Note on aliasing using Tzz. 2003-04-30 by C.C.Tscherning.
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A general study on aliasing is found on
http://cct/gfy.ku.dk/alias03.pdf
However, it is necessary to get more insight into what
happens using gridded Tzz data at GOCE altitude.
Therefore a number of tests have been conducted, using data
generated using EGM96 from degree 25 - 360, file
/cct/dgravsoft/egm9624_360 .
As degree-variances was used the error-degree-variances from degree
0 - 24, the degree-variances of EGM96 from 25 to 360 and the
degree-variances of GPM98A, file
/cct/dgravsoft/egm24egm.dgv .
The data were supposed to be at 250 km altitude and having
a noise standard deviation of 0.005 EU.
Job-files are denoted /cct/dgravsoft/sphgrid24_360X.job,
where X is equal to a, b, d, ...
a) Here EGM96 to degree 120 was used to generate the Tzz values.
1 deg. x 1 deg. values were used.
Data variance 0.021 EU while the one from the covariance function was
0.022 EU.
Coefficients up to degree 72 were computed.
In this example there is a large over-sampling, so the agreement
for degree 25-72 is very good, generally of the order of below 0.01 %.
However the error estimates are of the order of 1 % of the degree-
standard deviation at degree 54, decreasing for increasing degree.
b) Here EGM to degree 360 was used. Coefficients to degree 180 were computed.
1 deg. x 1 deg. values were used.
Since the data-configuration and noise was the same as in a) all the error
estimates were identical. At degree 180 the estimated error was 100 % of the
degree standard deviation. ( At 54 it was 1.2 %.)
The agreement with the input coefficients became a little worse.
d) Here EGM96 to degree 360 was used again, but now a 0.5 deg. x 0.5 deg. grid
was created. I expect to see a decrease of the aliasing for deg < 181.