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A review of time­‐frequency methods Slide 1 A review of time­‐frequency methods Slide 2 A review of time­‐frequency methods Slide 3 A review of time­‐frequency methods Slide 4

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A review of time­‐frequency methods Slide 8 A review of time­‐frequency methods Slide 9 A review of time­‐frequency methods Slide 10 A review of time­‐frequency methods Slide 11 A review of time­‐frequency methods Slide 12 A review of time­‐frequency methods Slide 13 A review of time­‐frequency methods Slide 14 A review of time­‐frequency methods Slide 15 A review of time­‐frequency methods Slide 16 A review of time­‐frequency methods Slide 17 A review of time­‐frequency methods Slide 18 A review of time­‐frequency methods Slide 19 A review of time­‐frequency methods Slide 20 A review of time­‐frequency methods Slide 21 A review of time­‐frequency methods Slide 22 A review of time­‐frequency methods Slide 23 A review of time­‐frequency methods Slide 24 A review of time­‐frequency methods Slide 25 A review of time­‐frequency methods Slide 26 A review of time­‐frequency methods Slide 27 A review of time­‐frequency methods Slide 28 A review of time­‐frequency methods Slide 29 A review of time­‐frequency methods Slide 30 A review of time­‐frequency methods Slide 31 A review of time­‐frequency methods Slide 32 A review of time­‐frequency methods Slide 33 A review of time­‐frequency methods Slide 34 A review of time­‐frequency methods Slide 35 A review of time­‐frequency methods Slide 36 A review of time­‐frequency methods Slide 37 A review of time­‐frequency methods Slide 38 A review of time­‐frequency methods Slide 39 A review of time­‐frequency methods Slide 40

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A review of time­‐frequency methods

Spectral estimation, and corresponding time-frequency representation for nonstationary signals, is a cornerstone in geophysical signal processing and interpretation. The last 10–15 years have seen the development of many new high-resolution decompositions that are often fundamentally different from Fourier and wavelet transforms. These conventional techniques, like the short-time Fourier transform and the continuous wavelet transform, show some limitations in terms of resolution (localization) due to the trade-off between time and frequency localizations and smearing due to the finite size of the time series of their template. Well-known techniques, like autoregressive methods and basis pursuit, and recently developed techniques, such as empirical mode decomposition and the synchrosqueezing transform, can achieve higher time-frequency localization due to reduced spectral smearing and leakage. We first review the theory of various established and novel techniques, pointing out their assumptions, adaptability, and expected time-frequency localization. We illustrate their performances on a provided collection of benchmark signals, including a laughing voice, a volcano tremor, a microseismic event, and a global earthquake, with the intention to provide a fair comparison of the pros and cons of each method. Finally, their outcomes are discussed and possible avenues for improvements are proposed.

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A review of time­‐frequency methods

