Geoscience Reference
In-Depth Information
Compressional waves (P-waves) differ from shear (S) waves in the direction of particle
motion as the wave propagates through the rock. For P-waves the motion is parallel to
the direction of travel of the wave, whereas for S-waves it is perpendicular. The P- and
S-wave velocities are related to different rock properties. When P-waves propagate
through a rock, there are changes in the volume of individual particles, whereas S-wave
propagation causes bending without change of volume. Standard seismic sources emit
P-waves almost entirely, so we usually see S-waves directly only when P-waves have
been partly converted to S-waves on reflection at an interface. Standard seismic pro-
cessing concentrates on using P-waves to form an image of the subsurface. However,
as we shall see, the shear properties of the rock are important to understanding AVO.
Sometimes a quantity called Poisson's ratio (
σ
) is used instead of the V p
/
V s ratio. It
is given by
V s
V p 2
0
.
5
σ =
.
V s
V p 2
1
Figures 5.1 and 5.2 show typical values of these parameters for some common rock
types.
Offset reflectivity
5.2
We saw in section 3.1.1 how the reflection coefficient at an interface depends on the
acoustic impedance contrast across it for the case of normal incidence. In the real
world, seismic data are always acquired with a finite separation between the source
and receiver (usually termed the offset ). This means that reflection will be much more
complicated, because part of the P-wave energy will be converted into a reflected and
transmitted shear wave. The equations describing how the amplitudes of the reflected
and transmitted P- and S-waves depend on the angle of incidence and the properties
of the media above and below the interface were published by Zoeppritz (1919) ; the
amplitudes depend on the contrast in Poisson's ratio across the interface, as well as
the acoustic impedance change. Figure 5.3 shows an example of how the amplitudes
depend on incidence angle for a particular interface.
For a plane interface the relationship between the P-wave angles of incidence and
transmission is given by Snell'sLaw ( fig. 5.4) :
sin
θ 2
V 2 =
θ 1
V 1
sin
.
If velocity increases with depth across the interface, then there will be an incidence
angle for which the transmission angle is 90 . This is the critical angle, at and beyond
which there is no transmitted P-wave, and therefore a high reflection amplitude.
 
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