Abstract
In our previous work [Ramouz et al. 2018], during the gravity field
determination via Least Squares Collocation (LSC) in Iran, it was
detected that localizing covariance modeling shows better performance
than using one uniform covariance for all the under investigation
regions. Now the question is which criteria should be used for dividing
the region into subareas for localization the covariance estimation?
Tscherning et al. 1994 stated that data distribution could significantly
affect the covariance estimation and consequently the LSC gravity
modeling. As Iran has a rough topography and at the same time suffers
from lack of a good coverage and homogenous terrestrial gravity network,
covariance analysis in this area is not a trivial task. Four local case
studies with different roughness and data distributions but with the
same window size were selected. In each case study and based on Remove
– Restore technique, the global and topographic parts of the gravity
signal were removed from the observations. To do so, global gravity
model EIGEN-6C4 up to d/o 360 and RTM method with the topographic
information supplied by SRTM 1 arc-second height model, were used
respectively. After that, residual gravity anomalies went through
analytical covariance estimation by make use of Tscherning – Rapp 1974
covariance model. Indeed, covariance estimation in LSC method consists
of two steps: calculation of an empirical covariance function from the
residual gravity anomalies, and fitting an analytical covariance model
to it. In this study, we focus on the considerations about data and its
distribution which must be taken into account during empirical and
analytical covariance determination. In case of not well-distributed
input data, excavating analytical covariance model parameters is a
challenging task. In some cases, this sensitivity causes difficulty even
in choosing initial values for inverse adjustment of these parameters,
which improper initial values lead to wrong parameters selections. Also,
the distribution of data in each case study was manipulated to analyze
its influence on the covariance estimation. To make an assessment, in
each case study, the residual gravity anomalies were split into two
datasets; first as observations input for LSC, and the second, as
control points to evaluate the accuracy of the LSC gravity modeling and
the covariance estimation. Then the interdependency and effect of
Tscherning – Rapp covariance model parameters on the covariance
estimation were investigated in each case study. Evaluation of the
results in the case studies shows that the accuracy of the gravity
modeling, directly dependent on the distribution of the data and the
roughness of the topography, among other parameters. Finally, enhancing
the covariance estimation based on presented approach, lead to about
10% improvement of the accuracy in terms of STD through LSC gravity
modeling.