Estimation of rocking and torsion associated with surface waves extracted from recorded motions

• Published in: Soil dynamics and earthquake engineering (1984) Vol. 80; pp. 225 - 240
• Main Authors: Meza-Fajardo, Kristel C., Papageorgiou, Apostolos S.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2016
• Subjects: Angular displacements; Cross-spectrum analysis; Displacement; Estimates; Ground motion variability; Harmonics; Horizontal; Love waves; Phase velocity; Phase velocity spectrum; Rocking; Surface waves; Time–frequency analysis; Torsion; Wave identification; PSE, New Zealand; ISEW, Taiwan; PSE, New Zealand, South I., Canterbury, Canterbury Basin; Rocking; Wave identification; torsion; Ground motion variability; Phase velocity spectrum; Time–frequency analysis; Cross-spectrum analysis; Angular displacements
• ISSN: 0267-7261; 1879-341X
• DOI: 10.1016/j.soildyn.2015.10.017

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. •We present a refined time–frequency technique to extract surface waves.•We present a method to estimate the angular displacements induced by surface waves.•We compute rocking from real seismograms recorded during an aftershock of the 1999 Chi-Chi earthquake in Taiwan from seismograms of an aftershock of the 1999 Chi-Chi earthquake.•We compute torsion from seismograms of the 2010 Darfield earthquake in New Zealand.