Inner Core - Seismology - Lecture Slides, Slides of Geology

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Inner core anisotropy

Seismic anisotropy

• In an anisotropic structure, seismic wave

propagate with different velocities in

different directions.

• The main causes of anisotropy are:
  • SPO (shape-Preferred Orientation)
  • LPO (lattice-preferred orientation)

! ij = "# ij $ kk

• 2 μ$ ij Isotropic medium (review): μ = shear modulus ! = " +

μ Compressional modulus

V

P

V

S

 Anisotropic medium – more general case: ! ij = C ijkl " kl Up to 21 independent elements of the elastic tensor Cijkl

SPO: Anisotropy due to layering ⇒ Radial anisotropy 5 independent elements of the elastic tensor: A,C,F,L,N (Love, 1911)

SPO Anisotropy

L = ρ V sv 2 N = ρ V sh 2 C = ρ V pv 2 A = ρ V ph 2 η = F/(A-2L)

• Radial anisotropy (A,C,F,L,N)
• Azimuthal anisotropy:
  • Velocity depends on the direction of propagation in the horizontal plane V = a + b cos 2! + c sin 2! + d cos 4! + e sin 4! Where ψ is the azimuth counted counterclockwise from North a,b,c,d,e are combinations of elastic elements Cijkl

Montagner, 2002 ξ = (Vsh/Vsv) 2 Radial Anisotropy Isotropic velocity Azimuthal anisotropy Hypothetical convection cell