Airborne Gravity Airborne Gravity Data Processing Data Processing Sandra Preaux May 2016 7701 Greenbelt Rd., Suite 400 Greenbelt, MD 20770 [email protected]
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Airborne Gravity Airborne Gravity Data ProcessingData Processing
Sandra PreauxMay 2016
7701 Greenbelt Rd., Suite 400Greenbelt, MD [email protected]
• Data & Metadata• Processing– Re-computing Raw Gravity– Corrections• Timing• Aircraft Motion• Tilt• Drift
– Filtering & Trimming–What’s not included
• Troubleshooting
Data: What is Collected
• Positioning System– GPS in Gravimeter– GPS in IMU– GPS Base Station
• Orientation System– IMU– Gravimeter Platform
• Gravimeter Sensor Data• Meta
– Absolute Gravity Tie– Lever Arm
• GPS antenna to Gravimeter • GPS antenna to IMU
– Height of Gravimeter above Tie
IMU GPS Antenna
GravimeterAbsolute Gravity Tie
Data: Aircraft• Time– GPS does not adjust for leap
seconds– Learn more about GPS vs UTC
or find out when leap seconds have been applied at http://tycho.usno.navy.mil/leapsec.html
– Common data rates• 1, 10, 20, 100 Hz
• Position– X, Y, Z
• Referenced to Earth center and rotation rate
– Latitude, Longitude, Height• Referenced to an ellipsoid
– Velocity and Acceleration
• Orientation– Rotation
• Pitch, Roll Yaw• From IMU or Avionics
– Rotation Rate– Horizontal and Vertical
Acceleration
Data: Gravimeter• Sensor– Raw Gravity• Spring Tension, Beam Position & Cross Coupling• Restoring force
– Calibration Factors• Environment– Temperature– Pressure– Ambient and in sensor box
• Platform– Horizontal Accelerometers (Cross and Long)– Calibration Factors
Data: Meta Data• For Each Installation or Airport– Lever Arms• GPS to Gravimeter• GPS to IMU• Gravimeter to IMU
– Vertical distance from gravimeter to tie Spot– Gravity and vertical gradient at tie spot
• Each Flight– Still readings pre- and post-flight– Start and end times of each data track–Winds and turbulence– Pilot actions: deicing, trim adjustments, etc.
• Data & Metadata• Processing– Re-computing Raw Gravity– Corrections• Timing• Aircraft Motion• Tilt• Drift
– Filtering & Trimming–What’s not included
• Troubleshooting
Processing
• Complicated by– Instrumentation issues– Timing issues– Positioning issues– Aircraft motion through a rotating
curvilinear coordinate system– Discrete computation– Variable aircraft and gravimeter
orientation– Noise
Processing: Raw Gravity
•
Processing: Aircraft Motion
• Variation in rotation rate Earth is very small• Eötvös correction – the vertical component of the Coriolis and centrifugal terms.– Varies with latitude, altitude, speed and heading– Simplified formula is often used for low and slow airborne or
marine surveys
• 1st term is the acceleration of the aircraft computed as the 2nd derivative of position
CoriolisCentrifugal
Eötvös CorrectionEast West
Derivatives
Derivatives1st derivative
order formal error sin test sin+0.005 spike sin+0.001 spike
2 8.333E-02 2.378E-01 5.006E-03 1.028E-03
4 1.667E-02 1.877E-04 6.719E-03 1.344E-03
6 3.571E-03 1.587E-07 7.650E-03 1.530E-03
8 7.937E-04 1.392E-10 8.255E-03 1.651E-03
10 1.804E-04 1.793E-12 8.688E-03 1.738E-03
12 4.163E-05 1.756E-12 9.017E-03 1.803E-03
14 9.713E-06 1.880E-12 9.278E-03 1.856E-03
16 2.285E-06 1.890E-12 9.492E-03 1.898E-03
18 5.413E-07 2.071E-12 9.672E-03 1.934E-03
20 1.877E-08 1.916E-12 9.825E-03 1.965E-03
Derivatives2nd derivative
order formal error sin test sin+0.005 spike sin+0.001 spike
2 8.333E-02 8.988E-03 1.732E-02 3.464E-03
4 1.111E-02 4.730E-06 2.216E-02 4.432E-03
6 1.786E-03 2.999E-09 2.445E-02 4.890E-03
8 3.175E-04 5.317E-12 2.580E-02 5.159E-03
10 6.013E-05 4.934E-12 2.668E-02 5.337E-03
12 1.189E-05 4.962E-12 2.732E-02 5.463E-03
14 2.428E-06 5.044E-12 2.779E-02 5.558E-03
16 5.078E-07 5.155E-12 2.816E-02 5.632E-03
18 1.083E-07 5.314E-12 2.845E-02 5.691E-03
20 1.083E-07 5.630E-12 2.870E-02 5.739E-03
Processing: Timing Issues• GPS and gravimeter readings have a sub-second
difference in timing.• GPS time is offset from UTC• Even in smooth conditions most of the measured vertical
acceleration (gRaw) is due to aircraft motion (aaircraft).– >95% in some segments– Routinely >85%
• Methods– Cross-Covariance Analysis to find the best delay to 0.01
seconds• For each 4 minute window during the flight • For each data track
Processing: Timing Issues
Processing: Tilt
•
Processing: Tilt
• Two ways to correct– Derive θ • using platform accelerometers and GPS derived
horizontal accelerations• using GPS derived horizontal accelerations and
platform control loop or damped pendulum model
– Use the difference in the sum of accelerations between the airplane and the meter to directly compute the correction
Processing: Tilt
Processing: Drift• To re-compute or not to re-compute still readings– Still readings are not so still (or how to pick a point)– Constant, linear or other drift model
• What is in the soup?
– Instrument drift– Earth tide– ???
Processing: Drift
Processing: Drift
• Data & Metadata• Processing– Re-computing Raw Gravity– Corrections• Timing• Aircraft Motion• Tilt• Drift
– Filtering & Trimming–What’s not included
• Troubleshooting
Processing: Filtering & Trimming
• Frequency Domain Filters–Must trim tracks first– Discrete FFT and IFFT
• Time Domain Filters– Trim after– Requires convolution
• Geographic Domain Filters–Must trim tracks first – Requires conversion to equal spatial distribution– Geophysical relevance
Processing: Filtering & Trimming
• Data & Metadata• Processing– Re-computing Raw Gravity– Corrections• Timing• Aircraft Motion• Tilt• Drift
– Filtering & Trimming–What’s not included
• Troubleshooting
Processing: Other Considerations
What we don’t correct – Variable rate of Earth’s rotation– Sensor temperature & pressure variation– Acceleration due to rotation of platform– Filter attenuation
Processing: Variability in Earth’s Rotation Rate
make dt equal one day, radius of the earth 6371000m and for an acceleration of 1 mGall1-l2=15.126 seconds
for acceleration of 0.1 mGal, l1-l2=1.513 seconds
Length of day variations are, in reality only, 2 or 3 ms,
So, consider l1-l2=5ms,
Then at the equator, arot = 3.3e-4 mGal
Clarkplanetarium.org
• Data & Metadata• Processing– Re-computing Raw Gravity– Corrections• Timing• Aircraft Motion• Tilt• Drift
– Filtering & Trimming–What’s not included
• Troubleshooting
Troubleshooting
Or Why we process in the field– Instrument Issues• Timing and control electronics• Temperature, pressure• Cables: GPS, Power, Data• Data Cards
– Aircraft• Autopilot: heading hunt, porpoise, roll, old• Vibration (particularly in twin engine aircraft)• Pilots
• Now on to quality assessment….
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