Anisotropy and azimuthal attributes: fractures and stress

Part 8 — Advanced QI Topics

Learning objectives

Recognize that real rocks are typically anisotropic (VTI, HTI, or orthorhombic)
Distinguish VTI (layer-induced, angle-dependent) from HTI (fracture-induced, azimuth-dependent)
Read a velocity rose: fast axis = fracture strike; anisotropy magnitude ≈ fracture density
Explain Thomsen parameters ε, δ, γ and what they control
Use AVAz (amplitude variation with azimuth) to detect and map aligned fractures from 3D seismic

Seismic processing and most Part 7 inversion workflows ASSUME the subsurface is isotropic: a wave traveling in any direction at a given point sees the same velocity. In reality, this is almost never exactly true. Sedimentary rocks are ANISOTROPIC by construction: horizontal layering makes them faster along bedding than across; aligned fractures create azimuthal velocity variations; combined layering + fractures produce full orthorhombic anisotropy. §8.3 is about measuring anisotropy, understanding what it reveals, and using it to map FRACTURES and STRESS — two of the most valuable geological unknowns.

The key practical payoff: AZIMUTHAL ATTRIBUTES. By analyzing how seismic amplitudes and velocities vary with AZIMUTH at a given location, you can extract (1) fracture density, (2) fracture strike, and (3) local stress direction. These maps drive horizontal-well targeting, fracture-stimulation design, and mud-weight windows. In unconventional plays (shale, tight sand), azimuthal attributes are the primary tool for identifying the best frac intervals.

Types of anisotropy

VTI (Vertical Transverse Isotropy): rotationally symmetric about a VERTICAL axis. Dominant in shales (fine-scale horizontal layering at grain scale) and in fine-bedded sandstones. Vp is faster along bedding than across. No azimuthal variation (the rose is a CIRCLE), but Vp depends on ZENITH ANGLE from vertical.
HTI (Horizontal Transverse Isotropy): rotationally symmetric about a HORIZONTAL axis — typically normal to aligned vertical fractures. Vp depends on AZIMUTH: fastest along the fracture strike (no fractures crossed), slowest perpendicular. The velocity rose is an ELLIPSE with the long axis along fracture strike.
Orthorhombic: VTI + HTI combined. Both horizontal layering AND aligned vertical fractures. Most realistic model for fractured sedimentary reservoirs. Has TWO axes of symmetry (bedding normal + fracture strike).
Lower-symmetry (monoclinic, triclinic): rarely modeled; assumes even more complex fracture networks or folding-induced fabrics. Industry standard is orthorhombic unless there’s clear evidence for more.

Exercise — rotate the fractures, grow the anisotropy

Open the widget in HTI (fracture-aligned) mode with ε = 0.08 (moderate fracture density) and fracture strike = 45° (NE–SW). The velocity rose is an ELLIPSE elongated along the NE–SW direction: Vp is fastest where the propagation azimuth matches the fracture strike (no fractures crossed), slowest in the orthogonal direction.
Drag the strike slider. Watch the ellipse rotate. The fast-axis indicator (yellow dashed line with “fast” label) follows the fracture strike. Real fracture sets might be NNE, WNW, or any other azimuth — this is exactly what AVAz inversion reveals.
Drag the ε slider to 0. The ellipse collapses to a circle (no anisotropy). At ε = 0.15 (maximum), the anisotropy is strong — fast-axis Vp is 15% faster than the slow axis. This is a HIGHLY FRACTURED reservoir.
Switch to Isotropic reference. The rose becomes a plain circle at baseline Vp = 3500 m/s. This is the assumption most legacy seismic processing uses.
Switch to Orthorhombic. The azimuthal rose is still HTI-like (we’re looking in plan view). The VTI part (zenith-angle dependence) is not visible in this rose — it would require a vertical-slice visualization. Real orthorhombic inversion needs BOTH wide-azimuth 3D data AND careful zenith-angle analysis.
Read the summary: Vp fast, Vp slow, anisotropy %, fast azimuth. An anisotropy of 5-10% is typical for mild fractures; 10-15% is strong (good frac target); > 15% suggests heavily fractured, possibly fault-related zones.

Thomsen parameters

Thomsen (1986) parameterized weak anisotropy with three dimensionless numbers for VTI media:

ε (epsilon): relative P-wave anisotropy between bedding-parallel and bedding-normal. Typical shales: ε ≈ 0.1-0.25. High-fracture-density HTI: ε ≈ 0.05-0.15.
δ (delta): the NEAR-vertical P-wave anisotropy parameter (governs the curvature at small zenith angles). Controls depth errors from isotropic imaging. Typical δ ≈ 0-0.15.
γ (gamma): S-wave (shear) anisotropy. Parameter in converted-wave and multicomponent data.

