Ultrasonic inverse scattering of multidimensional objects buried in multilayered elastic background structures

Area of Science:

• Geophysics
• Acoustics
• Applied Mathematics

Background:

• Inverse scattering problems are crucial for subsurface imaging.
• Objects buried in inhomogeneous elastic media pose significant challenges.
• Ultrasonic probing offers a non-invasive method for material characterization.

Purpose of the Study:

• To develop a multiparameter direct linear inversion method for multidimensional inverse scattering.
• To retrieve both the geometry (imaging) and constitutive parameters (inverse problem) of buried objects.
• To address the nonlinear and ill-posed nature of inverse scattering in inhomogeneous elastic backgrounds.

Main Methods:

• Formulating the problem within a vector integral equation elastic scattering framework.
• Linearizing the nonlinear inverse scattering problem using the Born approximation.
• Employing singular value decomposition (SVD) for solving the discretized forward operator matrix.
• Applying constrained least-squares inversion and Tikhonov regularization.

Main Results:

• Successfully demonstrated a 2-D inverse scattering method for object retrieval from synthetic data.
• Compared the performance of minimum-norm least-square estimation with Tikhonov regularization.
• Validated the feasibility of retrieving object geometry and constitutive parameters.

Conclusions:

• The developed multiparameter inversion technique is effective for imaging buried objects in inhomogeneous elastic media.
• Linearization via Born approximation and SVD provide a robust framework for solving this inverse problem.
• Regularization techniques are essential for obtaining stable and accurate solutions in ill-posed inverse scattering scenarios.