Geodetic and geophysical results from a Taiwan airborne...

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


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


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


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).


Comparison with Surface Gravity Data

Crossover Analysis

Repeatability Analysis



Crossover 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


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 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: 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


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


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


Data reduction

Geoid Models From Airborne and Other Gravity Data

Bouguer Anomaly

Conclusions

Airborne Gravity Survey

Filtering of along-line values

Crossover Analysis



Numerical differentiation of position

Upward and downward continuation of gravity value


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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