H:\EXCERC\GEOD98e.E11.wpd

Department of Geophysics, Juliane Maries Vej 30, 2000 Copenhagen Ø..

**Geodesy Course exercise 11.**

**Statistical analysis of gravity data and drawing of a gravity
map.**

11.1. Estimation of a gravity anomaly (empirical)covariance
function and variogram

The following data must be used, with format:

number, latitude, longitude, altitude and gravity anomaly in
mgal.

11 56.0 10.0 0.0 4.0

12 56.1 10.0 0.0 2.0

13 56.2 10.0 0.0 0.0

14 56.3 10.0 0.0 -2.0

15 56.4 10.0 0.0 -4.0

16 56.5 10.0 0.0 -6.0

17 56.6 10.0 0.0 -8.0

18 56.7 10.0 0.0 -9.0

19 56.8 10.0 0.0 -7.0

20 56.9 10.0 0.0 -5.0

21 57.0 10.0 0.0 -3.0

22 57.1 10.0 0.0 -1.0

23 57.2 10.0 0.0 1.0

24 57.3 10.0 0.0 5.0

25 57.4 10.0 0.0 4.0

The covariances are estimated by forming products of all data
with distances in the interval from 0 to 0.05 and then
0.05+n*0.1 to 0.05+n*0.1 for n=1, 2, 3, 4, 5, 6, 7, and counting how many points there are in each sampling interval (totally 8). (Divide the work between you, so each one takes one
interval). The variogram is estimated by forming sums of
products of differences.

Where is the first zero-point for the covariance function and
what is the correlation distance (the distance to where the
covariance first time becomes half the variance (and we have
50 % correlation).

11.2. Predict using collocation the gravity anomaly in a point
with latitude 56.65 and longitude 10.0 from point 18 only, and
then from point 17 and 18, and finally 17, 18, 19.

What is the theoretical error-estimate if only point 18 is
used ?

11.3. Drawing of a gravity map.

Make sure you have done last part of exercise 6, where data
have been extracted from the gravity data base and stored as a
file called gra.ex6. We will now use geoplot21 to do the
contouring. Remember after log-in on a UNIX machine to type
uniras.

There has been prepared a standard input-file, which can be
used for repeated runs called geoplot.ex11.

Note that you must answer **t** to the question on Contour plot.

The contouring can be made using different interpolation
methods to form a grid, which is the base for the calculation
of the contours. Try 2 of the possibilities (see UNIRAS manual
AGL/INTERPOLATIONS for details). Note the (large) differences.

The resolution of the contour plot is dependent of the number
of grid support points. Try first a small number ( 50 x 40)
and later 150 x 120.

It is possible to contour only within a region (e.g. land).
This is not used here, so answer **f** to the question whether a
region is to be used.

For COLOUR SCALE INDEX use either 3 (black/white), 6 colours,
but other are possible, see UNIRAS manual.

The plots can be printed in b/w if the driver MPOST is used.