An Empirical Model for the Interfrequency Correlation of Epsilon for Fourier Amplitude Spectra

2019 ◽  
Vol 109 (3) ◽  
pp. 1058-1070 ◽  
Author(s):  
Jeff Bayless ◽  
Norman A. Abrahamson
Keyword(s):  
Empirical Model ◽  
Fourier Amplitude ◽  
Amplitude Spectra

scholarly journals Preliminary empirical model for scaling Fourier Amplitude Spectra of strong ground acceleration in terms of earthquake magnitude, source-to-station distance, and recording site conditions

1976 ◽  
Vol 66 (4) ◽  
pp. 1343-1373 ◽  
Author(s):  
M. D. Trifunac
Keyword(s):  
Empirical Model ◽  
Fourier Spectrum ◽  
Epicentral Distance ◽  
Site Conditions ◽  
Fourier Amplitude ◽  
Recording Site ◽  
Ground Acceleration ◽  
Amplitude Spectra ◽  
Order Of Magnitude ◽  
Strong Ground

abstract An empirical model for scaling Fourier Amplitude Spectra of strong earthquake ground acceleration in terms of magnitude, M, epicentral distance, R, and recording site conditions has been presented. The analysis based on this model implies that: It has been shown that the uncertainties which are associated with the forecasting of Fourier amplitude spectra in terms of magnitude, epicentral distance, site conditions, and component direction are considerable and lead to the range of spectral amplitudes which for an 80 per cent confidence interval exceed one order of magnitude. A model has been presented which empirically approximates the distribution of Fourier spectrum amplitudes and enables one to estimate the spectral shapes which are not exceeded by the presently available data more than 100 (1 - p) per cent of time where p represents the desired confidence level (0 < p <1).

A frequency-dependent ground-motion spatial correlation model of within-event residuals for Fourier amplitude spectra

2021 ◽  
pp. 875529302098199
Author(s):  
Nan Wang ◽  
Kim B Olsen ◽  
Steven M Day
Keyword(s):  
Time Series ◽  
Spatial Correlation ◽  
Ground Motion ◽  
Empirical Model ◽  
Correlation Model ◽  
Motion Generation ◽  
Fourier Amplitude ◽  
Frequency Dependent ◽  
Spatial Correlation Structure ◽  
Amplitude Spectra

Ground motion time series recorded at stations separated by up to about 50 km show a frequency-dependent spatial coherency structure, and the corresponding ground motion intensity measures are found to be correlated. As omitting this correlation can result in underestimation of seismic losses in risk analysis, it is critical to quantify the spatial correlation structure for ground motion Fourier spectra estimated at different sites during a single event within a region. Toward this goal, we have developed an empirical frequency-dependent spatial correlation model for the within-event residuals of effective Fourier amplitude spectra from the Pacific Earthquake Engineering Research Center (PEER) Next Generation Attenuation (NGA) West2 database. The correlation model shows slower decrease of the spatial correlation with distance at lower frequencies compared with higher frequencies, in agreement with the underlying ground motion data, and no significant dependence on the magnitude of the earthquakes is observed. We use this empirical model to incorporate frequency-dependent spatial correlation into a hybrid deterministic-stochastic broadband ground motion generation module, which successfully generates synthetic time series for seven western US earthquakes with frequency-dependent spatial correlation that closely mimics that of the empirical model. Furthermore, the method also significantly improves the correlation for spectral accelerations, cumulative absolute velocities, and Arias intensities, compared with that derived from the original broadband module.

Spectral characteristics of central Nevada microearthquakes

1970 ◽  
Vol 60 (5) ◽  
pp. 1547-1559 ◽  
Author(s):  
Bruce M. Douglas ◽  
Alan Ryall ◽  
Ray Williams
Keyword(s):  
Spectral Characteristics ◽  
Propagation Path ◽  
Seismic Signals ◽  
Fourier Amplitude ◽  
Recording Site ◽  
Focal Distance ◽  
Amplitude Spectra ◽  
Spectral Frequency ◽  
Group Characteristics ◽  
Event Magnitude

Abstract Fourier amplitude spectra were computed for 40 central Nevada microearthquakes, selected to consider, independently, effects of azimuth and distance from known sources. Spectra were averaged for groups of events to eliminate peculiarities of individual records and emphasize group characteristics. Spectral characteristics did not behave systematically as a function of azimuth from the recording site to the source, but peak spectral frequency was found to correlate strongly with event magnitude and to some degree also with focal distance. These preliminary results suggest that recordings of small earthquakes and microearthquakes can be used to provide detailed information on the character of seismic signals related to properties of the source and propagation path.

Approximate method to estimate the short-period strong motion spectra on bedrock

1981 ◽  
Vol 71 (2) ◽  
pp. 491-505
Author(s):  
Katsuhiko Ishida
Keyword(s):  
Earthquake Swarm ◽  
Strong Motion ◽  
Fourier Amplitude ◽  
Period Range ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Short Period ◽  
Amplitude Spectra ◽  
Low Pass ◽  
Parkfield Earthquake

abstract The methodology to estimate the strong motion Fourier amplitude spectra in a short-period range (T ≦ 1 to 2 sec) on a bedrock level is discussed in this paper. The basic idea is that the synthetic strong motion Fourier spectrum F˜A(ω) calculated from smoothed rupture velocity model (Savage, 1972) is approximately similar to that of low-pass-filtered strong earthquake ground motion at a site in a period range T ≧ 1 to 2 sec: F˜A(ω)=B˜(ω)·A(ω). B˜(ω) is an observed Fourier spectrum on a bedrock level and A(ω) is a low-pass filter. As a low-pass filter, the following relation, A ( T ) = · a · T n a T n + 1 , ( T = 2 π / ω ) , is assumed. In order to estimate the characteristic coefficients {n} and {a}, the Tokachi-Oki earthquake (1968), the Parkfield earthquake (1966), and the Matsushiro earthquake swarm (1966) were analyzed. The results obtained indicate that: (1) the coefficient {n} is nearly two for three earthquakes, and {a} is nearly one for the Tokachi-Oki earthquake, eight for the Parkfield earthquake, and four for the Matsushiro earthquake swarm, respectively; (2) the coefficient {a} is related with stress drop Δσ as (a = 0.07.Δσ). Using this relationship between {a} and Δσ, the coefficients {a} of past large earthquakes were estimated. The Fourier amplitude spectra on a bedrock level are also estimated using an inverse filtering method of A ( T ) = a T 2 a T 2 + 1 .

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