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Analysis of high dimensional time series: Ocean bottom seismogram data

Analysis of high dimensional time series: Ocean bottom seismogram data

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Analysis of high dimensional time series: Ocean bottom seismogram data

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  1. Analysis of high dimensional time series: Ocean bottom seismogram data The Institute of Statistical Mathematics Genshiro Kitagawa Japan-US Seminar on Statistical Time Series Analysis June 22, 2001, Kyoto

  2. T. Takanami, H. Shimamura (Hokkaido University) S. Watanabe (Graduate Univ. for Advanced Study) (Schlumberger)

  3. Example Exploring Underground Structure by OBS (Ocean Bottom Seismogram) data T. Takanami and H. Shimamura Hokkaido Univ., Inst. Seismologyand Volcanology

  4. Exploring Underground Structure by OBS (Ocean Bottom Seismogram) Data Sea Surface OBS Bottom

  5. 4 Channel Time Series N=15360, 98239 series Experiment • Off Norway(Depth 1500-2000m) • 39 OBS, (Distance: 10-30km) • Air-gun Signal from a Ship (982 times: Interval 70sec., 200m) • Observation(dT=1/256sec., T =60sec., 4-Ch)

  6. 0 100 200 300 400 500 600 700 800 900 OBS-31 data K=982, N=15360

  7. Time Adjustment • Cross-Correlation • Locally stationary AR model

  8. Objectives Estimation of Underground Structure Detection of Reflection & Refraction Waves Estimation of parameters (hj, vj)

  9. t-p Transformation x: Epicentral distrance t;Travel time p: Slowness t: Origin travel time Slant Stacking

  10. Inverset-p Transformation Hilbert Transform Inverse of t-p

  11. h-v Transform(Hyperboric)

  12. t-p Trandform (OBS4)

  13. t-p Transform (OBS31)

  14. t-p Trandform (OBS4) 

  15. t-p filtering (OBS4)  0-150, 1-2000 150-320, 1-2000 320-400, 1-2000

  16. t-p filtering (OBS4) 320-400, 1-200 0-150, 601-1000 0-150, 400-1200 150-320, 1-200

  17. t-p filtering (OBS‐31)  Original 160-200, 1-3000 0-160, 1-3000

  18. Time-Varying AR model Model for the coefficients State Space Representation Power Spectrum

  19. Time-Varying Spectrum Ch-700 Ch-720 Ch-740 Ch-760

  20. Time-Varying Spectrum Ch-700 Ch-720 Ch-740 Ch-760

  21. Time series at hypocenter (D=0) Wave(011) Wave(00011) Wave(0) Wave(000) Wave(00000)

  22. Model for Decomposition Self-Organizing Model

  23. State Space Model

  24. State Vector Change of Variance Self-organizing SSM Self-organizing State Space Model

  25. Nonlinear Non-Gaussian State Space Model State Time Series Non-Gaussian System Noise Non-Gaussian Observation Noise

  26. Monte Carlo Filter System Noise Predictive Distribution Importance (Bayes) Factor Filter Distribution(by Resampling)

  27. Reflection Wave Direct Wave Tau 1 Tau 2 Decomposition of Ch-701 Observed

  28. Reflection Wave Direct Wave Decomposition of Ch-721 Observed

  29. Extracted Reflection Wave

  30. t-p Transform(OBS31-Reflection)

  31. Modeling Spatial-Temporal Structure • Correlation structure between adjacent series • Time-space model

  32. Modeling Space-Time Structure Multivariate Time Series Time Series Structure Relation Between Adjacent Series Time Series Model Spatial Model Spatio-Temporal Model

  33. Model of Propagation Path Parallel Structure Width Velocity

  34. Examples of Wave Path Wave(0) Wave(000) Wave(01) Wave(011) Wave(0121) Wave(000121) Wave(01221) Wave(012321) Wave(00012321)

  35. Time Series at Wave(0) Wave(000) Wave(00000)

  36. Velocity of Water Wavev0 a=-0.060

  37. Path Models and Arrival Times

  38. Assumed Parameters(Example)

  39. Path Models and Arrival Times Arrival Time(Sec.) ーD/6 Distance(km)

  40. Path models and arrival times(OBS4) Arrival Time (sec.) Distance (km)

  41. Spatial Filter k:Time-lag

  42. Spatial Model(Ignoring time series structure) Series j-1Series j : Time-lag=k

  43. Kalman-like Filter Initial Prediction Prediction Filter Filter

  44. Path Models and the Differences of the Arrival Times Between Adjacent Channels Epicentral Distance

  45. Local Cross-Correlation Function 場所 時間

  46. 8 7 6 5 4 3 2 1 0 Arrival Time -10 -8 -6 -4 -2 0 2 4 6 8 10 D: Distance Local Time Lag

  47. Estimation of Time Lag Log-likelihood Local log-likelihood

  48. OBS4 SHIFT=23

  49. OBS4 SHIFT=13 SHIFT=8 SHIFT=3