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Analysis of Transient Seismic Signals using Wigner-Ville Distributions Simon Lloyd(1), Götz Bokelmann(1), and Victor Sucic(2) MFT Wigner-Ville vs MFT Introduction Analysing Synthetic Seismograms With the widespread adoption of ambient noise tomography, and the increasing number of local earthquakes recorded worldwide due to dense seismic networks and many very dense temporary experiments, we consider it worthwhile to evaluate alternative methods to measure surface wave group velocity dispersions curves. Moreover, the increased comput- ing power of even a simple desktop computer makes it fea- sible to routinely use methods other than the typically em- ployed multiple filtering technique (MFT). MFT is a robust technique and thus often a good choice to measure disper- sion. However, it involves a certain amount of averaging across frequencies. The measured dispersion curve may therefore be too smooth, or span across a too broad frequency range. While it still makes sense to use MFT for most applications, it is im- portant to know how strong the potential bias due to this av- eraging may be. To that end we perform tests with synthetic and observed seismograms using the Wigner-Ville distribution (WVD) frequency time analysis, and compare dispersion curves measured with WVD and MFT with each other. References: Peterson, J., 1993. Observations and mod- elling of background seismic noise. Open- file report 93-322, U. S. Geological Survey, Albuquerque, New Mexico Contact: Simon Lloyd ([email protected]) Dept. of Meteorology and Geophysics Althanstraße 14 (UZA II) 1090 Vienna, Austria Zimmernummer: 2D508 T: +43-1-4277-53722 F: +43-1-4277-53799 Both multiple filtering and Wigner-Ville yield similar results when measuring group velocity dispersion. MFT appears more robust over a wider frequency range. Wigner-Ville is more sensitive and better constrains dispersion measurements. The two methods may complement each other, whereby Multiple Filtering allows measuring dispersion over a wider frequency range and Wigner-Ville tells us about the true quality of the measurements. Random noise is better suppressed in WV, potentially allowing better detection of events. 1) Dept. of Meteorology and Geophysics, University of Vienna, 2) Faculty of Engineering, University of Rijeka [email protected] Station Noise We first compare MFT to Wigner- Ville (WV) on an observed teleseis- smic event. The measured dispe- rsion is similar for both methods. However, WV produces a sharper outline of group velocity dispe- rsion. WV may introduce some art- ifacts, which can be reduced by smoothing (across time and fr- equency). Even after smoothing the dispersion curve as outlined by the contours is still sharper than using MFT. To test the performance of WV we proceed using synthetic wav- eforms The noise spectrum at seismic sta- tions is not flat, and the ampli- tudes can thus vary significantly. We simulate best/worst case sce- narios using Peterson’s (1993) noise models obtained from glo- baly analysing measured noise (left). The synthetic noise has the same amplitude spectrum as Peterson’s (1993) hi and low noise models. Randomness is obtained from arbitrary phases asigned to each frequency (right). The Multiple Filter Technique (MFT) was introduced by Dziewonski et al. in 1969, as a way to measure surface wave group velocities. Countless studies have used MFT to determine group velocity disper- sion curves of surface waves, which can be inverted for velocity structure. As im- plied by its name, the method requires filtering the same trace multiple times. Typically these filters are Gaussian shaped, and centred at the frequency for which group velocity is measured. After filtering, the arrival time of the maximum of the envelope is picked and used together with epicentral distance to calculate group velocity at the re- spective periods. Doing this with several filters, each centred at different periods, allows determining dispersion curves. To compare MFT and WV with each other we compuate a synthetic seismogram and measure the dispersion curve using both methods. The wave form is the vertical component of a Mw=3.2, 45° dip slip earthquake at 200 km distance using the PREM Earth model. We add random, but non-white noise to the sythnthetic waveforms with the amplitude spectra of the Peterson’s (1993) NLNM and NHNM. The resulting waveforms are shown on the right. We omit showing the noise free case in the dispersion measure- ments (below), as it is very close to the low noise model case. Simi- larly to the teleseismic event, both methods produce comparable dispersion curves. However, in the case where high noise is added to the synthetic waveform, the noise itself is more visible in the MFT plots than WV. Conclusions NLNM NHNM Seismogram + NLNM Noise Free Seismogram Seismogram + NHNM True Amplitudes Normalised Amplitudes T3-P13

