Applications of seismic anisotropy in the oil and gas industry

176 Pages·2009·9.574 MB·English

by  Grechka, V. I︠U︡

Applications of
Seismic Anisotropy in the
Oil and Gas Industry

Vladimir Grechka
© 2009 EAGE Publications by

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List of Figures
1.1 Block made of layers of steel (white) and rubber (black). The apparent stiffness of the block
under a compressive load depends on the direction of the load.
1.2 Fractures in sandstones of Checkerboard Mesa (Zion National Park, Utah, USA).
1.3 Anisotropic and isotropic depth-migrated sections obtained in (a) exact anisotropic model, (b)
anisotropic model estimated from surface reflection data, (c) isotropic model constructed via
conventional processing, and (d) isotropic model with the correct vertical velocity (after Han et
al., 2001).
1.4 Common-image gathers after prestack depth migration with (a) isotropic and (b) anisotropic
velocity model (after Sarkar and Tsvankin, 2004).
1.5 P- (a) and shear- wave (b) gathers after the azimuthally-invariant (isotropic) NMO correction.
The traces are sorted by the source-to-receiver azimuth. The apparent cosine-type dependence of
the residual moveout is indicative of azimuthal anisotropy. The jitter obscuring this dependence is
caused by slightly unequal offsets at different azimuths. The events at approximately 1.27 s (a)
and 2.35 s (b) are the reflections from the bottom of the Rulison reservoir (after Vasconcelos and
Grechka, 2007).
1.6 Isotropic (a) and anisotropic (b) PS-wave common-conversion-point stacks (after Grechka et al.,
2002c).
1.7 Errors in (a) the lateral position of the PS-wave conversion point and (b) the incidence angle of
the P-leg for PP- and PS-waves at the Siri reservoir caused by neglecting anisotropy (after
Grechka et al., 2002c).
1.8 Three-component record (a, b, c) of a shear microseismic event and the rotated 3C trace (d, e, f)
that reveals shear- wave splitting.
1.9 Fast (a) and slow (b) shear reflections from the Austin Chalk horizon (after Mueller, 1992).
1.10 Shale under a microscope (after Hornby et al., 1994).
1.11 Sets of well-developed joints in Caithness, Scotland, UK (source: Wikipedia,
http://en.wikipedia.org/wiki/File:Joints Caithness. JPG).
1.12 Equivalence of finely layered isotropic and homogeneous anisotropic solids for propagation of
long seismic waves.
1.13 Sonic (black), shear (blue), and density (red) logs acquired over a 500 m interval in a deepwater
oil field in the Gulf of Mexico (after Bakulin and Grechka, 2003).
2.1 Small tetrahedron whose three faces lie in the coordinate planes.
2.2 Normal (red) and shear (black) components of the stress tensor.
2.3 Deformation of (a) isotropic and (b) anisotropic solids under a compressive load.
2.4 Two systems of vertical cracks embedded in azimuthally isotropic host rock at oblique directions
with respect to each other generally result in monoclinic symmetry with a horizontal symmetry
plane (after Bakulin et al., 2000).
2.5 Fractured sandstones near Paria Canyon in Arizona, USA.
2.6 Orthorhombic media have three mutually orthogonal planes of mirror symmetry. One of the
orthotropic models contains vertically fractured fine horizontal layers (after Rüger, 1998).
2.7 Orthogonal fracture sets in sandstones of Cedar Mesa, Utah, USA (source: Jon Olson’s home
page, http://www.pe.utexas.edu/~jolson/Welcome.html).
|| ⊥
2.8 Sketch of an HTI model. Shear waves polarized parallel (S ) and normal (S ) to the isotropy
||
plane (cracks) propagate with different vertical velocities. The velocity of the S - wave is greater
⊥
than that of S (after Rüger, 1997).
2.9 Typical geometry of phase- velocity surfaces in orthorhombic media. Red arrow points to the
shear- wave singularity (after Grechka et al., 1999a).
2.10 Slowness (dashed blue) and phase velocity (solid red) of the SV wave in a VTI medium with the
density-normalized stiffness coefficients a = 16.2, a = 6.12, a = 9.0, a = 1.44, and a =
11 13 33 55 66
2 2
1.0 (all in km /s ). The vertical and horizontal lines indicate the symmetry axis and the isotropy
plane, respectively.
