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

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

Maxwell’s equations from elasticity

Mechanical model and circuit strain resistance capacitance

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

The analogy

EM

Energy in the time domain

The Debye-Zener analogy Creep function Permittivity

Fresnel’s formulae EM

Green’s analogies between elastic and light waves

Analogy

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

Backus’s averaging EM b.c. Long wavelengths

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

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

The reciprocity principle

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.

Forbidden directions

Analogy for diffusive fields Poroelasticity EM

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

Fresnel 1821

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

Analogy - Fresnel’s surface EM

Fresnel - Simulations

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

The analogy Thank you

Analogy