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Hilbert-Huang transformations

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Journal Article

Application of the empirical mode decomposition and Hilbert-Huang transform to seismic reflection data

Bradley Matthew Battista, Camelia Knapp, Tom McGee, Vaughn Goebel
Journal: Geophysics
Published: 02 March 2007
Geophysics (2007) 72 (2): H29–H37.
DOI: https://doi.org/10.1190/1.2437700
...) which combines with the Hilbert transform as the Hilbert-Huang transform (HHT). The EMD empirically reduces a time series to several subsignals, each of which is input to the same time-frequency environment via the Hilbert transform. The HHT allows for signals describing stochastic or astochastic...
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The Hilbert–Huang Transform: A High Resolution Spectral Method for Nonlinear and Nonstationary Time Series

Daniel C. Bowman, Jonathan M. Lees
Published: 01 November 2013
Seismological Research Letters (2013) 84 (6): 1074–1080.
DOI: https://doi.org/10.1785/0220130025
... between time and frequency resolution for nonstationary signals and the creation of spurious harmonics for nonlinear signals. We present an open‐source implementation of the Hilbert–Huang transform ( HHT ), an alternative spectral method designed to avoid the linearity and stationarity constraints...
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Hilbert–Huang Transform and Energy Rate Functions for Earthquake Source Characterization—A Study from the Japan Trench

Swapnil Mache, Avigyan Chatterjee, Kusala Rajendran, Chandra Sekhar Seelamantula
Published: 08 September 2022
Bulletin of the Seismological Society of America (2022) 112 (6): 2847–2858.
DOI: https://doi.org/10.1785/0120220099
...Swapnil Mache; Avigyan Chatterjee; Kusala Rajendran; Chandra Sekhar Seelamantula ABSTRACT The Hilbert–Huang Transform (HHT) has been sparsely applied to problems in seismology, although previous studies have pointed to its broad scope. In this maiden attempt, we use the HHT to represent earthquake...
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A Record-Based Method for the Generation of Tridirectional Uniform Hazard-Response Spectra and Ground Motions Using the Hilbert-Huang Transform

Ping Gu, Y. K. Wen
Published: 01 October 2007
Bulletin of the Seismological Society of America (2007) 97 (5): 1539–1556.
DOI: https://doi.org/10.1785/0120060127
... to the site and a simulation method recently developed for nonstationary random processes using the Hilbert-Huang Transform. The simulation method can reproduce the ground-motion intensity and spectral content variation with time and is thus suitable for near-fault ground motions with long- period pulses...
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<span class="search-highlight">Hilbert</span> energy spectra of the <span class="search-highlight">Hilbert</span>–<span class="search-highlight">Huang</span> <span class="search-highlight">transform</span> (HHT) with the same e...

Hilbert energy spectra of the Hilbert–Huang transform (HHT) with the same e...

Published: 01 November 2010
Fig. 14. Hilbert energy spectra of the Hilbert–Huang transform (HHT) with the same energy scaling for the Dedenborn, Erkensruhr, and Rollesbroich gauging stations from 1991 to 1993.
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▴ The <span class="search-highlight">Hilbert</span>-<span class="search-highlight">Huang</span> <span class="search-highlight">transform</span> was used to analyze GPS data at ACAP to obtai...

▴ The Hilbert-Huang transform was used to analyze GPS data at ACAP to obtai...

Published: 01 January 2009
Figure 5. ▴ The Hilbert-Huang transform was used to analyze GPS data at ACAP to obtain onset time, amplitude, and duration of SSE. (A), (B), and (C) are the ACAP GPS three-components displacement observation, unit: cm, The black circle is the inflection point. The black vertical bar marks
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<span class="search-highlight">Hilbert</span>-<span class="search-highlight">Huang</span> <span class="search-highlight">transform</span> of a signal composed of three frequencies −2, 20, a...

Hilbert-Huang transform of a signal composed of three frequencies −2, 20, a...

Published: 02 March 2007
Figure 2. Hilbert-Huang transform of a signal composed of three frequencies −2, 20, and 100 Hz . The time series in (a) is transformed to the time-frequency domain in (b). The Hilbert marginal spectrum shown in (c) is produced as the temporal sum of amplitudes for every frequency in (b).
Journal Article

Multiscale Analysis of Hydrologic Time Series Data using the Hilbert–Huang Transform All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.

J. Rudi, R. Pabel, G. Jager, R. Koch, A. Kunoth, H. Bogena
Published: 01 November 2010
Vadose Zone Journal (2010) 9 (4): 925–942.
DOI: https://doi.org/10.2136/vzj2009.0163
...Fig. 14. Hilbert energy spectra of the Hilbert–Huang transform (HHT) with the same energy scaling for the Dedenborn, Erkensruhr, and Rollesbroich gauging stations from 1991 to 1993. ...
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Prediction of fracture density using genetic algorithm support vector machine based on acoustic logging data

Tianyang Li, Ruihe Wang, Zizhen Wang, Mingyuan Zhao, Lei Li
Journal: Geophysics
Published: 24 January 2018
Geophysics (2018) 83 (2): D49–D60.
DOI: https://doi.org/10.1190/geo2017-0229.1
... and frequency domains by the Hilbert-Huang transform (HHT) and extracted 11 features in the time domain and nine features in the frequency domain. Then, we reduced the features in the time and frequency domain to three principal components by principal component analysis. Finally, a new prediction model...
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An Alternative Approach to Characterize Nonlinear Site Effects

