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.