New Matlab isoluminant colormap for azimuth data

I recently added to my Matlab File Exchange function, Perceptually improved colormaps, a colormap for periodic data like azimuth or phase. I am going to briefly showcase it using data from my degree thesis in geology, which I used before, for example in Visualization tips for geoscientists – Matlab. Figure 1, from that post, shows residual gravity anomalies in milligals.

data cube1_final_shading_slope

Figure 1

Often we’re interested in characterizing these anomalies by calculating the direction of maximum dip at each point on the surface, and for that direction display the azimuth, or dip azimuth.  I’ve done this for the surface of residual anomalies from Figure 1 and displayed the azimuth in Figure 2. Azimuth from 0 to 360 degrees are color-coded using Jet, Matlab’s standard colormap (until recently). Typically I do not trust azimuth values when the dip is close to zero because it is often contaminated by noise so I would use shading to de-saturate the colors where dip has the lowest values, but for ease of discussion I haven’t done so in this case.

Figure 2. Azimuth values color-coded with Jet.

Figure 2. Azimuth values color-coded with Jet.

There are two problems with Figure 2. First, the well-known problems with the jet colormap. For example, blue is too dark and blue areas appear as bands of constant colour. Yellow is much lighter than any other colour so we see artificial yellow edges that are not really present in the data. But there is an additional issue in Figure 2 because azimuths close in value to 0 and 360 degrees are colored with blue and red, respectively, instead of a single color as they should, causing an additional artificial edge.

In Figure 3 I recolored the map using a colormap that replicates those used in many geophysical software tools to display azimuth or phase data. This is better because it wraps around at 360 degrees but the perceptual issues are unresolved: in this case red, yellow and blue all appear as sharp perceptual edges.


Figure 3. Azimuth values color-coded with generic azimuth colormap.



Figure 4. Azimuth values color-coded with isoluminant azimuth colormap.


In Figure 4 I used my new colormap, called isoAZ (for isoluminant azimuth). This colormap is much better because not only does it wraps around at 360 degrees, but also lightness is held constant for all colors, which eliminates the perceptual anomalies. All the artificial yellow, red, and blue edges are gone, only real edges are left. This can be more easily appreciated in the figure below: if you hover with your mouse over it you are able to switch back and forth between Figure 3 and Figure 4.


From an interpretation point of view, azimuths 180 degrees apart are of opposing colours, which is ideal for dip azimuth data because it allows us to easily recognize folds where dips of opposite direction are juxtaposed at an edge. One example is the sharp edge in the northwest quadrant of Figure 4, where magenta is juxtaposed to green. If you look at Figure 1 you see that there’s a relative high in this area (the edge in Figure 4) with dips of opposite direction on either side (East and West, or 0 and 360 degrees).

The colormap was created in the Lightness-Chroma-Hue color space, a polar transform of the Lab color space, where lightness is the vertical axis and at each value of lightness, chroma is the radial coordinate and hue the polar angle. One limitation of this approach is that due to theirregular  shape of the color gamut section at each lightness value, we can never exceed  chroma values  of about 38-40 (at lightness = 65 in Matlab; in Python, with extensive trial and error, I have not been able to go past 36 using the Scikit-image Color module), which make the resulting colors pale, pastely.

it creates For those that want to experiment with it further, I used just a few lines of code similar to the ones below:

radius = 38; % chroma
theta = linspace(0, 2*pi, 256)'; % hue
a = radius * cos(theta);
b = radius * sin(theta);
L = (ones(1, 256)*65)'; % lightness
Lab = [L, a, b];

This code is a modification from an example by Steve Eddins on a post on his Matlab Central blog. In Steve’s example the colormap cycles through the hues as lightness increases monotonically (which by the way is an excellent way to generate a perceptual rainbow). In this case lightness is kept constant and hue cycles through the entire 360 degrees and wraps around. Also, instead of using the Image Processing Toolbox, I used  Colorspace, a free function from Matlab File Exchange, for the color space transformations.

