Effective fractional acoustic wave equations in one-dimensional random multiscale media

Area of Science:

• Wave propagation
• Random media physics
• Stochastic homogenization theory

Background:

• Understanding wave propagation in complex, random media is crucial for various scientific fields.
• Previous models often simplify correlation properties or neglect frequency-dependent effects.

Purpose of the Study:

• To develop an effective deterministic model for pulse propagation in a 1D non-lossy random medium.
• To characterize the frequency-dependent attenuation and phase properties of such media.

Main Methods:

• Application of stochastic homogenization theory.
• Derivation of an effective fractional wave equation.
• Analysis of frequency-dependent attenuation and phase relationships.

Main Results:

• Pulse propagation is described by a deterministic fractional wave equation.
• The medium exhibits frequency-dependent attenuation following a power law (exponent 0-2).
• The Hurst parameter characterizes the medium's correlation properties and influences the attenuation exponent.

Conclusions:

• The fractional wave equation provides an accurate model for wave propagation in random media.
• The model satisfies causality and Kramers-Kronig relations through frequency-dependent phase.
• This work offers insights into the behavior of waves in complex media.