  The Gaussian beam superposition method is an asymptotic method for computing
high frequency wave fields in smoothly varying inhomogeneous media. In this
paper we study the accuracy of the Gaussian beam superposition method and
derive error estimates related to the discretization of the superposition
integral and the Taylor expansion of the phase and amplitude off the center of
the beam. We show that in the case of odd order beams, the error is smaller
than a simple analysis would indicate because of error cancellation effects
between the beams. Since the cancellation happens only when odd order beams are
used, there is no remarkable gain in using even order beams. Moreover, applying
the error estimate to the problem with constant speed of propagation, we show
that in this case the local beam width is not a good indicator of accuracy, and
there is no direct relation between the error and the beam width. We present
numerical examples to verify the error estimates.
