Interpreting seismic amplitudes - 3-D Seismic Interpretation - page 144

Fluid Properties
(North Sea Example)

Density (g/cm 3 ) Fluid modulus (GPa)

0 1 2 3

0 0.5 1 1.5

0 0

500
1000
1500

500
1000
1500

2000
2500

2000
2500

Brine
38 ° API oil
Gas

brine
medium oil
gas

3000 3000

3500
4000
4500

3500
4000

4500
5000 5000

Fig. 5.19 Typical values of density and fluid modulus as a function of depth in the North Sea.

5.5.1.2 Calculating matrix parameters
Elastic moduli and densities for individual minerals can be taken from published values
such as those shown in fig. 5.20 . Where there is more than one mineral in a rock
then a weighted average has to be calculated of the parameters. For density this is a
straightforward weighting by fractional composition. For the bulk modulus, there are
several possible approaches (Mavko et al ., 1998) . The simplest is the Voigt-Reuss-Hill
average, which calculates the average of the arithmetic and harmonic weighted average
values. Thus, for a quartz-clay mixture we would calculate a Voigt bulk modulus:

K v = K qtz V qtz + K cl V cl

and a Reuss modulus:

1

K r =

V qtz
K qtz +

V cl
K cl

and then

K v + K r
2

K vrh = ,

where V is the volume fraction of the constituent denoted by the suffix. For the case
above, the clay volume fraction would be taken as the shale volume fraction derived
from petrophysical analysis.