2.11 Slowness (dashed blue) and phase velocity (solid red) shown in Figure 2.10, and group velocity
(solid black). The red, green and black arrows indicate the vectors nV, (∂V/∂θ ∂n/∂θ ) and g,
1 1
respectively. The gray arrows point to the phase- velocity extrema.
2.12 The same slowness (dashed blue), phase-velocity (solid red), and group-velocity (solid black)
surfaces as in Figure 2.11. The dark and light blue arrows are normals to the slowness surface.
Their lengths are equal to the group velocities g. The corresponding wavefront normals are shown
with red and brown arrows.
2.13 Shear- wave slowness (a, b) and group- velocity (c, d) surfaces in an orthorhombic solid with
density-normalized stiffness coefficients (in Voigt notation) a = 5.60, a = 4.97, a = 4.35,
11 12 13
2 2
a = 5.20, a = 3.55, a = 4.00, a = 0.012, a = 0.014, and a = 0.017 (all in km /s ). The
22 23 33 44 55 66
units of axes are s/km in (a, b) and km/s in (c, d).
3.1 Seismic wavefront at two consecutive time moments t and t + Δt. The dots indicate elementary
sources, the red arcs are the elementary wavefronts.
3.2 Rays emerging at observation surface typically do not arrive at predetermined receiver locations
(squares).
3.3 Ray trajectory through a sequence of homogeneous anisotropic layers.
inc
3.4 Kinematics of reflection-transmission problem in the local [p , b] - plane. If the incident wave
propagates in the upper half-space, the group-velocity vectors of reflected waves point up,
g3Q,refl < 0, while the group- velocity vectors of transmitted waves point down, g3Q,trans > 0 (Q
= P, S , S ).
1 2
3.5 Reflection traveltimes (top row) and ray trajectories (bottom row) of SV-waves in two-layer VTI
models. The relevant density-normalized stiffness coefficients in Voigt notation are: a11(1) =
12.60, a33(1) = 9.00, a55(1) = 2.25 in the top layer and a11(2) = 5.40, a13(2) = 6.81, a33(2) =
9.00, a55(2) = 2.25 in the bottom layer. Two models differ in the values of stiffness coefficient
a13(1) in the top layer. It is equal to a13(1) = 4.50 in (a) and a13(1) = 2.36 in (b). The units of all
2 2
a ’s are km /s . Red horizontal lines in the bottom panels are the model interfaces.
IJ
3.6 Detail of the multivalued traveltime in Figure 3.5b.
2 2
3.7 Same as Figure 3.5 but for a13(1) = −0.51 km /s .
4.1 P-wave phase velocity function (solid) for positive e and negative δ. The dashed line is a circular
arc whose radius is equal to the vertical velocity V .
P0
4.2 SV-wave phase velocity function (solid) for a positive σ. The dashed circular arc has a radius
equal to V .
S0
4.3 Dependence of the exact P-wave phase velocity (calculated with equation 4.17) on V in VTI
S0
media with ∈ = 0.7 and δ = 0.2. The legend indicates the V /V ratios. The corresponding
S0 P0
vertical shear- wave velocities are V = 0.8 km/s, 1.6 km/s, and 2.4 km/s.
S0
5.1 Ray trajectories in the reflector dip plane at zero and nonzero offsets. The vertical [x , x ] -plane
1 3
is assumed to be a symmetry plane so that the strike components of vectors p and g are equal to
zero (modified from Tsvankin, 1995).
5.2 Time-migrated seismic line. The gray bar indicates the locations of CMP gathers examined in
Figures 5.3 and 5.4 (after Alkhalifah and Tsvankin, 1995).
5.3 Constant- velocity stacks after the conventional isotropic NMO-DMO sequence. The velocity
values correspond to the NMO velocities of the subhorizontal reflectors (after Alkhalifah and
Tsvankin, 1995).
5.4 Anisotropic constant- velocity stacks. The velocities correspond to the stacking velocities of the
subhorizontal reflectors (after Alkhalifah and Tsvankin, 1995).
