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CWP-642P
Seismic anisotropy in exploration and reservoir
characterization: An overview
I. Tsvankin1, J. Gaiser2, V. Grechka3, M. van der Baan4, &
L. Thomsen51Colorado School of Mines, Department of Geophysics,
Center for Wave Phenomena, Golden, CO, USA.2Geokinetics, Denver,
CO, USA.3Shell Exploration & Production Company, Houston, TX,
USA.4University of Alberta, Department of Physics, CEB, 11322-89
Ave., Edmonton, Alberta, T6G 2G7, Canada.5Delta Geophysics,
Houston, TX, USA.
ABSTRACTRecent advances in parameter estimation and seismic
processing have allowedincorporation of anisotropic models into a
wide range of seismic methods. Inparticular, vertical and tilted
transverse isotropy are currently treated as an in-tegral part of
velocity fields employed in prestack depth migration
algorithms,especially those based on the wave equation. Here, we
briefly review the stateof the art in modeling, processing, and
inversion of seismic data for anisotropicmedia. Topics include
optimal parameterization, body-wave modeling methods,P-wave
velocity analysis and imaging, processing in the τ–p domain,
anisotropyestimation from vertical seismic profiling (VSP) surveys,
moveout inversion ofwide-azimuth data,
amplitude-variation-with-offset (AVO) analysis, processingand
applications of shear and mode-converted waves, and fracture
characteri-zation. When outlining future trends in anisotropy
studies, we emphasize thatcontinued progress in data-acquisition
technology is likely to spur transitionfrom transverse isotropy to
lower anisotropic symmetries (e.g., orthorhombic).Further
development of inversion and processing methods for such
realisticanisotropic models should facilitate effective application
of anisotropy parame-ters in lithology discrimination, fracture
detection, and time-lapse seismology.
Key words: Seismic anisotropy, velocity analysis, prestack
migration, pa-rameter estimation, transverse isotropy, AVO
analysis, multicomponent data,mode-converted waves, shear-wave
splitting, fracture characterization, verticalseismic profiling
1 INTRODUCTION
The area of applied seismic anisotropy is undergoingrapid
transformation and expansion. Whereas the theo-retical foundation
for describing anisotropic wave prop-agation had been developed a
long time ago, the multi-parameter nature of anisotropic models had
precludedtheir widespread application in seismic exploration
andreservoir monitoring. The role of anisotropy has dra-matically
increased over the past two decades due toadvances in parameter
estimation, the transition frompoststack imaging to prestack depth
migration, thewider offset and azimuthal coverage of 3D surveys,
andacquisition of high-quality multicomponent data. Cur-
rently, many seismic processing and inversion meth-ods operate
with anisotropic models, and there is littledoubt that in the near
future anisotropy will be treatedas an inherent part of velocity
fields.
A detailed historical analysis of developments inseismic
anisotropy can be found in Helbig and Thom-sen (2005), so here we
mention just several milestones.The work of Crampin (1981, 1985),
Lynn and Thomsen(1986), Willis et al. (1986), Martin and Davis
(1987),and others convincingly demonstrated that anisotropyhas a
first-order influence on shear and mode-convertedPS-waves, which
split into the fast and slow modeswith orthogonal polarizations.
Shear-wave processing
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354 I. Tsvankin, et al.
based on Alford (1986) rotation and its modificationshas helped
document ubiquitous azimuthal anisotropyin the upper crust
typically caused by near-vertical sys-tems of aligned fractures and
microcracks. Acquisitionand processing of high-quality
multicomponent offshoresurveys starting in the mid-1990’s clearly
showed thatPP- and PS-wave sections could not be tied in
depthwithout making the velocity model anisotropic.
In contrast, anisotropy-induced distortions in P-wave imaging
(the focus of the majority of explorationsurveys) are less
dramatic, especially for poststack pro-cessing of narrow-azimuth,
moderate-spread data. Also,incorporating anisotropy into velocity
analysis requiresestimation of several independent, spatially
variable pa-rameters, which may not be constrained by P-wave
re-flection traveltimes. Hence, the progress in P-wave pro-cessing
can be largely attributed to breakthroughs inparameterization of
transversely isotropic (TI) models,most notably the introduction of
Thomsen (1986) no-tation and the discovery of the P-wave
time-processingparameter η (Alkhalifah and Tsvankin, 1995). The
ex-ploding interest in anisotropy and the importance ofthe
parameterization issue have made Thomsen’s clas-sical ’86 article
the top-cited paper ever published in thejournal Geophysics.
More recently, the inadequacy of isotropic velocitymodels was
exposed by the advent of prestack depthmigration, which is highly
sensitive to the accuracy ofthe velocity field. As a result, TI
models with a verti-cal (VTI) and tilted (TTI) axis of symmetry
have be-come practically standard in prestack imaging projectsall
over the world. For instance, anisotropic algorithmsproduce
markedly improved images of subsalt explo-ration targets in the
Gulf of Mexico, which has long beenconsidered as a region with
relatively “mild” anisotropy.
The goal of this paper is to give a brief descriptionof the
state of the art in anisotropic modeling, process-ing, and
inversion and outline the main future trends.It is impossible to
give a complete picture of the fieldin a journal article, and the
selection of the materialinevitably reflects the personal research
experience andpreferences of the authors. For in-depth discussion
oftheoretical and applied aspects of seismic anisotropy, werefer
the reader to the books by Helbig (1994), Thomsen(2002), Tsvankin
(2005), and Grechka (2009).
2 NOTATION FOR ANISOTROPIC MEDIA
One of the most critical issues in seismic data analysisfor
anisotropic media is a proper design of model pa-rameterization.
Whereas the stiffness coefficients (cij)are convenient to use in
forward-modeling algorithms,they are not well-suited for
application in seismic pro-cessing and inversion. An alternative
notation for trans-verse isotropy was introduced by Thomsen (1986),
whosuggested to describe the medium by the symmetry-direction
velocities of P- and S-waves (VP0 and VS0,
respectively) and three dimensionless parameters (ǫ, δ,and γ),
which characterize the magnitude of anisotropy.The parameter ǫ is
close to the fractional difference be-tween the P-wave velocities
in the directions perpendic-ular and parallel to the symmetry axis,
so it defines whatis often simplistically called the “P-wave
anisotropy.”Likewise, γ represents the same measure for
SH-waves.While the definition of δ seems less transparent,
thisparameter also has a clear meaning – it governs the P-wave
velocity variation away from the symmetry axisand also influences
the SV-wave velocity.
Although Thomsen originally used the assump-tion of weak
anisotropy (i.e., |ǫ| ≪ 1, |δ| ≪ 1, and|γ| ≪ 1), his notation has
since emerged as the bestchoice in seismic processing for TI media
with any mag-nitude of velocity variations. Indeed, Thomsen
param-eters capture the combinations of the stiffness coeffi-cients
constrained by seismic signatures (for details, seeTsvankin, 2005).
In particular, P-wave kinematics forTI media with a given
symmetry-axis orientation de-pend on just three Thomsen parameters
(VP0, ǫ, andδ; the contribution of VS0 is negligible), rather
thanfour stiffness coefficients (c11, c33, c13, and c55). Thom-sen
notation is especially convenient for reflection dataprocessing
because it greatly simplifies expressions fornormal-moveout (NMO)
velocity, quartic moveout coef-ficient,
amplitude-variation-with-offset (AVO) response,and geometric
spreading. Linearization of exact equa-tions in ǫ, δ, and γ
provides valuable insight into the in-fluence of transverse
isotropy on seismic wavefields andhelps guide inversion and
processing algorithms.
Moreover, the contribution of anisotropy to time-domain
processing of P-wave reflection data for VTImedia is absorbed by
the single “anellipticity” parame-ter η close to the difference
between ǫ and δ
[η ≡ (ǫ− δ)/(1 + 2δ)] .
The interval values of η and the NMO velocity forhorizontal
reflectors [Vnmo(0)] are sufficient to performnormal-moveout and
dip-moveout corrections, prestackand poststack time migration for
VTI models witha laterally homogeneous overburden (Alkhalifah
andTsvankin, 1995). Most importantly, the time-processingparameters
Vnmo(0) and η can be estimated just from P-wave reflection
traveltimes using NMO velocity of dip-ping events or nonhyperbolic
moveout.
