability tensor leads to slightly different quasi-SV-wave velocities along the principal directions of propagation at ultrasonic frequencies.