Local Geoid Determination from GRACE Mission
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Date
2002-02
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Publisher
Ohio State University. Division of Geodetic Science
Abstract
An analysis is made about the feasibility of using in-situ GRACE measurements for
local gravity field determination as an alternative to global solution methods, which
yield solutions in terms of spherical harmonic coefficients. The method investigated is
based on integral inversion aided with regularization techniques. The observables
considered are potential differences (DT) and gravity disturbance differences (DGD).
Both observables are affected by position, velocity and acceleration errors. With
respect to position errors, the higher precision requirement is in relative position for
DT, which requires about 1 cm of absolute positional accuracy to produce 0.01 m2/s2
error. For velocities, the higher precision requirement is in relative velocity for both DT
and DGD. The observable DT required the higher precision 10−5 mgal in relative
acceleration.
The disturbing potential T at the Earth’s surface, assumed to be a sphere, can be
obtained from values of DT and DGD given at satellite’s altitude. The process turns out
to be ill-posed mainly due to gravity field attenuation at the operative altitude of the
GRACE mission (300-500 km).
Data error requirements are very demanding for downward continuation of both DT and
DGD. The Tikhonov regularization method was applied for the following configuration: a
grid of 0°.8 sampling interval for a 24° square area at 400 km altitude. Measurement
errors smaller than 1x10−5 m2/s2 in DT are required to achieve solution errors of the level
of 1 m2/s2 and with a relative error of about 10%. However, this increased to only 3 m2/s2
with 0.01 m2/s2 measurement error. It is found that model errors due to discrete and finite
sampling cause large mean solution errors.
The principal inversion methods employed were the Tikhonov, singular value
decomposition, the conjugate gradient and the 1-D fast Fourier transform (FFT) method.
Their performance was compared using simulations by employing three test areas with
the same configuration described above, but different geographical location. The
regularization methods were applied for both DT and DGD observables Overall, the
Tikhonov method performed better than the other methods. For the above configuration,
T was obtained with about 2.5 m2/s2 precision neglecting the mean error.
In the search of the best regularization parameter (α ), the L-curve method, which can be
applied to the Tikhonov, DSVD and the 1D-FFT, combined with Tikhonov, methods,
was analyzed and yielded good results when considering only random errors in the
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measurements. However, when considering model errors, the method did not produce
satisfactory results. A geometry adaptive method was formulated to find the best α . The
method consists of determining a k factor that relates the residual norm related to the
corner of the L-curve with the residual related to the best α .
Finally, the Tikhonov regularization combined with B-spline smoothing was applied. The
method yielded smaller solution errors using the above configuration. The solution errors
obtained were about 1.2 and 1.1 m2/s2 for 1°.2 resolution using DT and DGD,
respectively. The corresponding relative error was about 10%. This could potentially
produce about 10 cm geoid for about 150 km resolution. All simulations were made using
the geopotential model EGM96.
Description
This report was prepared by Ramon V. Garcia Lopez, a graduate research
assistant, Department of Civil and Environmental Engineering and Geodetic Science,
under the supervision of Professor Christopher Jekeli.
The research documented in this report was supported by a grant from the Center for Space Research, University of Texas, Austin; Contract No. UTA98-0223.
This report was also submitted to the Graduate School of The Ohio State University as a dissertation in partial fulfillment of the requirements for the PhD degree.
The research documented in this report was supported by a grant from the Center for Space Research, University of Texas, Austin; Contract No. UTA98-0223.
This report was also submitted to the Graduate School of The Ohio State University as a dissertation in partial fulfillment of the requirements for the PhD degree.