Difference between revisions of "Wyllie time-average equation"

From SubSurfWiki
Jump to navigation Jump to search
Line 1: Line 1:
The Wyllie time-average equation is an equation that relates sonic velocities with the [[porosity]] of a rock. The equation is as follows:
+
The Wyllie time-average equation is an equation that relates sonic velocities with the [[porosity]] of a rock. It was proposed by Wylie<ref Wyllie, M. R. J., Gregory, A. R., and Gardner, L. W., 1956, Elastic wave velocities in heterogeneous and porous media: Geophysics, 21, no. 1, 41-70>.
 +
 
 +
The equation is as follows:
  
 
:<math>\frac{1}{v}=\frac{\phi}{v_f}+\frac{1-\phi}{v_m}</math>
 
:<math>\frac{1}{v}=\frac{\phi}{v_f}+\frac{1-\phi}{v_m}</math>
Line 8: Line 10:
  
 
where, <math>\phi</math> is the total porosity, <math>v</math> is the wave's measured phase velocity, <math>v_m</math> is the velocity of the rock matrix, and <math>v_f</math> is the velocity of the fluid in the pores, <math>\Delta t</math> is the measured interval travel-time, <math>\Delta t_m</math> is the interval travel-time of the rock matrix, <math>\Delta t_f</math> is the interval travel-time of the saturating fluid.
 
where, <math>\phi</math> is the total porosity, <math>v</math> is the wave's measured phase velocity, <math>v_m</math> is the velocity of the rock matrix, and <math>v_f</math> is the velocity of the fluid in the pores, <math>\Delta t</math> is the measured interval travel-time, <math>\Delta t_m</math> is the interval travel-time of the rock matrix, <math>\Delta t_f</math> is the interval travel-time of the saturating fluid.
 +
 +
==References==
 +
<references/>
  
 
[[Category:Rock physics]]
 
[[Category:Rock physics]]

Revision as of 12:18, 15 September 2011

The Wyllie time-average equation is an equation that relates sonic velocities with the porosity of a rock. It was proposed by Wylie<ref Wyllie, M. R. J., Gregory, A. R., and Gardner, L. W., 1956, Elastic wave velocities in heterogeneous and porous media: Geophysics, 21, no. 1, 41-70>.

The equation is as follows:

and can be rewritten in terms of interval travel-times as,

where, is the total porosity, is the wave's measured phase velocity, is the velocity of the rock matrix, and is the velocity of the fluid in the pores, is the measured interval travel-time, is the interval travel-time of the rock matrix, is the interval travel-time of the saturating fluid.

References