Studying numerical dispersion of FEMs for the viscoacustic equation

FABIO IVÁN ZYSERMAN; PATRICIA M. GAUZELLINO

JOURNAL OF APPLIED GEOPHYSICS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2004 vol. 55 p. 279 - 289

0926-9851

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 viscoacoustic model yielding an approximately 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 normalized attenuation, phase and group velocities. We note that the NC-method introduces less numerical anisotropy anddispersion 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. By studying the numerical solution error as a function of the frequencywe show that methods are not pollution-free. It can be observed, however,  that  this effect is negligible for applications involving onlysmall frequencies.