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.
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. 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. 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. 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. 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. 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. Sponsors Meeting 2014
Data: hydraulic fracture treatment, western Canada.
Rolla, BC, 2011.
Field layout.
Eaton et al. (GJI, 2014)
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.
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
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. 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. 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. Sponsors Meeting 2014
Projection & Time Frequency Representation
320
210 ~210
~300
215
320
320
200
260
~230
P
Sv
Sh
AmplitudeAmplitudeAmplitude
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. 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. 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.
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. 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. 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. 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
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?
Title - Latest developments in time-frequency analysis Time-frequency analysis 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. This proposed 1/2-day PCWS intends to invite algorithm developers to explain their methods and show results 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.
This proposed 1/2-day PCWS intends to invite algorithm developers to explain their methods and show results 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.
3- Gliding tremor: Redoubt Volcano on March 31, 2009.
Frictional-faulting model for harmonic tremor before Redoubt Volcano eruptions. Nature Geosciences. 2013.
Hotovec-Ellis is a co-author of a second paper, published online July 14 in Nature Geoscience, that introduces a new "frictional faulting" model as a tool to evaluate the tremor mechanism observed at Redoubt in 2009. The lead author of that paper is Ksenia Dmitrieva of Stanford University, and other co-authors are Prejean and Eric Dunham of Stanford.Read more at: http://phys.org/news/2013-07-volcanoes-ever-higher-pitches-tops.html#jCp
Some volcanoes 'scream' at ever-higher pitches until they blow their tops
4- The fracturing is monitored by a toolstring of 6 downhole short-period geophones, with a sampling frequency of 2000 Hz. The signal shown
in Figure 8 corresponds to the recordings of a magnitude -1.7 microseismic event by the vertical component
of the deepest geophone.
5- The Mw9 Tohoku earthquake occurred on March 11, 2011
This proposed 1/2-day PCWS intends to invite algorithm developers to explain their methods and show results 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.
3- Gliding tremor: Redoubt Volcano on March 31, 2009.
Frictional-faulting model for harmonic tremor before Redoubt Volcano eruptions. Nature Geosciences. 2013.
Hotovec-Ellis is a co-author of a second paper, published online July 14 in Nature Geoscience, that introduces a new "frictional faulting" model as a tool to evaluate the tremor mechanism observed at Redoubt in 2009. The lead author of that paper is Ksenia Dmitrieva of Stanford University, and other co-authors are Prejean and Eric Dunham of Stanford.Read more at: http://phys.org/news/2013-07-volcanoes-ever-higher-pitches-tops.html#jCp
Some volcanoes 'scream' at ever-higher pitches until they blow their tops
The Mw9 Tohoku earthquake occurred on March 11, 2011, offshore the North-West coast of Japan where
the Pacific plate subducts under the Okhotsk plate (Tajima and Kennett, 2012). The seismogram presented
in Figure 10 was recorded by the borehole station KDAK from the IRIS IDA network located in Kodiak
Island on the Aleutian trench, South Alaska. This station has a 3-component broadband seismometer with
sampling frequency at 20 Hz giving an usable frequency band between around 0.003 and 10 Hz. The main
signal from the earthquake lasts for about half an hour, with a high SNR superior to 10.
The Mw9 Tohoku earthquake occurred on March 11, 2011, offshore the North-West coast of Japan where
the Pacific plate subducts under the Okhotsk plate (Tajima and Kennett, 2012). The seismogram presented
in Figure 10 was recorded by the borehole station KDAK from the IRIS IDA network located in Kodiak
Island on the Aleutian trench, South Alaska. This station has a 3-component broadband seismometer with
sampling frequency at 20 Hz giving an usable frequency band between around 0.003 and 10 Hz. The main
signal from the earthquake lasts for about half an hour, with a high SNR superior to 10.
The magnitude 9.0 Tohoku-Oki, Japan, earthquake on 11 March 2011 is the largest earthquake to date in Japan’s modern history and is ranked as the fourth largest earthquake in the world since 1900.
The signal shown in this Figure corresponds to the recordings of a magnitude -1.7 microseismic event by the vertical component
of the deepest geophone.
The T-F representation of these events is complicated mainly by their very short durations generally between 0.1 and 1 s. A clear separation of the different seismic phases is then
difficult to obtain due to the limits in time and frequency resolutions of conventional T-F methods.
Explain each method.
Time-frequency representations of the microseismic event in Figure 8), using the ST, ST-AR, KS,
CWT, SST, EMD and MP. The computing parameters are, ST: resolution parameter k=4; ST-AR: window
of 0.04 s with 90 % overlap and an AR order of 11; KS: AR order of 11; CWT and SST: Morlet wavelet
with 64 voices per octave; CEEMD: 100 realizations and random noise injection with 15 % of the signal
maximum amplitude; MP: Gabor dictionary.
The challenging synthetic signal:
- 20 Hz cosine wave, superposed 100 Hz Morlet atom at 0.3 s
two 30 Hz zero phase Ricker wavelets at 1.07 s and 1.1 s,
three different frequency components between 1.3 s and 1.7 s of respectively 7, 30 and 40 Hz.
