Matrix theory of elastic wave scattering

Upon invoking Huygen's principle, matrix equations are obtained describing the scattering of waves by an obstacle of arbitrary shape immersed in an elastic medium. New relations are found connecting surface tractions with the divergence and curl of the displacement, and conservation laws are discussed. When mode conversion effects are arbitrarily suppressed by resetting appropriate matrix elements to zero, the equations reduce to a simultaneous description of acoustic and electromagnetic scattering by the obstacle at hand. Unification with acoustic/electromagnetics should provide useful guidelines in elasticity. Approximate numerical equality is shown to exist between certain of the scattering coefficients for hard and soft spheres. For penetrable spheres, explicit analytical results are found for the first time.