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

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

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Maxwell’s equations from elasticity

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Mechanical model and circuit strain resistance capacitance

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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

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The analogy

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EM

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Energy in the time domain

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The Debye-Zener analogy Creep function Permittivity

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Fresnel’s formulae EM

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Green’s analogies between elastic and light waves

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Analogy

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

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Backus’s averaging EM b.c. Long wavelengths

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

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

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The reciprocity principle

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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.

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Forbidden directions

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Analogy for diffusive fields Poroelasticity EM

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

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Fresnel 1821

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

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Analogy - Fresnel’s surface EM

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Fresnel - Simulations

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Seismic waves and GPR waves Seismic waves: 0-100 Hz GPR waves: 20-2000 MHz Seismic processing Seismic Migration Seismic inversion Traveltime tomography Alford rotation

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The analogy Thank you

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Analogy

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