## Paraxial Super-Gaussian beams

**Ludek Klimes**
### Summary

In the conventional ray theory with real-valued travel time,
the initial amplitude profile is represented
by the initial conditions for amplitude.
Since the accuracy of the ray theory
suffers from the amplitude changes along wavefronts,
this approach is considerably inaccurate for beams,
because it does not provide the spreading of the beams
caused by diffraction.

The representation of the initial Gaussian amplitude profile
in terms of the imaginary part
of the initial complex-valued travel time
with the constant initial conditions for amplitude
yields satisfactorily accurate paraxial Gaussian beams.

In this paper, we demonstrate that
the representation of the initial Super-Gaussian amplitude profile
in terms of the imaginary part
of the initial complex-valued travel time
with the constant initial conditions for amplitude
yields the Super-Gaussian beams
whose lowest-order paraxial approximation is identical to
the conventional ray theory solution with real-valued travel time,
without the diffracted wavefield which could result
from the representation theorem.

### Keywords

Wave propagation, ray theory, complex-valued travel time,
paraxial approximation, Gaussian beams, Super-Gaussian beams.

### Whole paper

The paper is available in
PDF (81 kB).

In: Seismic Waves in Complex 3-D Structures, Report 23,
pp. 145-148, Dep. Geophys., Charles Univ., Prague, 2013.