  1. 1. Sponsors Meeting 2014 A review of time‐frequency methods with application to body-wave separation Roberto Henry Herrera, Jean-Baptiste Tary and Mirko van der Baan* University of Alberta, Canada Microseismic Industry Consortium
  2. 2. Objective – Value proposition Sponsors Meeting 2014 • Objective: – Review of best performing techniques for time-frequency analysis • Present our home-brewed algorithms with their recipes. • Possible applications: – Resonance frequency analysis & LP events. – Represent sharp events. Short duration and low energy. – Separate out close events in time and close frequency components. • Main problem • Latest review of TFA is from the past century (20 years ago). • Many new methods but hard to find best suited for specific problems. • Push the limits of the Gabor uncertainty principle. • Value Proposition • “a comprehensive set of essential tools for microseismic spectral analysis”. • Separation via differences in freq content. Requires hi-res time-freq transforms. Reconstruct P and S waves from the time-frequency map.
  3. 3. Sponsors Meeting 2014 TFA  a cornerstone in geophysical signal processing and interpretation. Why are we going to the T-F domain?  Study changes of frequency content of a signal with time. Useful for: - attenuation measurement (Reine et al., 2009) - direct hydrocarbon detection (Castagna et al., 2003) - stratigraphic mapping (ex. detecting channel structures) (Partyka et al., 1998). - Microseismic event detection (Das and Zoback, 2011)  Extract sub-features in seismic signals - reconstruct band‐limited seismic signals from an improved spectrum. - improve signal-to-noise ratio of the attributes. (Steeghs and Drijkoningen, 2001). - identify resonance frequencies (microseismicity). (Tary & van der Baan, 2012). Time-Frequency Analysis (TFA)
  4. 4. Sponsors Meeting 2014 Motivation: The last 10-15 years have seen the development of many new high-resolution decompositions Fourier and Wavelet Transforms. The “workhorses” of spectral analysis Methods 1. Short-time Fourier Transform (STFT) 2. Continuous Wavelet Transform (CWT) 3. Stockwell Transform (ST) 4. Matching Pursuit (MP) 5. Synchrosqueezing Transform (SST) 6. Short-time Autoregressive (ST-AR) 7. Kalman Smoother (KS) 8. Empirical mode decomposition (EMD) Benchmark signals 1. A Toy Example – Synthetic signal. 2. A laughing voice. 3. A volcano tectonic event – Gliding tremor. (Redoubt Volcano on March 31, 2009). 4. A microseismic event. (Rolla HyFrac. 2011) 5. And a global earthquake signal (Tohoku 2011, Mw9) “A comprehensive set of essential tools for microseismic spectral analysis” The review: Chapter 2: Spectral estimation – What’s new? What’s next?
  5. 5. Sponsors Meeting 2014 A representative volcano-seismic signal Gliding tremor: Redoubt Volcano on March 31, 2009. Some volcanoes 'scream' at ever-higher pitches until they blow their tops. http://www.sciencedaily.com/releases/2013/07/1307 14160521.htm Hotovec et al., 2013, Strongly gliding harmonic tremor during the 2009 eruption of Redoubt Volcano.Journal of Volcanology and Geothermal Research, 2013; 259: 89. Redoubt Volcano’s active lava. Dome. Alaska. Credit: Chris Waythomas, Alaska Volcano Observatory Swarms of small earthquakes can precede a volcanic eruption, sometimes resulting in "harmonic tremor" resembling sound from some musical instruments.
  6. 6. Sponsors Meeting 2014 A global seismology example: Megathrust earthquake: Tohoku-Oki, March 11, 2011, Mw9 STFT SSTCWT MPST ST-AR KSCEEMD The seismogram was recorded by the borehole station KDAK from the IRIS IDA network located in Kodiak Island on the Aleutian trench, South Alaska.
  7. 7. Sponsors Meeting 2014 Data: hydraulic fracture treatment, western Canada. Rolla, BC, 2011. Field layout. Eaton et al. (GJI, 2014)
  8. 8. Sponsors Meeting 2014 Microseismic event – Rolla, BC, 2011. STFT P-S converted wave - 320 Hz S-wave - 210 and 320 Hz. Signal TFR - is challenging  very short duration events (0.1 - 1 s). A clear separation of seismic phases is difficult to obtain due to the limits in time and frequency resolutions of conventional T-F methods. Microseismic event Mw -1.7. Vertical component, deepest geophone.
  9. 9. Sponsors Meeting 2014 Microseismic event – TFT with 8 methods +++ Smearing  + Smearing  + Smearing  STFT SSTCWT MPST ST-AR KSCEEMD --- Smearing  -- Smearing  - Smearing  - Smearing  +- Smearing 
  10. 10. SST – Steps Synchrosqueezing depends on the continuous wavelet transform and reassignment Sponsors Meeting 2014 Microseismic signal 𝑠(𝑡) Mother wavelet 𝜓(𝑡)  𝑓, Δ𝑓 CWT 𝑊𝑠(𝑎, 𝑏) IF 𝑤𝑠 𝑎, 𝑏 Reassignment step: Compute Synchrosqueezed function 𝑇𝑠 𝑓, 𝑏 Extract dominant curves from 𝑇𝑠 𝑓, 𝑏 + ICWT Time-Frequency Representation Signal Reconstruction - Sum of modes - Selected areas
  11. 11. Continuous Wavelet Transform vs Synchrosqueezing Transform Sponsors Meeting 2014 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -1 0 1 2Amplitude Synthetic trace s(t) CWT SST 100 Hz 30 Hz 7 Hz 30 Hz 40 Hz 20 Hz 20 Hz 20 Hz Morlet atom 100 Hz
  12. 12. Single-station separation of P- & S-waves? Sponsors Meeting 2014 • Objective: – Can we separate P & S waves at a single station w/o prior knowledge about polarities or waveforms? • Option 1: Separation of P & S waves via curl and divergence => Requires closely spaced multiple stations • Option 2: Separation via differences in freq content => Requires hi-res time-freq transforms
  13. 13. Microseismic event  STFT & SST 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -1 -0.5 0 0.5 1 x 10 4 Amplitude Time (s) s(t) S-wave P-wave P-wave S-wave Sponsors Meeting 2014
  14. 14. Sponsors Meeting 2014 Polarization + Move-out Analysis East North Vertical P-wave Sh-wave Sv-wave P- to Sv-wave a)- 3C microseismic traces at geophone 7, stage 2. b)- Polarization vectors for the waves modes. The polarity is reversed for display purposes only. East North Vertical
