Site response analysis of liquefiable soil employing continuous wavelet transform

Propagation of the earthquake motion towards the ground surface alters both the acceleration and frequency content of the motion. Acceleration time record and Fourier amplitude spectrum of the motion reveal changes in the acceleration and frequency content. However, Fourier amplitude spectrum fails to give frequency-time variation. Wavelet transform overcomes this difficulty. In the present study, site response analysis of a liquefiable soil domain has been investigated employing wavelet transform. Three earthquake motions with distinct predominant frequencies are considered. It is revealed that the moment soil undergoes initial liquefaction, it causes a spike in the acceleration time history. Frequency of the spikes is found to be greater than the predominant frequency of the acceleration-time history recorded at the ground surface from the analysis. Interestingly, the spikes belong to the sharp tips of the shear stress-shear strain curve. Immediately after the spike, acceleration deamplification is observed. Post-liquefaction deamplification (filtering) of the frequency components is also observed.

A Frequency-Dependent Model for the Shape of the Fourier Amplitude Spectrum of Acceleration at High Frequencies

ABSTRACT The high-frequency decay term of the acceleration spectrum κ is a commonly used parameter in engineering seismology. In recent years, the assumption of a linearly decaying spectrum in log–linear space has been recognized to not always be valid as the value of κ depends on the analyzed frequency band. We present an alternative model for the spectral falloff in which the frequency dependence is explicitly taken into account. This is motivated by observations that the quality factor Q has a power-law dependence on frequency at high frequencies. The new model describes the spectral decay with the help of two variables, opposite to the single parameter κ. The approach is applied to borehole data of the EUROSEISTEST site in Greece. The misfit between modeled and observed spectra is reduced with the new approach compared with the classical kappa model. The new estimates compare well with κ estimates if the same frequency interval is considered but additionally allows for the capture of the frequency dependence of the spectral shape.

A statistical approach to account for azimuthal variability in single-station HVSR measurements

SUMMARY The horizontal-to-vertical spectral ratio (HVSR) of ambient noise is commonly used to infer a site's resonance frequency (${f_{0,site}}$). HVSR calculations are performed most commonly using the Fourier amplitude spectrum obtained from a single merged horizontal component (e.g. the geometric mean component) from a three-component sensor. However, the use of a single merged horizontal component implicitly relies on the assumptions of azimuthally isotropic seismic noise and 1-D surface and subsurface conditions. These assumptions may not be justified at many sites, leading to azimuthal variability in HVSR measurements that cannot be accounted for using a single merged component. This paper proposes a new statistical method to account for azimuthal variability in the peak frequency of HVSR curves (${f_{0,HVSR}}$). The method uses rotated horizontal components at evenly distributed azimuthal intervals to investigate and quantify azimuthal variability. To ensure unbiased statistics for ${f_{0,HVSR}}$ are obtained, a frequency-domain window-rejection algorithm is applied at each azimuth to automatically remove contaminated time windows in which the ${f_{0,HVSR}}$ values are statistical outliers relative to those obtained from the majority of windows at that azimuth. Then, a weighting scheme is used to account for different numbers of accepted time windows at each azimuth. The new method is applied to a data set of 114 HVSR measurements with significant azimuthal variability in ${f_{0,HVSR}}$, and is shown to reliably account for this variability. The methodology is also extended to the estimation of a complete lognormal-median HVSR curve that accounts for azimuthal variability. To encourage the adoption of this statistical approach to accounting for azimuthal variability in single-station HVSR measurements, the methods presented in this paper have been incorporated into hvsrpy, an open-source Python package for HVSR processing.

The Influence of Typography on Algorithms that Predict the Speed and Comfort of Reading

1. The speed with which text can be read is determined in part by the spatial regularity and similarity of vertical letter strokes as assessed by the height of the first peak in the horizontal autocorrelation of the text. The height of this peak was determined for two passages in 20 fonts. The peak was unaffected by the size of the text or its content but was influenced by the font design. Sans serif fonts usually had a lower peak than serif fonts because the presence of serifs usually (but not invariably) resulted in a more even spacing of letter strokes. There were small effects of justification and font-dependent effects of font expansion and compression. 2. The visual comfort of images can be estimated from the extent to which the Fourier amplitude spectrum conforms to 1/f. Students were asked to adjust iBooks to obtain their preferred settings of font and layout. The preference was predicted by the extent to which the Fourier amplitude spectrum approximated 1/f, which in turn was jointly affected by the design of the font, its weight and the ratio of x-height to line separation. Two algorithms based on the autocorrelation and Fourier transformation of text can be usefully applied to any orthography to estimate likely speed and comfort of reading.

