Surface displacement amplitudes in the alluvial valley under sh wave

In an unbounded homogeneous medium, waves propagate without interruption at a constant speed and along a fixed path. But with the insertion of an obstacle in the medium, the path of the wave propagation is changed, and the obstacle, when excited by the otherwise undisturbed incident wave, acts as a secondary source which emits waves radially outward from itself. The aberration of the wave from its original path is known as the diffraction, and the radiation of secondary waves from the obstacle is called scattering. In an elastic medium, the obstacle may be in the form of a cavity or a crack, or a rigid body generally, a substance with elastic moduli and density different from the medium's. As a result of reflection and scattering, the stresses near the obstacle are different, sometimes higher, than the stresses at the same point produced by uninterrupted waves, a phenomenon known as dynamic stress concentration. The phenomenon of reflection is extremely valuable for our daily lives. For instance, the reflection of visible light allows us to see objects that do not produce their own light. The reflection of microwaves is quite useful for radar scanners. The reflection of sound waves in a theater or concert hall enlivens an onstage production. The reflection of seismic waves allows researchers to study the Earth's structure and to prospect for petroleum and other natural resources. The method of studying the reflection of elastic waves is not much different from methods used with other waves, owing to physical similarity and mathematical analogy. There is additional difficulty in the analysis, however, because of the presence in an isotropic elastic solid of two waves with different speeds, as opposed to one acoustical or electromagnetic wave in air. Another distinction, as a matter of interest, is that with elastic waves we are often dealing with waves at low frequencies), and in the region near the obstacle. Also, in connection with dynamic stress concentrations, the displacements and stresses associated with a wave at a point, instead of the overall wave scattering pattern, are what is sought. This may require in many cases a different computing technique. In the study, the elastic SH wave was dealt with, and the wave function expansion method was used in the calculation of the displacements. To show the essence of the methods without undue mathematical complexity, the diffraction of the SH wave by a cylindrical obstacles (valleys) are chosen as the illustrative example. Because the polarization of the SH waves is assumed to be parallel to the length of a endless cylindrical valleys, the scattered waves have the same polarization and wave velocity. As a result, only one type of wave, the SH wave, needs to be considered in the complete analysis. By emphasizing the basic equations of an elastic body motion, the analysis of the diffraction and scattering of the elastic waves is done. The assessments on the factors affecting reflection-scattering according to the dimensions of the valleys, their distances with each other, the material properties, and the changes of wave arrival angles was conducted.