Introduction

Last weekend I had a few hours to play with but needed a short break from writing about color palettes, so I decided to go back and finish up (for now) this series on geoscience visualization in Matlab. In the first post of the series I expanded on work by Steve Eddins at Mathworks on overlaying images using influence maps and demonstrated how it could be used to enhance the display of a single geophysical dataset.

Using transparency to display multiple data sets an example

At the end of the second post I promised I would go back and show an example of using transparency and influence maps for other tasks, like overlaying of different attributes. Here’s my favorite example in Figure 1. The image is a map in pastel colors of the Bouguer Gravity anomaly for the Southern Tuscany region of Italy, with three other layers superimposed using the techniques above mentioned.

It is beyond the objectives of this post to discuss at length about gravity exploration methods or to attempt a full interpretation of the map. I will go back to it at a later time as I am planning a full series on gravity exploration using this data set, but if you are burning to read more about gravity interpretation please check these excellent notes by Martin Unsworth, Professor of Physics at the Earth and Atmospheric Sciences department, University of Alberta, and note 4 at the end of this post. Otherwise, and for now, suffice it to say that warm colors (green to yellow to red) in the Bouguer gravity map indicate, relatively speaking, excess mass in the subsurface and blue and purple indicate deficit of mass in the subsurface.

The black and grey lines are lineaments extracted from derivatives of the Bouguer gravity data using two different methods [1]. The semitransparent, white-filled polygons show the location of some of the  basement outcrops (the densest rocks in this area).

Lineaments extracted from gravity data can correspond to contacts between geological bodies of different density, so a correlation can be expected between basement outcrops and some of the lineaments, as they are often placed in lateral contact with much lesser dense rocks. This is often exploited in mineral exploration in areas such as this where mineralization occurs at or in the vicinity of this contacts. As an example, I show in Figure 2 the occurrences (AGIP – RIMIN, unpublished industry report, 1989) of silicization (circles) and antimony deposits (triangles), superimposed on the distance from one of the set of lineaments (warm colors indicate higher distance) from Figure 1.

The fact that different methods give systematically shifted results is a known fact, often due the trade-off between resolution and stability, whereby the more stable methods are less affected by noise, but often produce smoother edges over deeper contacts, and their maxima may not correspond. This is in addition to the inherent ambiguity of gravity data, which cannot, by themselves, be interpreted uniquely. To establish which method might be more correct in this case (none is a silver bullet) I tried to calibrate the results using basement outcrops (i.e. does either method more closely match the outcrop edges?). Having done that, I would have more confidence in making inferences on possible other contacts in the subsurface suggested by lineament. I would say the black lines do a better overall job in the East, the gray perhaps in the West. So perhaps I’m stuck? I will get back to this during my gravity series.

Figure 1

Figure 2

Matlab code

As usual I am happy to share the code I used to make the combined map of Figure 1. Since the data I use is in part from my unpublished thesis in Geology and in part from Michele di Filippo at the University of Rome, I am not able to share it, and you will have to use your own data, but the Matlab code is simply adapted. The code snippet below assume you have a geophysical surface already imported in the workspace and stored in a variable called “dataI”, as well as the outcrops in a variable called “basement”, and the lineaments in “lnmnt1” and “lnmnt2”. It also uses my cube1 color palette.

 
% part 1 - map gravity data
figure; imagesc(XI,YI,dataI); colormap(cube1); hold on;
%
% part 2 - dealing with basement overlay
white=cat(3, ones(size(basement)), ones(size(basement)),...
 ones(size(basement)));
ttt=imagesc(Xb,Yb,white); % plots white layer for basement
%
% part 3 - dealing with lineaments overlays
black=cat(3, zeros(size(lnmnt1)), zeros(size(lnmnt1)),...
 zeros(size(lnmnt1)));
grey=black+0.4;
basement_msk=basement.*0.6;
kkk=imagesc(XI,YI,black); % plots black layer for lineament 1
sss=imagesc(XI,YI,gray); % plots gray layer for lineament 2
hold off
%
% part 4 - set influence maps
set(ttt, 'AlphaData', basement_msk); % influence map for basement
set(kkk, 'AlphaData', lnmnt1); % influence map for linement 1
set(sss, 'AlphaData', lnmnt2); % influence map for linement 2
%
% making it pretty
axis equal
axis tight
axis off
set(gca,'YDir','normal');
set(gcf,'Position',[180 150 950 708]);
set(gcf,'OuterPosition',[176 146 958 790]);

