Recovering Temporal Integrity with Data Driven Time Synchronization

1. Recovering Temporal IntegritywithData Driven Time Synchronization Martin Lukac CENS Seminar December 05, 2008

2. 50 standalone Caltech sites 62 wirelessly connected UCLA sites MesoAmerican Subduction Experiment MASE – 2005 to 2007 Wireless Seismic Array 500 Km - Stations 5-10 Km 3 Channels 24 bit -100Hz Keep all data 802.11b Directional antennae Splitters

3. Fix offset data?

4. Offset source Find offset with linear fit of event arrivals 20 stations had problem for 6 months average Up to 10% of data is incorrectly time stamped Typical drift without GPS: A few seconds a month Offsets in our data: 10’s seconds to 1000’s of seconds Reboot/reconfigure with disconnected/broken/misconfigured GPS Plots by R. Clayton

5. Data Driven Time Synchronization Use characteristics of the data Enable time correlation Fix time offsets Requires model of the characteristic Apply model Derive time correction shift Independent characteristic

6. Microseisms Microseisms, they are so hot right now Wave energy that travels through the crust Can see everywhere with broadband seismometer 3 to 30 second period 6 second period highest energy 16-22 second period next highest Opposing ocean surface waves Generated by weather Create pressure on ocean floor Correct depth + correct interference pattern + correct ocean floor = microseisms

7. Microseisms

8. Microseism Model Use microseisms to repair offset Model microseisms propagation - travel time Determine travel times with good data Apply travel times to bad data Correction shift

9. Computing Travel Time Cross-correlation: Dot product of two signals at different lags Measures similarity of signals at different offsets Tells us how signals line up: Peak of cross-correlation is the travel time

10. Computing Travel Time

12. Microseism Cross Correlation Larger data windows Better peaks Changing nature of microseisms creates randomness in signal for better cross correlation

13. Microseism Modeling Challenges Cross correlation provides travel time Microseism sources Affects travel time Velocity between stations Affects travel time Noise Affects travel time

14. Microseism Sources Weather changes: Pattern of interference changes ‘Sources’ of microseism change Can not just d/v=t Sources during ‘good time’ Different from source during offset time

15. Bias Receiver line Sources dA,B Station A Station B Microseism Sources With multiple random sources, only sources along receiver line stack constructively If pattern of sources on either side of receiver line is non-random, then from one day to the next travel times do not represent straight line time between stations -> introduce bias

16. Bias Receiver line Sources dA,B Station A Station B Microseism Sources Large windows of time -> off receiver line sources cancel out Shorter windows of time -> not enough sources to be random, so there is a bias which affects the phase and the travel time of the microseism The challenge is determining the bias

17. Microseism Noise Noise is good: Cross correlations work better Noise is bad: Larger window, averages more sources together so off receiver line sources cancel

18. Microseism Noise Large windows (360 days): Signal is only from sources along the receiver line Applying travel time from large window introduces error Short windows (1 day): Much more variance in travel time due to bias More error + less pronounced peaks in cross correlation The challenge is choosing the correct window size

19. Microseism Velocity Structure of crust varies Velocity between stations: Constant over time Different across array Can not just say 3 Km/s v4 v3 v2 v1

20. Model Details & Correcting Time

21. Model Processes Overview 4 Stations -> A, B, C, D First 12 months, no problems Month 13 station B has time offset Cross correlate all station pairs for first 12 months to find 6 second S to N microseisms and obtain parameters Cross correlate all station pairs for month 13 Time offset will show up as bad travel time for pairs with station B Use parameters to obtain time correction shift forstation B A B C D

22. Why does the model work? New observation: For nearly aligned station pairs, time series of daily travel times between pairs fluctuates up to two seconds The fluctuations are correlated with one another

24. Obtaining a Correction Suggest a common bias in the arriving energy Implies the bias in the sources is in the far-field because it is common-mode across the array Can use signal to fine tune the predicted travel time for station B

25. Microseism Propagation Model The model describes the phase change from biased energy introduced to the averaged energy traveling along the receiver line of two stations. Knows (constants): tt = travel time d = distance v = velocity T = angle between stations Unknowns (we solve for these): S = fraction of energy off receiver line θ= direction of off receiver line energy f = offset parameter

26. Computing Constants Know distance, angle between stations Velocity: Want accurate straight line measurement so we need to use large cross correlation window so there is no direction bias 360 day cross correlation windows

27. Velocity Computation Bandpass filter data around 6 second period Use sign bit method to remove large amplitude events: signal > 0, set value to 1 signal <= 0, set to 0 Cross correlate, choose phase peak from correlogram as travel time, divide into distance

28. Phase Peak vs. Group Peak

29. Phase Peak vs. Group Peak

30. Solving for parameters Have all constants now use model to derive S, θ, f during good month Use 24 hour cross correlation windows over one month to get travel times (filter data and use sign bit method) Gives us over determined set of equations: One θ per day One S per day One f per station pair 10 days, 5 station pairs = 10 θ’s, 10 S’s, 5 f’s, 50 tt’s 15 unknowns for 50 equations Non linear least squares

31. Predict Travel Time

32. Solving for parameters Have parameters for ‘good’ month. For bad month, do same process to get daily S’s and θ‘s Use ‘f’ from previous month Put all together to predict travel time for broken station The travel time provides the time offset shift

33. Evaluation Ground truth by faking time offsets in known good data: how well can we repair it • Pick one month to obtain parameters • Pick second month and ‘break’ one station pair • Use model + parameters to predict travel time for broken station pair • Compute RMSE of predicted travel time • Repeat 10x for random selection of station pairs Compute mean and stddev across 10 runs

34. Results With right selection of stations, always less than 0.2

35. Earthquake Localization How does error in time correction affect earthquake localization? Use multilateration on arrival of earthquake Pick one station and change arrival time to see how it affects the localization

37. Earthquake Localization

38. Earthquake Localization + - 1 second offset in 0.05 second increments

39. Results to Come How do time offsets affect other Allen Huskers’s deep tomography velocity model Comparison of our correction method to others: Eye ball data alignment using major events Some function of arrival time of major events Allen’s deep tomography velocity model can predict arrival times of events

40. We Can Do Better! Want to reach 0.05 second RMSE Understand where pattern/fluctuations are coming from – Trying to correlate with weather Understand where sources of the microseisms are – Trying alternate methods to get bearing on sources

41. Piles of weather data Wave height, wave period, wave direction, wind magnitude, wind direction

42. Wind Magnitude over March 20063 hour increments

43. Correlation with Weather How does this patter correlate with changing weather features?

44. Correlation with Wind Magnitude Best correlation is above .5 Correlation can reach above .6 with linear combination of regions

45. Correlation with Wave Period

46. Wind to Travel Time Correlation Red line is linear combination of two regions and then scaled to fit on this plot The correlation to the other lines is about .61