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Approaches to the infrasound Approaches to the infrasound signal denoising by using signal denoising by using
AR methodAR method
N. Arai, N. Arai, T. MurayamaT. Murayama, and M. Iwakuni, and M. Iwakuni
(Research Dept., Japan Weather (Research Dept., Japan Weather Association) Association)
2008 Infrasound Technology Workshop in Bermuda2008 Infrasound Technology Workshop in Bermuda
Table of ContentsTable of Contents
MotivationMotivation Denoising by using Denoising by using statistical modelsstatistical models Example of estimation resultExample of estimation result Conclusion and future planConclusion and future plan
MotivationMotivation Wind and other background noise are Wind and other background noise are
included in the Observed Infrasound Dataincluded in the Observed Infrasound Data
Therefore,…Therefore,…• It is difficult to detect exactly arrival time of signalIt is difficult to detect exactly arrival time of signal• The signal of small amplitude may not be detected The signal of small amplitude may not be detected
And then,…And then,…• We want to see pure signal each event sourceWe want to see pure signal each event source
We need remove the background noise !!We need remove the background noise !!
Way to denoising of infrasound data ?Way to denoising of infrasound data ?
Noise Noise bandband
Signal Signal bandband
Signal Signal bandband
Noise Noise bandband
Limit of the frequency Limit of the frequency decomposition filterdecomposition filter
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< CASE 1 >< CASE 1 >
< CASE 2 >< CASE 2 >
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Observed Observed
Noise Noise
Signal Signal
Undetectable Undetectable levellevel
Detectable Detectable levellevel
Need other Need other Denoising metodDenoising metod
Image of the Denoising and the Extraction of Image of the Denoising and the Extraction of Infrasound SignalInfrasound Signal
Observed Infrasound Data Observed Infrasound Data WaveformWaveform
Background Noise WaveformBackground Noise Waveform
Infrasound Signal Infrasound Signal WaveformWaveform
If we Subtract Noise data from Obs. data, we can get signal !?If we Subtract Noise data from Obs. data, we can get signal !?
- (minus)
= (equal)
Process flow diagram of the Denoising and ExProcess flow diagram of the Denoising and Extraction of signaltraction of signal
Step 1: Trend RemovalStep 1: Trend Removal
Step 2: Estimation of the Background Noise WaveformStep 2: Estimation of the Background Noise Waveform
Step 3: Extraction of the Infrasound Signal WaveformStep 3: Extraction of the Infrasound Signal Waveform
Step 1: Trend RemovalStep 1: Trend Removal
Polynomial trend modelPolynomial trend model
mnmn
nnn
xaxaat
wty
...110
TrendTrend
Observed Observed Infrasound Infrasound WaveformWaveform
Infrasound Infrasound WaveformWaveform removedremoved TrendTrend
Noise Noise areaarea
Signal + Noise areaSignal + Noise area
Noise areaNoise area
Step 2: Estimation of the Step 2: Estimation of the Background Noise WaveformBackground Noise Waveform
m
ininin vyay
1
Estimated Estimated Background Background Noise Noise WaveformWaveform
Signal arrival time: decide by Signal arrival time: decide by AIC (Akaike Information Criterion)AIC (Akaike Information Criterion)
Estimation of State Space model by using Estimation of State Space model by using AR (AR (AAutoutoRRegressive) methodegressive) method
Estimation of time series by using Estimation of time series by using Kalman filterKalman filter
mm: Order of AR model: Order of AR modelaa: AR cofficents: AR cofficentsvv: white noise (N(0,tau: white noise (N(0,tau22))))
Infrasound Infrasound Waveform Waveform RemovedRemoved TrendTrend
Step 3: Extraction of the Step 3: Extraction of the Infrasound Signal WaveformInfrasound Signal Waveform
- (minus)
= (equal)
Pure Pure SignalSignal
Observed Observed Infrasound Data Infrasound Data WaveformWaveform
Background Nise Background Nise WaveformWaveform
Infrasound Infrasound signal signal WaveformWaveform
If we Subtract Noise data from Obs. data, we can get pure signal If we Subtract Noise data from Obs. data, we can get pure signal
Ex. 1: Extraction of Infrasound Ex. 1: Extraction of Infrasound signal generated by earthquakesignal generated by earthquake
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___ Observed DATA
___ Trend
___ Time series removed trend
___ Estimated Noise data
___ Extracted Infrasound data
Co-sisemicCo-sisemic Infrasound Infrasound phasephase
< Step 1 >
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Ex.2: Extraction of Infrasound Ex.2: Extraction of Infrasound signal generated by - lightning signal generated by - lightning
flashes -flashes -
Amplitude of denoised signal is bigger than frequency decomposition signalAmplitude of denoised signal is bigger than frequency decomposition signal
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___ Observed DATA
___ Trend
___ Time series removed trend
___ Estimated Noise data
___ Extracted Infrasound data
< Step 1 >
< Step 2 >
< Step 3 >
Conclusions and future Conclusions and future planplan
We have only begun to study the denoising of InfrWe have only begun to study the denoising of Infrasound monitoring data by using asound monitoring data by using statistical modstatistical models (AR model, State space model, Kalman filterels (AR model, State space model, Kalman filter…)…)
We really do not understand a effect of the denoiWe really do not understand a effect of the denoising by using statistical models at this timesing by using statistical models at this time
In order to clear a effect of the denoising, we will In order to clear a effect of the denoising, we will give in-depth consideration to give in-depth consideration to statistical models statistical models by using more events databy using more events data
Thank Thank you !you !