Matlab code, explained

OK, let’s break it down starting from scratch. I want first to create a figure and display the gravity data, then hold it so I can overlay the other layers on top of it. I do this with these two commands:

figure;imagesc(XI,YI,dataI);

hold on;

The layer I want to overlay first is the one showing the basement outcrops. I make a white basement layer covering the full extent of the map, which is shown in Figure 3, below.

Figure 3

I create it and plot it with the commands:

white=cat(3, ones(size(basement)), ones(size(basement)), ones(size(basement)));

ttt=imagesc(Xb,Yb,white);

The handle  ttt is to be used in combination with the basement influence map to produce the partly transparent basement overlay: remember that I wanted to display the outcrops in white color, but only partially opaque so the colored gravity map can still be (slightly) seen underneath. I make the influence map, shown in Figure 4, with the command:

basement_msk=basement.*0.6;

Since the original binary variable “basement” had values of 1 for the outcrops and 0 elsewhere, whit the command above I assign an opacity of 0.6 to the outcrops, which will be applied when the next command, below, is run, achieving the desired result.

set(ttt, ‘AlphaData’, basement_msk); % uses basement influence map

Figure 4

For the lineaments I do things in a similar way, except that I want those plotted with full opacity since they are only 1 pixel wide.

As an example I am showing in Figure 5 the black layer lineament 1 and in Figure 6 the influence map, which has values of 1 (full opacity) for the lineament and 0 (full transparency) for everywhere else.

Figure 5

Figure 6

Now a few extra lines to make things pretty, and this is what I get, shown below in Figure 7: not what I expected!

Figure 7

The problem is in these two commands:

white=cat(3, ones(size(basement)), ones(size(basement)), ones(size(basement)));

ttt=imagesc(Xb,Yb,white);

I am calling the layer white but really all I am telling Matlab is to create a layer with maximum intensity (1). But the preceding colormap(cube1) command assigned a salmon-red color to the maximum intensity in the figure, and so that is what you get for the basement overlay.

Again, to get the result I wanted, I had to come up with a trick like in the second post examples. This is the trick:

I create a new color palette with this command:

cube1edit=cube1; cube1edit(256,:)=1;  

The new color palette has last RGB triplet actually defined as white, not salmon-red.

Then I replace this line:

figure; imagesc(XI,YI,dataI); colormap(cube1); hold on;

with the new line:

figure; imagesc(XI,YI,dataI, [15 45]); colormap (cube1edit); hold on;

The highest value in dataI is around 43. By spreading the color range from [15 43] to [15 45], therefore exceeding max(dataI) I ensure that white is used for the basement overlay but not in any part of the map where gravity is highest but there is no basement outcrop. In other words, white is assigned in the palette but reserved to the overlay.

Please let me know if that was clear. If it isn’t I will try to describe it better.

Notes

[1] One method is the total horizontal derivative. The other method is the hyperbolic tilt angle – using Matlab code by Cooper and Cowan (reference). This is how I produced the two overlays:  first I calculated the total horizontal derivative and the tilt angle, then I found the maxima to use as the overlay layers. This is similar to Figure 3e in Cooper and Cowan, but I refined my maxima result by reducing them to 1-pixel-wide lines (using a thinning algorithm).

Reference

Cooper, G.R.J., and Cowan, D.R. (2006) – Enhancing potential field data using filters based on the local phase  Computers & Geosciences 32 (2006) 1585–1591

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