2007/01/01 by Jonás D. De Basabe, Mrinal K. Sen · 202 citations
Earth and Planetary Sciences · Engineering · Mathematics · #Acoustics #Dispersion (optics) #Eigenvalues and eigenvectors #Finite element method #Geometry #Geophysical Methods and Applications #Grid #Isotropy #Mathematical analysis #Mathematics #Optics #Physics #Seismic Imaging and Inversion Techniques #Seismic Waves and Analysis #Wave propagation
paper · doi:10.1190/1.2785046
published in Geophysics 72(6), T81-T95 (Society of Exploration Geophysicists)
openalex publication_date 2007/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Abstract Purely numerical methods based on finite-element approximation of the acoustic or elastic wave equation are becoming increasingly popular for the generation of synthetic seismograms. We present formulas for the grid dispersion and stability criteria for some popular finite-element methods (FEM) for wave propagation, namely, classical and spectral FEM. We develop an approach based on a generalized eigenvalue formulation to analyze the dispersive behavior of these FEMs for acoustic or elastic wave propagation that overcomes difficulties caused by irregular node spacing within the element and the use of high-order polynomials, as is the case for spectral FEM. Analysis reveals that for spectral FEM of order four or greater, dispersion is less than 0.2% at four to five nodes per wavelength, and dispersion is not angle dependent. New results can be compared with grid-dispersion results of some classical finite-difference methods (FDM) used for acoustic or elastic wave propagation. Analysis reveals that FDM and classical FEM require a larger sampling ratio than a spectral FEM to obtain results with the same degree of accuracy. The staggered-grid FDM is an efficient scheme, but the dispersion is angle dependent with larger values along the grid axes. On the other hand, spectral FEM of order four or greater is isotropic with small dispersion, making it attractive for simulations with long propagation times.