Publications Details

Propagation of transient signals from a spherical source in a half-space with surface layers

Norwood, F.R.

The title problem is of particular interest for the analysis of seismic signals arising from underground nuclear explosions. Previous attempts at the solution have indicated that, although cylindrical symmetry exists, conventional methods cannot be applied because of the existence of plane and spherical boundaries. The present paper develops a ray-grouping technique for finding the solution to the title problem. This technique allows the separation of the problem into a series of canonical problems. Each such problem deals with a given boundary condition (e.g., continuity conditions at a material interface). Using this technique, one may follow waves along ray paths. It is easy to identify, after n reflections, (a) rays which arrive simultaneously at a given point and (b) the terms in the solution which need to be included at a given time. It is important to note that a cylindrical coordinate system is not employed, even though the problem is axially symmetric. Instead, the equations are carefully transformed making it possible to use a Cartesian coordinate system. This results in a spectral representation of the solution in terms of algebraic expressions in lieu of Bessel functions.