For data like fracture orientation where azimuths 180 degrees apart are equivalent it is better to stack two of these isoluminant colormaps in a row. In this way we place opposing colors 90 degrees apart, whereas color 180 degrees apart are the same. You can do it using Matlab commands repmat or vertcat, as below:

radius = 38; % chroma
theta = linspace(0, 2*pi, 128)'; % hue
a = radius * cos(theta);
b = radius * sin(theta);
L = (ones(1, 128)*65)'; % lightness
Lab = [L, a, b];

Seismic terrain displays


A couple of years ago I stumbled in a great 2001 paper by Beyer [1] on The Leading Edge. Being interested in visualization techniques I was drawn by the display in Figure 1 (which is a low resolution copy from Figure 2 in the paper). But what really amazed me was the suggestion that a display like this could be created in a few minutes, without doing any interpretation, by just manipulating instantaneous phase slices. With the only condition of having data of fair quality, this promised to be an awesome reconnaissance tool.


Figure 1 – Copyright SEG

The theory

The idea that instantaneous phase is a great attribute for interpretation has been around for a long time. There is, for example, a 1989 Exploration Geophysics paper by Duff and Mason [2]. These two authors argue that amplitude time slices are a suboptimal choice, and that instantaneous phase slices should be preferred. They give three reasons:

1) on amplitude time slices only relatively strong events remain above the bias level after gain and scaling. Weak events are submerged below the bias and remain unmappable.  Although it is the topic of a future post, it is worth mentioning I think this effect is exacerbated by the common but unfortunate choice of a divergent color palette with white in the middle. White is so bright (I call it white hole) that even more low amplitude events become indiscernible.

2) discrete boundaries corresponding to unique positions on the wavelet are displayed on instantaneous phase slices – this intra wavelet detail is lost on amplitude slices.

After-Duff-Mason 2

Figure 2 – after Duff and Mason, Figure 2

3) instantaneous time slices give DIRECTLY the sense of time dip for dipping events. In Figure 2 I show 2 parallel dipping reflectors, represented by 5 (non consecutive) traces, and 2 (non-consecutive) instantaneous phase slices (at arbitrary t1 an t2). I marked 5 discrete phase events for the top dipping reflector. The sense of time dip is given (with appropriate color palette) by the sense of color transition. Conversely, this intra wavelet detail would be lost on the amplitude time slices, with amplitudes between the black center trace and the red traces, and amplitudes between the red traces and the green traces lost within a single broad zone. The difference is probably not as dramatic nowadays with the increase in dynamic ranges available, but using instantaneous phase slices still remains advantageous for detailed mapping.

Beyer’s seismic terrain is just a natural extension of the instantaneous time slice as ( quoted from [1]):”… it then follows that the instantaneous phase (-180 deg to +180 deg) can simply be rescaled to the wavelength in ms of pseudoseismic two-way time… Seismic terrain can be thought of as a type of instantaneous wavelength generated from instantaneous phase along a time slice”. With reference to the top dipping reflector in Figure 3, the method allows generating converting the brown phase segment to the dipping blue segment (and similarly the yellow phase segment to the dipping green segment for bottom dipping event).


Figure 3

The practice – Petrel

Let’s see how we can create a terrain display similar to that in Figure 1 using Petrel.

Raw data

The process starts with migrated seismic data, from which we need generate both the phase and frequency component to get us the instantaneous wavelength.

For this tutorial I use a public seismic dataset (BPA9901) available on the Norwegian Public Data Portal. In Figure 4 below I am showing an amplitude time slice (above the Chalk) from the migrated seismic volume.


Figure 4

Step 1 – generate phase component

The first step is to generate an instantaneous phase attribute volume. This is found in the volume attributes. In Figure 5 below I am showing the instantaneous phase slice corresponding to the amplitude time slice of Figure 4.

*** N.B. *** If significant regional dips are observed in the seismic data, care should be taken in some cases  it may be beneficial (please see comment section) to remove them through flattening prior to the terrain generation.

Figure 5

Figure 5

Step 2 – generate frequency component

This is the trickiest part. In theory to get the instantaneous wavelength we would have to calculate the instantaneous frequency and divide the  instantaneous frequency attribute can be very noisy and can have spurious values in areas of low amplitude in the input data. A good practical alternative is to measure a single value of the dominant wavelet period T in an area of relatively flat reflections near the zone of interest as I am showing in Figure 6.

