The Fabric, or Internal Structure, of Rocks

The Patterns of Anisotropy, Part 1

Geology is the correct starting point for any geophysical discussion in AAPG. This two-part article starts with the rock, progresses to the wave and concludes with our increased understanding of the rock. If you, dear reader, can stay for both parts, you will gain a basic understanding of how anisotropy in P-P seismic reflection data can add to our understanding of the rocks, specifically the reservoir, at depth.

Rocks are composed of minerals and contain layers, porosity and pore fluids and are influenced by a tri-axial stress field (for the most part), plus local structure – faults, fractures, folds and small variations in curvature.

Four words provide the fundamental description of rocks: homogeneity, heterogeneity, isotropy and anisotropy.

“Homogeneity” means spatial invariance in a property laterally and/or vertically. For example, the P-wave velocity (VP), the shear-wave velocity (VS) and density – the three primary characteristics we seek to learn from seismic data – are spatially invariant laterally or vertically.

“Heterogeneity” means that there is a lateral or vertical change in VP, VS, and/or density: facies changes or the vertical stratigraphic column. The layers of sedimentary rocks are the primary heterogeneity that we map using reflections that arise at impedance (velocity times density) contrasts.

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Geology is the correct starting point for any geophysical discussion in AAPG. This two-part article starts with the rock, progresses to the wave and concludes with our increased understanding of the rock. If you, dear reader, can stay for both parts, you will gain a basic understanding of how anisotropy in P-P seismic reflection data can add to our understanding of the rocks, specifically the reservoir, at depth.

Rocks are composed of minerals and contain layers, porosity and pore fluids and are influenced by a tri-axial stress field (for the most part), plus local structure – faults, fractures, folds and small variations in curvature.

Four words provide the fundamental description of rocks: homogeneity, heterogeneity, isotropy and anisotropy.

“Homogeneity” means spatial invariance in a property laterally and/or vertically. For example, the P-wave velocity (VP), the shear-wave velocity (VS) and density – the three primary characteristics we seek to learn from seismic data – are spatially invariant laterally or vertically.

“Heterogeneity” means that there is a lateral or vertical change in VP, VS, and/or density: facies changes or the vertical stratigraphic column. The layers of sedimentary rocks are the primary heterogeneity that we map using reflections that arise at impedance (velocity times density) contrasts.

“Isotropy” means that, for a given volume of rock of interest, whatever measurement you wish to make shall yield to you the same value, no matter which direction in which it is measured.

“Anisotropy” means that, for this volume of rock, the direction in the measurement is made shall determine its value.

These four words usually exhibit scale-dependency. That is, the frequency used for the seismic measurement will determine your assessment of the rock. For the purposes of this article, I am speaking of the surface seismic reflection data, with frequencies of 5-100 Hertz (5-100 cycles per second).

Permeability and Velocity

Examples of anisotropic quantities are permeability and velocity. Engineers are familiar with the permeability (K) anisotropy of rocks: Kvertical is not equal to Khorizontal; some reservoirs exhibit a KHmax which is not equal to Khmin. VP and VS are notorious for being anisotropic in the sedimentary layers that can contain hydrocarbon reservoirs.

“All anisotropy arises from ordered heterogeneity smaller than the wavelength.”

This sweeping statement from Don Winterstein’s paper in Geophysics, “ Velocity anisotropy terminology for geophysicists,” remains unrefuted. The wavelength is determined by the frequency and the velocity (frequency x wavelength = velocity). The ordered heterogeneities smaller than the wavelength can include shale clay platelets and finely layered rocks. Other ordered heterogeneities may be one set of vertical aligned fractures. The word “fracture” is very unspecific: it lumps together stress-aligned microfractures (arising from unequal horizontal stresses) whose apertures are too small to flow fluids, and macrofractures that flow fluids. We would prefer to find (and document) a method that will empirically disentangle these two situations, even at the risk of arousing the ire of the theoreticians. If there are heterogeneities (“crack-like pores”) smaller than the wavelength, but they are disordered, then we are back to seismic isotropy. True matrix porosity will look the same for all azimuths. The word “azimuth” in this article is the direction from source to receiver that the wave travels.

