Identifiability limits in ultrasonic microstructure characterisation using attenuation and velocity features:...

Area of Science:

• Materials Science
• Acoustics
• Signal Processing

Background:

• Ultrasound is increasingly used for microstructure characterization, with performance often evaluated by inversion accuracy.
• The information content within measured ultrasonic responses fundamentally constrains characterization frameworks.
• Identifiability, the ability to uniquely determine microstructural parameters, is crucial for reliable characterization.

Purpose of the Study:

• To directly examine the identifiability of microstructural parameters using ultrasound.
• To analyze the geometry of the forward operator in both canonical and stochastic microstructure models.
• To understand the influence of parameter coupling, dimensional restrictions, and intrinsic variability on characterization accuracy.

Main Methods:

• Analysis of the forward operator's geometry using feature-level ultrasonic observables.
• Sensitivity analysis for a canonical pulse-echo model to identify information limits.
• Investigation of stochastic surrogate microstructures (Gaussian random fields) focusing on attenuation and velocity.
• Application of a variance-weighted Fisher framework to assess parameter recoverability.

Main Results:

• Canonical model analysis revealed information limits due to parameter coupling and dimensional restrictions.
• For stochastic microstructures, the forward map from correlation length and texture coherence to observables was full rank but anisotropic.
• Intrinsic microstructural variability significantly reduced practical identifiability.
• Recoverability depends on the balance between sensitivity magnitude and stochastic variability, not just structural rank.

Conclusions:

• Identifiability limits in feature-level ultrasonic microstructure characterization are primarily governed by forward-map structure and intrinsic variability.
• Single observables yield poorly constrained results, while combined observables improve conditioning.
• This work provides a foundation for developing optimal observable selection strategies for enhanced ultrasonic material characterization.