title: A comparison of stochastic and effective medium approaches to the backscattered signal from a porous layer in a solid matrix.
abstract: This paper reports a study of the backscattering behavior of a solid layer containing randomly spaced spherical cavities in the long wavelength limit. The motivation for the work arises from a need to model the responses of porous composite materials in ultrasonic NDE procedures. A comparison is made between models based on a summation over discrete scatterers, which show interesting emergent properties, and an integral formulation based on an ensemble average, and with a simple slab effective medium approximation. The similarities and differences between these three models are demonstrated. A simple quantitative criterion is established which sets the maximum frequency at which ensemble average or equivalent homogeneous medium models can represent echo signal generation in a porous layer for given interpore spacing, or equivalently, given pore size and concentration.
authors.affiliation: Electrical Systems and Optics Division, Faculty of Engineering, University of Nottingham, University Park, Nottingham, NG7 2RD United Kingdom. valerie.pinfield@nottingham.ac.uk
authors.forename: Valerie J
authors.initials: VJ
authors.lastname: Pinfield
authors.forename: Richard E
authors.initials: RE
authors.lastname: Challis
authors.forename: Robert A
authors.initials: RA
authors.lastname: Smith
mesh_terms: D003198:Computer Simulation; D004867:Equipment Design; D005583:Fourier Analysis; D008962:Models, Theoretical; D009038:Motion; D009716:Numerical Analysis, Computer-Assisted; D016062:Porosity; D012542:Scattering, Radiation; D013016:Sound; D013018:Sound Spectrography; D013269:Stochastic Processes; D013997:Time Factors; D014159:Transducers; D014465:Ultrasonics / Q000295:instrumentation