Interpreting seismic amplitudes - 3-D Seismic Interpretation - page 149

V p /V s

2500

Castagnas sandline
Castagnas mudline
Quartz line
Shales
Oseberg Qtz cement
Oseberg Clay Cement
Troll 5 MPa
Troll 10 MPa
Troll 20 MPa

2000 0.2

0.1

1500

V s

0.4

1000

0.3

0.45

Lines of equal Poisson
Ratio are also shown

500

0.49

0

1500 2000 2500 3000 3500 4000

V p

Fig. 5.24 Schematic plots of shear against compressional velocity (m/s) using various empirical
relations for a range of lithologies. Lines of constant Poisson's ratio are also shown.

where the velocities are in km/s. The shear velocity for the rock is calculated as the
average of the weighted arithmetic and harmonic averages:

V arith = V s i w i

and

1
w i
V s i

V harm =

where the summation is across the four possible constituents, each with a volume
fraction w and shear velocity V s .
Some typical schematic plots of V s against V p are shown in fig. 5.24 . The quartz
line, V s = 0 . 8029 V p − 0 . 7509 , was derived by one of the authors (R. W. S.) from
the work of Murphy et al. (1993) and other data and predicts higher V s than the
Castagna (1993) relations. With increasing velocity (in general, decreasing porosity),
Poisson's ratio decreases. For V p below about 2500 m / s, none of these relations
is applicable; they tend to predict too high a shear velocity, perhaps by a wide
margin.