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Fourier amplitude spectra

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Journal Article

Offshore Nonergodic Ground‐Motion Model of Fourier Amplitude Spectra for Subduction Earthquakes in the Japan Trench Area

Lei Hu, Yingmin Li, Hongwu Yang, Weihao Pan, Shuyan Ji
Published: 24 December 2024
Seismological Research Letters (2024)
DOI: https://doi.org/10.1785/0220240200
...Lei Hu; Yingmin Li; Hongwu Yang; Weihao Pan; Shuyan Ji Abstract Fourier amplitude spectra (FAS) offer a more direct representation of ground motion compared to acceleration response spectra, leading to significant attention on modeling of FAS in engineering seismology. Advances in ground‐motion...
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View PDF for article title, Offshore Nonergodic Ground‐Motion Model of <span class="search-highlight">Fourier</span> <span class="search-highlight">Amplitude</span> <span class="search-highlight">Spectra</span> for Subduction Earthquakes in the Japan Trench Area
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Early Publication
Includes: Supplemental Content
Journal Article

Investigation of Site Response in Xinjiang, Northwestern China, from S – Lg Fourier Amplitude Spectra

Zhen Guo, Lei Li
Published: 02 January 2024
Bulletin of the Seismological Society of America (2024) 114 (3): 1680–1694.
DOI: https://doi.org/10.1785/0120230141
... and site response in Xinjiang using broadband recordings at 44 stations from 118 earthquakes with magnitudes of 4.4–7.0 occurring in Xinjiang and adjacent areas between January 2009 and February 2022. We used linear regression analysis of the Fourier acceleration amplitude spectra in 18 frequency bands...
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View PDF for article title, Investigation of Site Response in Xinjiang, Northwestern China, from S – Lg <span class="search-highlight">Fourier</span> <span class="search-highlight">Amplitude</span> <span class="search-highlight">Spectra</span>
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Journal Article

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

Nan Wang, M.EERI, Kim B Olsen, Steven M Day
Published: 01 August 2021
Earthquake Spectra (2021) 37 (3): 2041–2065.
DOI: https://doi.org/10.1177/8755293020981995
... 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...
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View PDF for article title, A frequency-dependent ground-motion spatial correlation model of within-event residuals for <span class="search-highlight">Fourier</span> <span class="search-highlight">amplitude</span> <span class="search-highlight">spectra</span>
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Journal Article

Summary of the BA18 Ground‐Motion Model for Fourier Amplitude Spectra for Crustal Earthquakes in California

Jeff Bayless, Norman A. Abrahamson
Published: 10 September 2019
Bulletin of the Seismological Society of America (2019) 109 (5): 2088–2105.
DOI: https://doi.org/10.1785/0120190077
... of the two horizontal components leads to an amplitude spectrum that is compatible with the use of RVT to convert Fourier spectra to response spectra. The EAS is smoothed using the log 10 ‐scale Konno and Ohmachi (1998) smoothing window, which has weights and window parameter defined as follows...
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View PDF for article title, Summary of the BA18 Ground‐Motion Model for <span class="search-highlight">Fourier</span> <span class="search-highlight">Amplitude</span> <span class="search-highlight">Spectra</span> for Crustal Earthquakes in California
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Add to Citation Manager for Summary of the BA18 Ground‐Motion Model for <span class="search-highlight">Fourier</span> <span class="search-highlight">Amplitude</span> <span class="search-highlight">Spectra</span> for Crustal Earthquakes in California
Includes: Supplemental Content
Journal Article

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

Jeff Bayless, Norman A. Abrahamson
Published: 07 May 2019
Bulletin of the Seismological Society of America (2019) 109 (3): 1058–1070.
DOI: https://doi.org/10.1785/0120180238
...Jeff Bayless; Norman A. Abrahamson Abstract An empirical ground‐motion model (GMM) is presented for the interfrequency correlation of normalized residuals, epsilon ( ε ), for smoothed Fourier amplitude spectra (FAS). The interfrequency correlation of ε ( ρ ε ) model is developed for the smoothed...
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View PDF for article title, An Empirical Model for the Interfrequency Correlation of Epsilon for <span class="search-highlight">Fourier</span> <span class="search-highlight">Amplitude</span> <span class="search-highlight">Spectra</span>
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Includes: Supplemental Content
Journal Article

