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Estimation of rocking and torsion associated with surface waves extracted from recorded motions
Institution:1. Department of Civil Engineering, Universidad Nacional Autónoma de Honduras, Tegucigalpa, Honduras;2. Department of Civil Engineering, University of Patras, GR-26500 Patras, Greece;1. Sinochem Petroleum Exploration & Production Co. Ltd, Beijing 100031, China;2. China University of Petroleum, Beijing, Beijing 102249, China;3. PetroChina Research Institute of Petroleum Exploration & Development, Beijing 100083, China;4. Research Institute of Exploration and Development, PetroChina Jilin Oilfield Company, Songyuan 138000, China;1. Department of Civil, Environmental and Architectural Engineering, University of Colorado, Boulder, USA;2. Iranian National Committee on Large Dams, Tehran, Iran;3. Department of Civil Engineering, Ryerson University, 350 Victoria St., Toronto, ON, Canada M5B 2K3;1. University of Mons – UMONS, Faculty of Engineering, Department of Theoretical Mechanics, Dynamics and Vibrations, Place du Parc 20, B-7000 Mons, Belgium;2. University of Mons – UMONS, Faculty of Engineering, Department of Civil Engineering, Place du Parc 20, B-7000 Mons, Belgium;1. Chair of Geomechanics and Geotechnics, Kiel University, Ludewig-Meyn-Strasse 10, 24118, Kiel, Germany;2. Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bontchev St., bl. 4, 1113, Sofia, Bulgaria
Abstract:By exploiting the capability of identifying and extracting surface waves existing in a seismic signal, we can proceed to estimate the angular displacement (rotation about the horizontal axis normal to the direction of propagation of the wave; rocking) associated with Rayleigh waves as well as the angular displacement (rotation about the vertical axis; torsion) associated with Love waves.For a harmonic Rayleigh (Love) wave, rocking (torsion) would be proportional to the harmonic vertical (transverse horizontal) velocity component and inversely proportional to the phase velocity corresponding to the particular frequency of the harmonic wave (a fact that was originally exploited by Newmark (1969) 15] to estimate torsional excitation). Evidently, a reliable estimate of the phase velocity (as a function of frequency) is necessary. As pointed out by Stockwell (2007) 17], because of its absolutely referenced phase information, the S-Transform can be employed in a cross-spectrum analysis in a local manner. Following this suggestion a very reliable estimate of the phase velocity may be obtained from the recordings at two nearby stations, after the dispersed waves have been identified and extracted. Synthesis of the abovementioned harmonic components can provide a reliable estimate of the rocking (torsional) motion induced by an (extracted) Rayleigh (Love) wave.We apply the proposed angular displacement estimation procedure for two well recorded data sets: (1) the strong motion data generated by an aftershock of the 1999 Chi-Chi, Taiwan earthquake and recorded over the Western Coastal Plain (WCP) of Taiwan, and (2) the strong motion data generated by the 2010 Darfield, New Zealand earthquake and recorded over the Canterbury basin. The former data set is dominated by basin-induced Rayleigh waves while the latter contains primarily Love waves.
Keywords:Ground motion variability  Wave identification  Time–frequency analysis  Angular displacements  Phase velocity spectrum  Cross-spectrum analysis  Rocking  torsion
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