The parameters required for P-wave imaging andAVO analysis in
VTI media are listed in Table 1.Whereas ǫ usually quantifies the
magnitude of P-wavevelocity variations, the parameters of more
importancein seismic processing are δ and η. Laboratory
mea-surements of the anisotropy parameters for sedimen-tary rocks
from different regions are summarized byWang (2002). Both
rock-physics and seismic data indi-cate that vertical and tilted
transverse isotropy in sedi-mentary basins are mostly associated
with the intrinsicanisotropy of shales caused by aligned
plate-shaped clay
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Overview of seismic anisotropy 355
Full set Depth imaging Time imaging AVO (intercept,
gradient)
VP0 VP0 Vnmo(0) VP0
ǫ or η ǫ or η η –
δ δ – δ
VS0 – – VS0
Table 1. P-wave parameters for imaging and AVO analysis in VTI
media. The parameter Vnmo(0) = VP0√
1 + 2δ is the NMOvelocity for horizontal reflectors.
particles. Many sedimentary formations including sandsand
carbonates, however, contain vertical or steeply dip-ping fracture
sets and should be described by effectivesymmetries lower than TI,
such as orthorhombic (seebelow). The effective anisotropy
parameters are also in-fluenced by fine layering on a scale small
compared toseismic wavelength (Backus, 1962).
The principle of Thomsen notation has been ex-tended to
orthorhombic (Tsvankin, 1997; 2005), mono-clinic (Grechka et al.,
2000) and even the most general,triclinic (Mensch and Rasolofosaon,
1997) models. Forinstance, Tsvankin’s notation for orthorhombic
mediapreserves the attractive features of Thomsen parame-ters in
describing the symmetry-plane velocities, travel-times, and
plane-wave reflection coefficients of P-, S1-,and S2-waves. It also
reduces the number of parametersresponsible for P-wave kinematics
and provides a uni-fied framework for treating orthorhombic and TI
modelsin parameter-estimation methods operating with wide-azimuth,
multicomponent data (Grechka et al., 2005).
Estimation of anisotropy from P-wave vertical seis-mic profiling
(VSP) data acquired under a structurallycomplex overburden involves
expressing the verticalslowness component in terms of the
polarization direc-tion. This problem, discussed in more detail
below, leadsto the definition of Thomsen-style anisotropy
parame-ters specifically tailored to VSP applications (Grechkaand
Mateeva, 2007; Grechka et al., 2007).
Furthermore, Thomsen notation has been general-ized for
attenuative TI and orthorhombic media in orderto facilitate
analytic description and inversion of body-wave attenuation
coefficients (Zhu and Tsvankin, 2006,2007). For a model with VTI
symmetry of both the realand imaginary parts of the stiffness
matrix, this notation(in addition to Thomsen’s velocity-anisotropy
parame-ters) includes the vertical attenuation coefficients of
P-and S-waves (AP0 and AS0) and three dimensionless pa-rameters
(ǫ
Q, δ
Q, and γ
Q) responsible for attenuation
anisotropy. Linearization of the P-wave phase attenua-tion
coefficient in the anisotropy parameters yields anexpression that
has exactly the same form as Thom-sen’s (1986) weak-anisotropy
approximation for P-wavephase velocity.
Whereas the optimal choice of notation is a pre-
requisite for successful anisotropic parameter estimationand
processing, it is also important in forward modeling,which is
discussed next.
3 FORWARD MODELING OF BODYWAVES
The ability to compute synthetic seismograms has al-ways been a
high priority in geophysics since accu-rate forward modeling can be
a valuable aid in seis-mic interpretation and inversion.
Unfortunately, a fullyanisotropic (triclinic) Earth is
characterized by 21 stiff-ness coefficients (or Thomsen-style
parameters) anddensity, all of which may vary in space.
Full-waveform modeling can be implemented bysolving the wave
equation for a general 3D (an)elasticmedium using numerical
techniques such as finite-difference, finite-element,
pseudospectral and spectral-element methods (Kosloff and Baysal,
1982; Virieux,1986; Komatitsch and Tromp, 1999). Although
orig-inally many of these approaches were developed forisotropic
media, most have been extended to handleanisotropic, anelastic
media (Carcione et al., 1988; Ko-matitsch et al., 2000); for a
recent review, see Carcioneet al. (2002).
Despite the constantly increasing computationalpower, full
anisotropic (i.e., with 21 stiffnesses) model-ing using the above
techniques is still rarely attempteddue to the scale of the problem
and staggering number ofpossible models. In practice three avenues
are commonlyexplored to facilitate interpretation and reduce
compu-tation demands: (i) simplifications to theory; (ii)
re-duction of information content in the acquired data;and (iii)
limitations to considered structures, anisotropicsymmetries, and/or
medium types. For instance, seismicwaves are often represented
through rays, thereby in-voking a high-frequency approximation
(simplificationsto theory). Also, one can choose to analyze
traveltimesand/or amplitudes only (reduction in information
con-tent), treat only specific types of anisotropy, assumethat wave
motion can be described by P-wave propa-gation in acoustic media,
and/or impose lateral conti-nuity and consider only vertically
heterogeneous struc-
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356 I. Tsvankin, et al.
tures (constraints on media and/or structures). Obvi-ously,
several approaches can be combined to developan appropriate
interpretation strategy.
The earliest efforts to compute body-wave synthet-ics in
anisotropic media focused on either simulation offull waveforms for
simple models with at most one in-terface (Buchwald, 1959;
Lighthill, 1960) or traveltimecalculations by means of geometric
ray theory (Vlaar,1968; Červený, 1972). The former efforts were
motivatedby the development of ultrasonic techniques for the
mea-surement of dynamic elastic constants of pure crystalsand
metals (Musgrave, 1970; Auld, 1973). The latterapproach was largely
directed at explaining and under-standing anomalous body-wave
properties observed inrefraction experiments and seismic arrays
(Hess, 1964).
The ray method is a far-field, high-frequency,asymptotic
approximation, which can handle later-ally and vertically
heterogeneous anisotropic media un-der the assumption that the
medium parameters varysmoothly on the scale of wavelength. In
addition tobeing much less computationally intensive than
finite-difference schemes and similar numerical methods, raytheory
makes it possible to model individual wave typesrather than the
whole wavefield. Ray tracing can be usedto generate both
traveltimes and amplitudes; yet seriousdifficulties arise
(especially for amplitude computations)near singular areas, such as
caustics, cusps and conicalpoints on the wavefronts, shadow zones,
and propaga-tion directions for which the velocities of the split
S-waves are close (Gajewski and Pšenč́ık, 1987). Some ofthese
problems are related to wavefront folding whenmany rays pass
through a common focal point or focalline – a phenomenon that
complicates the evaluationof geometric spreading. Geometric ray
theory also ex-cludes head waves. Despite its limitations, ray
theoryis still at the heart of many migration algorithms thatemploy
ray tracing for efficient generation of traveltimetables. A more
detailed discussion of ray theory can befound in the paper by
Carcione et al. (2002) and mono-graphs by Červený (2001) and
Chapman (2004).
The reflectivity method takes an alternative avenueto compute
full-waveform synthetics in laterally homo-geneous media (Kennett,
1983). The technique is basedon plane-wave decomposition of
point-source radiationcombined with the solution of the plane-wave
reflec-tion/transmission problem for layered media obtainedusing
so-called “propagator matrices” (Haskell, 1953;Gilbert and Backus,
1966). It can model both kinematicand dynamic properties of
recorded wavefields includ-ing all primary and multiple
reflections, conversions andhead waves, as long as the 1D
assumption (i.e., the elas-tic properties vary only with depth) is
satisfied (Fuchsand Müller, 1971; Kennett, 1972). The anisotropic
re-flectivity method, originally developed for VTI mod-els and
symmetry-plane wave propagation (Keith andCrampin, 1977; Booth and
Crampin, 1983), has been
extended to azimuthally anisotropic media (Fryer andFrazer,
1984; Tsvankin and Chesnokov, 1990).
Despite its 1D model assumption, the reflectivitymethod has
proved to be a valuable tool for under-standing and interpreting
wave-propagation phenom-ena in both VSP and surface-seismic
acquisition geome-tries. For instance, Mallick and Frazer (1991)
employthis technique to study P-wave amplitude variationswith
offset and azimuth in a medium containing verti-cal fractures and
demonstrate how azimuthal amplitudeanomalies can help reveal
fracture orientation.
4 P-WAVE VELOCITY ANALYSIS ANDIMAGING
Most isotropic time- and depth-migration algo-rithms [Kirchhoff,
Stolt, phase-shift, phase-shift-plus-interpolation (PSPI), Gaussian
beam, finite-difference,etc.] have been generalized for VTI and, in
many cases,TTI media (e.g., Sena and Toksöz, 1993; Anderson etal.,
1996; Alkhalifah, 1997; Ren et al., 2005; Zhu et al.,2007a). The
key issue in anisotropic processing, how-ever, is reliable
estimation of the velocity model fromreflection data combined with
borehole and other infor-mation. The parameter η responsible for
time process-ing in VTI media can be obtained by inverting
eitherdip-dependent NMO velocity or nonhyperbolic (long-spread)
reflection moveout (Alkhalifah and Tsvankin,1995; Alkhalifah, 1997;
Toldi et al., 1999; Fomel, 2004;Tsvankin, 2005; Ursin and Stovas,
2006). Then the η-field can be refined in the migrated domain using
mi-gration velocity analysis (Sarkar and Tsvankin, 2004)
orreflection tomography (Woodward et al., 2008).
