Eight reasons you need to understand anisotropy:
•  Laterally misplaced targets below dipping wedges of anisotropic clastic sequences
•  Affects logging response in deviated bore holes or dipping layers
•  Changes critical angle calculations
•  First order effects on attributes such as  AVO
•  Changes ray paths for offset data
•  Influence on calculation of closure stresses
•  Effect on stress concentrations around a borehole, hence stability
• Time to depth conversion

Elastic anisotropy refers to having different elastic properties (moduli, velocities) in different directions. The number of different or unique constants is controlled by the symmetry of the feature or features causing the anisotropy. The features or fabric causing anisotropy  in sedimentary rock include typically a preferred alignment of anisotropic minerals such as clays, quartz, mica, etc., fractures or microfractures and stresses. One of the simplest and most ubiquitous symmetries displayed by these causes is hexagonal or transverse isotropy. The schematic below shows the principal directions and the required elastic constants for characterization.

Standard Three Plug Method
By far the most common measurement approach requires the extraction of three core plugs along prescribed orientations relative to the assumed symmetry axes. These orientations are parallel, perpendicular and typically 45 degrees to the vertical symmetry axis. The most difficult challenge in using this approach is defining the orientation of then elastic symmetry axes as these are not necessarily aligned with the visual fabric axes. Either static or dynamic measurements can be performed on these plugs to provide the magnitude of tensor elements c11, c33, c44, c66, and c13. These correspond to Young's moduli parallel and perpendicular to symmetry and three Poisson's ratios. These five elastic constants can be recast into more geophysically meaningful parameter (Thomsen, 1986), Vp, Vs, epsilon, delta  and gamma. Epsilon captures the difference between horizontally and vertically traveling P-waves. Gamma captures the same for S-waves. Delta is a noninutitive combination of elastic constants which controls the shape of the slowness surface at intermediate angles.  It directly affects AVO and logging responses.
Below is a histogram summarizing anisotropic measurements made on Kimmeridge shale. The values of epsilon, gamma and delta are shown.

ANISOTROPIC PARAMETER DISTRIBUTION IN KIMMERIDGE

Acoustic Tomography
 Acoustic tomography does not require a knowledge of the anisotropic symmetry class. It however, requires larger core specimens (3" to 6" diameter ). The sample is instrumented with a three dimensional array of transducers. Each element of the array can act as either a transmitter (T) or receiver (R). Waveforms are recorded for every possible T-R pair and travel times are measured along the computed geometric paths connecting each T-R pair. The velocities of each phase (P and S) along the various paths are input to an inversion program which solves for both the anisotropic symmetry and anisotropic elastic constants which minimize the error between observed and calculated phase velocities. Strong interplay between symmetry class and the magnitude of elastic constants makes many solutions equally probable. The inversion code can be forced to find the "most isotropic-like" solution. Tomography is limited to ambient conditions at this writing.

One of the major problems with the three-plug approach is shown in the figure below. This figure d shows the sensitivity of the measured value of delta to the error in the angle corresponding to the measurement of C13.  Errors as small as 1 to 2 degrees have large effects on delta. Experience demonstrates that relegating the simple task of core plugging to standard service providers often compromises the accurate measurement of anisotropic parameters.  Tomography overcomes these shortcomings.

Problems arise with all characterizations of anisotropy. The paramount problem is assuming or ascertaining the appropriate symmetry and the positioning the observations relative to them. Aside from this, measurements made at various scales can give widely differing values. There exists a formalism for upscaling core observation but not for downscaling field observations.  While there are some aspects of anisotropy we understand, there are many more in need of observation and investigation.

ANISOTROPY AND AVO

First order effects of anisotropy on AVO can be seen in the figure below. The exact isotropic reflectivity model is given by the red curve while the anisotropic responses are given by the blue and green curves. The green curve incorporates a positive delta value of 0.4 and the blue, a negative delta value of 0.3. These effects translate to a -16% and +30% amplitude change respectively at an offset of 30 degrees.

Applications

AVO interpretation
Borehole tool responses
Seismic depth migration
Time to depth conversion
Closure stress calculations
Borehole stability

Isaac, J. H. and D. C. Lawton, 1999, Image mispositioning due to dipping TI media: A physical seismic modeling study, Geophysics,
123-123.
Thomsen, L. A., 1986, Weak elastic anisotropy, Geophysics, 1954-1966
Vestrum, R. W., D. C. Lawton and R. Schmid, 1999, Imaging structures below dipping TI media, Geophysics, 123-123.
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