Identification and Extraction of Surface Waves from Three‐Component Seismograms Based on the Normalized Inner Product

Abstract

Identification of different wave types in a seismogram is an important step for the understanding of wave propagation phenomena. Because in most seismograms, different types of waves with different frequencies may appear simultaneously, separation of waves is more effectively achieved when a time-frequency analysis is performed. In this work, we propose a new time-frequency analysis procedure to identify and extract Rayleigh and Love waves from three-component seismograms. Exploiting the advantage of the absolute phase preservation by the Stockwell transform, we construct time-frequency filters to extract waves based on the normalized inner product (NIP). Because the NIP is the time-frequency counterpart of the correlation, Rayleigh and Love waves can be identified depending on the NIP between the Stockwell transforms of the horizontal and vertical displacement components. The novelty and advantage of the proposed procedure is that it does not require specifying a priori the direction of propagation of the surface waves, but instead such direction is determined. Furthermore, it is shown that the NIP is a more stable parameter in the time-frequency domain when compared to the instantaneous reciprocal ellipticity, and thus it avoids smoothing (and with it, altering) the data. The procedure has been successfully tested with real signals, specifically to extract Rayleigh and Love waves from seismograms of one aftershock of the 1999 Chi-Chi earthquake. With the proposed procedure, we found different directions of propagation for retrograde and prograde Rayleigh waves, which might suggest that they are generated by different mechanisms.

Response of tall buildings to base rocking induced by Rayleigh waves

“…An effective method to identify and extract surface waves from a recorded 3‐component time history of particle motion has been proposed by Meza‐Fajardo et al The basic idea of the method is to separate the waves by using as criterion the representation of their polarization characteristics in a time‐frequency correlation. The seismogram is first resolved in the time‐frequency domain by using the Stockwell Transform .…”

“…The NIP criterion allows one to identify the direction of propagation of Rayleigh waves that are present in the signal, as the direction corresponding to a minimum correlation between 2 orthogonal horizontal components. Because the NIP is also direct measure of the phase shift between 2 components of a signal, it can also differentiate between prograde and retrograde Rayleigh waves (see details in Meza‐Fajardo and Papageorgiou).…”

“…As explained above, to estimate rocking, we scale the vertical component of the velocity history by the horizontal phase velocity, also called the “apparent” velocity c app . Figure shows intermediate and final results of the estimation of rocking for 3 of the stations considered (detailed step‐by‐step explanations of the process can be found in Meza‐Fajardo and Papageorgiou). The first column contains the recorded displacement histories, which were obtained from time integration of accelerograms.…”

“…To reduce errors in the numerical integration, the acceleration histories were first band‐pass filtered between 0.05 and 20 Hz. Applying the time‐frequency polarization analysis (the NIP) of Meza‐Fajardo et al to the displacement histories, we determine the direction of propagation of the Rayleigh waves, which we call here the “radial” direction. Because of its dispersive characteristics, Rayleigh waves travel in “wave trains”; thus, the direction provided is an “average” direction of the wave train.…”

“…On the other hand, Meza‐Fajardo and Papageorgiou propose a procedure to compute the “apparent” phase velocity of Love and Rayleigh waves, which, for surface waves, is known to be frequency‐dependent. A necessary preliminary step is the separation of the surface waves from the body waves, something that now can be effectively achieved for a single station with the time‐frequency filtering procedure proposed by Meza‐Fajardo et al Recognizing that the phase velocity of Rayleigh waves is lower than that of body waves, rocking associated with Rayleigh waves is expected to be significant and the structural response is expected to be larger when the excitation contains Rayleigh waves.…”