ABSTRACT
The calculation of source fields, be it in full-space or on the surface of a half-space, certainly represents an important canonical problem of US-NDT; however, the real fundamental problem is sketched in Figure 15.1: A specimen volume VM with surface SM , often also being the stress-free measurement surface, contains (primary) sources of elastodynamic fields-source volumes VQ-and “defects”—scattering bodies with, say, a volume Vc with surface Sc. If the specimen material is assumed to be linear, time invariant, and locally reacting (very little may be done analytically without this assumption) but nevertheless inhomogeneous, anisotropic, and dissipative, where dissipation is expressed by the frequency dependence of complex valued material tensors ρ(e)
c (R,ω), c(e)
c (R,ω) (Section 4.4). The scattering bodies may be character-
ized by material tensors ρ(i) c (R,ω), c(i)
c (R,ω). The fundamental modeling273
problem is the following: Calculate elastodynamic field quantities-generally u(R, t)—on SM for given material tensors of VM and Vc, and for given sources f(R, t), h(R, t) in VQ; due to the assumed linearity and time invariance of the materials, we may formulate the fundamental modeling problem as in Figure 15.1 for the Fourier spectra.