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Analysis of Transient Seismic Signals using Wigner-Ville DistributionsSimon Lloyd(1), Götz Bokelmann(1), and Victor Sucic(2)

MFT

Wigner-Ville vs MFT

Introduction Analysing Synthetic SeismogramsWith the widespread adoption of ambient noise tomography, and the increasing number of local earthquakes recorded worldwide due to dense seismic networks and many very dense temporary experiments, we consider it worthwhile to evaluate alternative methods to measure surface wave group velocity dispersions curves. Moreover, the increased comput-ing power of even a simple desktop computer makes it fea-sible to routinely use methods other than the typically em-ployed multiple �ltering technique (MFT). MFT is a robust technique and thus often a good choice to measure disper-sion. However, it involves a certain amount of averaging across frequencies. The measured dispersion curve may therefore be too smooth, or span across a too broad frequency range. While it still makes sense to use MFT for most applications, it is im-portant to know how strong the potential bias due to this av-eraging may be. To that end we perform tests with synthetic and observed seismograms using the Wigner-Ville distribution (WVD) frequency time analysis, and compare dispersion curves measured with WVD and MFT with each other.

References:Peterson, J., 1993. Observations and mod-elling of background seismic noise. Open-�le report 93-322, U. S. Geological Survey, Albuquerque, New Mexico

Contact:Simon Lloyd ([email protected])Dept. of Meteorology and GeophysicsAlthanstraße 14 (UZA II)1090 Vienna, AustriaZimmernummer: 2D508T: +43-1-4277-53722F: +43-1-4277-53799

• Both multiple �ltering and Wigner-Ville yield similar results when measuring group velocity dispersion.• MFT appears more robust over a wider frequency range.• Wigner-Ville is more sensitive and better constrains dispersion measurements.• The two methods may complement each other, whereby Multiple Filtering allows measuring dispersion over a wider frequency range and Wigner-Ville tells us about the true quality of the measurements.• Random noise is better suppressed in WV, potentially allowing better detection of events.

1) Dept. of Meteorology and Geophysics, University of Vienna, 2) Faculty of Engineering, University of [email protected]

Station Noise

We �rst compare MFT to Wigner-Ville (WV) on an observed teleseis-smic event. The measured dispe-rsion is similar for both methods. However, WV produces a sharper outline of group velocity dispe-rsion. WV may introduce some art-ifacts, which can be reduced by smoothing (across time and fr-equency). Even after smoothing the dispersion curve as outlined by the contours is still sharper than using MFT. To test the performance of WV we proceed using synthetic wav-eforms

The noise spectrum at seismic sta-tions is not �at, and the ampli-tudes can thus vary signi�cantly. We simulate best/worst case sce-narios using Peterson’s (1993) noise models obtained from glo-baly analysing measured noise (left). The synthetic noise has the same amplitude spectrum as Peterson’s (1993) hi and low noise models. Randomness is obtained from arbitrary phases asigned to each frequency (right).

The Multiple Filter Technique (MFT) was introduced by Dziewonski et al. in 1969, as a way to measure surface wave group velocities. Countless studies have used MFT to determine group velocity disper-sion curves of surface waves, which can be inverted for velocity structure. As im-plied by its name, the method requires �ltering the same trace multiple times. Typically these �lters are Gaussian shaped, and centred at the frequency for which group velocity is measured. After �ltering, the arrival time of the maximum of the envelope is picked and used together with epicentral distance to calculate group velocity at the re-spective periods. Doing this with several �lters, each centred at di�erent periods, allows determining dispersion curves.

To compare MFT and WV with each other we compuate a synthetic seismogram and measure the dispersion curve using both methods. The wave form is the vertical component of a Mw=3.2, 45° dip slip earthquake at 200 km distance using the PREM Earth model. We add random, but non-white noise to the sythnthetic waveforms with the amplitude spectra of the Peterson’s (1993) NLNM and NHNM. The resulting waveforms are shown on the right.We omit showing the noise free case in the dispersion measure-ments (below), as it is very close to the low noise model case. Simi-larly to the teleseismic event, both methods produce comparable dispersion curves. However, in the case where high noise is added to the synthetic waveform, the noise itself is more visible in the MFT plots than WV.

Conclusions

NLN

MN

HN

M

Seismogram + NLNM

Noise Free Seismogram

Seismogram + NHNM

True Amplitudes Normalised Amplitudes

T3-P13