Post on 20-Mar-2020
Theory and Results of Taiwan Airborne Gravity Survey
Speaker: Yu-tsung Lo
REFERENCE
Cheinway Hwang, Yu-Shen Hsiao, Hsuan-Chang
Shih, Ming Yang, Kwo-Hwa Chen, Rene Forsberg,
and Arne V. Olesen (2007) Geodetic and
geophysical results from a Taiwan airborne
gravity survey: Data reduction and accuracy
assessment. Journal of Geophysical Research, vol.
112, B04407.
Cheinway Hwang, Yu-Shen Hsiao, Hsuan-Chang
Shih (2006) Data reduction in scalar airborne
gravimetry: Theory, software and case
study in Taiwan. Computers & Geosciences 32,
1573-1584.
Taiwan’s terrain is complex and mostly
inaccessible for gravity survey.
Ministry of the Interior (MOI) of Taiwan
sponsored an airborne gravity survey over
the period of May 2004 to May 2005.
The field work and data reduction were
carried out by the National Chiao Tung
University (NCTU), Taiwan, and the National
Survey and Cadastre (KMS), Denmark.
INTRODUCTION
INTRODUCTION
Objective…
Accuracies of GPS-derived position, velocity, and
acceleration
Achievable accuracy and spatial resolution of
airborne gravity data
Methods for data reductions and applications to
downward continuation, geoid modeling, and
Bouguer anomaly modeling.
OUTLINE
Taiwan Airborne Gravity Survey
Data Reduction
Geoid Models
Bouguer Anomaly
Conclusions
OUTLINE
Taiwan Airborne Gravity Survey
Data Reduction
Geoid Models
Bouguer Anomaly
Conclusions
Taiwan Airborne Gravity Survey
Vehicle King-Air Beechcraft-200
Instrumen
t
L&R Air-Sea Gravity System II 1Hz/85m
Trimble 5700 GPS Receiver 2Hz
Altitude 5156 m
Velocity 306 km/hour
Period 43 days(May 2004 to March
2005)
Over 200
hours
GPS
stationsYMSM、PKGM、KDNM、FLNM
TMAM、KMNM、MZUM、SNAM
Planning…
N-S 64 lines/4.5km
E-W
22 lin
es/20k
m
NE-SW 10 lines/5km
OUTLINE
Taiwan Airborne Gravity Survey
Data Reduction
Geoid Models
Bouguer Anomaly
Conclusions
Data reduction
GPS Positioning of Aircraft
Correction of gravimeter time
Correction of gravimeter position
Resolvable Wavelength
Error Sources and Filtering
Accuracy Assessment of Airborne Gravity Anomaly
Downward Continuation
Data reduction / Positioning
Precise aircraft position, velocity, and acceleration
are critical to the success of an airborne gravity
survey.
GPSurvey solution (broadcast ephemeris of GPS)
Bernese 5.0 solution (IGS precise ephemeris of GPS)
Data reduction /Velocity & Acceleration
Data reduction /Velocity & Acceleration
At a given epoch tFor numerical differentiations, a user-supplied function for interpolations is needed.
m/s10-6
Data reduction / Accuracy Assessment
We select 10 sessions of airborne
GPS data for the assessment.
Each session of about 4 hours in
data length was divided into two
independently processed
subsessions with a 30-min
overlap.
Two subsessions
Phase ambiguitiesTropospheric parameters
One session
Power Spectral Density(PSD)
Long-wavelength error
xffS )(
In theory…
a standard error of 0.293 m in vertical position will translate to a standard error
in vertical velocity
in vertical acceleration2585.02414.0 ms
1414.02293.0 ms
※1 gal=1 cm/s2
Correction of gravimeter time
The correlation function between two signals s1 and s2 is
The gravimeter time associated with gravity readings comes
from the clock of the computer attached to the gravimeter,
and it will not be as accurate as the GPS time.
where is the lag.
The computation is carried out in the frequency domain as
This time interval is the resolution of the correction and is the maximum of the sampling intervals of the GPS time and the gravimeter time.
Correction of gravimeter position
The position determined by GPS refers to the GPS
antenna phase center.
Data reduction / Resolvable Wavelength
The achievable spatial resolution of airborne gravimetry depends on
data noise and flight altitude.
First, gravity anomaly can be expanded into a series of spherical harmonics as [Heiskanen and Moritz, 1985]
The global average power of gravity anomaly to degree K is defined as
For the anomaly degree variances, we adopt
※IEEE=Institute of Electrical and Electronics Engineers
The resolvable degree at
an altitude z is a K such that
The resolvable wavelength at z
is then [Seeber, 2003, p. 469]
1410which is the limit of precision in the IEEE
double-precision computing environment.
This wavelength will be
degraded by data noise.