Building VTI velocity models in the depth domaintypically
requires a priori constraints because the verti-cal velocity VP0
and the parameters ǫ and δ can seldombe determined from P-wave
reflection moveout alone.In many cases, VP0 is found from check
shots or welllogs at borehole locations and used in combination
withthe stacking (NMO) velocity to compute the parame-ter δ. Note
that ignoring the contribution of δ to NMOvelocity in isotropic
processing leads to misties in time-to-depth conversion. Then the
velocity field can be con-structed by interpolating the parameters
VP0 and δ be-tween the boreholes and estimating η (and,
therefore,ǫ) from reflection data. Integration of seismic and
bore-hole data can be facilitated by applying geologic con-straints
in the process of interpretive model updating(Bear et al., 2005) or
rec asting the generation of a denseanisotropic velocity field as
an optimization problem.An efficient tool for building
heterogeneous VTI mod-els is postmigration grid tomography based on
iterativeminimization of residual moveout after prestack
depthmigration (Woodward et al., 2008).
Anisotropic migration with the estimated Thom-sen parameters
typically produces sections with betterfocusing and positioning of
reflectors for a wide range
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Overview of seismic anisotropy 357
of dips including steep interfaces, such as flanks of saltdomes.
The 2D line in Figure 1 is used by Alkhalifahet al. (1996) to
illustrate the improvements achievedby anisotropic time processing
in offshore West Africawhere thick TI shale formations cause
serious imagingproblems (Ball, 1995). For example, VTI
dip-moveoutand poststack migration algorithms succeeded in imag-ing
the fault plane at midpoint 7.5 km and depth 3 km(the right arrow
in Figure 1b), which is absent on theisotropic section (Figure 1a).
Also, the major fault planebetween the midpoints at 2 km and 8 km
(it stretchesup and down from the middle arrow in Figures 1a,b)and
gently dipping reflectors throughout the section ap-pear more crisp
and continuous. Accurate fault imagingbeneath the shales plays a
major role in prospect iden-tification in the area.
It is even more critical to properly account foranisotropy in
prestack depth migration because the re-sults of prestack imaging
are highly sensitive to thequality of the velocity model. The
section in Figure 2bwas produced by applying VTI migration velocity
anal-ysis (MVA) and Kirchhoff prestack depth migration tothe line
from Figure 1 (Sarkar and Tsvankin, 2006).MVA was carried out by
dividing the section into fac-torized VTI blocks, in which the
parameters ǫ and δ areconstant, while the velocity VP0 is a linear
function ofthe spatial coordinates. Factorized VTI is the
simplestmodel that allows for both anisotropy and heterogeneityand
requires minimal a priori information to constrainthe relevant
parameters (Sarkar and Tsvankin, 2004). Inthe absence of pronounced
velocity jumps across layerboundaries, knowledge of the vertical
velocity at thetop of a piecewise-factorized VTI medium is
sufficientto estimate the parameters VP0, ǫ, and δ along with
thevelocity gradients throughout the section using only P-wave data
(Figures 3a,c,d).
The velocity analysis revealed significant lateral ve-locity
gradients in some of the layers (Figure 3a), whichcould not be
handled by time-domain techniques. Asa result, the depth-domain
parameter estimation pro-duced a more reliable, laterally varying
η-field (Fig-ure 3b). The depth imaging facilitated structural
inter-pretation of the deeper part of the section by remov-ing the
false dips seen in Figure 2a. Also, most anti-thetic faults that
look fuzzy on the time section arewell focused, and subhorizontal
reflectors within theanisotropic layers are better positioned and
stacked.This and many other published case studies demon-strate
that a major advantage of anisotropic depthimaging is in providing
accurate well ties without sacri-ficing image quality.
In tectonically active areas or in the presence of dip-ping
fracture sets the symmetry axis of TI formationscan be tilted, and
the VTI model becomes inadequate.Tilted transverse isotropy is
common in the CanadianFoothills, where shale layers are often bent
and mayhave steep, variable dips (e.g., Vestrum et al., 1999).
Figure 1. Comparison between isotropic and VTI timeimaging
(after Alkhalifah et al., 1996, and Sarkar andTsvankin, 2006). A 2D
line from West Africa after (a)isotropic and (b) anisotropic time
imaging. The processingsequence included NMO and DMO corrections
and post-stack phase-shift time migration. Both time sections
arestretched to depth. The arrows point to the main improve-ments
achieved by taking anisotropy into account.
Also, uptilted shale layers near salt domes may causeserious
difficulties in imaging steeply dipping segmentsof the salt flanks
(Tsvankin, 2005). A detailed descrip-tion of distortions caused by
applying VTI algorithmsto data from typical TTI media can be found
in Beheraand Tsvankin (2009), who extend MVA to TI modelswith the
symmetry axis orthogonal to reflectors. In theircase studies from
the Gulf of Mexico, Huang et al. (2009)and Neal et al. (2009)
demonstrate that accounting forthe tilt of the symmetry axis
produces significant im-provements in imaging of steep dips, fault
resolution,and spatial positioning of reflectors. The inadequacy
ofVTI models for many subsalt plays in the Gulf of Mex-ico has
become especially apparent with acquisition ofwide-azimuth surveys.
In complicated structural envi-ronments, the full benefits of TI
imaging can be realizedwith reverse time migration (RTM) based on
solving thetwo-way wave equation (Huang et al., 2009). RTM withTTI
or VTI velocity models is already widely used inGoM subsalt imaging
projects.
Despite the recent successes, parameter estimationfor
heterogeneous TTI media remains a highly challeng-ing problem, even
with the common assumption that thesymmetry axis is orthogonal to
reflectors. Methods cur-rently under development combine TI
ray-based reflec-tion tomography with check shots and walkaway
VSP
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358 I. Tsvankin, et al.
0.0 4.0 8.0Midpoint (km)
2.0
4.0Dep
th (
km)
2.0
Dep
th (
km)
4.0
0.0 4.0 8.0Midpoint (km)
Figure 2. Comparison between VTI time and depth imag-ing (after
Sarkar and Tsvankin, 2006). The line from Figure 1after (a)
anisotropic time processing (same as Figure 1b) and(b) anisotropic
MVA and prestack depth migration. The ar-rows point to the main
differences between the two sections.
surveys (e.g., Bakulin et al., 2009). It is likely that
pro-cessing of high-quality wide-azimuth surveys in some areas will
require employing more complicated (but morerealistic),
orthorhombic velocity models. A promisingdirection for
high-resolution anisotropic velocity anal-ysis is full-waveform
inversion, which so far has beendeveloped mostly for acoustic
models.
5 SLOWNESS-BASED PROCESSING ANDINVERSION
Processing and inversion of surface seismic data ismostly done
in the time-offset domain; yet other do-mains may offer advantages
in terms of noise sup-pression and/or inversion for anisotropy
parameters.It is especially beneficial to transform seismic
datainto the slowness domain, with applications as diverseas
common-conversion-point sorting, anisotropy estima-tion,
geometric-spreading correction, and amplitude andfull-waveform
inversion.
Snell’s law states that the horizontal slowness pdoes not change
along a ray in 1D models. This facthelps identify correlated
pure-mode (PP) and converted(PS) reflections from the same
interface that have com-mon downgoing P-wave ray segments (and,
therefore,the same horizontal slownesses). Identification of
com-mon ray segments leads to a straightforward
common-conversion-point sorting scheme in both the time-offsetand
intercept time - horizontal slowness (τ -p) domains
80 4Midpoint (km)
2
0
4
Dep
th (
km)
2
4
Vertical velocity (km/s)
(a)
80 4Midpoint (km)
2
0
4D
epth
(km
)
η
0.0
0.1
(b)
80 4Midpoint (km)
2
0
4
Dep
th (
km)
ε
0.15
0.05
(c)
80 4Midpoint (km)
2
0
4
Dep
th (
km)
δ
0.05
0.00
(d)
Figure 3. Estimated parameters (a) VP0; (b) η; (c) ǫ; and(d) δ
used to generate the depth-migrated section in Fig-ure 2b (after
Sarkar and Tsvankin, 2006).
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Overview of seismic anisotropy 359
(Van der Baan, 2005). In the presence of lateral and ver-tical
velocity variations one can still identify PP and PSreflections
with the same takeoff angles (i.e., the samehorizontal slownesses)
at the source by matching theirtime slopes in common-receiver
gathers. This more gen-eral scheme called “PP+PS=SS” (discussed in
more de-tail below) is designed to construct the traveltimes
ofpure-mode SS reflections solely from acquired PP- andPS-waves
(Grechka and Tsvankin, 2002).
