Presence Of Transverse Isotropy Research Articles

Simulation of borehole sonic waveforms in dipping, anisotropic, and invaded formations

A numerical simulation study has been made of borehole sonic measurements that examined shoulder-bed, anisotropy, and mud-filtrate invasion effects on frequency-dispersion curves of flexural and Stoneley waves. Numerical simulations were considered for a range of models for fast and slow formations. Computations are performed with a Cartesian 3D finite-difference time-domain code. Simulations show that presence of transverse isotropy (TI) alters the dispersion of flexural and Stoneley waves. In slow formations, the flexural wave becomes less dispersive when the shear modulus (c44) governing wave propagation parallel to the TI symmetry axis is lower than the shear modulus (c66) governing wave propagation normal to the TI symmetry axis; conversely, the flexural wave becomes more dispersive when c44 > c66. Dispersion decreases by as much as 30% at higher frequencies for the considered case where c44 < c66. Dispersion of Stoneley waves, on the other hand, increases in TI formations when c44 > c66 and decreases when c44 < c66. Dispersion increases by more than a factor of 2.5 at higher frequencies for the considered case where c44 < c66. Simulations also indicate that the impact of invasion on flexural and Stoneley dispersions can be altered by the presence of TI. For the case of a slow formation and TI, where c44 decreases from the isotropic value, separation between dispersion curves for cases with and without the presence of a fast invasion zone increases by as much as 33% for the flexural wave and by as much as a factor of 1.4 for the Stoneley wave. Lastly, presence of a shoulder bed intersecting the sonic tool at high dip angles can alter flexural dispersion significantly at low frequencies. For the considered case of a shoulder bed dipping at 80°, ambiguity in the flexural cutoff frequency might lead to shear-wave velocity errors of 8%–10%.

Recovery of elastic parameters for a multi-layered transversely isotropic medium

A method for recovery of elastic anisotropic parameters of a multi-layered medium from three-component walkaway VSP data is presented. By analysing the multi-component signals recorded by any receiver in a walkaway VSP survey, the apparent transmission velocity field for the layered media above this receiver depth is inverted to yield the effective combined elastic constants of those layers. The interval elastic parameters and the velocity fields for the interval layer of interest between two receiver depths are also efficiently determined from these. The inversion technique adopted the Levenberg–Marquardt method to recover the elastic parameters from the qP-, qSV- and SH-wave transmission travel time data. For the layered media above a given receiver, the P- and S-wave velocities (α0, β0) along the symmetry axis, and the full set of Thomsen's anisotropic parameters are recovered by our inversion approach. For the combined layer's properties, the tilt angle (ψ) of the symmetry axis from the vertical is also inverted. The inversion software was first tested on synthetic data. It was then applied to actual field data and found to give plausible results. Anisotropic parameters recovered in this way may be used to improve data processing and imaging in the presence of transverse isotropy.

An effective anisotropy parameter in transversely isotropic media

An interesting physical meaning is presented for the anisotropy parameter δ, previously introduced by Thomsen to describe weak anisotropy in transversely isotropic media. Roughly, δ is the difference between the P-wave and SV-wave anisotropies of the medium. The observed systematic depth errors in the North Sea are reexamined in view of the new interpretation of the moveout velocity through δ. The changes in δ at an interface adequately describe the effects of transverse isotropy on the P-wave reflection amplitude, The reflection coefficient expression is linearized in terms of changes in elastic parameters. The linearized expression clearly shows that it is the variation of δ at the interface that gives the anisotropic effects at small incidence angles. Thus, δ effectively describes both the moveout velocity and the reflection amplitude variation, two very important pieces of information in reflection seismic prospecting, in the presence of transverse isotropy.

Love waves in a sedimentary layer lying over an anisotropic inhomogeneous half space

The effects of anisotropy and inhomogeneity on the propagation of Love waves in a sedimentary layer, overlying the inhomogeneous and transversely isotropic half space, are studied in this paper. The results of numerical analysis show an appreciable variation of phase- and group-velocity of Love waves in low frequency region compared to high frequency region due to the presence of transverse isotropy and inhomogeneity in the half space. The higher values for phase velocity are found for the increasing values of anisotropy factor as well as for the greater power of density variation. However, the presence of higher anisotropy factor and inhomogeneity in the half space reduce group velocity considerably in the lower frequency region.