[Seeber, 2003, p. 469]
Data reduction / Error Sources and Filtering
The basic formula for computing along-line gravity value at the flight altitude
The free-air gravity anomaly at z is computed by [Torge, 1989]
Normal gravity on a reference ellipsoid(GRS80)
The orthometric height(h) is determined by subtracting the geoidalheight of Hwang [1997] from the GPS-derived ellipsoidal height.
Eötvös effect
※Eötvös effect = formula correct for velocity relative to the Earth
Ignoring changes in gravimeter reading, airport gravity value, and off-levelcorrection, the differential change of gravity value
This relation can be used for computing accuracy requirements.
First computing the standard deviation of the differences between the raw and the initially filtered data.
If a difference exceeds three times of the standard deviation, the corresponding raw value is flagged as an outlier and its weight is reduced exponentially.
Further filtering is carried out with newly assigned data weights, and the filtering stops when no more outliers are found.
An ideal filter will be one that properly removes data noises while preserving
maximum gravity information - a iterative Gaussian filter
The filtered values is..
After some tests, it is decided to adopt a filter width of 150 s. This corresponds to a6-km spatial resolution (half wavelength).
Accuracy Assessment of Airborne Gravity Anomaly
Comparison with Surface Gravity Data
Crossover Analysis
Repeatability Analysis
Accuracy Assessment of Airborne Gravity Anomaly
Comparison with Surface Gravity Data
Crossover Analysis
Repeatability Analysis
Remove–restore procedure
GGM02C and EGM06 model are subtracted from the surface gravity values
Upward continued to the flight altitude
combined GGM02C and EGM06 model at z were then restored.
The differences caused by..
(1) Errors in airborne gravity
measurements
(2) Data density and quality of surface
gravity anomalies
(3) Large gravity gradients at areas of
rough gravity fields
(4) Possible computation error of upward
continuation
t
Accuracy Assessment of Airborne Gravity Anomaly Comparison with Surface Gravity Data
Crossover Analysis
Repeatability Analysis
A crossover difference is the difference of the two
gravity values at the intersection of two survey lines.
Least squares method →Observation equation
bias drift
Lines 18 and 54 were held fixed in the adjustment.
Given
Estimated-Given difference
Accuracy Assessment of Airborne Gravity Anomaly Comparison with Surface Gravity Data
Crossover Analysis
Repeatability AnalysisIn order to determine the airborne measurement repeatability and to identify the factors governing the repeatability, parts of lines 26 and 55.
Our filter width
Downward Continuation
Downward continuation of airborne gravity anomalies to sea level is needed for such applications as
Geoid modeling
Plate tectonic investigation
Orthometric correction
[cf. Moritz, 1980]
[cf. Buttkus, 2000]
Downward Continuation
Downward continuation: Fourier transform approach
Downward continuation: Least-squares collocation
Remove–restore procedure
GGM02C and EGM06 model are subtracted from the airborne gravity values
combined GGM02C and EGM06 model at z were then restored.
Downward continued to the sea level
(a)At flight
attitude(5156 m)
(b)At sea level (0
m)
(Unit:mgal)
OUTLINE
Taiwan Airborne Gravity Survey
Data reduction
Geoid Models
Bouguer Anomaly
Conclusions
Geoid Models
GGM02C+ EGM96 Prism method
※Prism method= Subtract Residual Terrain Model (RTM) gravity effect
Gravity anomaly (Δg)
Fourier transform Least-squares collocation
Terrain-assisted remove procedure
Terrain-assisted restore procedure
Stokes integral
KMS method NCTU methodResidual geoid grid
Geoid Models From Airborne and Other Gravity Data
The major improvement of current
geoid models over Hwang’s [1997]
model is in high mountains (the center
and south routes) where current land
gravity data are sparsely distributed
and geoid variation is large.
OUTLINE
Taiwan Airborne Gravity Survey
Data reduction
Geoid Models
Bouguer Anomaly
Conclusions
Bouguer Anomaly
Step 1: Interpolate the orthometric height at a surface point
Step 2: Compute the terrain effect using the same algorithm
Step 3: Subtract the terrain effect from Step 2 from the
downward-continued gravity to obtain Bouguer anomaly
at sea level.
Gauss quadrature method
Bouguer Anomaly
(Left)
At flight attitude(5156m)
(Right)
At sea level (0m)
OUTLINE
Taiwan Airborne Gravity Survey
Data reduction
Geoid Models From Airborne and Other Gravity Data
Bouguer Anomaly
Conclusions
Airborne Gravity Survey
Filtering of along-line values
Crossover Analysis
Repeatability Analysis
Correction of gravimeter time
Numerical differentiation of position
Upward and downward continuation of gravity value
Comparison with Surface Gravity Data
Bouguer Anomaly
Geoid Models Correction of gravimeter position
Data Reduction
Accuracy Assessment
Conclusions
Planning is NEW,
Result is GOOD,
Future will be BETTER.
Thanks for Your Attention!
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