Bayesian inference for the ultrasonic characterization of rigid porous materials using reflected waves by the first...

Area of Science:

• Geophysics
• Materials Science
• Acoustics

Background:

• Characterizing porous media is crucial for various applications.
• Ultrasonic methods offer non-destructive evaluation capabilities.
• Accurate determination of porosity, tortuosity, and characteristic lengths is challenging.

Purpose of the Study:

• To present a novel ultrasonic method for characterizing air-saturated porous media.
• To infer porosity, tortuosity, and viscous/thermal characteristic lengths using reflected waves.
• To solve the inverse problem using Bayesian inference and Markov-Chain Monte-Carlo methods.

Main Methods:

• Utilizing reflected pressure signals from the first interface under multiple obliquely incident waves.
• Employing a first-level Bayesian inference method for numerical inverse problem solving.
• Exploring posterior probability densities using a Markov-Chain Monte-Carlo approach.

Main Results:

• Successfully inferred viscous and thermal characteristic lengths despite low sensitivity to the reflection coefficient.
• Achieved simultaneous determination of all physical parameters governing the reflection operator.
• Constrained the problem and improved thermal length definition using a specific incident angle, revealing a statistical relationship between tortuosity and characteristic length ratio.

Conclusions:

• The proposed ultrasonic method enables comprehensive characterization of air-saturated porous media.
• Bayesian inference combined with MCMC provides a robust framework for solving inverse problems in acoustics.
• The study demonstrates the feasibility of extracting key material properties from reflected wave analysis.