# The Fabric, or Internal Structure, of Rocks: Part 2

Continuation of 'The Patterns of Anisotropy'

Part 1 of this series explained that the wave acquires the symmetry of the rock: by examining azimuthal travel times and amplitudes, we document the symmetry of the wave and learn of the symmetry of the rock (“symmetry” is the fabric or order in the heterogeneities). I introduced the terms “homogeneous,” “heterogeneous,” “isotropic” and “anisotropic,” schematically reviewed in figure 1.

In the anisotropic category, TI (transverse isotropy) is used to indicate that a plane of isotropy exists.

### Image Caption

Figure 1. Sketches of possible scenarios to illustrate the four terms. Length of black arrow is proportional to velocity (as measured in direction arrow is pointing). Figure courtesy of Satinder Chopra.

Part 1 of this series explained that the wave acquires the symmetry of the rock: by examining azimuthal travel times and amplitudes, we document the symmetry of the wave and learn of the symmetry of the rock (“symmetry” is the fabric or order in the heterogeneities). I introduced the terms “homogeneous,” “heterogeneous,” “isotropic” and “anisotropic,” schematically reviewed in figure 1.

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In the anisotropic category, TI (transverse isotropy) is used to indicate that a plane of isotropy exists.

Its normal can be vertical (VTI, for the layer anisotropy) or horizontal (HTI, for the fracture or azimuthal anisotropy). Orthorhombic (ORT) is VTI + HTI, or flat layers plus one set of vertical fractures. Flat layers plus two sets of orthogonal vertical fractures can also give rise to ORT symmetry.

The words “orthorhombic,” “monoclinic” and “triclinic” are like a family: they are related because now we are talking about how many right angles are there among the three axes (or principal planes of the anisotropy). If there are three right angles, we have orthorhombic: flat layers plus one set of vertical fractures. If there are two right angles, we have monoclinic: for example, dipping layers plus one set of vertical aligned fractures or vertical faults; or flat layers plus one set of dipping fractures or dipping faults. If there are no right angles, we have triclinic: for example, dipping layers plus two different non-orthogonal sets of fractures (possibly the stress-aligned micro-fractures from the unequal horizontal stresses, and the dipping faults or macro-fractures that flow fluids), wherein all these planes are non-orthogonal to each other.

Geologists: which of these symmetries is likely present in the dataset your team is working?

Our industry state-of-the-art processing is 3-D P-P full azimuth full offset migration in the orthorhombic or tilted orthorhombic symmetry. To build the correct velocity model, the data can be 5-D interpolated into four, six or eight azimuth-sectors (more is better), and the TTI model is used to build the velocity field for that azimuth. Then, an algorithm takes the azimuth-dependent velocities and builds the ORT velocity field from the observed travel times. There are other methods for preserving azimuth and offset during the migration step, but lack of space precludes me from digressing to there. If you haven’t reprocessed your data within the last five years, it is now time to reprocess to obtain the uplift, new gathers and additional attribute volumes.

## 360 Degrees

Geophysicists map the travel times (structure, VINT) and the amplitudes – the wave acquires the symmetry of the medium through which it travels. If the rocks contain the symmetry that the processing algorithm requires (i.e., expects), then all is fine. If the rocks are more complicated than the processing algorithm’s expectation, poorer images can result.

Figure 2 (c and d) compare the images obtained with two different assumptions about the symmetry of the rocks. This area of offshore Vietnam is fairly complex structure, and so the ORT assumptions are being “pushed” (that is, I would not argue that these rocks are ORT). Dipping reflectors and dipping faults are clearly visible. Perhaps this explains why the deeper reflectors on the gather (2b) appear to have some remnant azimuthal time wobble present. Note especially the time wobble on the near offsets of the deep reflectors. Possibly, further subsequent processing did remove those azimuthal travel time variations.

Risking arguments, I assert that for monoclinic and triclinic symmetries, we would do well to process P-P reflection data 0-360, and not 0-180. How can we know what is going on in the field data unless we look at it? My whole career has been one long series of arguments, starting in 1980 at Amoco, when I was asked to process two SH-SH reflection lines that tied at Devil’s Elbow, Pa. These two SH-SH reflection lines happened to lie in the principal planes of the anisotropy and exhibited a time-variant (dynamic) mis-tie at the tie point. This was the first published evidence of shear-wave splitting in oil company reflection seismic data. This field dataset sparked Rusty Alford’s ( of Amoco) interest in split shear waves, so he went to Dilley, Texas, and acquired 2-D four-component shear wave reflection profiles (SH and SV sources recorded by the inline and crossline horizontal geophones). The shear wave splitting contained in Alford’s data were published at the 1986 Society of Exploration Geophysicists’ Annual Meeting “Anisotropy” session; Alford was subsequently presented with the Kaufmann Gold Medal for his important contribution to the industry.

Rocks that are folded or curved can exhibit various regions of aligned fractures, curved layers being held in extension or in compression. A neutral plane can separate layers held in extension from layers held in compression. We often observe the azimuth of VINTfast to change by 90 degrees when comparing one layer held in extension to a (lower) layer held in compression, for example, as in a mild anticline. For a mild syncline, the upper layer is held in compression, but the lower layer is held in extension. In 1994, Bruno and Winterstein published an important study into the relationship of stress variations within folds (using shear-wave data and modeling).

## Conclusion

The internal structure of the rock, its fabric, can be studied by examining the anisotropy exhibited by the layer. Geophysicists routinely measure the interval velocity azimuthal anisotropy to compare to support data showing in situ stress (e.g. borehole breakout) and macrofractures; and the azimuthal amplitude anisotropy is compared to support data for macrofractures and in situ stress. To understand the AVO gradient change with azimuth (the industry standard), the azimuthal variation of the far offset amplitudes is quantified and mapped; as well as the azimuthal variation of the near offset amplitudes (see Lynn, SEG Expanded Abstracts, 2014, 2015, 2016). HTI amplitude modeling, through the CREWES website TI Explorer programs, is also employed to document “what we expect.” Azimuth-dependent prestack elastic inversions are also important for obtaining the azimuthal variation in P-impedance, S-impedance and density (third term). All these measurements are tied to the local calibration data to assure management that “our interpretation is consistent with all the observations.”

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