On the Correlation of Seismic Intensity with Fourier Amplitude Spectra

V. Yu Sokolov, Yu K. Chernov
Published: 01 November 1998
Earthquake Spectra (1998) 14 (4): 679–694.
DOI: https://doi.org/10.1193/1.1586022
...V. Yu Sokolov; Yu K. Chernov This paper presents a method for estimating the seismic intensity (MMI or MSK scale) using Fourier amplitude spectra of ground acceleration. The method implies that the severity of earthquake ground motion is determined by spectral amplitudes in a relatively narrow...
View PDF for article title, On the Correlation of Seismic Intensity with <span class="search-highlight">Fourier</span> <span class="search-highlight">Amplitude</span> <span class="search-highlight">Spectra</span>
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Journal Article

Empirical models for estimating Fourier-amplitude spectra of ground acceleration in the northern Caucasus (Racha seismogenic zone)

Vladimir Yu Sokolov
Published: 01 December 1997
Bulletin of the Seismological Society of America (1997) 87 (6): 1401–1412.
DOI: https://doi.org/10.1785/BSSA0870061401
... Society of America, Vol. 87, No. 6, pp. 1401-1412, December 1997 Empirical Models for Estimating Fourier-Amplitude Spectra of Ground Acceleration in the Northern Caucasus (Racha Seismogenic Zone) by Vladimir Yu Sokolov Abstract A collection of ground-motion recordings of small to moderate (Ms <= 6.2...
View PDF for article title, Empirical models for estimating <span class="search-highlight">Fourier</span>-<span class="search-highlight">amplitude</span> <span class="search-highlight">spectra</span> of ground acceleration in the northern Caucasus (Racha seismogenic zone)
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Add to Citation Manager for Empirical models for estimating <span class="search-highlight">Fourier</span>-<span class="search-highlight">amplitude</span> <span class="search-highlight">spectra</span> of ground acceleration in the northern Caucasus (Racha seismogenic zone)
Journal Article

The Mexico Earthquake of September 19, 1985—An Empirical Model to Predict Fourier Amplitude Spectra of Horizontal Ground Motion

R. Castro, S. K. Singh, E. Mena
Published: 01 November 1988
Earthquake Spectra (1988) 4 (4): 675–685.
DOI: https://doi.org/10.1193/1.1585497
...R. Castro; S. K. Singh; E. Mena We analyze Fourier acceleration amplitude spectra of 14 coastal earthquakes (5.6 ≤ Ms ≤ 8.1) recorded at a hill zone site in Ciudad Universitaria (CU), Mexico City (282 ≤ R ≤ 466 km, R= closest distance from CU to the rupture area). The observed smoothed spectra...
View PDF for article title, The Mexico Earthquake of September 19, 1985—An Empirical Model to Predict <span class="search-highlight">Fourier</span> <span class="search-highlight">Amplitude</span> <span class="search-highlight">Spectra</span> of Horizontal Ground Motion
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Journal Article

A simple model for estimating fourier amplitude spectra of horizontal ground acceleration

Robin K. McGuire
Published: 01 June 1978
Bulletin of the Seismological Society of America (1978) 68 (3): 803–822.
DOI: https://doi.org/10.1785/BSSA0680030803
...Robin K. McGuire abstract A simple model for estimating Fourier amplitude spectra ( FS ) is calibrated using the horizontal components of 70 strong-motion records from California, chosen so that the results are not biased by the effects of one earthquake nor by the effects of a single site...
View PDF for article title, A simple model for estimating <span class="search-highlight">fourier</span> <span class="search-highlight">amplitude</span> <span class="search-highlight">spectra</span> of horizontal ground acceleration
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Journal Article

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

M. D. Trifunac
Published: 01 August 1976
Bulletin of the Seismological Society of America (1976) 66 (4): 1343–1373.
DOI: https://doi.org/10.1785/BSSA0660041343
...M. D. Trifunac 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: the Fourier amplitude...
View PDF for article title, Preliminary empirical model for scaling <span class="search-highlight">Fourier</span> <span class="search-highlight">Amplitude</span> <span class="search-highlight">Spectra</span> of strong ground acceleration in terms of earthquake magnitude, source-to-station distance, and recording site conditions
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Add to Citation Manager for Preliminary empirical model for scaling <span class="search-highlight">Fourier</span> <span class="search-highlight">Amplitude</span> <span class="search-highlight">Spectra</span> of strong ground acceleration in terms of earthquake magnitude, source-to-station distance, and recording site conditions
Journal Article