  15. 15. Sponsors Meeting 2014 Phase identification: Move-out Vertical Component. Ringing P-wave arrival Picking of P-to-S wave P-wave Sh-wave Sv-waveP to Sv-wave 2 3 5 7 Very similar move- outs. - 2 wave packets for P-waves picks, w/ similar apparent velocities but different polarizations. (P + P-to-S waves) - 2 S-waves w/ slightly different: apparent velocities, arrival times and polarizations. - The “fast” S-wave on the East-North components is the Sh and the “slow” S-wave on the vertical is the Sv. Move-out analysis compatible with the results of the analysis of the time series & polarizations.
  16. 16. Sponsors Meeting 2014 Microseismic event – Rolla, BC, 2011. a)- Hodograms for the stage 2 event. b)- Vectors corresponding to the hodograms. P-wave Sh-wave Sv-wave P- to Sv-wave
  17. 17. Sponsors Meeting 2014 Projection & Time Frequency Representation 320 210 ~210 ~300 215 320 320 200 260 ~230 P Sv Sh AmplitudeAmplitudeAmplitude
  18. 18. Sponsors Meeting 2014
  19. 19. Sponsors Meeting 2014 P-wave S-wave 0.325 0.33 0.335 0.34 0.345 0.35 200 250 300 350 Frequency(Hz) 0.325 0.33 0.335 0.34 0.345 0.35 -2000 0 2000 Amplitude Time(s) s(t) sr (t) 0.36 0.365 0.37 0.375 0.38 0.385 0.39 200 250 300 350 Frequency(Hz) 0.36 0.365 0.37 0.375 0.38 0.385 0.39 -1 0 1 x 10 4 Amplitude Time(s) s(t) sr (t) Signal extraction from time-freq map
  20. 20. Conclusions Sponsors Meeting 2014 SST: • High-resolution time-frequency decomposition – Attractive for detailed analysis of variety of signals • Microseismic + earthquake data, any other signals • SST also permits signal reconstruction: – SST can extract individual components (= time-varying monochromatic signals) – Sum of individual components ≈ original signal • Very acceptable reconstruction error • We are developing a complete toolset for High- Res TFA.
  21. 21. Acknowledgments Sponsors Meeting 2014 • Sponsors of the Microseismic Industry Consortium for financial support • David Eaton: – For providing microseismic data • Sergey Fomel: – For many encouraging discussions on SST and P/S wave separation • Melanie Grob and Shawn Maxwell: – For their interesting suggestions that helped to improve the interpretation of our results.
  22. 22. Conclusions Sponsors Meeting 2014 SST: • High-resolution time-frequency decomposition – Attractive for detailed analysis of variety of signals • Microseismic + earthquake data, any other signals • SST also permits signal reconstruction: – SST can extract individual components (= time-varying monochromatic signals) – Sum of individual components ≈ original signal • Very acceptable reconstruction error • We are developing a complete toolset for High- Res TFA.
  23. 23. Rolla Experiment. Stage A2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -1 -0.5 0 0.5 1 x 10 4 Amplitude Time (s) s(t) S-wave P-wave P-wave S-wave
  24. 24. Rolla Experiment. Mode Decomposition 0.2 0.4 0.6 0.8 1 -1 0 1 x 10 4 Original trace Amplitude 0.2 0.4 0.6 0.8 1 -5000 0 5000 Mode 1 Amplitude Time (s) 0.2 0.4 0.6 0.8 1 -6000 -4000 -2000 0 2000 4000 Mode 2 Amplitude Time (s) 0.2 0.4 0.6 0.8 1 -1000 0 1000 Mode 3 Amplitude Time (s) 0.2 0.4 0.6 0.8 1 -500 0 500 Mode 4 Amplitude Time (s) 0.2 0.4 0.6 0.8 1 -1 0 1 Mode 5Amplitude Time (s)
  25. 25. Signal extraction from Rolla Stage A2 P-wave S-wave 0.325 0.33 0.335 0.34 0.345 0.35 200 250 300 350 Frequency(Hz) 0.325 0.33 0.335 0.34 0.345 0.35 -2000 0 2000 Amplitude Time(s) s(t) sr (t) 0.36 0.365 0.37 0.375 0.38 0.385 0.39 200 250 300 350 Frequency(Hz) 0.36 0.365 0.37 0.375 0.38 0.385 0.39 -1 0 1 x 10 4Amplitude Time(s) s(t) sr (t)
  26. 26. P-wave SH? 0.325 0.33 0.335 0.34 0.345 0.35 290 300 310 320 330 Frequency(Hz) 0.325 0.33 0.335 0.34 0.345 0.35 -2000 0 2000 Amplitude Time(s) s(t) sr (t) 0.36 0.37 0.38 0.39 0.4 0.41 180 200 220 240 Frequency(Hz) 0.36 0.37 0.38 0.39 0.4 0.41 -1 0 1 x 10 4 Amplitude Time(s) s(t) sr (t) 0.37 0.38 0.39 0.4 280 300 320 340 Frequency(Hz) 0.37 0.38 0.39 0.4 -1 0 1 x 10 4 Amplitude Time(s) s(t) sr (t) SV? Signal extraction from Rolla Stage A2
  27. 27. 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 150 200 250 300 350 Frequency(Hz) 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 -1 0 1 x 10 4 Amplitude Time(s) s(t) sr (t) Signal extraction from Rolla Stage A2
  28. 28. Rolla Experiment. Well A Stage 3 Fig 11. Eaton et. al., 2014 0 0.5 1 1.5 -2 0 2 x 10 -7 Amplitude Time(s) s(t) S-wave P-wave P S Time-Frequency Rep. by SST Scattered waves?
  29. 29. Rolla Experiment. Well A Stage 3 0.7 0.705 0.71 0.715 0.72 0.725 0.73 200 250 300 350 Frequency(Hz) 0.7 0.705 0.71 0.715 0.72 0.725 0.73 -0.2 -0.1 0 0.1 Amplitude Time(s) s(t) s r (t) P-wave 0.75 0.76 0.77 0.78 0.79 150 200 250 300 Frequency(Hz) 0.75 0.76 0.77 0.78 0.79 -0.5 0 0.5 Amplitude Time(s) s(t) sr (t) S-wave
  30. 30. Rolla Experiment. Stage A3 East North Vert. P-wave Sh-wave Sv-wave Vectors corresponding to the hodograms The three phases P, Sv, and Sh are approximately mutually perpendicular.
  31. 31. Rolla Experiment. Stage A3 P-wave Sh-wave Sv-wave 3C data projected on P vector SST 510 Hz400 Hz 270 Hz 290 Hz 195 Hz - P-waves at 400 Hz - Remnants of P-Sv converted waves at 270 Hz? - Difficulties to separate P- and Sv-waves - Sv contributions at 290 Hz (see next slide) - Patch at ~195-200 Hz present in all components - Patch at 510 Hz ?
  32. 32. Rolla Experiment. Stage A3 P-wave Sh-wave Sv-wave 3C data projected on Sv vector SST 455 Hz330 Hz 225 Hz 310 Hz 210 Hz - Sv-waves at 310 Hz - P-Sv converted waves at 330 and 225 Hz? - Patch at 455 Hz?
  33. 33. Rolla Experiment. Stage A3 P-wave Sh-wave Sv-wave 3C data projected on Sh vector SST 350Hz 295 Hz 190 Hz - Sh-waves between 295 and 350 Hz
  34. 34. Rolla Experiment. Stage A2 3C data projected on vectors SST P Sv Sh
  35. 35. Questions TLE. 2012. Brad Birkelo et. al. 1- Are the two components of the P-wave related to a compensated linear vector dipole (CLVD), instead of a double couple (DC) fracture type?. 1a)- CLVD a possible mechanism for microseismic fractures (Baig, A., and T. Urbancic ,2010) 2- We are able to extract regions on the Time-Freq map. Do you envision any application of waveform separation in microseismic analysis? 3- Is full-waveform based moment tensor inversion a possible application? 4- We would appreciate your collaboration in future related work, what are the main challenges you would like to work on?
  36. 36. Review Paper Signals and TFR
  37. 37. Review Paper Signals and TFR
  • PengHan5

