[GRASSLIST:3561] Re: Geophysical framework: WHITE PAPER

[Craig Funk]

Thanks Michael and Benjamin, I have several comments/questions:

Acquisition/Raw data:
<quote>
If the data are a set of vector points recorded in an orthogonal grid, 
they can be georeferenced using ***v.transform*** and a simple first 
order transformation. This requires only that the real-world 
coordinates (e.g. UTM's) be known for 3-4 of the original data points 
(i.e., ground control points or GCP's). The corners of the original 
survey area are convenient places to do this, but any well-spaced set 
of points will do in theory.
</quote>

In my experience, the data is rarely uniform. For mineral exploration, 
data is often collected in less then hospitable terrain which means 
that certain points on the proposed acquisition grid cannot be accessed 
in the real world. For the surveys I have been involved in where the 
instrument does not have a GPS, a coordinate was obtained using a 
technique appropriate for the accuracy desired ie GPS instrument or 
using laser Theodolites. Even in this case though, the data could still 
be imported as vectors as you described after some manipulation:

x-coordinate, y-coordinate, other data (ID, values, dates, etc)

Regarding corrections that need to be performed on the data (also often 
referred to as reductions):

1) Drift correction. Some instruments like gravimeters or magnetometers 
tend to drift over time and this correction needs to be applied to raw 
data. The drift can result from numerous factors such as moon/celestial 
tides, magnetic storms, atmospheric conditions, or mechnical/electrical 
drift in the instrument. The drift correction could be performed on the 
raw data prior to import into GRASS or on the vector data after import.

2) Latitude correction. This is grav data correction accounting for the 
non-spherical shape of the earth. It is a function of latitude and 
elevation. I suppose this could probably be performed using r.mapcalc. 
One would need to be able to obtain a latitude and elevation for a 
given coordinate pair in order to compute the correction.

3) Eötvos correction. Corrects for Coriolis force (due to rotating 
earth) and a moving gravity instrument (at sea or in the air). 
Correction depends on velocity latitude and heading of object which is 
measuring gravity. Again, this could probably be computed in r.mapcalc 
as long as one can get a latitude for a given location.

4) Reduction to the pole. Correction needed for mag data so that 
anomalies are transformed into what would be observed if the magnetic 
north pole was at the geographic north pole. Mag north drifts, so this 
correction is needed to provide data consistency. This correction is 
pretty straight forward in the frequency domain but is not very 
reliable at low latitudes. So to do this correction a combination of 
i.fft and r.mapcalc could be used.

5) Free air and Bouger correction. Corrects for the reduction in 
gravity as one moves away from the center of the earth, and also 
corrects for the gravitational attraction of the underlying mass WRT 
some datum. Correction is simple and could be done in r.mapcalc.

5) Terrain corrections. There is no industry consensus on the best 
approach to take for these grav corrections. It is logical to use a DEM 
as input into this correction but there are many algorithms that could 
be used. For a fairly accurate grav survey the elevations needs to have 
a measurement error of 3 cm or less. I am still looking into the best 
approach - anyone have any recommendations? Regardless, a GRASS module 
would likely have to be written for this one although simpler 
approaches could probably be implemented in r.mapcalc.

6) Trend surface removal. This applies to grav and mag data. Usually 
involves fitting a 1st or 2nd order surface to the data and then 
differencing that surface with the data set to get the residual data. 
There are many ways to do this. I recently came across a paper from 
Paolo Zatelli and Andrea Antonello titled "New GRASS modules for 
multiresolution analysis with wavelets". Multiresolution analysis would 
be a great way to do this reduction, although a more traditional 
approach would be to use least squares to fit a 1st or 2nd order 
surface.

To summarize: All the standard corrections (except maybe terrain 
correction) could be applied using existing GRASS modules. These 
corrections could be implemented either in shell scripts or in a new 
GRASS module. My inclination is to write a GRASS module to do this. Any 
comments?


Craig

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