# Reflectivity versus water saturation

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Series Geophysical References Series Problems in Exploration Seismology and their Solutions Lloyd P. Geldart and Robert E. Sheriff 5 141 - 180 http://dx.doi.org/10.1190/1.9781560801733 ISBN 9781560801153 SEG Online Store

## Problem 5.8

What shale velocities are consistent with the Figure 5.8a oil-sand data?

### Solution

We determine velocities and reflectivities for two values of water saturation for each of the three depths, neglecting differences between sand and shale densities. Setting ${\displaystyle \rho _{ss}=\rho _{sh}}$, equation (3.6a) becomes {\displaystyle {\begin{aligned}R=\left(V_{ss}-V_{sh}\right)/\left(V_{ss}+V_{sh}\right),\\V_{sh}=V_{ss}\left(1-R\right)/\left(1+R\right).\end{aligned}}}

Figure 5.8a.  Effect of water saturation on velocity (i) and reflectivity (ii) (after Domenico, 1974). Solid curves are for gaseous, dashed curves for liquid hydrocarbons.
Table 5.8a. Oil-sand data from Figure 5.8a.
Depth Water saturation ${\displaystyle R}$ ${\displaystyle V_{ss}}$ ${\displaystyle V_{sh}}$
610 m 30% –0.08 1.7 km/s 2.0 km/s
70 –0.03 1.8 1.9
1830 30 –0.10 2.3 2.8
70 –0.07 2.4 2.8
3050 30 –0.10 2.7 3.3
70 –0.07 2.8 3.2

From Figures 5.8a(i,ii) we obtain the data in Table 5.8a for oil sands. These are plotted as triangles on Figure 5.6a.