5.5 Stack of horizontal layers.
5.6 (a) Average P-wave vertical velocity from a check shot (gray), the effective NMO velocity
(black), and (b) the interval Thomsen coefficient δ (after Alkhalifah et al., 1996).
5.7 Zero-offset ray (blue) reflected from a dipping interface beneath a layered anisotropic medium.
The dashed lines indicate nonexisting interfaces that would generate zero-offset reflected rays
with exactly the same trajectories as the one shown with the solid blue line (modified from
Alkhalifah and Tsvankin, 1995).
5.8 Influence of transverse isotropy on the P- wave NMO velocity. Calculations are done with
equation 5.6 normalized by V ,p(0)/ cos ϕ (after Alkhalifah and Tsvankin, 1995). The
nmo
horizontal axes approximately correspond to sinϕ; the dip angles range from 0° to 70°. (a) Models
with the same η = 0.2 but different e and δ: ∈ = 0.1, S = −0.071 (solid black); ∈ = 0.2, δ = 0
(gray); and ∈ = 0.3, δ = 0.071 (dashed). The three curves in (a) nearly overlap. (b) Models with
different η values: η = 0.1 (solid black); η = 0.2 (gray); and η = 0.3 (dashed).
5.9 Parameters of a 2D VTI model: (a) the P-wave vertical velocity V , the Thomsen coefficients (b)
P0
∈ and (c) 5 and (d) the anellipticity coefficient η (after Han et al., 2001).
5.10 Interval (a) P- wave NMO velocity and (b) anellipticity coefficient η (solid lines) as functions of
the two-way vertical time estimated from subhorizontal and dipping reflections at midpoints
between 4.9 km and 6.7 km in Figure 5.9. The dashed line in (b) indicates the true values of η
(after Han et al., 2001).
5.11 Same as Figure 5.10 but for midpoints in the range 11.0 km – 16.8 km (after Han et al., 2001).
5.12 Ray trajectories and pure-mode reflection traveltime in wide- azimuth CMP geometry (after
Grechka et al., 1999b).
5.13 NMO ellipse that has the azimuth β of the major axis and the semi-axes Vnmo(1)=1/λ1 and
Vnmo(2)=1/λ2.
5.14 NMO ellipse in a dipping VTI layer.
5.15 The strike-line P-wave NMO velocity V (n/2,p) (normalized by the zero-dip NMO velocity) as
nmo
a function of the ray parameter p for dips ranging from 0° to 90° (after Grechka and Tsvankin,
1998b). (a) Different models with the same η = 0.2 but different ∈ and δ:∈ = 0.1, δ = −0.071
(solid); ∈ = 0.2, 5 = 0.0 (dashed); ∈ = 0.3, 5 = 0.071, (dotted). (b) Models with different η
values: η = 0.1 (solid); η = 0.2 (dashed); η = 0.3 (dotted).
5.16 Dipping reflector beneath a horizontally layered overburden. The effective NMO ellipse in this
model can be obtained from the generalized Dix equation 5.40 (after Grechka et al., 1999b).
5.17 Plan view of the source and receiver positions (small circles) in a single superbin. The superbin
contains approximately 400 source-receiver pairs with a common-midpoint scatter of about 80 m
or 2% of the maximum offset (after Grechka and Tsvankin, 1999b).
5.18 Semblance curves obtained by the conventional velocity analysis, which ignores the azimuthal
dependence of moveout velocity (dashed) and by the azimuthal velocity analysis (solid). Arrows
indicate the major reflection evens (after Grechka and Tsvankin, 1999b).
5.19 Effective NMO eccentricities at (a) t = 2.14 s and (b) t = 2.57 s (after Grechka and Tsvankin,
0 0
1999b).
5.20 Interval NMO eccentricities for the horizon between 2.14 s and 2.57 s (after Grechka and
Tsvankin, 1999b).
6.1 Hyperbolic (solid) and nonhyperbolic (dashed) moveout terms normalized by their values at the
offset-to-depth ratio equal to two. Equation 6.7 with the parameters t = 2 s, V = 3 km/s, and η
0 nmo
= 0.2 was used for this computation.