    May. 9, 2018
  • DrRoshanKumar1

    Jan. 5, 2017
  • septt0

    Jan. 2, 2017
  • iskandarsyahMahmuddi

    Jun. 17, 2015
  • 7877039929

    Apr. 6, 2015

Spectral estimation, and corresponding time-frequency representation for nonstationary signals, is a cornerstone in geophysical signal processing and interpretation. The last 10–15 years have seen the development of many new high-resolution decompositions that are often fundamentally different from Fourier and wavelet transforms. These conventional techniques, like the short-time Fourier transform and the continuous wavelet transform, show some limitations in terms of resolution (localization) due to the trade-off between time and frequency localizations and smearing due to the finite size of the time series of their template. Well-known techniques, like autoregressive methods and basis pursuit, and recently developed techniques, such as empirical mode decomposition and the synchrosqueezing transform, can achieve higher time-frequency localization due to reduced spectral smearing and leakage. We first review the theory of various established and novel techniques, pointing out their assumptions, adaptability, and expected time-frequency localization. We illustrate their performances on a provided collection of benchmark signals, including a laughing voice, a volcano tremor, a microseismic event, and a global earthquake, with the intention to provide a fair comparison of the pros and cons of each method. Finally, their outcomes are discussed and possible avenues for improvements are proposed.

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