Numerical modeling of ultrasonic coda wave interferometry in a multiple scattering medium with a localized nonlinear defect

In this paper, the spectral element method is used to perform a parametric sensitivity study of the nonlinear coda wave interferometry (NCWI) method in a homogeneous or heterogeneous sample with localized damage. The influence of a strong pump wave on localized nonlinear damage is modeled as modifications to the elastic properties of an effective damage zone (EDZ), depending on the pump wave amplitude. These modifications are quantified with coda wave interferometry through an overall wave velocity variation probed by a reverberated or multiple scattered coda wave. Results demonstrate that the NCWI observables are independent of the source/receiver positions. Also, relations between the EDZ parameters and method observables are established, e.g. the relative velocity variation is found to be proportional to the product of the change in elastic modulus and the EDZ area. The numerical results reported constitute another step towards quantification and forecasting of the nonlinear acoustic response of a cracked material, which proves to be necessary for a quantitative non-destructive evaluation. Furthermore, it is shown numerically that NCWI sensitivity and applicability are similar for the cases of reverberated waves in a cavity and multiply scattered waves in a heterogeneous medium.