Slowness-based traveltime inversion can also in-crease the
accuracy of interval parameter estimation.Anisotropic traveltime
inversion is often based on move-out approximations that become
unnecessary if seismicdata are processed by means of a plane-wave
decom-position, such as the τ -p transform. Indeed,
plane-wavepropagation is directly governed by phase rather
thangroup velocities because the interval τ (p) curves repre-sent
rescaled versions of the slowness functions (Hake,1986). Note that
phase velocities generally are less com-plex mathematically
compared to group velocities.
A τ -p domain approach has been applied by Gaiser(1990) to
analysis of VSP data, by Hake (1986) andVan der Baan and Kendall
(2002, 2003) to inversionof reflections traveltimes, and by Mah and
Schmitt(2003) to processing of ultrasonic measurements. Sim-ilar
gains in accuracy can be obtained by formulat-ing slowness-based
inversion algorithms directly in thetime-offset domain (Douma and
Van der Baan, 2008;Fowler et al., 2008; Dewangan and Tsvankin,
2006a;Wang and Tsvankin, 2009). It should be mentioned thatthe
velocity-independent layer-stripping method of De-wangan and
Tsvankin (2006a) is valid for an arbitrarilyheterogeneous target
horizon. An important feature ofslowness-based algorithms is that
they replace Dix-typedifferentiation of moveout parameters with
traveltimestripping (Figure 4), which increases the accuracy
andstability of interval parameter estimates.
Plane-wave decomposition also represents a conve-nient tool for
geometric-spreading correction in horizon-tally layered media.
Indeed, plane waves in 1D mod-els are not subject to geometric
spreading (in contrastto spherical waves); this is implicitly used
in the re-flectivity method discussed above (Fuchs and
Müller,1971; Kennett, 1983; Fryer and Frazer, 1984). Wangand
McCowan (1989), Dunne and Beresford (1998) andVan der Baan (2004)
explicitly employ plane-wave de-composition to remove the
geometric-spreading factorfrom the amplitudes of all primary and
multiple re-flections (including mode conversions)
simultaneously.Subsequent moveout correction and stacking in the τ
-p domain (Stoffa et al., 1981, 1982) generates higher-quality
stacked sections compared to those produced bythe standard
time-offset stacking process (Figure 5). In-terestingly, stacking
in the slowness domain preserveshead waves suppressed by
conventional processing (Vander Baan, 2004).
Finally, plane-wave decomposition may facilitate
amplitude analysis at far offsets near and beyond thecritical
angle, where the wavefield in the time-offset do-main cannot be
described by plane-wave reflection co-efficients (Van der Baan,
2004; Van der Baan and Smit,2006; Tsvankin, 1995a). Thus,
slowness-based process-ing and inversion has many advantages for
data fromanisotropic media. Indeed, it has been suggested in
theliterature that seismic inversion techniques should beapplied to
slant-stacked data obtained after a plane-wave decomposition
(Müller, 1971; Fryer, 1980; Trei-tel et al., 1982). This approach
is also suitable for full-waveform inversion in stratified media
(Kormendi andDietrich, 1991; Martinez and McMechan, 1991; Ji
andSingh, 2005) and separation of interfering PP and PSwaves (Van
der Baan, 2006).
6 ANISOTROPY ESTIMATION FROM VSPDATA
The concept of operating with slowness measurementsis also
essential in processing of vertical seismic profilingsurveys.
Although anisotropic velocity models have tobe built based on
surface reflection data for most appli-cations in seismic
exploration, VSP can often provideuseful complementary anisotropy
estimates. Becausethose estimates are made at seismic frequencies,
theyhave an important advantage over well-log
anisotropymeasurements, which pertain to the frequency range of103
− 104 Hz and require upscaling for use in seismicprocessing. The
anisotropy parameters constrained byVSP data strongly depend on
both the acquisition de-sign and the magnitude of lateral
heterogeneity of theoverburden.
The simplest VSP experiment involves a single geo-phone placed
in a well. First-break P-wave times pickedfrom such VSP data
reflect the influence of effectiveanisotropy between the earth’s
surface, where the seis-mic sources are located, and the geophone’s
depth. Be-cause this depth is known, P-wave walkaway VSP data(or
the combination of surface reflection data and checkshots) for
laterally homogeneous VTI media yield the ef-fective Thomsen
parameter δ. Whether or not it is pos-sible to estimate another
anisotropy parameter (η or ǫ)governing P-wave kinematics depends on
the presenceof sufficiently large offsets in the data. While the
useful-ness of such low-resolution anisotropy estimates mightbe
questioned, P-wave traveltimes recorded in any VSPgeometry help
build an exact depth-migration operatorsuitable for constructing a
subsurface image near thegeophone.
The opposite “end member” is a wide-azimuth,multicomponent VSP
survey recorded by a string of geo-phones placed beneath a
laterally homogeneous over-burden. Such VSP data make it possible
to obtain acomplete (triclinic) local stiffness tensor near the
bore-hole. This is demonstrated by Dewangan and Grechka(2003) who
apply the so-called slowness-polarization
-
360 I. Tsvankin, et al.
a) b) c)
Figure 4. Layer stripping in the τ -p domain (after Van der Baan
and Kendall, 2002). A hyperbolic moveout curve in thetime-offset
domain maps onto an ellipse in the τ -p domain, and nonhyperbolic
moveout manifests itself by a deviation fromthe ellipse. (a)
Moveout curves in the τ -p domain are created by summing the
contributions of the individual layers. Removingthe influence of
(b) the top layer or (c) the two top layers yields the moveout in
the corresponding interval. The first and thirdlayers are
isotropic, whereas the second layer is anisotropic, as evidenced by
the strong deviation of its interval moveout froman ellipse on plot
(b).
Position (km) Position (km)
Tim
e (
s)
Tim
e (
s)
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
00.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0
a) b)
Figure 5. Comparison of stacking techniques on field data (after
Van der Baan, 2004). (a) A conventional t-x stacked sectionafter
the geometric-spreading correction. (b) The same section obtained
by stacking in the τ -p domain after applying
plane-wavedecomposition to remove geometric spreading. The two
sections are structurally similar but τ -p processing produced a
highersignal-to-noise ratio at small traveltimes and somewhat
different reflector amplitudes between 1.3 s and 1.6 s.
method (White et al., 1983; de Parscau, 1991; Hsu et al.,1991;
Horne and Leaney, 2000) to estimate anisotropyfrom the traveltimes
and polarization directions of P-,S1-, and S2-waves recorded at
Vacuum Field (New Mex-ico, USA). They conclude that the VSP
measurementscan be well-described by an orthorhombic model witha
near-horizontal symmetry plane. Unfortunately,
theslowness-polarization method can be successfully imple-mented
only when lateral heterogeneity of the overbur-den is negligible.
Then the horizontal slowness compo-nents, which are measured on
common-receiver gathers
and pertain to seismic sources at the earth’s surface, canbe
used to reconstruct the slowness surface at geophonelocations
(Gaiser, 1990; Miller and Spencer, 1994; J́ıleket al., 2003).
Strong lateral heterogeneity (for instance, due tothe presence
of salt in the overburden) renders recon-struction of the slowness
surfaces inaccurate and of-ten makes shear-wave arrivals too noisy
for anisotropicinversion. Consequently, anisotropy has to be
inferredfrom P-waves only, which leads to the introduction
ofThomsen-style parameters for P-wave VSP inversion.
-
Overview of seismic anisotropy 361
6.40
6.46
6.52
6.58
6.70
6.64
Dep
th (
km)
0 0.05 0.1 0.15
21
21.1
21.2
21.3
21.4
21.5
21.6
21.7
21.8
21.9
22
δVSP
Dep
th (
kft)
a
40 60 80 100 120
21
21.1
21.2
21.3
21.4
21.5
21.6
21.7
21.8
21.9
22
Gamma−ray log
b
shale
shale
sand
sand
Figure 6. Comparison of (a) the anisotropy parameter δ VSP (bold
line) estimated from VSP for subsalt sediments in the Gulfof Mexico
with (b) a gamma-ray log (after Grechka and Mateeva, 2007). The
thin lines on plot (a) mark the standard deviationof δ VSP.
The measured quantities include the P-wave verticalslowness
component, q, expressed as a function of thepolar (ψ) and azimuthal
(ϕ) angles of the polarizationvector. The values of q, ψ, and ϕ do
not depend on thestructural complexity of the overburden and
correspondto the vicinity (with the spatial extent
approximatelyequal to the wavelength) of downhole geophones. If
themedium around the borehole is VTI, the vertical slow-ness q is
independent of the polarization azimuth ϕ,and the weak-anisotropy
approximation for q(ψ) takesthe form (Grechka and Mateeva,
2007)
q(ψ) =cosψ
VP0
`
1 + δVSP sin2 ψ + ηVSP sin
4 ψ´
, (1)
where
δVSP =δ
(VP0/VS0)2 − 1and
ηVSP = η(VP0/VS0)
2 + 1
(VP0/VS0)2 − 1(2)
are the anisotropy parameters responsible for the P-wave
slowness-of-polarization dependence.
