# On Satellite Gravity Gradiometry

Abstract (Summary)

Satellite gravity gradiometry measures the second-order partial derivatives of the
Earth’s gravitational potential based on differential accelerometry. Measuring the
gravitational gradients at satellite level opens a new way to compute a precise and
high resolution geopotential model from space. The upcoming satellite mission
gravity field and steady-state ocean circulation (GOCE) is dedicated to provide
precise gradiometric data in this respect. It is claimed to achieve geoid and gravity
anomaly with 1 cm and 1 mGal accuracies, respectively with 1 ? ×1 ? resolution using
the delivered Earth gravitational model from GOCE data.
In this thesis new expressions for the gravitational gradients are developed. A new
expression for tensor spherical harmonics are presented and used to solve the
gradiometric boundary value problems and to compute a geopotential model. It is
found that the vertical-horizontal gradients are more suited than the other gradients in
geopotential modeling. Topographic and atmospheric effects on the satellite gravity
gradiometry data are formulated in spherical harmonics, and numerically
investigations in Fennoscandia and Iran show that the topographic effect is in the 1
and 2 E level in these areas. A new atmospheric density model is proposed, and the
atmospheric effect based on this model is within 5 mE. Second-order partial
derivatives of the extended Stokes’ formula are modified in a least-squares sense to
validate the satellite gravity gradiometry data. Downward continuation of each
element of the gravitational tensor is studied using the Tikhonov regularization. The
gravitational gradients T
zz
, T
xx
,T yy , T
xz
, T
yz
and T
xy
are suited for determining
gravity anomaly at sea level. Combination of the satellite data to recover the global
and local gravity field is investigated. It is shown that the combination of integral
solutions of the gradiometric boundary value problems using variance component
estimation, is beneficial in geopotential modeling. In local gravity field
determination, it is concluded that a grid of 1 ? ×1 ? gravity anomalies with 1 mGal
accuracy is achievable from directly combined continuation of the satellite
gradiometric data. The polar gaps due to an inclined orbit are studied, and it is shown
that T
xy
and T
yz
are better than the other gradients for estimating the gravity anomaly
in the polar gaps. The combined inversion of the satellite gradiometric data (after
biased-correction step) can determine 1 ? ×1 ? gravity anomalies with 1 and 3 mGal
accuracy in the north and south polar gaps, respectively.
Bibliographical Information:

Advisor:

School:Kungliga Tekniska högskolan

School Location:Sweden

Source Type:Doctoral Dissertation

Keywords:NATURAL SCIENCES; Earth sciences; satellite orbit; atmosphric desity model; lateral density variation; validation downward continuation; joint inversion; ring modification

ISBN:978-91-85539-42-0

Date of Publication:01/01/2009