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 Motivation Denoising by using statistical models Denoising by using statistical models Example of estimation result Example of estimation result Conclusion and future plan Conclusion and future plan

3. Motivation Wind and other background noise are included in the Observed Infrasound Data Wind and other background noise are included in the Observed Infrasound Data Therefore, … Therefore, … It is difficult to detect exactly arrival time of signal It 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 source 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 band Noise band Limit of the frequency decomposition filter f Power spectrum f f ??? filtering filtering f Power spectrum Observed Noise Signal Undetectable level Detectable level Need other Denoising metod

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

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 Polynomial trend model Trend Observed Infrasound Waveform Infrasound Waveform removed Trend

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

9. Step 3: Extraction of the Infrasound Signal Waveform - (minus) = (equal) Pure Signal Observed Infrasound Data Waveform Background Nise Waveform 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 ___ Observed DATA ___ Trend ___ Time series removed trend ___ Estimated Noise data ___ Extracted Infrasound data Co-sisemic Infrasound phase

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