Uniformly Processed Fourier Spectra Amplitude Database for Recently Compiled New Zealand Strong Ground Motions

Elena F. Manea, Sanjay S. Bora, Jesse A. Hutchinson, Anna E. Kaiser
Published: 19 December 2023
Seismological Research Letters (2024) 95 (1): 239–252.
DOI: https://doi.org/10.1785/0220230228
... intensity measures (i.e., smoothed and down‐sampled Fourier spectral amplitudes, Arias intensity, cumulative absolute velocity, and duration measures) of the processed ground motions are presented in the database. Finally, the database includes station site parameters sourced directly from the 2022 NSHM...
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View PDF for article title, Uniformly Processed <span class="search-highlight">Fourier</span> <span class="search-highlight">Spectra</span> <span class="search-highlight">Amplitude</span> Database for Recently Compiled New Zealand Strong Ground Motions
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Journal Article

Impact of Geometric Spreading in the Fourier Domain on Source Spectra: Observations of Steep Amplitude Decay and Frequency Dependence from the 2019 Ridgecrest, California, Earthquake, Sequence

Gail M. Atkinson
Published: 26 July 2024
Bulletin of the Seismological Society of America (2024)
DOI: https://doi.org/10.1785/0120240005
...Gail M. Atkinson ABSTRACT This study characterizes the impact of attenuation on source spectra for events of the 2019 Ridgecrest, California, sequence, for M ∼4–7 at distances from ∼5 to 400 km. Fourier amplitudes display a steep rate of apparent geometric spreading: R − 1.6 within 60 km. Over...
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View PDF for article title, Impact of Geometric Spreading in the <span class="search-highlight">Fourier</span> Domain on Source <span class="search-highlight">Spectra</span>: Observations of Steep <span class="search-highlight">Amplitude</span> Decay and Frequency Dependence from the 2019 Ridgecrest, California, Earthquake, Sequence
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Add to Citation Manager for Impact of Geometric Spreading in the <span class="search-highlight">Fourier</span> Domain on Source <span class="search-highlight">Spectra</span>: Observations of Steep <span class="search-highlight">Amplitude</span> Decay and Frequency Dependence from the 2019 Ridgecrest, California, Earthquake, Sequence
Early Publication
Journal Article

Estimating Various Response Spectra from a Fourier Amplitude Spectrum

Rui Zhang, Haizhong Zhang, Yan‐Gang Zhao
Published: 21 April 2025
Bulletin of the Seismological Society of America (2025)
DOI: https://doi.org/10.1785/0120240242
... for estimating different response spectra from the Fourier amplitude spectrum (FAS). Our proposed approach for calculating spectral velocity (SV) and spectral acceleration (SA) has high accuracy. Our new method can be used in seismic hazard studies, especially in region with limited earthquake data...
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View PDF for article title, Estimating Various Response <span class="search-highlight">Spectra</span> from a <span class="search-highlight">Fourier</span> <span class="search-highlight">Amplitude</span> Spectrum
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Early Publication
Image
Fourier amplitude spectra of synthetic velocities at stations along profile A–A′. The numbers in the legend show how far stations are off the fault to the NW in the unit of kilometers. (a) Fourier amplitude spectra of the fault‐parallel component averaged over H11, H21, H31, and H41. (b) Fourier amplitude spectra of the fault‐normal component averaged over H11, H21, H31, and H41. (c) Fourier amplitude spectra of the fault‐parallel component averaged over R1 and R2. (d) Fourier amplitude spectra of the fault‐normal component averaged over R1 and R2.

Fourier amplitude spectra of synthetic velocities at stations along profile...

Published: 05 June 2018
Figure 10. Fourier amplitude spectra of synthetic velocities at stations along profile A–A′. The numbers in the legend show how far stations are off the fault to the NW in the unit of kilometers. (a) Fourier amplitude spectra of the fault‐parallel component averaged over H11, H21, H31, and H41
Image
Smoothed Fourier amplitude spectra and response spectra of the raw accelerogram and the processed accelerograms using the two methods and the PEER database (MYG013 record). (a) Smoothed Fourier amplitude spectra. The spectra were computed from accelerograms after tapering, with taper length setting as 2% of the total length. The smoothing of the spectrum was achieved using the Konno–Ohmachi smoothing algorithm (Konno and Ohmachi, 1998). The sampling interval is 0.0031 Hz. (b) Response spectra. The color version of this figure is available only in the electronic edition.