The pairs {δVSP, ηVSP} and {δ, η} play compara-ble roles for
processing of P-wave VSPs acquired alongvertical boreholes and of
P-wave surface reflection data,respectively, in VTI media. Indeed,
equation 1 revealsthat δVSP is responsible for the near-vertical
variation ofq(ψ), while ηVSP governs the vertical slowness at
largerpolarization angles. Importantly, δVSP and ηVSP absorbthe
shear-wave velocity VS0, rendering its value unneces-sary for
fitting the P-wave slowness-of-polarization func-tions. Grechka and
Mateeva (2007) illustrate this pointand present estimates of δVSP
and ηVSP in a salt bodyand subsalt sediments in the deepwater Gulf
of Mexico.Wheras the salt proved to be nearly isotropic, δVSP inthe
subsalt sediments exhibits a clear correlation withlithology
(Figure 6). As is usually the case for the pa-rameter δ, the value
of δVSP is larger in shales than ina predominantly sandy
interval.
This technique of anisotropy estimation from P-
-
362 I. Tsvankin, et al.
wave VSP surveys has been extended to azimuthalanisotropy. For
example, Grechka et al. (2007) invertwide-azimuth VSP data acquired
at tight-gas RulisonField (Colorado, USA) for Tsvankin’s (1997)
parame-ters of orthorhombic media and show that the
estimatedanisotropic model is consistent with the presence of
gas-filled vertical fractures in a VTI host rock.
7 AZIMUTHAL MOVEOUT ANALYSIS
Azimuthal variation of traveltimes, amplitudes, and at-tenuation
coefficients of reflected waves can providevaluable information
about anisotropy associated withnatural fracture systems,
nonhydrostatic stresses, ordipping TI layers (e.g., Lynn et al.,
1999; Rüger, 2002).Wide-azimuth P-wave data are often acquired on
landfor purposes of fracture characterization via azimuthalmoveout
and AVO analysis. The rapid advent of wide-azimuth offshore
technology, designed primarily for bet-ter imaging of subsalt
exploration targets, is expected tofurther stimulate development of
processing algorithmsfor azimuthally anisotropic models.
Moveout analysis of wide-azimuth, conventional-spread data is
based on the concept of the NMO ellipseand on the generalized
Dix-type averaging equations(Grechka and Tsvankin, 1998; Grechka et
al., 1999).The normal-moveout velocity of pure
(non-converted)reflected waves expressed as a function of the
azimuthα of the CMP line is given by the following
quadraticform:
V −2nmo(α) = W11 cos2 α + 2W12 sinα cosα
+W22 sin2 α , (3)
where W is a symmetric 2×2 matrix determined bythe medium
properties around the zero-offset ray. If thetraveltime increases
with offset in all azimuthal direc-tions (i.e., in the absence of
reverse move out), Vnmo(α)traces out an ellipse even for
arbitrarily anisotropic,heterogeneous media. Furthermore, equation
3 can beapplied to mode-converted waves, if their moveout inCMP
geometry is symmetric with respect to zero offset(this is the case
for horizontally layered models with ahorizontal symmetry
plane).
The equation of the NMO ellipse provides a simpleway to correct
for the azimuthal variation in stackingvelocity often ignored in
conventional processing. Evenmore importantly, the semiaxes and
orientation of theNMO ellipse can be used in anisotropic parameter
esti-mation and fracture characterization. A critical issue
inmoveout analysis of wide-azimuth data is separation ofthe
influence of anisotropy and lateral heterogeneity (inthe form of
velocity gradients, dipping interfaces, veloc-ity lenses, etc.) on
reflection traveltimes (e.g., Jenner,2009).
A data-driven correction of the NMO ellipse for lat-eral
velocity variation in horizontally layered media is
suggested by Grechka and Tsvankin (1999), who presenta complete
processing sequence for azimuthal moveoutinversion that also
includes 3D “global” semblance anal-ysis and generalized Dix
differentiation of effective NMOellipses. They show that the
orientation of the P-waveinterval NMO ellipses produced by this
methodologyin the Powder River Basin (Wyoming, USA) is
well-correlated with the depth-varying fracture trends in
thefield.
P-wave azimuthal moveout analysis has proved tobe effective in
predicting the dominant fracture orien-tation in many other
exploration regions (e.g., Corriganet al., 1996; Lynn et al., 1999;
Tod et al., 2007). Jen-ner (2001), who has developed a
trace-correlation ap-proach for estimating the NMO ellipse, shows
that thefast NMO-velocity direction at Weyburn field in Canadais
aligned with the dominant fracture strike and the po-larization
vector of the fast S-wave; this implies thatthe medium symmetry is
HTI or orthorhombic. Still, insome cases the NMO ellipse is rotated
with respect tothe shear-wave polarization directions, which may
indi-cate the presence of lower symmetries.
Since the P-wave NMO ellipse constrains only threecombinations
of the medium parameters, its inversionfor the physical properties
of fractures (e.g., fracturecompliances) suffers from ambiguity,
which can be re-duced by using the NMO ellipses of the split
S-waves,nonhyperbolic moveout, or other (amplitude,
borehole)information. For instance, joint inversion of the NMO
el-lipses of P- and S-waves with a priori constraints helpsbuild
even orthorhombic and monoclinic velocity models(Grechka et al.,
2000; Vasconcelos and Grechka, 2007);more details are given in the
section on fracture charac-terization.
Among the first to recognize the benefits of em-ploying
nonhyperbolic (long-spread) reflection moveoutin anisotropic
parameter estimation was Sena (1991),whose analytic traveltime
expressions for multilayered,weakly anisotropic media are based
upon the “skewed”hyperbolic moveout formulation of Byun et al.
(1989).Long-spread, wide-azimuth P-wave traveltime in az-imuthally
anisotropic media can be accurately describedby generalizing the
nonhyperbolic moveout equationsof Tsvankin and Thomsen (1994) and
Alkhalifah andTsvankin (1995) originally designed for VTI
media.Vasconcelos and Tsvankin (2006) develop a moveout-inversion
algorithm for horizontally layered orthorhom-bic media based on the
extended Alkhalifah-Tsvankinequation:
t2(x, α) = t20 +x2
V 2nmo(α)(4)
−2η(α) x4
V 2nmo(α) [ t20 V
2nmo(α) + (1 + 2η(α)) x2]
,
where t0 is the zero-offset time, Vnmo(α) is the NMOellipse
(equation 3), and η(α) is the azimuthally vary-ing anellipticity
parameter. Equation 5 can be combined
-
Overview of seismic anisotropy 363
with the velocity-independent layer-stripping method(Dewangan
and Tsvankin, 2006a) to compute the in-terval traveltime in the
target layer and estimate theinterval NMO ellipse and anellipticity
parameters η(1),η(2), and η(3) (Wang and Tsvankin, 2009).
Nonhyper-bolic moveout inversion of wide-azimuth data not
onlyrepresents a promising fracture-characterization tech-nique
(see the case study in Vasconcelos and Tsvankin,2006), but also
provides the input parameters for P-wave time imaging and
geometric-spreading correctionin layered orthorhombic media.
8 PRESTACK AMPLITUDE ANALYSIS
Angle-dependent reflection and transmission coefficientscontain
valuable information about the local mediumproperties on both sides
of an interface. Therefore,analysis of amplitude variations with
incidence angle(usually called AVO – amplitude variation with
offset)and/or azimuth is often used in reservoir characteriza-tion.
Because reflection coefficients are determined bythe elastic
properties averaged on the scale of seismicwavelength, AVO analysis
can achieve a much highervertical resolution than traveltime
methods.
Exact equations for plane-wave reflection coeffi-cients are
cumbersome even for isotropy and, therefore,rarely used in
processing. Whereas exact reflection co-efficients for VTI media
and symmetry planes of or-thorhombic media can still be obtained in
closed form(Daley and Hron, 1977; Rüger, 2002), for lower
sym-metries it is necessary to apply computational schemes(e.g.,
Fryer and Frazer, 1984; J́ılek, 2002a,b). Impor-tant insight into
anisotropic reflectivity is provided bylinearized weak-contrast,
weak-anisotropy approxima-tions, which have a much simpler form and
often reducethe number of free parameters. The approximate
P-wavereflection coefficient for VTI media depends on the
con-trasts in the vertical P- and S-wave velocities (VP0 andVS0),
density, and the parameters δ and ǫ (Banik, 1987;Thomsen, 1993;
Rüger, 1997). Although the contribu-tion of δ distorts the AVO
gradient, the P-wave AVOsignatures in isotropic and VTI media are
generally sim-ilar, which complicates amplitude inversion for the
fiveindependent parameters. Indeed, as shown by de Nico-lao et al.
(1993), only two parameters can be resolvedfrom the isotropic
reflection coefficient.
