Recovering Temporal Integrity with Data Driven Time Synchronization

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Recovering Temporal IntegritywithData Driven
Time Synchronization

• Martin Lukac
• CENS Seminar
• December 05, 2008

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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

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Fix offset data?
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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
• 10s seconds to 1000s of seconds
• Reboot/reconfigure with
• disconnected/broken/misconfigured GPS

Plots by R. Clayton
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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

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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

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Microseisms
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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

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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

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Computing Travel Time
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Microseism Cross Correlation

• Larger data windows
• Better peaks
• Changing nature of microseisms creates
• randomness in signal for better
• cross correlation

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Microseism Modeling Challenges

• Cross correlation provides travel time
• Microseism sources
• Affects travel time
• Velocity between stations
• Affects travel time
• Noise
• Affects travel time

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Microseism Sources

• Weather changes
• Pattern of interference changes
• Sources of microseism change
• Can not just d/vt
• Sources during good time
• Different from source during
• offset time

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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 -gt introduce bias

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Microseism Sources

• Large windows of time -gt off receiver line
  sources cancel out
• Shorter windows of time -gt 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

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Microseism Noise

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

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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

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Microseism Velocity

• Structure of crust varies
• Velocity between stations
• Constant over time
• Different across array
• Can not just say 3 Km/s

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v3
v2
v1
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• Model Details
• Correcting Time

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Model Processes Overview

• 4 Stations -gt 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
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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

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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

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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
• ? direction of off receiver line energy
• f offset parameter

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Microseism Propagation Model

• Bias consists of energy that constructively
  interferes along the receiver path (the normal
  assumption) combined with a fraction S (lt1) that
  arrives off-path at an angle Theta
• By adding two phasors one with unity amplitude
  and phase given by the travel time delay and a
  second, with amplitude S and phase determined by
  the incident angle, we can predict the travel
  times

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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

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Velocity Computation

• Bandpass filter data around 6 second period
• Use sign bit method to remove large amplitude
  events
• signal gt 0, set value to 1
• signal lt 0, set to 0
• Cross correlate, choose phase peak from
  correlogram as travel time, divide into distance

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Phase Peak vs. Group Peak
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Computing Travel Time
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Phase Peak vs. Group Peak

• Cross correlation provides phase
• velocity and group velocity
• Group velocity is the velocity of the packet of
  energy containing the 6 second period oscillation
• Phase velocity is the velocity of the phase for
  the 6 second period oscillation within the group
• Choosing the max peak is an approximation of the
  group velocity only accurate when collides with
  envelope peak

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Phase Peak vs. Group Peak

• Phase velocity is faster than
• the group velocity
• Phases move earlier in time with increasing
  distances
• Cycle skips occur after the phase arrival peak
  has moved y one period earlier than the group
  peak
• Shows up as 6 second travel time jump across the
  array

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Phase Peak vs. Group Peak

• How often does the cycle skip happen?
• Phase period 6 seconds
• Group velocity 2.5 Km/s
• Phase velocity 3.0 Km/s
• Get D 90Km

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Phase Peak vs. Group Peak
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Phase Peak vs. Group Peak
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Solving for parameters

• Have all constants now use model to derive S, ?,
  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 ? per day
• One S per day
• One f per station pair
• 10 days, 5 station pairs 10 ?s, 10 Ss, 5 fs,
  50 tts
• 15 unknowns for 50 equations
• Non linear least squares

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Predict Travel Time
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Solving for parameters

• Have parameters for good month.
• For bad month, do same process to get daily Ss
  and ?s
• Use f from previous month
• Put all together to predict travel time for
  broken station
• The travel time provides the time offset shift

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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

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Results

• With right selection of stations, always less
  than 0.2

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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

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Earthquake Localization
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Earthquake Localization
- 1 second offset in 0.05 second increments
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Results to Come

• How do time offsets affect other Allen Huskerss
  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
• Allens deep tomography velocity model can
  predict arrival times of events

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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

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Piles of weather data

• Wave height, wave period, wave direction, wind
  magnitude, wind direction

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Wind Magnitude over March 20063 hour increments
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Correlation with Weather

• How does this patter correlate with changing
  weather features?

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Correlation with Wind Magnitude

• Best correlation is above .5
• Correlation can reach above .6 with linear
  combination of regions

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Correlation with Wave Period
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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

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Wave-Wave Interaction Intensity

• Following others works
• Can combine
• wave direction
• wave height
• wave period
• bathymetry
• To obtain wave-wave interaction
• The correlate with patter to try and find sources