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doi:10.2204/iodp.proc.335.202.2015

Methods and materials

Principles of sonic anisotropy analysis

Sonic anisotropy analysis of downhole logging data utilizes the physical phenomenon of shear wave splitting. When a shear wave propagates through anisotropic media, it is polarized, or “split,” into two directions aligned with the fast and slow axis of the formation. In the case of aligned fractures and/or other structural features, the fast direction is along the strike of these features; for stress-induced anisotropy, the fast shear aligns with the direction of the far-field maximum principal stress (Ellis and Singer, 2007; Sinha and Kostek, 1996). Thus, by measuring the polarization direction and the difference in the arrival times of the fast and slow shear waves, it is possible to infer the direction and degree of formation anisotropy. For most downhole logging measurements, sonic waves travel along the borehole axis and are polarized in various azimuthal orientations with respect to the axis (Fig. F3). They are, therefore, most sensitive to the azimuthal variability of formation properties in the plane perpendicular to the borehole axis. In a vertical borehole, this means that the highest sensitivity to azimuthal variations occurs in the horizontal plane (e.g., produced by subvertical features and/or unequal horizontal stresses). Such media are classified as transversely isotropic with a horizontal axis of symmetry, or TI-H.

The DSI that was deployed in Hole 1256D utilizes directional sources and receivers, allowing for oriented recording of polarized shear waves in an anisotropic formation (Ellis and Singer, 2007). Four waveforms are analyzed simultaneously at each depth from two source-receiver pairs (two in-line and two cross-line). In order to determine the fast and slow directions for an arbitrary azimuthal orientation of the tool in the borehole, the four wave fields are numerically rotated into the principal planes using the Alford rotation procedure (Alford, 1986). In this procedure, the following parameters characterize the measured anisotropy and are simultaneously derived: the fast shear azimuth (FSH), cross-energy, and traveltime anisotropy. The numerically rotated fast and shear wave forms are processed to determine fast-shear and slow-shear slownesses (inverse of V_S) and to compute shear slowness anisotropy. The details of the processing algorithms can be found in Ellis and Singer (2007), Sinha and Kostek (1996), and Sinha et al. (1994). The next section summarizes the main anisotropy parameters needed to understand the outcomes of the sonic anisotropy analysis conducted in Hole 1256D.

Key anisotropy parameters

In total, three parameters quantifying the amount of anisotropy, slowness anisotropy, traveltime anisotropy, and energy anisotropy, are computed during these processing steps:

• Slowness anisotropy is the difference between the fast and slow slowness calculated on rotated waveforms and normalized to the average slowness. It is the main indicator of the magnitude of shear wave anisotropy (in percent of average V_S).
• Traveltime anisotropy is the arrival-time difference between the rotated fast and shear waves averaged across the receiver array and normalized by the average arrival time to compute a percentage difference. This serves as a secondary indicator of anisotropy and requires good borehole conditions to be meaningful.
• Energy anisotropy is a spectral parameter that quantifies the amount of energy in the cross-component waveforms and is computed as a percentage of total energy in all four rotated wave field components. Two related parameters are also computed: the minimum and the maximum cross-energy. The minimum cross-energy, when close to zero, indicates that the Alford rotation procedure was successful. The maximum cross-energy is proportional to the degree of anisotropy and should be significantly greater than the minimum cross-energy if, in fact, shear wave splitting is observed.

Sonic anisotropy analysis is most reliable when the following measurement conditions are satisfied:

• The tool is consistently rotating while logging the borehole, thus providing full azimuthal coverage, and the FSH does not track the tool orientation. Tool rotation is recorded during data acquisition with the Pad 1 azimuth (P1AZ). Typically, tools rotate during logging, but they may become “locked” at a particular azimuth due to irregularities in the well bore. Tool azimuth is an important quality control parameter to make sure that calculated FSH is independent of the tool orientation in the borehole.
• Borehole conditions are good and borehole diameter is not significantly enlarged in any orientation around the hole. Hole quality can be checked using a caliper log, which measures borehole diameter in two orthogonal directions.
• The minimum cross-energy is small or close to zero and the maximum cross-energy is significantly greater than the minimum cross-energy. This indicates that shear wave splitting has been measured and the Alford rotation procedure was successful. Slow and fast velocity components can then be reliably separated.

Under these conditions, both slowness and traveltime anisotropy estimates should be similar and allow for a reliable magnitude estimate of anisotropy in the formation. The FSH indicates the strike of the formation anisotropy, the intrinsic features that are potentially responsible for causing it, and/or the orientation of the maximum horizontal stress in the formation.

Frequency-slowness analysis (dispersion plots)

An additional and powerful tool for detecting the presence of shear wave anisotropy and understanding its nature is the analysis of shear wave dispersion. Shear waves in boreholes are produced by flexural waves created by directional sources, locally deforming the borehole perpendicular to its axis. These flexural waves are inherently dispersive (i.e., their velocity depends on frequency; Sinha et al., 1994). In an anisotropic formation, curves of the slow and fast shear wave velocity separate as a function of frequency, and the pattern of this separation on a dispersion plot may allow for stress-induced and intrinsic sources of anisotropy to be distinguished (Fig. F4). For intrinsic anisotropy, for example, the fast shear wave travels parallel to the strike of formation features and the slow shear wave travels perpendicularly to them. The fast and slow shear wave dispersion curves are nonintersecting over the entire frequency band. The fast-shear direction determined form the rotated waveform indicates the strike of anisotropic features in the formation. For stress-induced anisotropy, when anisotropy is due to stress imbalance in the borehole cross-sectional plane, the fast shear aligns with the direction of the far-field stress and the fast and slow shear wave dispersion curves cross over at an intermediate frequency (Fig. F4; Sinha et al., 2000). For an isotropic formation, the fast and slow shear slownesses are identical and overlap in the dispersion plot.

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