Huygens principle versus exploding reflector ? theoretical and numerical aspects

Abstract

Huygens principle states that wave motion can be described by exploding secondary sources along the wavefront. The envelope of the resulting spheres constitute successive wavefronts which progress in time. This fundamental concept elucidates the nature of wave motion for virtually any field, such as electromagnetism, optics, acoustics and elasticity. We have deviated slightly from Huygens principle, advocating that the explosions take place not along the wavefronts, but rather on the reflectors of the medium where the wave propagates. The magnitude of each explosion is directly proportional to the reflection coefficient of that reflector. Each explosion point emits particles at each reflector point of the receivers yields the wavefields. If the reflection coefficient vanishes, no additional explosion occurs at this point of time and space. The validity of this exploding reflection straight trajectory modelling is demonstrated with reference to a two layer acoustic case. Comparison of the synthetic seismogram with that obtained by ray theory shows good time agreement. It is shown that for such a simple model the new modelling technique also yields correct amplitudes.