Detecting Site Resonant Frequency Using HVSR: Fourier versus Response Spectrum and the First versus the Highest Peak Frequency

ABSTRACT In this investigation, we examine the uncertainties using the horizontal-to-vertical spectral ratio (HVSR) technique on earthquake recordings to detect site resonant frequencies at 207 KiK-net sites. Our results show that the scenario dependence of response (pseudospectral acceleration) spectral ratio could bias the estimates of resonant frequencies for sites having multiple significant peaks with comparable amplitudes. Thus, the Fourier amplitude spectrum (FAS) should be preferred in computing HVSR. For more than 80% of the investigated sites, the first peak (in the frequency domain) on the average HVSR curve over multiple sites coincides with the highest peak. However, for sites with multiple peaks, the highest peak frequency (fp) is less susceptible to the selection criteria of significant peaks and the extent of smoothing to spectrum than the first peak frequency (f0). Meanwhile, in comparison to the surface-to-borehole spectral ratio, f0 tends to underestimate the predominant frequency (at which the largest amplification occurs) more than fp. In addition, in terms of characterizing linear site response, fp shows a better overall performance than f0. Based on these findings, we thus recommend that seismic network operators provide fp on the average HVSRFAS curve as a priority, ideally together with the average HVSRFAS curve in site characterization.

The Influence of Typography on Algorithms That Predict the Speed and Comfort of Reading

The speed with which text can be read is determined in part by the spatial regularity and similarity of vertical letter strokes as assessed by the height of the first peak in the horizontal autocorrelation of the text. The height of this peak was determined for two passages in 20 fonts. The peak was unaffected by the size of the text or its content but was influenced by the font design. Sans serif fonts usually had a lower peak than serif fonts because the presence of serifs resulted in a more even spacing of letter strokes. There were small effects of justification and font- dependent effects of font expansion and compression. The visual comfort of images can be estimated from the extent to which the Fourier amplitude spectrum conforms to 1/f. Students were asked to adjust iBooks to obtain their preferred settings of font and layout. The preference was predicted by the extent to which the Fourier amplitude spectrum approximated 1/f, which in turn was jointly affected by the design of the font, its weight and the ratio of x-height to line separation. The above algorithms can be usefully applied to any orthography to estimate likely speed and comfort of reading.

Feature Extraction Method for Hydraulic Pump Fault Signal Based on Improved Empirical Wavelet Transform

There are many interference components in Fourier amplitude spectrum of a contaminated fault signal, and thus the segment obtained based on the spectrum can lead to serious over-decomposition of empirical wavelet transform (EWT). Aiming to resolve the above problems, a novel method named improved empirical wavelet transform (IEWT) is proposed. Because the power spectrum is less sensitive to the contaminated interference and manifests the presence of fault feature information, IEWT replaces the Fourier amplitude spectrum of EWT with power spectrum in segment acquirement, and threshold processing is also introduced to eliminate the bad influence on the acquirement, and thus the best decomposition result of IEWT can be obtained based on feature energy ratio (FER). The loose slipper fault signal of hydraulic pump is tested and verified. The result demonstrates that the proposed method is superior and can extract the fault feature information accurately.

NGA-West2 Empirical Fourier and Duration Models to Generate Adjustable Response Spectra

Adjustment of median ground motion prediction equations (GMPEs) from one region to another region is one of the major challenges within the current practice of seismic hazard analysis. In our approach of generating response spectra, we derive two separate empirical models for a) Fourier amplitude spectrum (FAS) and b) duration of ground motion. To calculate response spectra, the two models are combined within the random vibration theory (RVT) framework. The models are calibrated on recordings obtained from shallow crustal earthquakes in active tectonic regions. We use a subset of NGA-West2 database with M3.2–7.9 earthquakes at distances 0–300 km. The NGA-West2 database expanded over a wide magnitude and distance range facilitates a better constraint over derived models. A frequency-dependent duration model is derived to obtain adjustable response spectral ordinates. Excellent comparison of our approach with other NGA-West2 models implies that it can also be used as a stand-alone model.

Seismic Response of Anchor + Hinged Block Ecological Slope by Shaking Table Tests

Landslides caused by earthquakes and other natural disasters may cause serious economic and personal losses. Slope protections are usually applied in engineering practice to prevent significant slope slides and damages. Based on the mechanical and ecological requirements on slope protections, this paper put forward a new type of anchor + hinged block ecological slope and carried out shaking table tests on it and other three traditional slope protections for comparing. By shaking table tests, the acceleration amplification factors and Fourier amplitude spectrums of four different slope types are analyzed and compared to verify the suitability of this new slope protection under earthquakes. The results indicated that the natural frequency and the acceleration Fourier amplitude spectrum of the four tested slope protections change according to internal materials. The anchor + hinged block ecological slope has higher natural frequency comparing to traditional slopes, so the resonance cycle from earthquake excitation can effectively be avoided and as a result the anchor + hinged block ecological slope can achieve better seismic performance.