In HTI media the same parameters are DEFINED relative to the symmetry axis (fracture normal), often noted as ε_V, δ_V, γ_V. Orthorhombic uses SIX Thomsen-style parameters to capture both VTI and HTI contributions. These numbers are what inversion actually solves for.

AVAz: amplitude variation with azimuth

The practical workhorse of HTI inversion. At a given reservoir interface, the reflection amplitude at a FIXED OFFSET varies with propagation azimuth if the rock below is HTI. The amplitude is a SINUSOID with period 180° (fractures look the same forward or back):

A(φ) = A₀ + B · cos(2(φ − φ_fast))

where A₀ is the azimuthally averaged amplitude, B is the anisotropy magnitude, and φ_fast is the fast-axis azimuth (= fracture strike for simple HTI). Inversion per voxel: fit the 2φ sinusoid to amplitude vs azimuth. Outputs: B (fracture density proxy) and φ_fast (fracture strike).

Requires WIDE-AZIMUTH data: traditional narrow-azimuth marine streamer surveys don’t sample enough of the azimuth space for reliable AVAz. Ocean-bottom-node, wide-azimuth towed-streamer, and land 3D (multi-component vibrator arrays) are all AVAz-capable.

Practical applications

Fractured reservoirs: the strongest use case. Carbonate reservoirs, tight sandstones, and fractured basement all have aligned-fracture networks that HTI inversion maps directly. Fracture density (from ε) predicts permeability; fracture strike (from φ_fast) guides horizontal-well azimuth selection.
Stress-direction mapping: aligned fractures respond to the current stress field. Open fractures align with MAXIMUM HORIZONTAL STRESS (σH); compressed fractures close normal to σH. AVAz fast-axis = current σH azimuth, directly useful for wellbore-stability and frac-design.
Imaging correction: below a VTI overburden (shale caps, clay packages), isotropic migration mis-positions reflectors in depth. Adding ε and δ to the imaging model removes these errors — TOC (top-of-carbonate) and other critical events image much more accurately.
Shear-wave splitting (converted waves): in HTI media, a shear wave splits into FAST (polarized along fracture strike) and SLOW (normal to strike) components. Time delay between them is another direct fracture-density measurement.
Unconventional plays (shale + frac): identify “sweet spots” where natural fractures already exist. Drive completion design: hit fracture corridors with multi-stage fracs oriented transverse to the natural-fracture strike.

When anisotropy matters and when it doesn’t

Must-model situations: (1) Imaging below a VTI overburden (most sedimentary basins — shales are almost always VTI). (2) Fractured reservoirs where fractures are PRODUCTION-CONTROLLING. (3) AVAz inversion for stress/fracture maps. (4) Anisotropic velocity analysis for accurate depth conversion.
Optional (but improving): (1) Conventional reservoirs with weak anisotropy (ε < 0.05) and no fractures of interest. (2) Basins with well-calibrated legacy isotropic velocity models.
Required cost: anisotropic processing adds ∼15-30% to the compute time for pre-stack depth migration. Wide-azimuth acquisition is ∼30-50% more expensive than narrow-azimuth. But the payoff is cleaner imaging + new information (fracture/stress maps) that isotropic can’t deliver.
Common mistake: using narrow-azimuth data for AVAz. Doesn’t work. The math requires samples from MANY azimuths at the same CDP; narrow-azimuth just doesn’t have them. AVAz projects always start with “do we have the data?” before “can we do the analysis?”.

Anisotropy is the acknowledgment that the subsurface has STRUCTURE at scales smaller than the wavelength — layering, alignments, stress fabrics — and that structure is itself MEASURABLE from seismic. For QI, anisotropy is both a NUISANCE (isotropic inversion is biased when ε is large) and an OPPORTUNITY (AVAz maps directly answer fracture and stress questions that no other seismic attribute can). §8.4 takes the next step: full-waveform inversion, which abandons the simple convolutional model entirely and solves the full wave equation — naturally handling anisotropy, attenuation, and complex geology in one integrated framework.

References

Rüger, A. (2002). Reflection Coefficients and Azimuthal AVO Analysis in Anisotropic Media. Society of Exploration Geophysicists.
Aki, K., & Richards, P. G. (2002). Quantitative Seismology (2nd ed.). University Science Books.
Mavko, G., Mukerji, T., & Dvorkin, J. (2009). The Rock Physics Handbook (2nd ed.). Cambridge University Press.
Chopra, S., & Marfurt, K. J. (2007). Seismic Attributes for Prospect Identification and Reservoir Characterization. Society of Exploration Geophysicists.