6.2 (a) Synthetic seismogram of the P- wave reflected from the bottom of a VTI layer described by
parameters t = 1 s, V = 2 km/s, and V = 2.3 (η = 0.16). The spread length is equal to two
0 nmo hor
reflector depths; the source pulse is a Ricker wavelet with central frequency of 40 Hz. (b)
Semblance contours in the coordinates {V , V } calculated with equation 6.11 for t = 1 s.
nmo hor 0
(c) Same as (b) but plotted in the coordinates {V , η} (after Grechka and Tsvankin, 1998a).
nmo
6.3 Semblance contours for the model from Figure 6.2 after addition of linear traveltime error that
changes from +4 ms at zero offset to −4 ms at the offset x = 2 km. The semblance maximum
corresponds to η = 0.085 (after Grechka and Tsvankin, 1998a).
6.4 Traveltimes for different source positions (dots) recorded by a single downhole receiver and the
best-fit nonhyperbolic moveout curve (solid) computed using equation 6.11. The offsets and
traveltimes are doubled to simulate a reflection experiment (after Grechka and Tsvankin, 1998a).
6.5 RMS time residuals (in ms) calculated with equation 6.11 for different pairs {V , V }. The
nmo hor
residual for the best-fit model at the center of the contours is 6.7 ms (after Grechka and Tsvankin,
1998a).
6.6 Time-migrated seismic line (after Alkhalifah, 1997).
6.7 Semblance analysis for CMP 300 in Figure 6.6 at different zero-offset times t . Gray lines
0
correspond to contours of the effective η. The maximum offset in the data is 4.3 km (after
Alkhalifah, 1997).
6.8 Interval V and η (black) as functions of t at CMP 300 in Figure 6.6. The gray curves show
nmo 0
the error bars caused by the picking uncertainties (after Alkhalifah, 1997).
6.9 Magnitude of the azimuthally-varying quartic coefficient A4(vti)(α,ϕ) computed using equation
6.13 for a VTI layer above a planar reflector with the dip (a) ϕ = 15°, (b) ϕ = 30°, and (c) ϕ = 45°.
The arrows mark the azimuth of the reflector dip plane (after Pech et al., 2003).
6.10 Source-receiver geometry for a superbin used for azimuthal NH move- out analysis. Each blue
dot marks a source-receiver pair; the polar angle corresponds to the source-receiver azimuth from
the north (see the numbers on the perimeter), whereas the radius is the offset. The total fold for
this superbin is 2,491 (after Vasconcelos and Tsvankin, 2006).
6.11 Seismic data at superbin in Figure 6.10 after a conventional hyperbolic NMO correction. The
gather is sorted by increasing offset and contains all azimuths, which are irregularly sampled
(Figure 6.10). Non- hyperbolic moveout manifests itself through the curvature of the NMO-
corrected events at long offsets (so-called hockey sticks). The jittery character of the reflections
suggests the presence of traveltime variations with azimuth (after Vasconcelos and Tsvankin,
2006).
6.12 Results of nonhyperbolic moveout inversion for the reflections from the Viking horizon (the
maximum offset-to-depth ratio is 2.5), the Blairmore ( ODR = 2.0), the Lower Vanguard ( ODR =
1.9) and the Mississippian Unconformity ( ODR = 1.8). The arrows mark the estimated direction
of the semi-major axis of the NMO ellipse. The number by each arrow is the azimuth of the axis
with respect to the north. All η parameters are the effective values for a given reflection event
(after Vasconcelos and Tsvankin, 2006).
7.1 First-break P- wave times (in ms) recorded by a geophone placed at a depth of 4,509 ft (1,374 m)
in a vertical well at Rulison Field, Colorado, USA. The data were acquired by the Reservoir
Characterization Project, Colorado School of Mines (after Grechka et al., 2007).
7.2 Measurements carried out for estimating anisotropy in a typical VSP geometry. The traveltime
difference, dt, between geophones (dots) located at a distance dh along a wellbore defines the
apparent slowness, q = dt/dh. Three-component traces recorded by each downhole geophone yield
the direction of particle motion, U, defined by the polar polarization angle, ψ, and azimuth, φ. The
azimuths of the horizontal components (X and X ) of the geophones usually vary along the tool
1 2
string and should be treated as unknown unless independently measured (after Grechka et al.,
2007).
