Weak elastic anisotropy and the tube wave

Abstract

Tube‐wave speed in the presence of a weakly anisotropic formation can be expressed in terms of an effective shear modulus for an equivalent isotropic formation. When combined with expressions for the speeds of the SH‐ and quasi‐SV‐waves along the borehole axis, a simple inversion procedure can be obtained to determine three of the five elasticities of a transversely isotropic (TI) formation tilted at some known angle with respect to the borehole axis. Subsequently, a fourth combination of elastic moduli can be estimated from the expression for the qP‐wave speed along the borehole axis. The possibility of determining all five elasticities of a TI formation based on an assumed correlation between two anisotropy parameters is discussed.

Estimation of rock anisotropic constants using sonic data from deviated wellbores

“…Norris and Sinha [3] have developed approximate equations for calculating plane wave velocities along arbitrary directions in a TI-material. These equations have been used to develop inversion algorithms for weak anisotropic formations to calculate all 5 TI elastic constants using the compressional and two cross-dipole shear wave velocities from wellbore with two different deviations or relative dips with respect to the TI-symmetry axis.…”

Theoretical estimate of tube-wave modulus in arbitrarily anisotropic media: comparisons between semi-analytical, FEM, and approximate solutions

“…Today, more borehole sonic measurements are conducted in highly deviated or horizontal wells penetrating strongly transverse isotropic (TI) formations (either with a vertical axis of symmetry called VTI or a tilted axis of symmetry called TTI) or lower symmetries such as orthorhombic or monoclinic due for instance to the presence of fractures. In this context it is important to more accurately relate the three or four available sonic slowness measurements from sonic tools, i.e., one compressional, one or two dipole shear, and one tube-wave slowness, to the five elastic constants of intrinsic TI formations (Norris and Sinha, 1993;Walsh et al, 2006;Sinha et al, 2006;Walsh et al, 2007). For a vertical well within a VTI medium, each sonic measurement can be uniquely related to one component of the stiffness tensor, i.e., the components c 33 , c 55 , and c 66 are respectively related to one compressional, one dipole shear, and one tube-wave shear slowness (see Figure 1; the stiffnesses are expressed using Voigt notation).…”

A numerical investigation of the acoustic mode waves in a deviated borehole penetrating a transversely isotropic formation

“…Dispersion curves can be obtained from the results in time domain [18][19]. The perturbation method is also used when the TI formation shows weak anisotropy [3,[20][21][22]. Laboratory measurement is also realized to observe the wave propagation phenomena [23,24], especially for the flexural waves excited by a dipole source.…”