development of state-of-the-art models include optical data, radio Doppler and radio
interferometry observations, Satellite Laser Ranging (SLR), DORIS and
satellite-to-satellite tracking data from the GPS constellation to low Earth orbiters.
Despite these advances, these tracking data types are incapable of resolving the fine
structure of the field, due to the attenuation of the gravitational signal with altitude.
Moreover, the available satellites do not sample uniformly the range of inclinations; this
causes strong correlation among coefficients of higher degrees and necessitates the use of
a priori constraints in the development of such models (Lerch et al., 1979).
Satellite altimetry has enabled an unsurpassed mapping of the field over the oceans,
both in terms of accuracy and in terms of resolution. TOPEX/POSEIDON (Fu et aI.,
1994) provides measurements of the sea surface which, for the first time, are not
significantly contaminated by radial orbit error (RMS radial orbit error at the 3.5 cm
level). However, altimetric measurements are confined over the ocean areas bounded by
the satellite's inclination, and furthermore provide a mapping of the sum of the geoid
undulation plus the Sea Surface Dynamic Topography (SSDT). These aspects weaken the
contribution of altimeter data in the determination of the long wavelength gravitational
signal and necessitate the appropriate modeling of the SSDT when altimeter data are used
in combination solutions for the gravitational field.
Surface gravimetry is in principle capable of resolving both long and short wavelength
features of the gravity field. This however requires uniform global coverage with dense
gravity data of uniformly high accuracy. Unfortunately, because surface gravimetry is an
expensive and time consuming process, the best available data at present (Kenyon and
Pavlis, this issue) represent information derived from over 4000 sources of detail gravity
data collected over several decades. Even in this comprehensive compilation of most land
gravity material presently available, the accuracy and density of point data vary
substantially with geographic region, with extended regions (e.g., Antarctica) being
practically void of gravity measurements. Airborne gravity surveys have demonstrated
their ability to provide rapid and accurate gravity coverage over areas that are difficult to
access such as Greenland (Forsberg and Brozena, 1993), and are expected to provide
similar improvement over the Antarctic in the future. Gravity anomaly data from different
sources may also have different systematic errors associated with them (Heck, 1990).
These systematic errors, in conjunction with the non uniformity of coverage, degrade the
long wavelength integrity of the gravitational information which can be extracted from
surface gravimetry. Nevertheless, surface gravimetry presently provides the only data that
can resolve short wavelength gravity features over land. In addition, ship borne gravity
measurements aid the separation of the geoid from the SSDT signal when used in
combination with satellite altimetry.
The complimentary character (both in a spectral as well as in a geographic sense) of
satellite tracking, altimetry and surface gravimetry data, enables the determination of the
gravitational field in combination solutions, over a wider band of its spectrum, with
improved accuracies than can be obtained by using any of the three data types alone.
ESTIMATION TECHNIQUES
The major factors influencing the choice of an estimation technique for the development
of a high-degree combination solution are: 1) the available computer resources, 2) the
treatment of satellite altimeter data, and 3) the availability of (near) global gravity
anomaly databases in gridded form. An ideal estimation strategy can be outlined as
follows:
112
interferometry observations, Satellite Laser Ranging (SLR), DORIS and
satellite-to-satellite tracking data from the GPS constellation to low Earth orbiters.
Despite these advances, these tracking data types are incapable of resolving the fine
structure of the field, due to the attenuation of the gravitational signal with altitude.
Moreover, the available satellites do not sample uniformly the range of inclinations; this
causes strong correlation among coefficients of higher degrees and necessitates the use of
a priori constraints in the development of such models (Lerch et al., 1979).
Satellite altimetry has enabled an unsurpassed mapping of the field over the oceans,
both in terms of accuracy and in terms of resolution. TOPEX/POSEIDON (Fu et aI.,
1994) provides measurements of the sea surface which, for the first time, are not
significantly contaminated by radial orbit error (RMS radial orbit error at the 3.5 cm
level). However, altimetric measurements are confined over the ocean areas bounded by
the satellite's inclination, and furthermore provide a mapping of the sum of the geoid
undulation plus the Sea Surface Dynamic Topography (SSDT). These aspects weaken the
contribution of altimeter data in the determination of the long wavelength gravitational
signal and necessitate the appropriate modeling of the SSDT when altimeter data are used
in combination solutions for the gravitational field.
Surface gravimetry is in principle capable of resolving both long and short wavelength
features of the gravity field. This however requires uniform global coverage with dense
gravity data of uniformly high accuracy. Unfortunately, because surface gravimetry is an
expensive and time consuming process, the best available data at present (Kenyon and
Pavlis, this issue) represent information derived from over 4000 sources of detail gravity
data collected over several decades. Even in this comprehensive compilation of most land
gravity material presently available, the accuracy and density of point data vary
substantially with geographic region, with extended regions (e.g., Antarctica) being
practically void of gravity measurements. Airborne gravity surveys have demonstrated
their ability to provide rapid and accurate gravity coverage over areas that are difficult to
access such as Greenland (Forsberg and Brozena, 1993), and are expected to provide
similar improvement over the Antarctic in the future. Gravity anomaly data from different
sources may also have different systematic errors associated with them (Heck, 1990).
These systematic errors, in conjunction with the non uniformity of coverage, degrade the
long wavelength integrity of the gravitational information which can be extracted from
surface gravimetry. Nevertheless, surface gravimetry presently provides the only data that
can resolve short wavelength gravity features over land. In addition, ship borne gravity
measurements aid the separation of the geoid from the SSDT signal when used in
combination with satellite altimetry.
The complimentary character (both in a spectral as well as in a geographic sense) of
satellite tracking, altimetry and surface gravimetry data, enables the determination of the
gravitational field in combination solutions, over a wider band of its spectrum, with
improved accuracies than can be obtained by using any of the three data types alone.
ESTIMATION TECHNIQUES
The major factors influencing the choice of an estimation technique for the development
of a high-degree combination solution are: 1) the available computer resources, 2) the
treatment of satellite altimeter data, and 3) the availability of (near) global gravity
anomaly databases in gridded form. An ideal estimation strategy can be outlined as
follows:
112