Adrianus T. de Hoop

Simultaneous nonlinear reconstruction of two-dimensional permittivity and conductivity

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.

Generation of acoustic waves by an impulsive point source in a fluid/porous‐medium configuration with a plane boundary

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.

Time‐domain reciprocity theorems for acoustic wave fields in fluids with relaxation

Time‐domain reciprocity theorems of the time‐convolution and the time‐correlation type for acoustic wave fields in linear, time‐invariant, and locally reacting fluids are discussed. Inhomogeneity, inertial anisotropy, and arbitrary relaxation effects in inertia and compressibility properties, both of the active and the passive type, are included. The theorems also apply to the ‘‘equivalent fluid model’’ of a solid in which only compressional waves are considered and shear is neglected. The analysis is entirely carried out in space‐time, without intermediate recourse to the frequency or the wave vector domains. The application to inverse source and inverse constituency (or inverse profiling/scattering, or imaging) problems is briefly indicated.

Elastic wave up/down decomposition in inhomogeneous and anisotropic media: an operator approach and its approximations

Abstract A structural operator approach to the up/down decomposition of elastic waves in inhomogeneous and anisotropic media is presented. First, the up/down decomposition is carried out; next, a decomposition of the wave field into its polarization constituents is worked out. The procedure is discussed in detail for the class of orthorhombic media and includes lateral variations. The high-frequency approximation to the operator approach is shown to be amenable to matrix manipulations in the horizontal Fourier transform domain. Two-level parabolic approximations are carried out to find sparse matrix (finite-difference) representations of the relevant operators. Finally, the space-time peculiarities and artifacts associated with the parabolic approximation to the particle velocity of the wave motion generated by a point force in a homogeneous and isotropic solid are discussed.

The moving-load problem in soil dynamics—the vertical displacement approximation

Abstract The moving point load problem in soil dynamics is analyzed in the vertical particle displacement approximation. Prior to its motion, the load is stationary. From the instant at which it is set into motion it moves, with constant speed, along a straight path on the (horizontal) planar surface of a semi-infinite elastic medium. The modified Cagniard method for solving transient wave problems is used to determine closed-form expressions for the vertical component of the particle displacement from the elastodynamic wave equation of which only the vertical component is taken into account. The relevant approximation is standard in soil dynamics. Both the cases of “subsonic” and “supersonic” surface load speeds are considered. Methods to include losses in the model are briefly discussed. The study has been initiated with a view to the application of the results to the analysis of the ground motion generated by high-speed trains traveling on a poorly consolidated soil.

Generalized Ray Theory for Time-Domain Electromagnetic Fields in Horizontally Layered Media

Generalized-ray theory for time-domain electromagnetic fields in a horizontally layered medium is developed. It can be considered as the time-domain equivalent of the intensively studied Greens function formulation in frequency domain. After introducing appropriate integral transformations and source-type field representations, the solution is written out in terms of generalized ray constituents whose space-time counterparts are constructed with the aid of the Cagniard–DeHoop technique. The formulation lays the foundation to rigorously study time-domain field behavior in numerous practical topologies where a stratified multilayer is involved, such as planar antennas and circuits, but also electromagnetic compatibility (EMC) and propagation problems. Illustrative numerical results are presented.

Time-domain reciprocity theorems for elastodynamic wave fields in solids with relaxation and their application to inverse problems

Abstract Time-domain reciprocity theorems of the time-convolution and the time-correlation type for elastodynamic wave fields in linear, time-invariant, and locally reacting solids are discussed. Inhomogeneity, anisotropy, and arbitrary relaxation effects, both of the active (anti-causal) and passive (causal) kind, are included. The analysis is entirely carried out in space-time, without intermediate recourse to the frequency or the wavevector domains. The application to inverse source and inverse constituency (inverse profiling or scattering) problems is discussed.

Impulsive sound reflection from an absorptive and dispersive planar boundary

The impulsive sound reflection from a planar boundary with absorptive and dispersive properties is investigated. The acoustic properties of the boundary are modeled via a local impedance transfer function whose complex frequency domain representation is taken to be a Pade (2,2) expression. The coefficients in this representation are matched to frequency domain acoustic wave reflection measurements. With the aid of the Cagniard–De Hoop method, a closed-form space-time expression is derived for the acoustic pressure of the reflected wave arising from the incidence of a point-source monopole excited spherical pulse. Depending on the acoustic impedance properties of the boundary, large-amplitude oscillating surface effects can occur. These surface phenomena differ in nature from the true surface waves like the Rayleigh, Scholte, and Stoneley waves in elastodynamics. Illustrative numerical results are presented.

Pulsed Electromagnetic Field Radiation From a Wide Slot Antenna With a Dielectric Layer

Analytic time-domain expressions are derived for the pulsed electromagnetic field radiated by a wide slot antenna with a dielectric layer in a two-dimensional model configuration. In any finite time window of observation, exact pulse shapes for the propagated, reflected and refracted wave constituents are constructed with the aid of the modified Cagniard method (the Cagniard-DeHoop method). Numerical results are presented for field pulse shapes at the dielectric/free-space interface, the pulse time widths of the excitation being chosen such that the separate arrivals from the two edges of the slot can be distinguished. Applications are found in any system whose operation is based on pulsed electromagnetic field transfer and where digital signals are detected and interpreted in dependence on their pulse shapes.

Seismic waves generated by an impulsive point source in a solid/fluid configuration with a plane boundary

The space‐time acoustic wave motion generated by an impulsive point source in a solid/fluid configuration with a vertical plane boundary is calculated with the aid of the modified Cagniard method. Two types of sources are considered in detail, viz. (1) a point source of expansion (model for an explosive source), and (2) a point force parallel to the vertical interface (model for a mechanical vibrator). Numerical results are presented for the transmitted scalar traction in the fluid in those regions of space where head wave contributions occur. There is a marked difference in the time response observed for the two types of sources and for the different positions of the receiver in the fluid with respect to the position of the source in the solid. These waveform differences are important when the transmitted wave in the fluid is used to determine experimentally the elastic properties of the solid. Scholte waves are observed only when the source is close to the fluid/solid interface. As compared with the tra...