Ray Ruichong Zhang, M.EERI, Stephen Hartzell, Jianwen Liang, Yuxian Hu
Published: 01 February 2005
Earthquake Spectra (2005) 21 (1): 243–274.
DOI: https://doi.org/10.1193/1.1853390
...Ray Ruichong Zhang, M.EERI; Stephen Hartzell; Jianwen Liang; Yuxian Hu This paper examines the rationale of a method of nonstationary data processing and analysis, referred to as the Hilbert-Huang transform (HHT), for its application to a recording-based approach in quantifying influences of soil...
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Multidimensional EMD with marginal Hilbert-Huang spectrum applications for engineering geophysics — Technical tutorial and field example

Chih-Sung Chen, Yih Jeng
Journal: The Leading Edge
Published: 01 May 2022
The Leading Edge (2022) 41 (5): 347–356.
DOI: https://doi.org/10.1190/tle41050347.1
... in engineering geophysics. A newer methodology, Hilbert-Huang transform (HHT), has been developed as a remedy. In this article, a systematic review and technical tutorial on the evolving advanced data processing method, multimarginal HHT spectral analysis, which is derived from HHT, will be the main theme...
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Identification of Pulse Periods in Near‐Fault Ground Motions Using the HHT Method

Xiaoyu Chen, Dongsheng Wang, Rui Zhang
Published: 24 September 2019
Bulletin of the Seismological Society of America (2019) 109 (6): 2384–2398.
DOI: https://doi.org/10.1785/0120190046
... attention should be paid to the frequency components in the ground motion. Based on the identification of frequency components in the original record, a new method based on the Hilbert–Huang transform (HHT) is proposed here. A ground‐motion record can be decomposed into several intrinsic mode functions...
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A Method to Estimate the Phase Velocities of Microtremors Using a Time-Frequency Analysis and Its Applications

Hitoshi Morikawa, Shizuo Udagawa
Published: 01 April 2009
Bulletin of the Seismological Society of America (2009) 99 (2A): 774–793.
DOI: https://doi.org/10.1785/0120080100
... in short-time range and propose a method that can find the instantaneously corresponding portions of microtremor records at two different sites and that can estimate the apparent phase velocities between the two sites. We use the technique of a time-frequency analysis for which the Hilbert–Huang Transform...
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Dedenborn site data from 1990 to 1999: (A) <span class="search-highlight">Hilbert</span> energy spectrum of the H...

Dedenborn site data from 1990 to 1999: (A) Hilbert energy spectrum of the H...

Published: 01 November 2010
Fig. 10. Dedenborn site data from 1990 to 1999: (A) Hilbert energy spectrum of the Hilbert–Huang transform (HHT), (B) Morlet and (C) Mexican hat wavelet spectra, and (D) Fourier spectrogram.
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Dedenborn site data from 1991 to 1993: (A) <span class="search-highlight">Hilbert</span> energy spectrum of the H...

Dedenborn site data from 1991 to 1993: (A) Hilbert energy spectrum of the H...

Published: 01 November 2010
Fig. 12. Dedenborn site data from 1991 to 1993: (A) Hilbert energy spectrum of the Hilbert–Huang transform (HHT), (B) Morlet and (C) Mexican hat wavelet spectra, and (D) Fourier spectrogram.
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COMPARISON OF SUBSIDENCE RATE AT GRAND ISLE RELATIVE TO THREE DIFFERENT REF...

COMPARISON OF SUBSIDENCE RATE AT GRAND ISLE RELATIVE TO THREE DIFFERENT REF...

Published: 01 June 2015
TABLE 1. COMPARISON OF SUBSIDENCE RATE AT GRAND ISLE RELATIVE TO THREE DIFFERENT REFERENCE STATIONS FROM LINEAR REGRESSION AND HILBERT-HUANG TRANSFORM
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Relationship between Baker’s pulse indicators and the maximum energy change...

Relationship between Baker’s pulse indicators and the maximum energy change...

Published: 24 September 2019
Figure 5. Relationship between Baker’s pulse indicators and the maximum energy changes of IMFs that are obtained by the Hilbert–Huang transform (HHT) method. PEER, Pacific Earthquake Engineering Research Center.
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Plot of tide gauge data at Grand Isle, Louisiana (GRIS) referenced to Pensa...

Plot of tide gauge data at Grand Isle, Louisiana (GRIS) referenced to Pensa...

Published: 01 June 2015
Figure 3. Plot of tide gauge data at Grand Isle, Louisiana (GRIS) referenced to Pensacola, Florida (PCLA) (gray dots) and comparison between average long-term subsidence rate (black line) and change of rate (dash line) obtained from linear regression (reg.) analysis, compared to Hilbert-Huang
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Comparison of three different spectrograms of the model data. (a) Synthetic...

Comparison of three different spectrograms of the model data. (a) Synthetic...

Published: 27 July 2007
of the short-time Fourier transform. (c) Spectrogram of the Hilbert-Huang transform. (d) Spectrogram of the wavelet transform. The values for the shading codes in (b–d) indicate amplitude in relative scale. The normalized scale should refer to the shading in (d).
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(a) Comparison between observed and modeled tide gauge records inside Acapu...

(a) Comparison between observed and modeled tide gauge records inside Acapu...

Published: 27 September 2022
Figure 6. (a) Comparison between observed and modeled tide gauge records inside Acapulco Bay. (b) Comparison of observed and modeled waveform envelopes constructed from the Hilbert transform of each. (c) Hilbert‐Huang spectrogram of the observed data and integrated amplitude spectrum constructed