This paper investigates acoustoelastic effects on guided waves in a fluid-filled pressurized borehole in a biaxial prestressed formation, and develops a simplified formula that explicitly expresses the dependence of velocity dispersions on the stresses, the third-order elastic constants, and the azimuthal angle of multipole source polarization. The simplified formula shows that only in the flexural wave is there a crossover of the dispersion curves, and this phenomenon does not appear in every other guided wave. In particular, as a transformed result from the simplified expression, the square difference of flexural wave velocity dispersions is only dependent on the difference of the biaxial stresses, and neither the square sum of the flexural dispersions nor the velocity dispersions of the other guided waves is dependent on it. Computational results show that the sensitivity coefficients for the flexural dispersions induced by the biaxial stresses at low frequency asymptotically approach the corresponding coefficients of shear-waves in the formation, like the asymptotic behavior of velocities.

In this paper, the acoustic field excited by multipole sources in a fluid-filled borehole surrounded by a transversely isotropic elastic solid is systematically analyzed and numerically simulated. Not only have the mode waves been analyzed thoroughly, but the propagation mechanism of the critical refracted P and S waves corresponding to the multipole branch cut integration for the transversely isotropic formation has also been investigated for the first time. In the presence of a fast or a slow transversely isotropic elastic solid formation, the component waves excited by a monopole, a dipole, and a quadrupole source have been studied in the time and frequency domains. It is found that the critical refracted arrival of the S wave is a dominant factor, while the mode wave is not in the low-frequency multipole direct shear wave logging. When the formation is changed from isotropic to transversely isotropic, the amplitudes of the component waves vary significantly, but the variation of the cutoff frequencies of the mode waves and the resonant frequencies of the P and S waves is less pronounced.

A new and effective analytical perturbation method is presented for the multipole acoustic logging in a transversely isotropic elastic solid whose symmetric principal axis is perpendicular to the borehole axis. The transversely isotropic elastic solid is regarded as a relevant isotropic elastic solid added to the perturbations, and three perturbation quantities about moduli deviated from the isotropic medium are introduced. By selecting a group of displacement potentials and a cylindrical coordinate system oriented along the borehole axis, the zero- and first-order perturbation solutions of the multipole acoustic field are derived for the weak transversely isotropic elastic solid which has its symmetric principal axis perpendicular to the borehole axis. The acoustic fields inside and outside the borehole excited by a multipole source are investigated. It is found that not only the nth multipole acoustic field can be excited by an nth multipole source, but the multipole fields whose orders are higher and lower than n also can be excited by an nth multipole source.

Anisotropic formation is modeled as a transversely isotropic two‐phase medium whose symmetric principal axis is perpendicular to the borehole axis. An effective analytical perturbation method is presented for the multipole acoustic logging in this formationborehole model. The anisotropic formation is regarded as the perturbations added to the relevant isotropic two‐phase medium. Five perturbation quantities about moduli deviated from the isotropic formation are introduced. The acoustic multipole logging in anisotropy is theoretically studied and analyzed. The zero‐ and first‐ order perturbation solutions of the multipole acoustic fields inside and outside the borehole are derived. It is found that not only the nth multipole acoustic field can be excited by the nth multipole source, but the multipole fields whose orders are higher and lower than n can also be excited in such a formation‐borehole system.

The nonsplitting perfectly matched layer (NPML) absorbing boundary condition (ABC) was first provided by Wang and Tang (2003) for the finite-difference simulation of elastic wave propagation in solids. In this paper, the method is developed to extend the NPML to simulating elastic wave propagation in poroelastic media. Biot's equations are discretized and approximated to a staggered-grid by applying a fourth-order accurate central difference in space and a second-order accurate central difference in time. A cylindrical twolayer seismic model and a borehole model are chosen to validate the effectiveness of the NPML. The results show that the numerical solutions agree well with the solutions of the discrete wavenumber (DW) method.