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                         SEISMIC ANISOTROPY:
                     YESTERDAY, TODAY, TOMORROW
                                                     Vladimir Grechka
                                   Center for Wave Phenomena, Department of Geophysics
                                     Colorado School of Mines, Golden, Colorado, USA
A look back                                                                 Thomsen’s (1986) paper did not cause any applause either
   Directional dependence of elastic properties of crystals, or their   because at first glance it looked like no more than a manipulation
seismic anisotropy, was recognized a long time ago. By the end of       with known equations that describe the velocities of waves propa-
the nineteenth century the first laboratory measurements of seismic     gating in transversely isotropic (VTI) media. The deeper truth,
velocities in sedimentary rocks were made and the main theoretical      however, is that his now famous parameters ε, δ, and γ capture the
result in elastic wave propagation ( the Christoffel equation ( was     combinations of stiffness coefficients (which come from the stan-
obtained. It was also noticed that earth formations are not isotropic   dard formulations of linear elasticity) responsible for such com-
(White and Sengbush, 1953) and that fine layering, observed in          monly measured seismic signatures as the normal-moveout (NMO)
many sedimentary basins, always creates effective anisotropy            velocities and amplitude-versus-offset (AVO) responses. Moreover,
(Backus, 1962). Still, my M.Sc. thesis “Ray tracing in layered          Thomsen-type parameters have since been shown to have exactly
anisotropic media”, defended in 1984, was deemed by my thesis           the same physical meaning and significance in lower-symmetry
committee an exercise in programming that had almost no rele-           orthorhombic and monoclinic media (Tsvankin, 1997; Grechka et
vance to the issues of seismic exploration.                             al., 2000), the models that are believed to be adequate for describing
                                                                        seismic data acquired over naturally fractured reservoirs.
    It is clear why things used to be this way. Not having sufficient
computing power in the past, geophysicists acquired and processed           Thomsen parameterization helped to determine that P-wave
P-wave reflection data at short offsets (approximately equal to the     reflection traveltimes, which are routinely used for building macro-
reflector depths) only, which automatically implied a relatively        velocity models, are governed by fewer independent quantities
small angular ray coverage. Seismic anisotropy, being the direction-    than those formally appearing in the expressions for velocities of
al dependence of elastic properties of the earth, went unnoticed for    waves propagating through VTI media. This observation led to the
years because we usually looked at the subsurface through too nar-      introduction of the anellipticity coefficient η ≈ ε – δ that, along with
row fans of rays. Even though mis-ties in time-to-depth conversion,     conventional NMO velocity, enables one to perform time process-
caused by the difference between stacking and vertical velocities       ing of P-waves in laterally homogeneous VTI media (Alkhalifah
due to anisotropy, were routinely observed, geophysicists dealt         and Tsvankin, 1995). Once superior quality of anisotropic time
with them by simply stretching isotropic images.                        images over the isotropic ones became apparent, and correlation
                                                                        between the estimated values of η and lithology was established,
    The situation changed some fifteen years ago due to rapid           many oil and service companies incorporated Alkhalifah-Tsvankin
advances in the whole suite of methodologies employed by the            methodology into their processing flow.
seismic industry. As the quality of seismic data increased, even rel-
atively small violations of our conventional isotropic assumptions          While VTI models are generally considered to be acceptable for
became noticeable. With the technological progress in acquisition,      sedimentary basins, they are clearly insufficient for describing
which made acquiring long-offset and multicomponent data feasi-         azimuthally varying seismic signatures recorded over fractured
ble and cost-effective, anisotropy showed up, requiring geophysi-       reservoirs. Although one might expect that complicated rheology of
cists do something about it and with it.                                fractured media should produce seismic responses that would be
                                                                        difficult to interpret, this turned out not to be the case. Grechka and
Current state of affairs                                                Tsvankin (1998) showed that the azimuthal dependence of pure-
                                                                        mode (e.g., P-P and S-S) NMO velocities is an ellipse under the
   The day of practical treatment and use of seismic anisotropy in      same general assumptions that result in the familiar hyperbolic
exploration and exploitation contexts probably began in 1986 when       form of reflection moveout. In addition, azimuthal behavior of
two cornerstone papers of Alford (1986) and Thomsen (1986) were         prestack reflection amplitudes of pure modes was also found to be
published. Both papers apparently appeared ahead of their time          approximately quadratic in sines and cosines of the azimuth as long   ˆ
and for this reason were not immediately appreciated. The extreme-      as offsets do not exceed the reflector depth (Rüger, 1997; Vavrycuk
                                                                              ˆ   ˆ                                                   Vavrycuk
ly clear result of Alford (1986) that shear-wave data cannot be              Psencík,
                                                                        and PöencÌk, 1998). Having realized that seismic signatures are suf-
processed without taking azimuthal anisotropy into account was          ficiently sensitive to certain fracture parameters (called the excess
regarded by some part of the exploration community as an unfor-         fracture compliances), Bakulin et al. (2000) devised a suite of tech-
tunate complication that could be avoided by simply not dealing         niques for quantitative fracture characterization.
with S-waves.

