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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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

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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

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ininin vyay

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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

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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

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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 !