The ellipticity (H/V-ratio) of Rayleigh surface waves
It has long been observed that damage to human settlements during earthquakes depends greatly both on the local properties of the soil, and on other features such as irregular surface topography and underground morphology. One of the most efficient ways to define the soil properties is the H/V-method, which yields an estimation of the ratio between the Fourier amplitude spectra of the horizontal (H) to vertical (V) components of the ambient noise vibrations recorded at one single station. Considering that the most dominant contributions to ambient vibrations are known to come from surface waves, although the exact composition may change depending on the particular site, the aim of this thesis is to more deeply investigate the behavior of the H/V-ratio curve of Rayleigh waves, and thereby contribute to the further development of the established H/V-method. The method of the thesis is to study the H/V-ratio of Rayleigh waves, working from simple to complex models. The model complexity ranges from the easiest model, ``homogeneous half-space'', to the most general model: ``inhomogeneous layer over homogeneous half-space''. The thesis concentrates on the peaks and the troughs of H/V curves which play an important role in the H/V calculation, and how specific parameters affect them. I additionally study the motion of an individual particle. By studying the peaks and troughs, I construct maps showing their frequency relationships with parameters of the model and propose applications to the study of natural disasters. The thesis is also devoted to determining the H/V-ratio of a body incident wave which is generated from deep inside the substrate, for example by an earthquake. I show the similarity of the H/V-ratio in this scenario to the H/V-ratio of a surface wave with a turbulence noise. It turns out that these two H/V-ratios are identical if the phase velocity is that of a Rayleigh wave.