Analysis of azimuthal amplitude variations showsconsiderably
more promise, in particular for estima-tion of dominant fracture
directions in naturally frac-tured (e.g., tight-gas and tight-oil)
reservoirs (Mallickand Frazer, 1991; Gray et al., 2002). Linearized
P-wave reflection coefficients were derived for HTI mediaand
symmetry planes of orthorhombic media by Rüger(1997, 1998) and for
arbitrary anisotropy by Vavryčukand Pšenč́ık (1998); for
details, see Rüger’s (2002) com-prehensive monograph. Application
of these analytic ex-pressions in quantitative AVO inversion,
however, is hin-
dered by nonuniqueness in parameter estimation. In-stead, it is
more common to reconstruct the azimuthalvariation (which is close
to elliptical) of the magni-tude of the AVO gradient (Gray et al.,
2002; Hall andKendall, 2003). For HTI and orthorhombic media,
theextrema of the AVO gradient lie in the orthogonal ver-tical
symmetry planes of the model.
If azimuthal anisotropy is caused by one set of verti-cal
fractures, the maximum AVO gradient may be eitherparallel or
perpendicular to the fractures, which gener-ally leads to a
90◦-uncertainty in the fracture azimuth.Despite this ambiguity, the
azimuthally varying P-waveAVO response has been successfully used
for estimatingthe dominant fracture orientation and, in some
cases,mapping “sweet spots” of intense fracturing (e.g., Grayet
al., 2002; Gray and Todorovic-Marinic, 2004; Xu andTsvankin, 2007).
For instance, Hall and Kendall (2003)demonstrate that the direction
of the minimum AVOgradient at Valhall field is well-aligned with
faults in-ferred from coherency analysis (Figure 7).
For HTI and orthorhombic media with a singlefracture set, the
difference between the symmetry-planeAVO gradients is proportional
to the fracture density(which is close to the shear-wave splitting
parameter)and also depends on the fracture infill (Rüger,
2002).Therefore, even for such simple models the inversionof the
P-wave AVO gradient for the fracture proper-ties is generally
nonunique. In principle, fracture den-sity and saturation can be
constrained by combiningthe P-wave AVO response and NMO ellipse,
but thisapproach is applicable only to relatively thick,
weaklyheterogeneous reservoirs (e.g., Xu and Tsvankin,
2007).Additional complications may be caused by multiplefracture
sets (which lower the symmetry to at least or-thorhombic) and the
presence of fractures on both sidesof the target reflector. For
such realistic fractured reser-voirs, it is highly beneficial to
employ multicomponentdata in azimuthal AVO analysis (Bakulin et
al., 2000;J́ılek, 2002a,b; DeVault et al., 2002). In particular,
J́ılek(2002b) presents a methodology for joint nonlinear
AVOinversion of wide-azimuth PP and PS reflections for TIand
orthorhombic media.
Another interesting possibility is to combine az-imuthal AVO and
attenuation analysis, which helps re-move the uncertainty in
estimating the fracture ori-entation for HTI media (Clark et al.,
2009). Fur-thermore, body-wave attenuation coefficents are
highlysensitive to anisotropy and fracturing and may po-tentially
provide powerful fracture-characterization at-tributes (Chapman,
2003; Zhu et al., 2007b; Chichin-ina et al., 2009; Maultzsch et
al., 2009). On the otherhand, in some cases azimuthally varying
attenuation (ifunaccounted for) may distort the AVO signature.
Effi-cient velocity-independent techniques for estimating in-terval
offset- and azimuth-dependent attenuation fromfrequency-domain
reflection amplitudes are suggestedby Behura and Tsvankin (2009)
and Reine et al. (2009).
-
364 I. Tsvankin, et al.
N
Figure 7. Application of P-wave azimuthal AVO analysisto
fracture detection at Valhall field (after Hall and Kendall,2003).
The fracture azimuths (ticks) estimated from the az-imuthally
varying AVO gradient for the top-chalk horizonare compared with
interpreted fault traces. Note the gen-eral alignment of fractures
with large-scale faulting, espe-cially near the faults trending
from northwest to southeast.In the southeast corner, fractures also
appear to be perpen-dicular to the surface curvature defined by the
time contours(the contours are plotted at 20-ms intervals, with the
redcolor indicating deeper areas).
AVO analysis is designed to operate with the plane-wave
reflection coefficient at the target interface. Therecorded
amplitude of reflected waves, however, also de-pends on the
source/receiver directivity and such propa-gation factors as
geometric spreading, transmission co-efficients, and attenuation
(Martinez, 1993; Maultzschet al., 2003). Anisotropic layers in the
overburden focusor defocus seismic energy like an optical lens,
thus dis-torting the amplitude distribution along the wavefrontand
causing pronounced angle variations of geometricspreading
(Tsvankin, 1995b, 2005; Stovas and Ursin,2009). In that case,
robust reconstruction of the angle-dependent reflection coefficient
requires an anisotropicgeometric-spreading correction.
Geometric spreading in the time-offset domain isrelated to the
convergence or divergence of ray beams(Gajewski and Pšenč́ık,
1987) and, therefore, can becomputed directly from the spatial
derivatives of trav-eltime (Vanelle and Gajewski, 2003). This
ray-theoryresult is exploited in the moveout-based
geometric-spreading correction devised for horizontally layeredVTI
models by Ursin and Hokstad (2003) and extendedto wide-azimuth,
long-spread PP and PS data from az-imuthally anisotropic media by
Xu and Tsvankin (2006,2008). In particular, this correction has
proved to be es-sential in azimuthal AVO analysis of reflections
from thebottom of relatively thick fractured reservoirs (Xu
andTsvankin, 2007).
On the whole, recent developments have laid thegroundwork for
transforming anisotropic AVO analysisinto a valuable
reservoir-characterization tool.
9 PROCESSING AND APPLICATIONS OFMULTICOMPONENT DATA
Early applications of shear-wave seismology had to copewith
erratic and unpredictable data quality and mistiesbetween SS-wave
reflections at the intersection of 2D ac-quisition lines (Lynn and
Thomsen, 1986; Willis et al.,1986). This caused serious
difficulties in generating in-terpretable shear-wave sections and
using multicompo-nent data in lithology discrimination and fracture
char-acterization. Alford (1986) suggested that these prob-lems are
related to shear-wave splitting due to azimuthalanisotropy and
proposed simple rotation operators totransform SS data into two
principal sections contain-ing the fast and slow modes. Likewise,
Martin and Davis(1987) discuss the need to rotate converted
PS-wavesacquired for fracture-characterization purposes at
SiloField (Colorado, USA).
Shear waves in anisotropic media exhibit birefrin-gence
(shear-wave splitting) and travel as two separatemodes with
different velocities and orthogonal (for thesame phase direction)
polarizations. If the medium isHTI or orthorhombic with a
horizontal symmetry plane,the vertically traveling split S-waves
are polarized in thesymmetry planes of the model. The magnitude of
shear-wave splitting at vertical incidence is described by
theparameter γ(S), which is close to the fractional differ-ence
between the velocities of the fast (S1) and slow(S2) modes and can
be estimated as γ
(S) ≈ (ts − tf )/tf ,where ts and tf are the traveltimes of the
waves S2 andS1, respectively. After separating the split shear
waveson prestack data, it may be possible to evaluate theirNMO
ellipses and AVO signatures.
9.1 Pure-mode SS-waves
Processing surface shear-wave data for azimuthalanisotropy
analysis has primarily involved 1D compen-sation for splitting at
near-vertical propagation direc-tions. Alford’s (1986) rotation
algorithm operates onfour-component, stacked (supposed to be
equivalent tozero-offset) data excited by two orthogonal sources
andrecorded by two orthogonal receivers. Data can be ac-quired on a
2D line, with sources and receivers orientedparallel (inline) and
perpendicular (crossline) to the ac-quisition azimuth. The four
recorded S-wave displace-ment components can be represented in the
form of thefollowing 2×2 matrix:
D =
„
DXX DXYDY X DY Y
«
, (5)
where X denotes inline and Y crossline; the first letterin the
subscript refers to the source orientation, and thesecond letter to
the receiver orientation. Prestack shear-wave data depend on the
anisotropic velocity field andhave polarization properties
controlled by the azimuthof the line with respect to the symmetry
planes. How-ever, stacking or performing AVO inversion of 4C
data
-
Overview of seismic anisotropy 365
Figure 8. (a) Polarization azimuth of the PS1-wave and (b) the
shear-wave splitting coefficient (in percent) above the
GessosoSolfifera formation at Emilio Field (after Gaiser et al.,
2002). The north direction is rotated about 15◦ clockwise.
can provide an estimate of the difference between
thenormal-incidence reflection coefficients (i.e., AVO inter-cepts)
of the split S-waves, which is governed by theparameter γ(S)
regardless of the original propagationazimuth.