Smoothed Fourier amplitude spectra and response spectra of the raw accelero...

Published: 13 September 2024
Figure 7. Smoothed Fourier amplitude spectra and response spectra of the raw accelerogram and the processed accelerograms using the two methods and the PEER database (MYG013 record). (a) Smoothed Fourier amplitude spectra. The spectra were computed from accelerograms after tapering, with taper
Image
Smoothed Fourier amplitude spectra and response spectra of the raw accelerogram and the processed accelerograms using the two methods and the PEER database (El centro record). (a) Smoothed Fourier amplitude spectra. The spectra were computed from accelerograms after tapering, with taper length setting as 2% of the total length. The smoothing of the spectrum was achieved using the Konno–Ohmachi smoothing algorithm (Konno and Ohmachi, 1998). The sampling interval is 0.0062 Hz. The color version of this figure is available only in the electronic edition.

Smoothed Fourier amplitude spectra and response spectra of the raw accelero...

Published: 13 September 2024
Figure 11. Smoothed Fourier amplitude spectra and response spectra of the raw accelerogram and the processed accelerograms using the two methods and the PEER database (El centro record). (a) Smoothed Fourier amplitude spectra. The spectra were computed from accelerograms after tapering
Image
In the panels, the dotted line shows the Fourier amplitude spectra of the original seismic data and the solid line displays the Fourier amplitude spectra of the Q-compensated seismograms produced by the proposed method. (a) For data at the well position. (b) For data near the well position. (c and d) The normalized Fourier amplitude spectra of those shown in (a and b), respectively.

In the panels, the dotted line shows the Fourier amplitude spectra of the o...

Published: 28 September 2018
Figure 10. In the panels, the dotted line shows the Fourier amplitude spectra of the original seismic data and the solid line displays the Fourier amplitude spectra of the Q -compensated seismograms produced by the proposed method. (a) For data at the well position. (b) For data near
Image
The estimated Fourier amplitude spectra at SGR for the 2009 Suruga Bay earthquake. The horizontal component (gray trace) is the composition of two components. These spectra were computed by multiplying the Fourier amplitude spectra at MKN (Fig. 10) with the average spectral ratios (Fig. 9).

The estimated Fourier amplitude spectra at SGR for the 2009 Suruga Bay eart...

Published: 01 April 2011
Figure 11. The estimated Fourier amplitude spectra at SGR for the 2009 Suruga Bay earthquake. The horizontal component (gray trace) is the composition of two components. These spectra were computed by multiplying the Fourier amplitude spectra at MKN (Fig.  10 ) with the average spectral ratios
Image
Relative amplitude of Fourier amplitude spectra at 4.0 Hz as a function of distance from the source computed for the two cross sections. The S-wave window was Fourier transformed, smoothed by an octave band filter, and the values at 0.5 Hz were normalized by their amplitude at a 50 km epicentral distance. These results include the TMVB.

Relative amplitude of Fourier amplitude spectra at 4.0 Hz as a function of ...

Published: 01 February 2009
Figure 7. Relative amplitude of Fourier amplitude spectra at 4.0 Hz as a function of distance from the source computed for the two cross sections. The S -wave window was Fourier transformed, smoothed by an octave band filter, and the values at 0.5 Hz were normalized by their amplitude at a 50 km
Image
(a) Observed Fourier amplitude spectra for earthquake number 7 (thick line is average, thin lines are average ± standard deviation [Av. St. dev.]). (b,c) Observed Fourier amplitude spectra compared to the theoretical spectra Af(f) calculated by equation (1) (dashed lines), for average − standard deviation and for average + standard deviation spectra, respectively.

(a) Observed Fourier amplitude spectra for earthquake number 7 (thick line ...

Published: 10 March 2020
Figure 8. (a) Observed Fourier amplitude spectra for earthquake number 7 (thick line is average, thin lines are average ± standard deviation [Av. St. dev.]). (b,c) Observed Fourier amplitude spectra compared to the theoretical spectra A f ( f ) calculated by equation  (1) (dashed