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. 2021 May 10;21(9):3292.
doi: 10.3390/s21093292.

Horizontal-to-Vertical Spectral Ratio of Ambient Vibration Obtained with Hilbert-Huang Transform

Maik Neukirch  1 , Antonio García-Jerez  2 , Antonio Villaseñor  3 , Francisco Luzón  2 , Mario Ruiz  1 , Luis Molina  4
Affiliations

Horizontal-to-Vertical Spectral Ratio of Ambient Vibration Obtained with Hilbert-Huang Transform

Maik Neukirch et al. Sensors (Basel). .

Abstract

The Horizontal-to-Vertical Spectral Ratio (HVSR) of ambient vibration measurements is a common tool to explore near surface shear wave velocity (Vs) structure. HVSR is often applied for earthquake risk assessments and civil engineering projects. Ambient vibration signal originates from the combination of a multitude of natural and man-made sources. Ambient vibration sources can be any ground motion inducing phenomena, e.g., ocean waves, wind, industrial activity or road traffic, where each source does not need to be strictly stationary even during short times. Typically, the Fast Fourier Transform (FFT) is applied to obtain spectral information from the measured time series in order to estimate the HVSR, even though possible non-stationarity may bias the spectra and HVSR estimates. This problem can be alleviated by employing the Hilbert-Huang Transform (HHT) instead of FFT. Comparing 1D inversion results for FFT and HHT-based HVSR estimates from data measured at a well studied, urban, permanent station, we find that HHT-based inversion models may yield a lower data misfit χ2 by up to a factor of 25, a more appropriate Vs model according to available well-log lithology, and higher confidence in the achieved model.

Keywords: HVSR; data processing; non-stationary.

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Conflict of interest statement

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

Figures

Figure 1
Figure 1
Basic Empirical Mode Decomposition. Note that the sifting stop criteria (point 5) above is given in its original form and various alternatives have been discussed in the literature [27]. However, the exact formulation of the stopping criteria for the sifting process (points 3 to 5) is not central to our work as the EMD algorithm performs with any chosen criteria.
Figure 2
Figure 2
ICJA results for FFT- and MEMD-based processing.
Figure 3
Figure 3
Weighted distribution of tested ICJA inversion models’ χ2 for FFT and MEMD curves.
Figure 4
Figure 4
Well-log, models and data for ICJA station obtained with FFT. Well-log column taken from [35].
Figure 5
Figure 5
Well-log, models and data for ICJA station obtained with MEMD. Well-log column taken from [35].
Figure 6
Figure 6
EJDN results for FFT- and MEMD-based processing.
Figure 7
Figure 7
Weighted distribution of tested EJDN inversion models’ χ2 for FFT and MEMD curves.
Figure 8
Figure 8
Model results and data fit for the inversion of EJDN data processed by MEMD and FFT.
See this image and copyright information in PMC

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