Superposition method for modelling boundaries between media in viscoelastic finite difference time domain simulations

Area of Science:

• Geophysics
• Computational Seismology
• Wave Propagation Modeling

Background:

• Finite-difference time domain (FDTD) methods are essential for modeling viscoelastic wave propagation in heterogeneous media.
• Modeling liquid-solid interfaces on Cartesian grids with standard FDTD schemes introduces significant 'staircasing' errors.
• High spatial resolution to mitigate these errors is often computationally prohibitive.

Purpose of the Study:

• To present a modified FDTD scheme, the superposition method, to reduce staircasing errors at liquid-solid interfaces.
• To maintain manageable computational costs while improving simulation accuracy.
• To validate the effectiveness of the superposition method for viscoelastic wave propagation.

Main Methods:

• Developed a superposition method as a modification to the Virieux staggered-grid FDTD scheme.
• Validated the method by comparing low-resolution simulations with high-resolution simulations across various incident angles.
• Analyzed root-mean-square stress amplitude maps to quantify artifactual wave reduction.

Main Results:

• The superposition method significantly reduces staircasing effects in FDTD simulations.
• Artifactual wave amplitudes were reduced by several orders of magnitude compared to the standard Virieux staggered-grid FDTD method.
• Accurate results were achieved at low spatial resolutions for all incident angles.

Conclusions:

• The superposition method offers a computationally efficient way to accurately model viscoelastic wave propagation across liquid-solid interfaces.
• This technique overcomes the limitations of traditional FDTD methods in complex media.
• It enables more reliable seismic and wave propagation simulations in geophysics and related fields.