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ARTICLE                     Cont’d
Continued from Page 9

    The progress in multicomponent ocean-bottom technology,               References
which already resulted in acquiring high-quality converted-wave           Alford R.M., 1986, Shear data in the presence of azimuthal anisotropy: 56th SEG
(PS) reflection data, put an additional emphasis on seismic                  meeting, Expanded Abstracts, 476-479.
anisotropy. The reason for this becomes clear once we recognize           Alkhalifah, T., and Tsvankin, I., 1995, Velocity analysis for transversely isotrop-
that one-half of the ray trajectories of converted PSV reflections is        ic media: Geophysics, 60, 1550-1566.
composed of SV-waves whose velocity anisotropy is often about an          Backus, G.E., 1962, Long-wave elastic anisotropy produced by horizontal layering:
order of magnitude greater than that of P modes. Therefore, while            J. Geophys. Res., 67, 4427-4440.
ignoring P-wave anisotropy may be sometimes acceptable, it is no
                                                                          Bakulin, A., Grechka, V., and Tsvankin, I., 2000, Estimation of fracture param-
longer possible for converted waves. Such a conclusion could have            eters from reflection seismic data. Part I-III: Geophysics, 65, 1788-1830.
meant the end of multicomponent seismic exploration some fifteen
                                                                          Grechka, V., Contreras, P., and Tsvankin, I., 2000, Inversion of normal moveout
years ago; however, perception of anisotropy by the exploration              for monoclinic media: Geophysical Prospecting, 48, 577-602.
community has changed . Many geophysicists now recognize that
                                                                          Grechka, V., and Tsvankin, I., 1998, 3-D description of normal moveout in
shear-wave velocities and anisotropic parameters, which can be
                                                                             anisotropic inhomogeneous media: Geophysics, 63, 1079-1092.
inferred from PP and PS reflection data, might help to discriminate
                                                                          Rüger A., 1997, P-wave reflection coefficients for transversely isotropic models
lithology, predict pore pressure, and characterize fractures or stress.
                                                                            with vertical and horizontal axis of symmetry: Geophysics, 62, 713-722.
The benefits of obtaining such information significantly overweigh
the difficulties of dealing with anisotropy.                              Thomsen, L., 1986, Weak elastic anisotropy: Geophysics, 51, 1954-1966.
                                                                          Thomsen, L., 2001, Seismic anisotropy: Geophysics, 66, 40-41.
A look ahead                                                              Tsvankin, I., 1997, Anisotropic parameters and P-wave velocity for orthorhombic
   There is no doubt that the existing technologies will be refined          media: Geophysics, 62, 1292-1309.
and developed further to make estimates of anisotropy and related         Tsvankin, I., 2001, Seismic signatures and analysis of reflection data in anisotrop-
rock properties more accurate. Advances can be expected in the fol-          ic media: Elsevier Science Publ.
                                                                                 ˆ               ˆ    ˆ
lowing areas.                                                             VavrycukV., and Psencík, I., 1998, PP-wave reflection coefficients in weakly
                                                                          Vavrycuk,       PöencÌk,
                                                                              anisotropic elastic media: Geophysics, 63, 2129-2141.
Imaging                                                                   White, J.E., and Sengbush, R.L., 1953, Velocity measurements in near-surface
                                                                            formations: Geophysics, 18, 54-69. R
    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        The very publishing of this article, a similar review written by Thomsen (2001), as well
                                                                          as the comprehensive monograph of Tsvankin (2001), who discusses methodologies
time or depth processing. As more studies are done, we will gain a        of seismic processing in anisotropic media, indicates that anisotropy is no longer con-
better understanding of the influence of various trade-offs on the        sidered an academic subject irrelevant to exploration needs.
estimated anisotropic velocity fields and, consequently, on the qual-
ity of the obtained migration images.
                                                                                            HAVE YOU
Multicomponent seismology                                                                   MOVED?
   Measuring shear-wave velocities (as opposed to computing
them from the P-wave ones using some empirical relationships) has
                                                                                                             DO YOU KNOW
clear benefits for many exploration tasks. Since S-waves are difficult                                           SOMEONE
to excite on land and virtually impossible offshore, converted                                                       THAT
waves will become the primary source of S-wave information. It
remains to be seen how much can be gained from the obtained S-
                                                                                                              HAS MOVED?
wave velocities and anisotropies for different subsurface plays.
                                                                                            LET US
Reservoir characterization                                                                  KNOW . . .
   Techniques for estimating local reservoir anisotropy from vari-
ous borehole and vertical seismic profiling (VSP) data will continue
to evolve. We can anticipate development of more accurate meth-
ods that relate measured anisotropy to such important reservoir
characteristics as in situ stress, fractures, pore pressure, and perme-
ability. Once we learn how to make these methods more robust, the
same measurements will be used in a time-lapse sense to optimize                                                fax: 403-262-7383
reservoir production.                                                                                           email:
                                                                                                                call: 403-262-0015

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