Simultaneous anisotropy inversion and type identification in the frequency domain for flexural waves in horizontal transverse isotropic media

Abstract

The anisotropy of elastic waves has been widely used to obtain information about the formation structure in geosciences research. The splitting of flexural waves is generally applied to evaluate anisotropy using geophysical inversion methods. However, most of these methods must be combined with other methods, such as dispersion analysis, to distinguish stress-induced and intrinsic anisotropies. The objective function proposed by Tang and Chunduru has been improved by a new objective function that introduces an amplitude ratio of the slow to fast flexural waves in a horizontal transverse isotropic formation. By considering the amplitude difference in flexural wave splitting under stress-induced or intrinsic anisotropy, the new method can perform anisotropy inversion and type identification in the frequency domain. The calculated azimuth of the fast flexural wave as a function of frequency is used to distinguish the anisotropy type. The results from synthetic examples indicate that the intrinsic anisotropy commonly leads to a smooth azimuth curve, whereas the stress-induced anisotropy leads to a sharp step change. Therefore, the distribution of the azimuth in the frequency domain is a better indicator of the anisotropy type than the traditional slowness dispersion curve. Moreover, a new objective function and a new quality indicator for simultaneous anisotropy inversion and type identification have been developed and validated by synthetic and field data sets.

Crack‐Induced Shear‐Wave Orthorhombic Anisotropy: Modeling and Inversion of Shear‐Wave Borehole Measurements

“…In the presence of VTI anisotropy, the flexural‐wave velocity is faster than its isotropic counterpart, especially in the medium to high frequency range (Xu et al, 2017). However, in the presence of HTI anisotropy, the flexural wave splits into the fast‐ and slow‐flexural waves (Sinha et al, 1994; Tang & Cheng, 2004; Zeng et al, 2018) that can be determined by the 4C dipole tool. The tool measures four data sets XX , XY , YX , and YY , with the first (second) letter referring to the source (receiver) orientation of the two orthogonal dipole systems X and Y of the tool.…”

“…It is interesting to note that shear‐wave logging with a four‐component (4C) dipole acoustic tool in a vertical borehole penetrating orthorhombic rock formations can determine both the background and azimuthal anisotropy parameters, such that the tasks of formation evaluation and fracture characterization can be performed in an efficient manner. For this evaluation, the shear‐wave VTI property is determined from borehole monopole Stoneley‐wave (Tang, 2003) and dipole flexural‐wave (Xu et al, 2017) measurements, while shear‐wave HTI property is determined from dipole flexural‐wave measurements (Tang & Chunduru, 1999; Walker et al, 2015; Zeng et al, 2018). In the following, we develop an inversion method for estimating the shear‐wave anisotropy parameters.…”

“…Although the transversely isotropic medium with a horizontal axis of symmetry (HTI) is the simplest model for modeling the HTI anisotropy caused by parallel vertical fractures around a borehole (e.g., Bakulin et al, 2000), an exact analytical solution for borehole wave propagation with an HTI formation is not available, in contrast to the VTI formation case where an analytical solution exists. Hence, perturbation techniques (e.g., Ellefsen, 1990;Sinha et al, 1994Sinha et al, , 2000 and finite-difference or finite-element techniques (e.g., Cheng, 1994;Liu & Sinha, 2003;Zeng et al, 2018) have been used for the HTI case. On the other hand, because of the importance of fracture-induced HTI, numerous methods have been developed for the inversion of shear-wave azimuthal anisotropy (i.e., HTI) parameters (e.g., Alford, 1986;Collins & Cheng, 2016;Esmersoy et al, 1994;Tang & Chunduru, 1999;Zeng et al, 2018).…”

“…Hence, perturbation techniques (e.g., Ellefsen, 1990;Sinha et al, 1994Sinha et al, , 2000 and finite-difference or finite-element techniques (e.g., Cheng, 1994;Liu & Sinha, 2003;Zeng et al, 2018) have been used for the HTI case. On the other hand, because of the importance of fracture-induced HTI, numerous methods have been developed for the inversion of shear-wave azimuthal anisotropy (i.e., HTI) parameters (e.g., Alford, 1986;Collins & Cheng, 2016;Esmersoy et al, 1994;Tang & Chunduru, 1999;Zeng et al, 2018). Interestingly, Zeng et al (2018) developed a frequency domain inversion method where the Tang and Chunduru (1999) method was modified by introducing an amplitude ratio term in the objective function for the inversion of anisotropy parameters.…”