  We introduce new numerical integration operators which compose the mass and
stiffness matrices of a modified spectral element method for simulation of
elastic wave propagation. While these operators use the same quadrature nodes
as does the original spectral element method, they are designed in order that
their harmonic responses have errors of the same ratio, and that the respective
dispersion errors of the mass and stiffness matrices cancel each other. As a
result, the modified spectral element method yields two extra-orders of
accuracy, and is comparable to the original method of one order higher. The
theoretical results are confirmed by numerical dispersion analysis and examples
of computation of waveforms using our operators. Replacing the ordinary
operators by those proposed in this study could be a non-expensive solution to
improve the accuracy.
