Numerical Analysis Of Fem's For The Viscoacustic Wave Equation

Abstract

We investigate the numerical dispersive properties of two nite element methods
yielding a rst order spatial approximation, a nonconforming one (NC-method) and
the Q1 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
xed frequency range. The study 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. It is observed that the NC-method
introduces less numerical anisotropy and dispersion than the C-method. Moreover, for a
given xed frequency, the NC-method nearly halves the number of points per wavelength
necessary to reach a given accuracy when calculating the mentioned derived quantities.