Thus, even for 2D acquisition geometry, pureshear modes can
yield information about azimuthalanisotropy. When the acquisition
line is parallel to avertical symmetry plane and the medium is
laterallyhomogeneous, no reflection energy should be presenton the
off-diagonal components in equation 5. Out-of-plane (obliquely
oriented) lines, however, may containsignificant coherent energy on
DXY and DY X . Alford’s(1986) 4C operator simultaneously rotates
the sourcesand receivers in order to estimate the
symmetry-planeazimuths and traveltime difference between the fast
andslow S-waves:
D′ = RS D RTR , (6)
where R is a 2×2 matrix of rotation around the verticalaxis for
sources (RS) and receivers (RR), and T denotestranspose. Rotation
is applied to each CDP consistingof a 4C group of traces. For a
certain rotation anglethat corresponds to the minimum energy on the
off-diagonal components D′XY and D
′
Y X , the data appear
as if they were acquired in one of the symmetry planes.This
means that the diagonal components, D′XX andD′Y Y , correspond to
the fast and slow shear waves andcan be processed to estimate the
splitting coefficient.
The 4C rotation dramatically improves the qualityof shear-wave
reflection data and makes them suitablefor lithology discrimination
(Alford, 1986). By combin-ing Alford rotation of VSP data with
layer stripping,Winterstein and Meadows (1991) evaluate S-wave
split-ting related to in-situ stress and fractures at Cymricand
Railroad Gap oil fields (California, USA). WhereasAlford’s method
assumes the principal anisotropy direc-tions (i.e., the azimuths of
the symmetry planes) to beinvariant with depth, Winterstein and
Meadows (1991)identify well-resolved, abrupt changes in the
splittingcoefficient at several depth levels that could be
im-portant for reservoir characterization. Thomsen et al.(1999)
extend the layer-stripping technique to reflectedS-waves and
discuss the analytic basis for separating thesplit shear modes on
both 4C and 2C (single-source)data.
There have been numerous successful applicationsof shear-wave
splitting for purposes of fracture charac-terization (e.g.,
Mueller, 1990; Crampin, 2003; Vascon-celos and Grechka, 2007).
Traveltime and amplitude dif-
-
366 I. Tsvankin, et al.
ferences between the fast and slow shear waves, as wellas their
NMO ellipses, can help estimate fracture ori-entation, density and,
in some cases, make inferencesabout fluid saturation. Also, Angerer
et al. (2000) showthat shear-wave splitting is a more sensitive
time-lapse(4D) indicator of pressure changes in response to
CO2injection than P-wave velocities. Their synthetic seis-mograms
based on the anisotropic poroelastic theory ofZatsepin and Crampin
(1997) match stacked data beforeand after injection. Terrell et al.
(2002) arrive at sim-ilar conclusions in their time-lapse study of
CO2 floodat Weyburn Field in Canada. There is little doubt
thatmoveout and amplitude inversion of multicomponent,multiazimuth
data offers the best hope of estimatingthe anisotropy parameters of
subsurface formations.
9.2 Mode-converted PS-waves
The majority of multicomponent surveys is acquiredwithout
shear-wave sources, so the reflected wave-field is largely composed
of compressional waves andmode-converted PS-waves. The most
prominent P-to-S conversion typically happens at the reflector;
suchPS events are sometimes called “C-waves” (Thomsen,1999). For
horizontally layered, azimuthally isotropicmedia converted PS-waves
are polarized in the incidence(sagittal) plane (i.e., they result
from P-to-SV conver-sion). However, if the incident P-wave
propagates out-side vertical symmetry planes of azimuthally
anisotropicmedia, the reflected PS-wave splits into the fast
(PS1)and slow (PS2) modes, neither of which is generally po-larized
in the sagittal plane (e.g., J́ılek, 2002a).
An important processing step for mode conversionsin the presence
of azimuthal anisotropy is rotation ofreceiver directions from an
acquisition coordinate sys-tem to a source-centered, radial and
transverse coordi-nate system (Gaiser, 1999). This procedure
reveals az-imuthal traveltime variations of PS1- and PS2-waves
onthe stacked radial components, as well as polarity rever-sals in
the principal anisotropy directions on the stackedtransverse
components (Li and MacBeth, 1999).
Similar to pure-mode SS reflections, the fast andslow PS-waves
have to be separated for further pro-cessing. The feasibility of
PS-wave splitting analysis isdemonstrated by Garotta and Granger
(1988) who an-alyze the amplitude ratios of the transverse and
radialcomponents and apply 2C rotation and layer stripping.Gaiser
(1997) shows that Alford rotation and layer strip-ping (a method
similar to that of Winterstein and Mead-ows, 1991), are applicable
to PS-waves in reverse VSPgeometry. His technique operates with 4C
data fromequation 5 where the two rows correspond to
source-receiver azimuths 90◦ apart. The principle of Alford
ro-tation is extended to wide-azimuth PS-wave surveys byDellinger
et al. (2002) who replace stacking of PS1 andPS2 reflections with
an appropriately designed tensormigration. Their results from
Valhall Field are mixed,
which suggests that azimuthal and lateral velocity varia-tions
may seriously complicate PS-wave processing. Re-cently there has
been renewed interest in developing amore formal inversion approach
to the PS-wave layer-stripping problem where the objective function
is for-mulated in terms of the PS1-wave polarization azimuthand the
traveltime difference between the split PS-waves(e.g., Bale et al.,
2009; Haacke et al., 2009; Simmons,2009).
In addition to such well-documented applications asimaging
beneath gas clouds and lithology discrimina-tion, mode-converted
data provide valuable attributesfor fracture/stress
characterization (Gaiser, 2000). Af-ter performing layer stripping
of 3D ocean-bottom-cable(OBC) PS-wave data over Valhall Field,
Olofsson etal. (2002) describe a dramatic “ring of anisotropy”
inthe overburden where the PS1-wave is polarized trans-versely
around the production platform. The correla-tion of this anisotropy
pattern with sea-floor subsidencecaused by the reservoir collapse
after years of productionsuggests that shear waves are highly
sensitive to local,deformation-induced stresses. Sensitivity of the
polar-ization direction of the PS1-wave to local stresses
overanticlines has also been observed at Emilio Field in
theAdriatic Sea (Gaiser et al., 2002), and at Pinedale Fieldin
Wyoming, USA (Gaiser and Van Dok, 2005). As il-lustrated by Figure
8, the PS1-wave at Emilio Field ispolarized parallel to the crest
of a doubly plunging anti-cline (thick black arrows), where
anisotropy is generallyhigher.
Finally, it is important to note that the moveoutasymmetry of
PS-waves (i.e., their traveltime generallydoes not stay the same
when the source and receiver areinterchanged) helps constrain the
parameters of tiltedTI media (Dewangan and Tsvankin, 2006b) and
char-acterize dipping (non-vertical) fracture sets (Angerer etal.,
2002).
9.3 Joint processing of PP and PS data
Conventional isotropic processing of high-quality
mul-ticomponent offshore OBC surveys routinely producesdepth
misties between PP and PS sections, in large partdue to the strong
influence of anisotropy on PS-wavemoveout. The high sensitivity of
mode conversions toanisotropy represents an asset for joint
anisotropic in-version of PP and PS data (e.g., Grechka et al.,
2002a;Foss et al., 2005). For example, the parameters VP0, ǫ,and δ
influence the kinematics of both P- and SV-wavesin TI media, which
underscores the importance of mul-ticomponent data in anisotropic
velocity analysis.
Widespread use of converted waves, however, ishindered not just
by the higher acquisition cost ofmulticomponent surveys, but also
by difficulties inPS-wave processing. Such properties of mode
conver-sions as moveout asymmetry, reflection point disper-sal, and
polarity reversals present significant challenges
-
Overview of seismic anisotropy 367
VTI Isotropic
7 118 9 10 12 13 7 8 9 10 11 12 13
4.0
t, s
3.5
3.0
2.5
2.0
1.5
Top Balder
Figure 9. Common-conversion-point stacks of PSV-wavesfor a 2D
line above the Siri reservoir in the North Sea (af-ter Grechka et
al., 2002b). Acquired PP- and PSV-waveswere processed using the
PP+PS=SS method to compute thetraveltimes of the corresponding SS
(SVSV) reflections. Thesection on the left was computed with a VTI
velocity modelobtained from stacking-velocity tomography of the
recordedPP-waves and constructed SS-waves. The section on the
rightwas produced without taking anisotropy into account.
for velocity-analysis and imaging algorithms. Theseproblems
motivated the development of the so-called“PP+PS=SS” method
designed to construct primarySS (in general, both S1 and S2)
reflections with thecorrect kinematics from PP and PS data (Grechka
andTsvankin, 2002). The key idea of the method, which op-erates on
PP and PS reflections acquired in split-spreadgeometry, is to match
the time slopes (horizontal slow-nesses) of PP- and PS-waves on
common-receiver gath-ers. This procedure helps identify PP and PS
events re-flected at the same (albeit unknown) subsurface
points,and the SS-wave traveltime can be obtained as a sim-ple
linear combination of the PP and PS times. Toavoid time picking,
Grechka and Dewangan (2003) de-vised the full-waveform
(interferometric) version of thePP+PS=SS method based on a
specially designed con-volution of PP and PS traces.
