Equivalent permittivity of binary objects obtained by inversion of their response to impressed potentials
Résumé
This investigation addresses the following problem: (a) a binary
inhomogeneous dielectric (two distinct permittivities; those of the
core and of the mantle) object B is subjected to a quasistatic
electric potential P and the response F to this field is measured at
various points outside the object. (b) Find the so-called ‘equivalent’
permittivity ε of the homogeneous object H , having the same shape
and size as B , which gives rise to the same response F as B to the
solicitation P . This is treated as an inverse problem, in which F is
the simulated data and the parameter retrieval model is that of the
interaction of P with H . We show, for B a filled tube-like object, that:
(1) this inverse problem can be solved for the retrieved value E of ε
in a mathematically-explicit form, (2) and E can provide consistent,
meaningful, physical and geometric information as to the nature and
proportion of the core and mantle components of the object, provided
uncertainties concerning the measurement of F are small.