Rock Physics

BasicsDynamic and Static ElasticityDvorkin/RockPhysics 1WAVE EQUATIONε ~ 10 -7u(z)CompressionalExperimentAσ(z)dzσ(z+dz)zAdzρ«« u = A[σ(z + dz) − σ(z)] = Adz∂σ / ∂z ⇒ ρ∂ 2 u / ∂t 2 = ∂σ / ∂zσ = Mε = M∂u / ∂z ⇒ ∂ 2 u / ∂t 2 = (M / ρ)∂ 2 u / ∂z 2 ≡ V p2∂ 2 u / ∂z 2Dynamic definitions:V p= M / ρ = (K + 4G / 3)/ρ; V s= G / ρ;M = ρV p 2 ; G = ρV s 2 ; K = ρ(V p 2 − 4V s 2 / 3); λ = ρ(V p 2 − 2V s 2 )STATIC UNIAXIAL EXPERIMENTε ~ 10 -2 Courtesy Ali Mese70Sample 10156-5860Axial Stress (MPa)50403020Pc = 2000 psi = 14.1 MPaPc = 500 psi = 3.52 MPaPc = 0100RADIALAXIAL-0.005 0 0.005 0.01 0.015 0.02Strain