7.3 P- wave slowness surface (in s/km) constructed from 3D VSP data (after Dewangan and Grechka,
2003).
7.4 Horizontal projections of the P-wave polarization vectors (tick lengths are proportional to the
magnitudes of the projections) plotted at the source locations with respect to the well, which is
placed at the coordinate origin (after Dewangan and Grechka, 2003).
7.5 Exact q(ψ) functions for various V /V ratios but fixed parameters V = 10 kft/s (3 km/s),
S0 P0 P0
δ = 0.033 and η = 0.417 (symbols). The dashed line shows the WAA of q(ψ) given by
VSP VSP
equation 7.2 (after Grechka and Mateeva, 2007).
7.6 Geometry of walkaway VSP (after Grechka and Mateeva, 2007). Surface shot locations are
shown in red. Positions of 3C receivers in the borehole are marked in cyan. Depth-migrated
surface seismic data are displayed on the background of the isotropic P-wave depth-velocity
model (white color corresponds to the P-wave velocity in water, magenta to the velocity in salt).
7.7 Particle-motion hodogram for a typical source-receiver pair used in the inversion. The geophone
axis X is vertical; the axes X and X are horizontal but their azimuths are unknown. Open
3 1 2
circles indicate the picked first-break time, dots mark the particle motions at 2 ms time
increments. The hodogram corresponds to approximately one quarter of the dominant period of P-
waves (after Grechka and Mateeva, 2007).
7.8 P-wave traveltimes (a) and polarization angles (b). The dots indicate the quantities picked from
several traces in a common-shot gather. The solid lines are the linear traveltime fit (a) and the
mean polarization angle (b). They give the slowness- polarization pair, q(ψ), which is one data
point for the inversion. The dashed lines correspond to ± one standard deviation from the best-fit
lines. These standard deviations are 0.25 ms for the times and 1° for the polarization angles (after
Grechka and Mateeva, 2007).
7.9 Slowness- polarization data and estimated parameters (a) in the salt at a depth of 18,500 ft (5,639
m) and (b) beneath the salt at a depth of 21,750 ft (6,629 m). Crosses associated with each data
point (black dot) indicate the standard deviations in the picked ψ and q values. The solid circles
correspond to the best-fit q(ψ) VTI functions, open circles – to those functions ± one standard
deviation. The obtained P-wave vertical velocities in SI units are (a) V = 4,471 ± 4 m/s and (b)
P0
V = 2, 837 ± 3 m/s. The solid red lines show the isotropic q(ψ) dependencies implied by those
P0
V (after Grechka and Mateeva, 2007).
P0
7.10 Vertical velocities (a) and anisotropy coefficients (b). The thin solid lines in (b) are the standard
deviations of δ and η estimated from the uncertainties in the ψ and q picks (after Grechka and
Mateeva, 2007).
7.11 Anisotropy coefficient δ (a) and gamma-ray log for subsalt sediments (b). Thin lines in (a)
VSP
show the standard deviation of δ (after Grechka and Mateeva, 2007).
VSP
7.12 Azimuthal variation of the fitted vertical slowness (in s/kft) corrected for isotropy as a function of
the P-wave horizontal polarization components for the best-fit orthorhombic model in the depth
range 4,510 ft4,910 ft (1,375 m1,497 m). The white circles indicate the slowness variations
expected in the absence of azimuthal anisotropy (after Grechka et al., 2007).
8.1 Effective stiffness coefficients (a) c and (b) c for a single set of dry cracks. The
e,11 e,22
3
background velocities are V = 3.0 km/s, V = 1.0 km/s, and density is ρ = 2.2 g/cm ; they
P,b S,b b
yield the Lamé coefficients λ = 15.4 GPa, μ = 2.2 GPa. Symbols indicate different theoretical
b b
predictions: ∇ - the first-order Hudson’s (equations 8.20 and 8.21), Δ – the second-order
Hudson’s (equations 8.21 and 8.26 − 8.28), * – Schoenberg’s (equations 8.4, 8.12, 8.13, and
o
8.15), and – the NIA (equations 8.4 and 8.19), which takes into account nonzero crack aspect
ratios (Θ = 0.05 for all fractures). The bars cor​respond to the 95% confidence intervals (the mean
values ± two standard deviations) of the numerically computed stiffness coefficients obtained for
100 random realizations of the fracture locations (after Grechka and Kachanov, 2006c).
