Zannat, Umma Jamila

### Description

Geocentre motion is the motion of the centre of mass of the Earth
system with
respect to the geometric centre of figure of the solid Earth
surface because of
the continual deformation of the Earth by geophysical processes.
This motion is
important both in theory and in practice to understand and
interpret various
mass transport phenomena and their consequences, such as sea
level rise,
postseismic relaxation, polar ice melting, and glacial...[Show more] isostatic
adjustment.
Global reference frames for space geodetic point positioning are
realised using
measurements of the relative motion between satellites orbiting
around the
centre of mass on one hand and stations placed on the Earth's
surface on the
other. Therefore, reliable modelling of the geocentre motion is
vital for the
stability and the accuracy of these reference frames. In turn,
the
interpretation of many geodynamical quantities of current
interest, such as the
mean sea level, depends heavily on the quality of the adopted
reference frame.
Space geodetic measurement of the true geocentre motion, however,
is difficult
due to the discrete and therefore incomplete sampling of the
Earth's surface by
geodetic stations. In other words, there is a discrepancy between
the centre of
figure of the Earth surface and the centre of network of the
stations, called
the network effect, arising from the sampling bias of the
geodetic network.
In this work, we develop a method to estimate the magnitude of
the network
effect for a network of a given size \(N\). For a given crustal
deformation
model, we consider the Helmert parameters of transformation, that
is, the
parameters characterising a Euclidean similarity transformation,
between the
centre of figure frames before and after the deformation event.
Our proposed
estimate for the network effect, which we call the `expected
bias', is the
standard deviations of the changes in these parameters by the
event as measured
by a random network of the size \(N\). We show that, in
accordance with
probability theory, the expected bias scales as \(1/\sqrt{N}\),
and we provide
an explicit formula for this estimate in terms of the vector
spherical harmonics
expansion of the displacement field.
We assess the effectiveness of the expected bias as an estimate
of the network
effect by simulating the displacement fields for two illustrative
geodynamical
processes: (instantaneous) coseismic deformation due to great
earthquakes, and
(time-dependent) elastic deformation due to surface water
movements. We
accordingly concentrate on the instantaneous changes and the
secular drifts in
the Helmert parameters for the two cases respectively.
We found that, in both case studies, the network effect is often
as large as the
changes in the Helmert parameters themselves. Hence, current
space geodetic
networks are indeed inadequate for verifying the geocentre motion
predictions by
geophysical models accurately. Nevertheless, our simulations
validate the
expected bias to be a reasonable estimate of the network effect.
Finally, we propose an alternative definition of the centre of
network frame
that assigns a weight proportional to the area a station
represents to its
measurements. We show that it can significantly reduce the
network effect and
improve the detection of geocentre motion in most cases.

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