View source for Reflectivity versus water saturation

{{publication
 | name    = Problems in Exploration Seismology and their Solutions
 | image   = [[File:897.Def.Lz-cropped.png|frameless|180px|link=Problems in Exploration Seismology and their Solutions]]
 | width   = 120px
 | series  = Geophysical References Series
 | title   = [[Problems in Exploration Seismology and their Solutions]]
 | part    = 
 | chapter = 5
 | pages  = 141 - 180
 | author  = [[Lloyd P. Geldart]] and [[Robert E. Sheriff]]
 | doi     = 10.1190/1.9781560801733
 | pdf     = 
 | store   = https://shop.seg.org/shop/products/detail/897
 | isbn    = ISBN 9781560801153
}}
== 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 <math>\rho_{ss} = \rho_{sh}</math>, equation (3.6a) becomes
<math>
\begin{align}
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{align}
</math>

[[file:Ch05_fig5-8a.png|thumb|center|{{figure number|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.]]

{|class="wikitable" style="text-align:center; width:300px; height:200px; "border="1"
|+ '''Table 5.8a. Oil-sand data from Figure 5.8a.'''
|-
! Depth
! Water saturation
! <math>R</math>
! <math>V_{ss}</math>
! <math>V_{sh}</math>
|-
| 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.

== Continue reading ==
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| align="center" | [[:Category:Geometry of seismic waves| Geometry of seismic waves]]
| align="center" | [[:Category:Characteristics of seismic events|Characteristics of seismic events]]
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[[Problems_in_Exploration_Seismology_and_their_Solutions|Table of Contents (book)]]
|}

== Also in this chapter ==
* [[Maximum porosity versus depth]]
* [[Relation between lithology and seismic velocities]]
* [[Porosities, velocities, and densities of rocks]]
* [[Velocities in limestone and sandstone]]
* [[Dependence of velocity-depth curves on geology]]
* [[Effect of burial history on velocity]]
* [[Determining lithology from well-velocity surveys]]
* [[Reflectivity versus water saturation]]
* [[Effect of overpressure]]
* [[Effects of weathered layer (LVL) and permafrost]]
* [[Horizontal component of head waves]]
* [[Stacking velocity versus rms and average velocities]]
* [[Quick-look velocity analysis and effects of errors]]
* [[Well-velocity survey]]
* [[Interval velocities]]
* [[Finding velocity]]
* [[Effect of timing errors on stacking velocity, depth, and dip]]
* [[Estimating lithology from stacking velocity]]
* [[Velocity versus depth from sonobuoy data]]
* [[Influence of direction on velocity analyses]]
* [[Effect of time picks, NMO stretch, and datum choice on stacking velocity]]

== External links ==
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