Seismic Anisotropy: Yesterday, Today, Tomorrow

A look back

Directional dependence of elastic properties of crystals, or their seismic anisotropy, was recognized a long time ago. By the end of the nineteenth century the first laboratory measurements of seismic velocities in sedimentary rocks were made and the main theoretical result in elastic wave propagation ( the Christoffel equation ( was obtained. It was also noticed that earth formations are not isotropic (White and Sengbush, 1953) and that fine layering, observed in many sedimentary basins, always creates effective anisotropy (Backus, 1962). Still, my M.Sc. thesis “Ray tracing in layered anisotropic media”, defended in 1984, was deemed by my thesis committee an exercise in programming that had almost no relevance to the issues of seismic exploration.

It is clear why things used to be this way. Not having sufficient computing power in the past, geophysicists acquired and processed P-wave reflection data at short offsets (approximately equal to the reflector depths) only, which automatically implied a relatively small angular ray coverage. Seismic anisotropy, being the directional dependence of elastic properties of the earth, went unnoticed for years because we usually looked at the subsurface through too narrow fans of rays. Even though mis-ties in time-to-depth conversion, caused by the difference between stacking and vertical velocities due to anisotropy, were routinely observed, geophysicists dealt with them by simply stretching isotropic images.

The situation changed some fifteen years ago due to rapid advances in the whole suite of methodologies employed by the seismic industry. As the quality of seismic data increased, even relatively small violations of our conventional isotropic assumptions became noticeable. With the technological progress in acquisition, which made acquiring long-offset and multicomponent data feasible and cost-effective, anisotropy showed up, requiring geophysicists do something about it and with it.

Current state of affairs

The day of practical treatment and use of seismic anisotropy in exploration and exploitation contexts probably began in 1986 when two cornerstone papers of Alford (1986) and Thomsen (1986) were published. Both papers apparently appeared ahead of their time and for this reason were not immediately appreciated. The extremely clear result of Alford (1986) that shear-wave data cannot be processed without taking azimuthal anisotropy into account was regarded by some part of the exploration community as an unfortunate complication that could be avoided by simply not dealing with S-waves.

Thomsen’s (1986) paper did not cause any applause either because at first glance it looked like no more than a manipulation with known equations that describe the velocities of waves propagating in transversely isotropic (VTI) media. The deeper truth, however, is that his now famous parameters ε, δ, and γ capture the combinations of stiffness coefficients (which come from the standard formulations of linear elasticity) responsible for such commonly measured seismic signatures as the normal-moveout (NMO) velocities and amplitude-versus-offset (AVO) responses. Moreover, Thomsen-type parameters have since been shown to have exactly the same physical meaning and significance in lower-symmetry orthorhombic and monoclinic media (Tsvankin, 1997; Grechka et al., 2000), the models that are believed to be adequate for describing seismic data acquired over naturally fractured reservoirs.

Thomsen parameterization helped to determine that P-wave reflection traveltimes, which are routinely used for building macrovelocity models, are governed by fewer independent quantities than those formally appearing in the expressions for velocities of waves propagating through VTI media. This observation led to the introduction of the anellipticity coefficient η ≈ ε – δ that, along with conventional NMO velocity, enables one to perform time processing of P-waves in laterally homogeneous VTI media (Alkhalifah and Tsvankin, 1995). Once superior quality of anisotropic time images over the isotropic ones became apparent, and correlation between the estimated values of η and lithology was established, many oil and service companies incorporated Alkhalifah-Tsvankin methodology into their processing flow.

While VTI models are generally considered to be acceptable for sedimentary basins, they are clearly insufficient for describing azimuthally varying seismic signatures recorded over fractured reservoirs. Although one might expect that complicated rheology of fractured media should produce seismic responses that would be difficult to interpret, this turned out not to be the case. Grechka and Tsvankin (1998) showed that the azimuthal dependence of puremode (e.g., P-P and S-S) NMO velocities is an ellipse under the same general assumptions that result in the familiar hyperbolic form of reflection moveout. In addition, azimuthal behavior of prestack reflection amplitudes of pure modes was also found to be approximately quadratic in sines and cosines of the azimuth as long as offsets do not exceed the reflector depth (Rüger, 1997; Vavrycuk and PöencÌk, 1998). Having realized that seismic signatures are sufficiently sensitive to certain fracture parameters (called the excess fracture compliances), Bakulin et al. (2000) devised a suite of techniques for quantitative fracture characterization.

The progress in multicomponent ocean-bottom technology, which already resulted in acquiring high-quality converted-wave (PS) reflection data, put an additional emphasis on seismic anisotropy. The reason for this becomes clear once we recognize that one-half of the ray trajectories of converted PSV reflections is composed of SV-waves whose velocity anisotropy is often about an order of magnitude greater than that of P modes. Therefore, while ignoring P-wave anisotropy may be sometimes acceptable, it is no longer possible for converted waves. Such a conclusion could have meant the end of multicomponent seismic exploration some fifteen years ago; however, perception of anisotropy by the exploration community has changed¹. Many geophysicists now recognize that shear-wave velocities and anisotropic parameters, which can be inferred from PP and PS reflection data, might help to discriminate lithology, predict pore pressure, and characterize fractures or stress. The benefits of obtaining such information significantly overweigh the difficulties of dealing with anisotropy.

A look ahead

There is no doubt that the existing technologies will be refined and developed further to make estimates of anisotropy and related rock properties more accurate. Advances can be expected in the following areas.

Imaging

Progress in anisotropic parameter estimation has revealed the types of subsurface structures for which reflection data can be unambiguously inverted for the anisotropic parameters that control time or depth processing. As more studies are done, we will gain a better understanding of the influence of various trade-offs on the estimated anisotropic velocity fields and, consequently, on the quality of the obtained migration images.

Multicomponent seismology

Measuring shear-wave velocities (as opposed to computing them from the P-wave ones using some empirical relationships) has clear benefits for many exploration tasks. Since S-waves are difficult to excite on land and virtually impossible offshore, converted waves will become the primary source of S-wave information. It remains to be seen how much can be gained from the obtained Swave velocities and anisotropies for different subsurface plays.

Reservoir characterization

Techniques for estimating local reservoir anisotropy from various borehole and vertical seismic profiling (VSP) data will continue to evolve. We can anticipate development of more accurate methods that relate measured anisotropy to such important reservoir characteristics as in situ stress, fractures, pore pressure, and permeability. Once we learn how to make these methods more robust, the same measurements will be used in a time-lapse sense to optimize reservoir production.