Lamb's problem on random mass density fields with fractal and Hurst effects.

Area of Science:

• Solid Mechanics
• Computational Physics
• Geophysics

Background:

• Lamb's problem is a classic benchmark in seismology and solid mechanics.
• Understanding wave propagation in heterogeneous media is crucial for geophysical exploration and material science.
• Previous models often simplified the complexity of natural material properties.

Purpose of the Study:

• To generalize Lamb's problem to an infinite elastic half-space with random fields (RFs) of mass density.
• To investigate the impact of uncorrelated and correlated RFs (with fractal and Hurst characteristics) on wave propagation.
• To analyze stochastic imperfection sensitivity in the planar stochastic Lamb's problem.

Main Methods:

• Generalization of Lamb's problem for random fields of mass density.
• Simulation of wave propagation using Cellular Automata (CA).
• Evaluation of CA response to uncorrelated (white-noise) and correlated (Cauchy, Dagum) mass density RFs.
• Analysis of fractal dimension and Hurst parameter effects on wave propagation.

Main Results:

• CA successfully simulates wave propagation in elastic half-spaces with random mass density fields.
• The study quantifies the response to varying coarseness of uncorrelated RFs.
• The impact of multiscale mass density RFs (Cauchy, Dagum) on wave propagation is evaluated.
• Stochastic imperfection sensitivity is assessed by comparing response variations to RF variations.

Conclusions:

• Cellular automata provide a viable method for simulating wave propagation in complex media.
• Both fractal dimension and Hurst parameter significantly influence the solution to the planar stochastic Lamb's problem.
• The study highlights the importance of characterizing RFs for accurate modeling in geophysics and material science.