Geology Reference
In-Depth Information
minimum
horizontal stress
direction
σ
3
Shear source
E-W
φ
Fractures
oriented
N 45 W
θ
Χ
1
maximum
horizontal
stress
direction
σ
2
Shear wave
splitting - time
delay
maximum principal
stress direction
σ
1
Figure 5.47
Modelling fractures as polar anisotropy with
horizontal axis of symmetry or horizontal transverse anisotropy
(HTI). Reflectivity depends on the angle of incidence (θ) and the
azimuth (
ϕ
). Fracture orientation is interpreted with respect to
changes in the AVO gradient.
Figure 5.46
Shear wave splitting in azimuthally anisotropic media
(after Martin and Davis,
1987
; Crampin,
1990
).
In areas with significant azimuthal anisotropy the
P wave AVO response is dependent on the azimuth of
the seismic. A simple model that is commonly used to
describe this situation is polar anisotropy with hori-
zontal axis of symmetry.
Figure 5.47
illustrates that
the AVO at an interface between an isotropic layer
and one with vertical cracks will vary depending on
the azimuth.
Rüger (
1998
) derived a reflectivity equation, again
similar to the Shuey equation, to characterise this
situation. Following Jenner (
2002
), for angles up to
about 35° it can be written:
regime are likely to be open and fluid filled. It is these
fractures that effectively contribute to azimuthal
anisotropy. Closed fractures do not contribute signifi-
cantly because of a lack of impedance contrast across
the fracture. Some oil and gas fields rely almost
entirely on fractures for their production. It follows
then that exploiting azimuthal anisotropy may pro-
vide direct information on fracture presence and pos-
sibly on permeability. There are generally two
approaches to exploiting azimuthal anisotropy for
detection of fractures, namely the analysis of
sin
2
I+ G
1
+G
2
cos
2
R
ðÞ¼
θ
,
ð
ϕ
β
Þ
θ
,
ð
5
:
8
Þ
'
shear
wave splitting
on land and the analysis of P wave
AVO differences with azimuth (commonly referred to
with an array of different acronyms such as AVOA,
AzAVO, AVD, AVOZ).
Shear wave techniques commonly employed for
fracture detection on land are based on the fact that a
shear wave entering an azimuthally anisotropic rock
unit at an angle oblique to the fractures splits into two
waves with different polarizations (
Fig. 5.46
). A fast
shear wave (S1) is polarized parallel to the fractures
whereas the slower shear wave (S2) is polarized per-
pendicular to the fractures. The anisotropy is com-
monly described by the time delay (i.e. T
s1
'
where
R(
reflection coefficient as a function of
incidence angle (
θ
,
ϕ
)
¼
receiver azimuth
with respect to a pre-defined direction, such as true
north),
β ¼
θ
) and
ϕ
(source
-
angle between chosen zero azimuth and either
the isotropy or symmetry axis plane I
¼
P wave
impedance contrast divided by 2 G1
¼
isotropic
AVO gradient G2
¼
anisotropic gradient
defined by:
"
#
,
2
Δγ
1
2
2
g
Δδ
ðÞ
+2
¼
ð
:
Þ
G
2
5
9
T
s2
)/T
s2
)
and an estimate of relative crack density can be made
on the basis of the delay (e.g. Crampin et al.,
1986
).
An example of shear wave splitting is shown in
Chap-
ter 7
and the reader is referred to Lynn (
2004
) for a
thorough introduction.
where g
V
p
/V
s
(average P wave velocity / average
S wave velocity),
Δδ
¼
(
υ
)
the difference in the Thomsen style
parameter
¼
δ
for HTI,
88
