Rock Physics in a Nutshell F dP dV

Some Rock Physics Definitions Hooke’s Law F = k X Robert Hooke 1635 - 1703 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 – 1829 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.

m Some Rock Physics Definitions Bulk Modulus K dP 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

Some Rock Physics Definitions Poisson’s Ratio s Simeon Poisson 1781 – 1841 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 – 1829 English “polymath”, and physician. Contemporary of W. Herschel. F A (area) Uniaxial stress DL E = Uniaxial strain Lo E = Modulus of elasticity

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

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

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

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