Alternative Estimation Techniques for Global High-Degree Gravity
Modeling
Nikolaos K. Pavlis and Joseph C. Chan
Hughes STX Corp., 7701 Greenbelt Rd., Greenbelt, MD 20770, USA
e-mail: zmnkp@gibbs.gsfc.nasa.gov
Francis J. Lerch
Space Geodesy Branch, NASA/Goddard Space Flight Center, Greenbelt, MD, USA
ABSTRACT
High-degree (Nmax=360) gravitational models require surface gravity data to resolve the
fine structure of the field. Given a global gravity anomaly data set, one can extract this
information using either quadrature formulre (orthogonality relations) or by solving a
system of observation equations. Under certain conditions such a system yields a normal
matrix of block-diagonal structure. To determine accurately the lower part of the
spectrum requires the least-squares combination of the surface gravity information with a
satellite-only gravity model. Depending on the technique employed to develop the
sUrface gravity solution, the estimation of a combined model can be performed in
different ways.
We have used a global set of 30' mean gravity anomalies and a satellite-only model to
produce combination solutions using both quadratures and the block-diagonal adjustment
technique. In both cases the complete covariance matrix of the satellite-only model was
used. Global geoid height difference (to Nmax=360) between the two types of solution is
at the ± 20 cm level. The error spectra obtained from the two techniques are in excellent
agreement. The models from the two techniques perform equally well in orbit fit tests.
Absolute comparisons with GPSlLeveling-derived undulations over British Columbia and
the US indicated that the block-diagonal technique yields slightly better results. However,
relative GPSlLeveling undulation comparisons seem to indicate a problem with the
higher degree harmonics obtained from the block-diagonal technique which requires
further study.
INTRODUCTION
The development of global high-resolution models of the Earth's gravitational potential
currently relies on the combination of long wavelength information obtained from the
analysis of satellite tracking data, with short wavelength information from satellite
altimetry and surface (and airborne) gravimetry observations (Rapp, 1989).
The availability of more accurate tracking data due to a continuously expanding
constellation of Earth orbiters, has resulted in a remarkable improvement of the accuracy
and resolution of satellite-only gravitational models over the last thirty years. Presently,
satellite-only models extend to degree and order 70 and incorporate information from
over 30 satellites (Nerem et aI., this issue). Tracking data which have been used in the
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Modeling
Nikolaos K. Pavlis and Joseph C. Chan
Hughes STX Corp., 7701 Greenbelt Rd., Greenbelt, MD 20770, USA
e-mail: zmnkp@gibbs.gsfc.nasa.gov
Francis J. Lerch
Space Geodesy Branch, NASA/Goddard Space Flight Center, Greenbelt, MD, USA
ABSTRACT
High-degree (Nmax=360) gravitational models require surface gravity data to resolve the
fine structure of the field. Given a global gravity anomaly data set, one can extract this
information using either quadrature formulre (orthogonality relations) or by solving a
system of observation equations. Under certain conditions such a system yields a normal
matrix of block-diagonal structure. To determine accurately the lower part of the
spectrum requires the least-squares combination of the surface gravity information with a
satellite-only gravity model. Depending on the technique employed to develop the
sUrface gravity solution, the estimation of a combined model can be performed in
different ways.
We have used a global set of 30' mean gravity anomalies and a satellite-only model to
produce combination solutions using both quadratures and the block-diagonal adjustment
technique. In both cases the complete covariance matrix of the satellite-only model was
used. Global geoid height difference (to Nmax=360) between the two types of solution is
at the ± 20 cm level. The error spectra obtained from the two techniques are in excellent
agreement. The models from the two techniques perform equally well in orbit fit tests.
Absolute comparisons with GPSlLeveling-derived undulations over British Columbia and
the US indicated that the block-diagonal technique yields slightly better results. However,
relative GPSlLeveling undulation comparisons seem to indicate a problem with the
higher degree harmonics obtained from the block-diagonal technique which requires
further study.
INTRODUCTION
The development of global high-resolution models of the Earth's gravitational potential
currently relies on the combination of long wavelength information obtained from the
analysis of satellite tracking data, with short wavelength information from satellite
altimetry and surface (and airborne) gravimetry observations (Rapp, 1989).
The availability of more accurate tracking data due to a continuously expanding
constellation of Earth orbiters, has resulted in a remarkable improvement of the accuracy
and resolution of satellite-only gravitational models over the last thirty years. Presently,
satellite-only models extend to degree and order 70 and incorporate information from
over 30 satellites (Nerem et aI., this issue). Tracking data which have been used in the
111