Approaches to the infrasound signal denoising by using AR method

1. Approaches to the infrasound signal denoising by using AR method N. Arai, T. Murayama, and M. Iwakuni (Research Dept., Japan Weather Association) 2008 Infrasound Technology Workshop in Bermuda

2. Table of Contents • Motivation • Denoising by using statistical models • Example of estimation result • Conclusion and future plan

3. Motivation • Wind and other background noise are included in the Observed Infrasound Data Therefore,… • It is difficult to detect exactly arrival time of signal • The signal of small amplitude may not be detected And then,… • We want to see pure signal each event source We need remove the background noise !! Way to denoising of infrasound data ?

4. Noise band Signal Observed Noise Power spectrum Power spectrum Signal band f f Signal band Noise band ??? Power spectrum Power spectrum f f Limit of the frequency decomposition filter < CASE 1 > Detectable level filtering < CASE 2 > Undetectable level Need other Denoising metod filtering

5. Image of the Denoising and the Extraction of Infrasound Signal Observed Infrasound Data Waveform - (minus) Background Noise Waveform = (equal) Infrasound Signal Waveform If we Subtract Noise data from Obs. data, we can get signal !?

6. Process flow diagram of the Denoising and Extraction of signal Step 1: Trend Removal Step 2: Estimation of the Background Noise Waveform Step 3: Extraction of the Infrasound Signal Waveform

7. Step 1: Trend Removal • Polynomial trend model Trend Observed Infrasound Waveform Infrasound WaveformremovedTrend

8. Noise area Noise area Signal + Noise area Step 2: Estimation of the Background Noise Waveform Signal arrival time: decide by AIC (Akaike Information Criterion) Infrasound Waveform RemovedTrend Estimated Background Noise Waveform Estimation of time series by using Kalman filter Estimation of State Space model by using AR (AutoRegressive) method m: Order of AR model a: AR cofficents v: white noise (N(0,tau2))

9. Pure Signal Step 3: Extraction of the Infrasound Signal Waveform Observed Infrasound Data Waveform - (minus) Background Nise Waveform = (equal) Infrasound signal Waveform If we Subtract Noise data from Obs. data, we can get pure signal

10. Ex. 1: Extraction of Infrasound signal generated by earthquake < Step 1 > ___ Observed DATA ___ Trend < Step 2 > ___ Time series removed trend ___ Estimated Noise data < Step 3 > ___ Extracted Infrasound data Infrasound phase Co-sisemic

11. Ex.2: Extraction of Infrasound signal generated by - lightning flashes - < Step 1 > ___ Observed DATA ___ Trend Amplitude of denoised signal is bigger than frequency decomposition signal < Step 2 > ___ Time series removed trend ___ Estimated Noise data < Step 3 > ___ Extracted Infrasound data

12. Conclusions and future plan • We have only begun to study the denoising of Infrasound monitoring data by using statistical models (AR model, State space model, Kalman filter…) • We really do not understand a effect of the denoising by using statistical models at this time • In order to clear a effect of the denoising, we will give in-depth consideration to statistical models by using more events data

13. Thank you !