8.2 Anisotropy coefficients (a) ∈(V) (b) δ(V) and (c) γ(V) of effective HTI media. The symbols are
the same as those in Figure 8.1 (after Grechka and Kachanov, 2006c).
8.3 Horizontal cross-section of the stress component τ through a model containing dry fractures
11
(wire spheroids). The crack density is e = 0.15. The arrow indicates the direction of applied
remote load, whose magnitude is 1 MPa (after Grechka and Kachanov, 2006c).
8.4 Horizontal cross-sections of the stress component τ for arrays of (a) non-intersecting and (b, c,
11
d) intersecting fractures. The aspect ratios Θ of the fractures lie in the range 0.04 ≤ 9 ≤ 0.08. The
arrows indicate the directions of applied uniaxial remote load whose magnitude is 1 MPa (after
Grechka and Kachanov, 2006d).
8.5 Effective anisotropy coefficients of fractured media. The bars correspond to the 95% confidence
intervals (the mean ± two standard deviations) of the numerically computed coefficients. The
triangles indicate their values for models with intersecting cracks. The predictions of the linear-
slip theory, which ignores the nonzero crack aspect ratios (equations 8.4, 8.12, 8.13, and 8.15)
and the non-interaction approximation, which accounts for them (equations 8.4 and 8.19), are
shown with * and •, respectively. All numerical effective models are triclinic but only Tsvankin’s
orthorhombic coefficients are displayed (after Grechka and Kachanov, 2006d).
8.6 Fracture geometries created to study the influence of crack shape on the effective properties. All
fractures are vertical and planar; their normals are parallel to the x -axis. Geometries 4, 5, and 6
1
contain rock islands inside the cracks and model partially closed fractures (after Grechka et al.,
2006).
8.7 Misfits Δcnrm (equation 8.38) for the six fracture shapes in Figure 8.6 (after Grechka et al.,
2006).
8.8 Models containing three sets of vertical rectangular cracks. Fractures that intersect their neighbors
are shaded, isolated cracks are transparent. The background Poisson’s ratio is v = 0.44 (after
b
Grechka et al., 2006).
ort
8.9 Relative deviations Δ (equation 8.39) from orthotropy of the numerically computed effective
stiffness tensors for intersecting crack arrays such as those shown in Figure 8.8 (after Grechka et
al., 2006).
8.10 P-wave seismic section at Rulison Field. The arrows mark the reflection events used for
azimuthal velocity analysis (after Vasconcelos and Grechka, 2007).
8.11 Output of the fracture characterization: the background velocities V and V of P- (a) and S-
P,b S,b
waves (b), and the principal crack densities e (c) and e (d). The directions of the principal
1 2
fracture sets are shown with ticks; their lengths are proportional to the eccentricities of the
interval P- wave NMO ellipses (Figure 8.14b). The star indicates the well location from where the
FMI log shown in Figure 8.12 was acquired (after Vasconcelos and Grechka, 2007).
8.12 Fracture count (blue) in well shown with star in Figure 93 and the 90% confidence interval
(dashed red) corresponding to the azimuth of the fracture set with the density e estimated from
1
seismic data (after Vasconcelos and Grechka, 2007).
8.13 Vertical velocities (a) V , (b) V and anisotropy coefficients (c) ∈(1), (d) ∈(2). (e) γ(1), and (f)
P0 S0
(2)
γ at Rulison reservoir (after Vasconcelos and Grechka, 2007).
(S)
8.14 The shear-wave splitting coefficient γ (a) and the eccentricity of the P-wave NMO ellipses
(1) (2)
δ − δ (b) at Rulison reservoir (after Vasconcelos and Grechka, 2007).
List of Tables
3.1 Summary of kinematic ray-tracing methods.
4.1 Phase and group velocities of P-, SV- and SH-waves in the vertical symmetry- axis direction, θ =
0, and in the horizontal isotropy plane, θ = π/2.
4.2 Average values of anisotropic coefficients measured on core samples by Wang (2002).