Numerical Modelling of Time-Harmonic Seismic Wave Fields in Simple Structures by the Gaussian Beam Method. Part I.

Gaussian beam summation method is used for numerical modelling of seismic wave fields in several simple types of models of media. Main attention is paid to the waves reflected from a plane interface, namely from the vicinity of a critical point. Comparison with exact solutions shows that the Gaussian beam summation method yields sufficiently accurate results even in the singular region of the critical point. By summation of Gaussian beams of waves reflected in the overcritical region even head waves are obtained. In the second part of this work, we shall investigate sensitivity of the results to various parameters, for example, to the initial width of a Gaussian beam, to the parameters of the summation of Gaussian beams, etc.