@article{TranThanhTuanScherbaumMalischewsky2011,
  author    = {Tran Thanh Tuan, and Scherbaum, Frank and Malischewsky, Peter G.},
  title     = {On the relationship of peaks and troughs of the ellipticity (H/V) of Rayleigh waves and the transmission response of single layer over half-space models},
  series = {Geophysical journal international},
  volume    = {184},
  journal   = {Geophysical journal international},
  number    = {2},
  publisher = {Wiley-Blackwell},
  address   = {Malden},
  issn      = {0956-540X},
  doi       = {10.1111/j.1365-246X.2010.04863.x},
  pages     = {793 -- 800},
  year      = {2011},
  abstract  = {One of the key challenges in the context of local site effect studies is the determination of frequencies where the shakeability of the ground is enhanced. In this context, the H/V technique has become increasingly popular and peak frequencies of H/V spectral ratio are sometimes interpreted as resonance frequencies of the transmission response. In the present study, assuming that Rayleigh surface wave is dominant in H/V spectral ratio, we analyse theoretically under which conditions this may be justified and when not. We focus on 'layer over half-space' models which, although seemingly simple, capture many aspects of local site effects in real sedimentary structures. Our starting point is the ellipticity of Rayleigh waves. We use the exact formula of the H/V-ratio presented by Malischewsky \& Scherbaum (2004) to investigate the main characteristics of peak and trough frequencies. We present a simple formula illustrating if and where H/V-ratio curves have sharp peaks in dependence of model parameters. In addition, we have constructed a map, which demonstrates the relation between the H/V-peak frequency and the peak frequency of the transmission response in the domain of the layer's Poisson ratio and the impedance contrast. Finally, we have derived maps showing the relationship between the H/V-peak and trough frequency and key parameters of the model such as impedance contrast. These maps are seen as diagnostic tools, which can help to guide the interpretation of H/V spectral ratio diagrams in the context of site effect studies.},
  language  = {en}
}
@article{TranThanhTuanPhamChiVinhOhrnbergeretal.2016,
  author    = {Tran Thanh Tuan, and Pham Chi Vinh, and Ohrnberger, Matthias and Malischewsky, Peter and Aoudia, Abdelkrim},
  title     = {An Improved Formula of Fundamental Resonance Frequency of a Layered Half-Space Model Used in H/V Ratio Technique},
  series = {Pure and applied geophysics},
  volume    = {173},
  journal   = {Pure and applied geophysics},
  publisher = {Springer},
  address   = {Basel},
  issn      = {0033-4553},
  doi       = {10.1007/s00024-016-1313-0},
  pages     = {2803 -- 2812},
  year      = {2016},
  abstract  = {The resonance frequency of the transmission response in layered half-space model is important in the study of site effect because it is the frequency where the shake-ability of the ground is enhanced significantly. In practice, it is often determined by the H/V ratio technique in which the peak frequency of recorded H/V spectral ratio is interpreted as the resonance frequency. Despite of its importance, there has not been any formula of the resonance frequency of the layered half-space structure. In this paper, a simple approximate formula of the fundamental resonance frequency is presented after an exact formula in explicit form of the response function of vertically SH incident wave is obtained. The formula is in similar form with the one used in H/V ratio technique but it reflects several major effects of the model to the resonance frequency such as the arrangement of layers, the impedance contrast between layers and the half-space. Therefore, it could be considered as an improved formula used in H/V ratio technique. The formula also reflects the consistency between two approaches of the H/V ratio technique based on SH body waves or Rayleigh surface waves on the peak frequency under high impedance contrast condition. This formula is in explicit form and, therefore, may be used in the direct and inverse problem efficiently. A numerical illustration of the improved formula for an actual layered half-space model already investigated by H/V ratio technique is presented to demonstrate its new features and its improvement to the currently used formula.},
  language  = {en}
}