Although the PP+PS=SS method should be pre-ceded by PP-PS event
registration, it does not requireinformation about the velocity
field and is valid for arbi-trarily anisotropic, heterogeneous
media. The moveoutsof the recorded PP-waves and computed SS-waves
canbe combined in anisotropic velocity analysis using, forexample,
3D stacking-velocity tomography (Grechka etal., 2002a). The case
study from the North Sea in Fig-ure 9 demonstrates that this
methodology greatly im-proves the quality of PS-wave stacked
sections (Grechkaet al., 2002b). Application of the PP+PS=SS
methodfollowed by VTI processing provided a much better im-age of
the reservoir top (top Balder, the deepest ar-row on the left) and
a crisp picture of faulting in theshallow layers. Accounting for
anisotropy also boosted
higher frequencies in the stack and, therefore,
increasedtemporal resolution.
10 FRACTURE CHARACTERIZATION
By some estimates, fractured reservoirs contain aboutone-third
of the world’s hydrocarbon reserves. Sincealigned fractures create
velocity and attenuationanisotropy on the scale of seismic
wavelength, seis-mic fracture characterization is largely based
onthe anisotropic processing/inversion methods discussedabove.
In the past few years, significant progress has beenachieved
both in effective media theories and seismiccharacterization of
multiple fracture sets. The theoreti-cal advances are mainly
attributed to increased comput-ing power, which made it possible to
construct so-calleddigital rocks and examine how such realistic
features ascrack intersections, shape irregularities,
microcorruga-tion, and partial contacts of the fracture faces
influencethe effective elastic properties. It has been shown
thatmultiple sets of irregular, possibly intersecting fracturesthat
have random shape irregularities are well approx-imated by
isolated, penny-shaped cracks (Grechka andKachanov, 2006, and
references therein).
Another important result, known from theoreticalstudies of
Kachanov (1980, 1993) and confirmed nu-merically by Grechka et al.
(2006), is that multiple,arbitrarily oriented sets of fractures
embedded in anotherwise isotropic host rock yield an effective
mediumof approximately orthorhombic symmetry. This state-ment is
valid for both dry and liquid-filled fractures.The former are close
to so-called scalar cracks (in ter-minology of Schoenberg and
Sayers, 1995), which al-ways yield effective orthotropy (i.e.,
orthorhombic sym-metry) in the non-interaction approximation. The
lattercontribute mainly to shear-wave anisotropy (i.e., to
pa-rameters analogous to the splitting coefficient γ(S)) andalso do
not produce any substantial deviations from or-thorhombic
symmetry.
The closeness of the effective elasticity of crackedsolids to
orthotropy implies that multiple systems offractures appear to long
(compared to the fracture sizes)seismic waves as three orthogonal
or principal sets. Forinstance, N sets of dry fractures that have
the individualcrack densities e(k) and the normals n(k) (k = 1, . .
. , N)to the fracture faces are equivalent to three
“principal”sets, whose densities and orientations are found as
theeigenvalues and eigenvectors of the crack-density
tensor(Kachanov, 1980, 1993):
αij =N
X
k=1
e(k) n(k)i n
(k)j , (i, j = 1, 2, 3) . (7)
Vasconcelos and Grechka (2007) employ this the-ory to
characterize multiple vertical fracture sets fromwide-azimuth,
multicomponent seismic reflection data
-
368 I. Tsvankin, et al.
recorded at Rulison Field. The fracture orientations ob-tained
from seismic data are consistent with the FMI(Formation
MicroImager) log acquired in the studyarea. In addition,
Vasconcelos and Grechka (2007) con-struct an orthorhombic velocity
model of the Ruli-son reservoir by jointly inverting P- and S-wave
NMOellipses. This inversion is possible primarily
becausecrack-induced orthotropy is governed by fewer inde-pendent
parameters than general orthorhombic media,making estimation of
these parameters better posed andea sier to implement. Still,
comparison of the spatiallyvarying crack densities with the
estimated ultimate re-covery (EUR) of the available wells shows
little correla-tion. This problem, typical for a number of other
tight-gas fields in North America, should motivate
furtherdevelopment of robust seismic technologies capable
ofdetecting accumulations of hydrocarbons in
fracturedformations.
11 THE ROAD AHEAD
Progress in geophysics is usually driven by data; when-ever we
acquire a new type of data, we can expect todiscover unexpected
features that cannot be handledby existing methodologies. In
hindsight, these surprisesshould have been foreseen (and maybe were
foreseen bya few savants), but they always do surprise most of
us.
Today, the industry routinely acquires high-qualitywide-azimuth
3D marine data with the goal of better il-luminating subsalt
targets. When processing such data,we are discovering that
azimuthally variable seismic ve-locity is often required to flatten
the wide-azimuth im-age gathers. This will surely lead us to
further developmethods dealing with azimuthal anisotropy, which
havebeen applied primarily to land data sets. Also, it is al-ready
clear that horizontal transverse isotropy (HTI) isnot an
appropriate model for most formations with ver-tical cracks, and
TTI is probably an oversimplified sym-metry for dipping beds.
Future developments will in-clude extension of velocity-analysis
and migration algo-rithms to more realistic orthorhombic models.
Althougha solid foundation for parameter estimation and imagingin
orthorhombic media has already been built, findingrobust and
cost-effective processing solutions is a seri-ous challenge,
especially for tilted orthotropy. Also, itwould not be practical to
operate with a parameter setthat is not constrained by available
seismic data. An-other direction of future research with a high
potentialpayoff in velocity analysis is anisotropic
full-waveforminversion of reflection data, which should become
feasi-ble with continuing increase in computing power.
An interesting feature of anisotropy is that, al-though usually
it is weak (i.e., the dimensionlessanisotropy parameters typically
are much smaller thanunity), in many contexts it has a strong
influence on seis-mic data. In particular, the contribution of
anisotropyto reflection coefficients is comparable to the
isotropic
“fluid” and “lithology” factors, which is particularlynoticeable
in the azimuthally varying P-wave AVO re-sponse. Anisotropy in the
overburden also causes pro-nounced distortions in the
geometric-spreading factorfor reflected waves. Hence, it is easy to
predict that moreemphasis will be placed on understanding and
utiliz-ing amplitude signatures in anisotropic media, likely
in-cluding attenuation measurements. Experimental dataindicate that
attenuation anisotropy, especially thatproduced by fluid-saturated
fractures, may be ordersof magnitude higher than velocity
anisotropy. There-fore, azimuthally varying (and, possibly,
frequency-dependent) attenuation coefficients may provide
sensi-tive reservoir-characterization attributes.
Anisotropic phenomena are especially noticeable inshear and
mode-converted wavefields; it is usually im-possible to deal with
shear data without consideringanisotropy. In so doing, completely
new concepts (un-known in isotropy) arise, such as shear-wave
splitting.For example, acquisition of high-quality PS-wave data
inrecent years revealed strong conversion of energy (P-to-S) at
near-normal incidence, which is prohibited by thestandard model of
plane-wave reflection from a planarboundary between isotropic or
VTI halfspaces. Someof candidate explanations of these anomalous PS
ar-rivals involve anisotropy (e.g., tilted TI on either sideof the
reflector). Whatever the eventual solution to thisproblem, it will
likely entail a revision of conventionalAVO models and algorithms
for both PP- and PS-waves.Also, wide-azimuth, multicomponent data
will play amajor role in robust parameter estimation for
realisticorthorhombic and, in some cases, lower-symmetry me-dia.
Note that the split shear-wave primary reflections(S1 and S2) with
the correct kinematics can be gener-ated from wide-azimuth PP and
PS data using the 3Dversion of the PP+PS=SS method.
Whereas anisotropic P-wave imaging essentiallyamounts to looking
“past” anisotropy at explorationtargets, progress in
processing/inversion techniques isputting more emphasis on
employing anisotropy pa-rameters as attributes in reservoir
characterization andlithology discrimination. One of interesting
emergingapplications of anisotropic attributes is in
time-lapseseismic for compacting reservoirs because the shear-wave
splitting coefficient, traveltime shifts and
othercompaction-related signatures are strongly influencedby
stress-induced anisotropy. Physical characterizationof the
subsurface in terms of lithology, fluids, fractures,pore pressure,
and permeability will require improvedrock-physics and geomechanics
methods operating withanisotropic models.
12 ACKNOWLEDGMENTS
We are grateful to our numerous colleagues for their
con-tributions discussed in the paper and for fruitful discus-sions
that improved our understanding of the subject.
-
Overview of seismic anisotropy 369
We appreciate the reviews by K. Helbig, A. Rüger andA. Stovas,
who made a number of helpful suggestions.I.T. acknowledges the
support of the Center for WavePhenomena at Colorado School of
Mines.
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