Rock Symmetry

In the world of anisotropy, there are four words or phrases that need to be known: transverse isotropy, orthorhombic, monoclinic and triclinic. These words indicate a certain symmetry (order in the heterogeneities) that we want to know about. The symmetry of the rock is imprinted upon the wave. By recording and displaying the symmetry of the wave, we deduce the symmetry of the rock. Although the more accurate statement is that the wave is influenced by the symmetry of the last layer through which the wave travels, geophysicists have various means to try to peer through the upper layers in order to see the reservoir conditions. We have to strip off the effect of the upper layers, in order to see the properties of the layer of interest (the reservoir). To “display the symmetry of the wave,” I refer to inspecting interval travel times, amplitudes, frequencies, etc., as a function of azimuth and offset, from 0-180 (north to south) or from 0-360 (north to south to north), preferably the latter.

The principal order in the heterogeneities smaller than the wavelength is the layering of the rocks: we routinely expect to find a plane of isotropy in the bedding plane. If there is a plane of isotropy we have transverse isotropy (TI). Now we have to state the normal to the plane of isotropy. Transverse isotropy with a vertical axis, VTI, is the layer anisotropy (see figure 1). Transverse isotropy with a tilted axis is TTI (dipping beds). VTI or TTI means that the P wave traveling parallel to the bedding plane will have the same (faster) velocity whether it travels north or east or south, etc. However, normal to the bedding plane, the P wave velocity will be slower. Figure 2 presents schematically the symmetry terms.

Transverse isotropy with a horizontal axis, HTI, is the symmetry of one set of vertical fractures: the P-wave traveling parallel to the fractures will travel faster, while the P-wave traveling normal to the fractures will travel slower. Evidence of azimuthal P-P travel times is visible in figure 3 (a) where the farther offsets show the travel time variation by source-receiver azimuth (a wobble, red arrow). The data are sorted first by offset group, then by azimuth within each offset group. The corrected travel times for orthorhombic processing are shown in Figure 2(b). The red arrow indicates where the azimuthal travel time variation is greatly reduced.

This medium is also bi-refringent (“two waves”) for the shear-wave: the vertically propagating shear wave with particle motion parallel to the fractures will travel faster; the vertically propagating shear wave with particle motion perpendicular to the fractures will travel slower. Shear-wave splitting occurs when the shear-wave with arbitrary polarization (particle motion skew to the fabric of the rock) enters the medium with one set of vertical aligned fractures: the one shear wave will become two shear waves.

Orthorhombic (ORT) is flat layers with one set of vertical aligned fractures; flat layers with two sets of orthogonal fractures is also allowed in the ORT symmetry. Note that you don’t know whether I’m referring to stress-aligned micro-cracks or macrofractures that flow fluids or some combination thereof. It turns out that across North America (and the rest of the world) about a 2 percent azimuthal variation in the P-wave V RMS is common (according to Ed Jenner, a senior geophysicist at NEOS). The word “azimuth” refers to the source-to-receiver direction (usually referenced to north when data is delivered to the client). We know that macro-fractures that flow fluids are rather rare, not found everywhere all the time. Therefore, our seismic data is telling us that there is a background ubiquitous effect across continents that causes azimuthal variation in the P-wave velocities: it is likely the unequal horizontal stresses. When our migration (imaging) algorithms accurately specify the velocity field that changes with space (heterogeneity) and offset (layer anisotropy) and azimuth (unequal horizontal stress and/or vertical aligned fractures), then our images are clear and crisp.

ORT is the current standard symmetry for the industry … plus we have as “attribute” volumes the quantification of the velocity fields – and these we use in interpretation. Velocity is affected by lithology, porosity, pore fluids, horizontal stress (in the direction of source to receiver) and fracture sets. From laboratory studies, we know that stress in the direction of source to receiver has a proportional effect upon the P-wave velocity. The standard explanation for the laboratory observations is that increasing the stress in one direction will close the micro-cracks that are normal or near normal to the increased stress; this closure of the cracks normal to the increased stress will increase the P-wave velocity. Interval velocities (VINT) average large volumes of rock, bounded by reflectors, and tend to change slowly spatially. The reflection amplitudes, however, are a spatially high-resolution dataset: they record the local contrast in impedance. The macro-fractures that flow fluids usually govern the azimuthal amplitude signatures: at least, this can be an initial hypothesis, to be tested against your own seismic data and calibration data. Since azimuthal VINT and azimuthal amplitudes are arising from different volumes of rock, they need not agree. If they do agree, that’s fine. When they don’t agree, we note the heterogeneity between the two different rock volumes.

To be continued in next month’s Explorer.

Acknowledgements: My thanks to Mike Perz of TGS-Calgary for his kindness to supply figure 1 in this article. I thank Satinder Chopra for requesting this article after he soldiered through my Geophysical Society of Houston webinar, “Azimuthal P-P for Better Imaging, Fractures, and Stress Analysis” in December 2017.

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