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A new inversion algorithm for the simultaneous reconstruction of permittivity and conductivity recasts the nonlinear inversion as the solution of a coupled set of linear equations. The algorithm is iterative and proceeds through the minimization of two cost functions. At the initial step the data are matched through the reconstruction of the radiating or minimum norm scattering currents; subsequent steps refine the nonradiating scattering currents and the material properties inside the scatterer. Two types of basis functions are constructed for the nonradiating currents: “invisible” (global) basis functions, which are appropriate for discrete measurements and nonradiating (local) basis functions, which are useful in studying the limit of continuous measurements. Reconstructions of square cylinders from multiple source receiver measurements at a single frequency show that the method can handle large contrasts in material properties.

The space–time acoustic wave motion generated by a two-dimensional, impulsive, monopole line source in a fluid/solid configuration with a plane boundary is calculated with the aid of the modified Cagniard technique. The source is located in the fluid, and numerical results are presented for the reflected-wave acoustic pressure, especially in those regions of space where head wave contributions occur. There is a marked difference in time response in the different regimes that exist for the wave speed in the fluid in relation to the different wave speeds (compressional, shear, Rayleigh) in the solid. These differences are of importance to the situation where the reflected wave in the fluid is used to determine experimentally the elastic properties of the solid.

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Time-domain reciprocity theorems of the time-convolution and the time-correlation type for electromagnetic fields in linear, time-invariant, and locally reacting media are discussed. Inhomogeneous, anisotropic, and arbitrarily dispersive, both active and passive, media are included. The analysis is entirely carried out in space-time, without intermediate r•ourse to the frequency or the wave vector domain. The application to inverse source and inverse constituency (or inverse profiling) problems is briefly indicated.