Waves in an elastic medium generated by a point source moving in an overlying fluid medium

Summary

Elastic waves coupled to atmospheric compressional waves radiated from a supersonic moving point source are considered. The point source has the form.

$$\operatorname{Re} [(vt - z\cos \alpha )^2 - r^2 \sin ^2 \alpha ]^{ - 1/2} fort > zcos\alpha /v,0< \alpha \leqslant \frac{\pi }{2},$$

describing a conic shock wave whose vertex is moving uniformly with a velocity δ, δ=v/cosα>v. An exact expression is derived for the motion of an elastic half-space excited by the moving point source in an overlying fluid half-space.