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The acoustic-electromagnetic analogy José M. Carcione OGS, Trieste, Italy.

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Presentation on theme: "The acoustic-electromagnetic analogy José M. Carcione OGS, Trieste, Italy."— Presentation transcript:

1 The acoustic-electromagnetic analogy José M. Carcione OGS, Trieste, Italy

2 Maxwell’s equations from elasticity R = electric field, E -4  E 2 = dielectric constant h = Displacement, D

3 Maxwell’s equations from elasticity

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6 Mechanical model and circuit strain resistance capacitance

7 TM Maxwell and SH elastic 2D propagation in the (x,z)-plane. H 2 and v 2 perpendicular to the plane. TM SH: plane of symmetry of a monoclinic medium

8 The analogy

9 EM

10 Energy in the time domain

11 The Debye-Zener analogy Creep function Permittivity

12 Fresnel’s formulae EM

13 Green’s analogies between elastic and light waves

14 Analogy

15 3-D Maxwell’s equations - biaxial medium Dielectric-permittivity components >>> Zener Magnetic-permeability components >>> Zener Conductivity - Ohm’s law >>> Kelvin-Voigt

16 Backus’s averaging EM b.c. Long wavelengths

17 The time-average and CRIM equations Time-average equation EM - CRIM equation n layers of thickness h i and velocity v i

18 The Kramers-Kronig relations EM Electric susceptibility J = J 1 + i J 2 : Creep function

19 The reciprocity principle

20 Babinet’s principle EM: Babinet's principle for thin conducting complementary screens implies that the sum, beyond the screen plane, of the electric and the magnetic fields equals the incident (unscreened) electric field. In elastodynamics, the principle holds for the same field (particle velocity or stress), but for complementary screens satisfying different types of boundary conditions, i.e, if the original screen is weak (stress- free condition), the complementary screen must be rigid. On the other hand, if the original screen is rigid, the complementary screen must be weak.

21 Forbidden directions

22 Analogy for diffusive fields Poroelasticity EM

23 Fresnel’s wave surface Optically biaxial crystal s: slowness components

24 Fresnel 1821

25 Orthorhombic (anisotropic) elastic medium C IJ = c IJ / 

26 Analogy - Fresnel’s surface EM

27 Fresnel - Simulations

28 Seismic waves and GPR waves Seismic waves: Hz GPR waves: MHz Seismic processing Seismic Migration Seismic inversion Traveltime tomography Alford rotation

29 The analogy Thank you

30 Analogy


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