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On planar seismic wavefront modeling for estimating rotational ground motions: Case of 2-D SH line-source
Institution:1. Department of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India;1. College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang 330063, PR China;2. School of Science, Beijing University of Chemical Technology, Beijing 100029, PR China;3. CEMA, Central University of Finance and Economics, Beijing 100081, PR China;1. United Technologies Research Center Inc., 2855 Telegraph Avenue Suite 410, Berkeley, CA 94705, USA;2. University of Illinois Urbana–Champaign, USA;1. Department of Structural and Geotechnical Engineering, Sapienza University of Rome (formerly Technical University of Bari), via Eudossiana 18, 00184 Rome, Italy;2. Department of Civil, Chemical, Environmental and Materials Engineering, University of Bologna, via Terracini 28, 40131 Bologna, Italy;3. Department of Civil, Environmental, Building Engineering and Chemistry, Technical University of Bari, via Orabona 4, 70125 Bari, Italy;1. University of Göttingen, Institute for Mathematical Stochastics, Goldschmidtstraße 7, 37077 Göttingen, Germany;2. Saarland University, Department of Mathematics, Postfach 151150, 66041 Saarbrücken, Germany
Abstract:At large hypocentral distances, it is convenient to approximate the curved transient seismic wavefronts as planar to estimate rotational ground motions from the single-station recordings of translational ground motions. In this paper, we investigate whether and when this approximation, referred to as the ‘plane-wave’ approximation, can be considered adequate close to the source. For this, we consider a simplistic source model comprising a two-dimensional, kinematic shear dislocation SH line-source buried in a homogenous, elastic half-space and assume this to be an equivalent representation of a finite-sized fault. The ‘plane-wave’ rotational motion is then synthesized from the exact translational motion solution to the assumed model and compared with the exact rotational motion solution for this model. The comparison between the two sets of rotational amplitudes in frequency domain suggests that the plane-wave approximation may be adequate, when the wavelengths of the seismic waves are much smaller than the source depth. When this is not true, the plane-wave approximation is seen to underestimate the Fourier amplitudes close to the source by several orders, particularly when the fault planes are vertically oriented. A similar comparison in the time domain indicates that a severe underestimation may also occur when the source rise time is longer than the shear-wave arrival time at the epicenter. Significant discrepancies are also observed between the waveforms of the exact and plane-wave rotational motions.
Keywords:Rotational ground motion  Plane-wave approximation  Two-dimensional SH line-source  Dislocation theory
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