1. Rock Physics in a NutshellF dP dV

2. Some Rock Physics Definitions
Hooke’s Law
F = k X
Robert Hooke
English gentleman scientist, paleontologist, experimential scientist. Contemporary of Issac Newton. Assisted Robert Boyle in the study of the physics of gases. F
DF = k DX
Just a constant of proportionality. This is a function of both material and geometry.
Young’s Modulus E
Thomas Young
1773 – English “polymath”, and physician. Contemporary of W. Herschel. F
A (area)
Uniaxial stress DL
E =
Uniaxial strain Lo
E =
Modulus of elasticity
This is just a function of the material; the geometry has been unitized.

3. m Some Rock Physics Definitions Bulk Modulus KdP dV
Ratio of stress to volumetric strain
K = dP dV
Shear Modulus m
Ratio of shear stress to shear strain
A (area) DX m
F I = F DX A I

4. Some Rock Physics Definitions
Poisson’s Ratio s
Simeon Poisson
1781 – French mathematician and physicist. Succeeded Fourier and Laplace. Contemporary of Faraday. Dx
Spring constants from Hook’s law: Dy ex dx ey dy = = x y ex
Poisson’s ratio = ey
Lateral expanshion =
Longitudinal contraction
Young’s Modulus E
Thomas Young
1773 – English “polymath”, and physician. Contemporary of W. Herschel. F
A (area)
Uniaxial stress DL
E =
Uniaxial strain Lo
E =
Modulus of elasticity

5. m m m s m s, m s m m Vp Vs r r r r r r K + K, m E, m 4 3 2 1 - 1 - 2
Compressional velocity
Shear velocity Vp Vs
Bulk modulus, Shear modulus 4 3 m m
K +
K, m r r
Poisson’s ratio, Shear modulus m s m
s, m 2
1 - r s
1 - 2 r
Young’s modulus, Shear modulus m
4m - m
E, m E r
3m - E r

6. Poisson’s ratio related to Vp/Vs ratio
C. A little rock physics
- Poisson’s ratio
Poisson’s ratio related to Vp/Vs ratio
Reduces to .5 (fluid) 2 Vp .6
- 2 s 1 Vs = 2 2 .5 Vp
- 1 Vs s .4 .3 Vp
Poisson’s ratio is another measure of the Vp/Vs ratio.
Here we see that the value of Poisson’s ratio converges to a value of .5 which represents a fluid, and on the other end, the Vp/Vs ratio converges to a value equal to the square root of 2.0 which is 1.14
A typical Vp/Vs ratio of 2.0 corresponds to a Poisson’s ratio of .333 s 2
- 2 .2 = s Vs 2
- 1 .1 2 4 6 8 Vp Vs
Reduces to 2
C - 28

7. So what’s the “Big Deal” about the
Vp / Vs ratio and Poisson’s ratio s ???
Answer: they explain the reflection coefficients and AVO

8. r r s s Vp r - r r + r Vp q Vp Vp Vp Vp Ds q q q
= 0
The R Reflection Coefficient r Vp Vp r - Vp r 1 1 2 2 1 1
R = r Vp r + Vp r Vp 2 2 1 1 2 2
The Shuey Equation 2 Ds 9 2
R = R
Cos q +
Sin q q 4 10 20 30 40
.20 q
.15
.10 s
.05 1 R
.00 s
Wet
-.05 2
-.10
-.15
Gas
-.20 10 20 30 40