Time-frequency representations of the microseismic event in Figure 8), using the ST, ST-AR, KS,
CWT, SST, EMD and MP. The computing parameters are, ST: resolution parameter k=4; ST-AR: window
of 0.04 s with 90 % overlap and an AR order of 11; KS: AR order of 11; CWT and SST: Morlet wavelet
with 64 voices per octave; CEEMD: 100 realizations and random noise injection with 15 % of the signal
maximum amplitude; MP: Gabor dictionary.
Small ringing problem for this geophone. Especially Vert.
Small ringing problem for this geophone. Especially Vert.
Taking all the first P-wave picks, the Vp apparent is ~11810 m/s
The East comp. gives the right Vp/Vs ratio, being different from the theoretical 1.73 by 15%. This includes errors in time-picks, effects from non-ideal rocks and slightly different ray paths between P- and S-waves.
It seems there are 2 wave packets for P-waves picks, having similar apparent velocities but different polarizations. (P + P-to-S waves)
Similarly, two S-waves are present. They have slightly different apparent velocities, different arrival times and different polarizations. The “fast” S-wave on the East-North components is the Sh and the “slow” S-wave on the vertical is the Sv. The measurements of apparent velocities can change quickly even for small errors in time-picks.
Delay between P and P-to-Sv wave ranging between 0.002 and 0.0085 s
Considering a S-wave velocity of 5500/1.73 ~ 3180 m/s, and with delay Dt = distance*(1/Vp – 1/Vs), it gives distances between 15 and 64 m
So conversion likely in the hosting rock close to the borehole.
Small ringing problem for this geophone. Especially Vert.
Taking all the first P-wave picks, the Vp apparent is ~11810 m/s
The East comp. gives the right Vp/Vs ratio, being different from the theoretical 1.73 by 15%. This includes errors in time-picks, effects from non-ideal rocks and slightly different ray paths between P- and S-waves.
It seems there are 2 wave packets for P-waves picks, having similar apparent velocities but different polarizations. (P + P-to-S waves)
Similarly, two S-waves are present. They have slightly different apparent velocities, different arrival times and different polarizations. The “fast” S-wave on the East-North components is the Sh and the “slow” S-wave on the vertical is the Sv. The measurements of apparent velocities can change quickly even for small errors in time-picks.
Delay between P and P-to-Sv wave ranging between 0.002 and 0.0085 s
Considering a S-wave velocity of 5500/1.73 ~ 3180 m/s, and with delay Dt = distance*(1/Vp – 1/Vs), it gives distances between 15 and 64 m
So conversion likely in the hosting rock close to the borehole.
Frequency content analysis
Similar frequency components on the two geophones. The P-wave and the P-to-Sv waves have similar frequency contents (320 Hz) and their arrival times are very close. Despite its high-resolution the SST is unable to clearly separate them. They are somewhat distinguishable by their polarization.
The Sv-wave consists of two components located at 210 and 280-340 Hz. The tails that are observed on geophone 7 only could be related to instrument self-excitation.
The Sh-wave has two components, one at 200-215 and one at 260-275 Hz.
The component at 200-210 Hz for all waves might correspond to energy leakage between components due to non-linear polarization or to instruments ringing.
Zoom in of the area in the rectangles shows a better P and S wave separation.
A global mode extraction from the Wavelet’s ridges drives to the next slide.
Mode decomposition: useful of noise suppression and extraction of individual components. This is unsupervised mode extraction.
Only Mode 2 seems to separate P and S wave, which is useful if we want on a clean time domain signal.
But if we manually extract the Region of Interest (ROI), then the next slide shows promising results.
Extracting a vertical rectangle comprising only P wave Time-Frequency component drives to a P wave only reconstruction.
The same with the rectangle gathering S wave spectral content.
The bottom plots shows in Blue the actual P-wave (left) and S-wave (right) and in red their corresponding reconstructed P and S waves.
Something interesting is that both P and S waves are built of two frequency components.
Extracting just one of these components give a different time domain signal. And this observation brings more questions than answers to our research.
This slide can be deleted to save time.
This is a hidden slide just in case some one wants to see to reconstruction from the entire section.
Change converted waves by scattered waves.
Eaton, D., Baan, M. van der, Tary, J., & Birkelo, B. (2013). Broadband microseismic observations from a Montney hydraulic fracture treatment, northeastern BC, Canada. Recorder, (3). Retrieved from http://csegrecorder.com/articles/view/broadband-microseismic-observations-from-a-montney-hydraulic-fracture-treat
Examples of high-frequency microseismic events, which are generally dominated by S arrivals. Upper panels: signal and noise spectra. Lower panels: recorded waveforms and corresponding spectrograms obtained using the short-time Fourier transform.
Waveform examples of high-frequency microseismic events are presented in Figure 4. In this case, the S-wave
arrival has the highest amplitudes. The frequency content of these signals is predominantly concentrated above 100 Hz, and the
bandwidth decreases with distance due to the effects of attenuation.
Again we see Two frequency components for the P waves and two Freq components for the S wave.
Again we see two frequency components for the P waves and two freq components for the S wave.
If we take the components the reconstruction is almost exact to the original waveform.