On the Scattering of Elastic Waves by the Small Obstacles

[摘要] In the theory of the Electromagnetic wave, we know that an incident wave may be scattered by small particles having a small difference in that dielectric conatant with the surrounding medium, and its intensity is invensely proportional to the fourth power of the wave-length. In this paper we investigatod what phenomenon will be expected in the elastic problem.As a simple example, we took the special case in which a small spherical obstacle having a little difference in the elastic constant with the surrounding medium, was buried in the latter, and its radius was supposed to be very small compared with the wave-length of the incident wave.We consider here dilatational waves as shown in equation (1) for incident ones. Substituting (1), (2) and (3) in the boundary conditions (4), we obtain (8) as the coeficients of the seattering waves. Taking main terms of (8), we get the scettering wavs shown by (9).From the present calculation, we can derive the following results _??_ when elastic dilatitional waves propagete in a medium in which small spherical obstacles of radius a exist and if the elastic constants of both material from one antother, the amplitudes of scattered waves are proportional to (ha)3, so that their intensities should be proportional to (ha)6 at the most. It must be noticed that the amplitudes of the polarized component are not greater than the order of (ha)5. Thus it becomes evident from what above stated that a hsterogeneous construction supposed to exist in the vicinity of the earth's surface may not be the cause of such distinct phenomenon as “Blue sky” in the optical problem.

[学科分类] 大气科学