Recent Applications and Advances of Numerical Modeling and Wavefield Inversion in Nondestructive Testing

Abstract

Abstract. This paper presents recent advances and future challenges of the application of different linear and nonlinear inversion algorithms in acoustics, electromagnetics, and elastodynamics. The presented material can be understood as an extension of our previous work on this topic. The inversion methods considered in this presentation vary from linear schemes, like the Synthetic Aperture Radar (SAR) applied electromagnetics and the Synthetic Aperture Focussing Technique (SAFT) as its counterpart in ultrasonics, and the linearized Diffraction Tomography (DT), to nonlinear schemes, like the Contrast Source Inversion (CSI) combined with different regularization approaches. Inversion results of the above mentioned inversion schemes are presented and compared for instance for time-domain ultrasonic data from the Fraunhofer-Institute for Nondestructive Testing (IZFP, Saarbrücken, Germany). Convenient tools for nondestructive evaluation of solids can be electromagnetic and/or elastodynamic waves; since their governing equations, including acoustics, exhibit strong structural similarities, the same inversion concepts apply. In particular, the heuristic SAFT algorithm can be and has been utilized for all kinds of waves, once a scalar approximation can be justified. Relating SAFT to inverse scattering in terms of diffraction tomography, it turns out that linearization is the most stringent inherent approximation. A comparison of the inversion results using the linear time-domain inversion scheme SAFT and well tested nonlinear frequency-domain inversion schemes demonstrates the considerable potential to extend and improve the ultrasonic imaging technique SAFT while consulting the mathematics of wavefield inversion, yet, in particular if the underlying effort is considered, the relatively simple and effective SAFT algorithm works surprisingly well. Since SAFT is a widely accepted imaging tool in ultrasonic NDE it seems worthwhile to check its formal restrictions and assumptions whether they could be overcome and whether they would outperform the standard and original SAFT algorithm.

Edge Illumination and Imaging of Extended Reflectors

“…It is easy to implement, it is not demanding computationally, and it is widely used in several applied areas such as seismic imaging [9,10,3,2], radar imaging [15,7], and nondestructive evaluation of materials [34]. There are, of course, more accurate broadband imaging methods such as full wave migration [2,Chapter 4] and full least squares inversion [2,Chapter 9].…”

Subspace projection filters for imaging in random media

“…The numerical simulations are in two dimensions, in a regime that is often used in ultrasonic array imaging in concrete [24,25]. In this paper, elastic wave propagation in concrete is simplified to a scalar acoustic problem.…”

GPR Estimation of the Geometrical Features of Buried Metallic Targets in Testing Conditions

“…In this work, we consider solution schemes based on a simplified model of the electromagnetic scattering such as Kirchhoff approximation [40][41][42][43]. Under the Kirchhoff approximation, the reconstruction provides an image corresponding to the support of the induced surface-current distribution on the illuminated region [40][41][42] and the unknown-to-data mapping is linear.…”

“…Under the Kirchhoff approximation, the reconstruction provides an image corresponding to the support of the induced surface-current distribution on the illuminated region [40][41][42] and the unknown-to-data mapping is linear. This linear inverse problem is regularized by using the Singular Values Decomposition (SVD) [26]; the absence of local minima favorably affects the reliability of the results and the low computational burden allows us to deal with 'large' (in terms of wavelengths) investigation domains, as the ones considered in the following.…”