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