Dispersion analysis of FEM's for the viscoacustic wave equation

FABIO IVÁN ZYSERMAN

MECANICA COMPUTACIONAL

AMCA

Lugar: Bahia Blanca; Año: 2003 vol. 22 p. 1569 - 1582

We investigate the numerical dispersive properties of two finite element methods yielding a first order spatial approximation, a nonconforming one (NC-method) and the Q_1 conforming method (C-method) when applied to solve the scalar wave equation in dispersive media in the space-frequency domain. The dispersive properties of the subsurface are simulated via a viscoacustic model yielding a constant quality factor in a given fixed frequency range. Thestudy is performed by constructing and analyzing the numeric dispersion relations, and  by evaluating derived quantities such as the frequency dependent normalizedattenuation, phase and group velocities. It isobserved that the NC-method introduces less numerical anisotropy and dispersion than the C-method. Moreover, for a given fixed frequency, the NC-method nearly halves the number of points per wavelength necessary to reach a given accuracy when calculating the mentioned derived quantities.