For the more avid readers, this is all explained quite nicely in Beyer (quoted from [1]): “Complex trace relationships dictate that the wavelength is the phase component divided by the frequency component. Thus one may be compelled to derive the seismic terrain by dividing the extracted instantaneous phase by the  extracted instantaneous frequency (carefully applying unit conversion of 1000 ms/ 360 deg or 2.78). However extracted instantaneous frequency tends to include spurious values in low amplitudes (approaching infinity according to literature and practice which correspond to poor data quality zones. Instantaneous frequency or even averaged instantaneous frequency renders the seismic terrain noisy, unrealistic, and misleading. Years of extensive use have shown that  single value of visually estimated dominant wavelet period (i.e. cycles per second) produces a very high-quality seismic terrain that closely fits the seismic events over wide areas”.


Figure 6

Step 3 – generate the instantaneous wavelength (seismic terrain)

Having estimated the dominant wavelet period T (in ms) , I can now use it to generate the instantaneous wavelength. We are essentially converting the data from the range [-180 180] deg to the range [-T/2 T/2] ms.

In Petrel I do it in the calculator with a formula of the type:

terrain=(((instantaneous phase +180)*T/2)/180)

The actual formula used is shown on the top row of Figure 7 below. You will notice that it isn’t exactly the same as the above formula. I added 1 to 180 to avoid division of zero values, e.g.:

(([-180 180]+180)*28/180) = ([0 180]*28/180) = ([0 5040]/180) % not good!


(([-180 180]+181)*28/180) = ([1 181]*28/180) = ([28 5068]/180) % good!

Once the division is performed I subtract T/2 again.

Notice from Figure 7 that because we added 181 but divided by 180 there is a small adjustment to be made by hand. I get this small adjustment by double clicking on the output volume to get the statistics. In this case it is +-0.16 ms, so I run a second time the formula (bottom row, Figure 7), this time subtracting T/2 +0.16 instead of just T/2.


Figure 7

Step 4 – display seismic terrain.

There are two options in Petrel to display the resulting seismic terrain volume:

Option 1 – display bump mapped terrain slices in 2D or 3D window

This is my preferred option for scanning up and down through the terrain slices. The bump mapping effect is done by double clicking on the terrain survey with a 2D or 3D window open and selected, in the Style tab>Intersection  tab. In Figure 8 I am showing the bump mapped terrain slice corresponding to the instantaneous phase time slice of Figure 5.


Figure 8

Option 2 – display selected horizons of interest in 3D window

One may want to create a display such as the one in Figure 1, which for me is intended for a later stage, when integrating perhaps with extracted amplitude or attribute anomalies highlighting hydrocarbon presence.

As often in Petrel there are different ways of achieving the same result. This is how I do it. First, I create a flat surface, with a TWT value corresponding to the slice I am interested in (as in Figure 9, left panel). Then I extract and append to this surface the terrain values from that slice of interest (as in Figure 9, right panel).

Figure 9

Figure 9

Figure 10

Figure 10

Finally, in the calculations tab, I add a constant time shift corresponding to the time associated with the slice  of interest: notice the difference in Z value between the left panel in Figure 10 (before the calculation), and the right panel (after the calculation). It is also necessary to use the extracted value as visual vertical position as illustrated in Figure 11.

Figure 11

Figure 11

I am showing the result in Figure 12. This is the same terrain slice as in Figure 8.

terrain_slice extracted

Figure 12


As a quick QC I am displaying in Figure 13 a vertical section (corresponding to the thick black line in Figure 12) from the input seismic data, with the extracted surface drawn as a thin black line.

The terrain deteriorates to the far left as we approach the edge of the survey, with fold decreasing and noise increasing, and there is a cycle skip towards the far right. But all in all I think  this is a very good result: it captures the faults well, and the whole process took less than 20 minutes with no picking.


Figure 13


This method has one limitation: the maximum fault throws or stratigraphic relief (in milliseconds) that can be mapped is equal to the period T.


I wish to thank DONG Energy for agreeing to the publication of the seismic images, which were generated using company licensed Petrel.

** UPDATE **

A few readers asked clarifications on what the benefits and potential uses are of using this attribute. The short answer is that this is in fact a pseudo-horizon that tracks dipping  seismic events accurately within the range of the period of the dominant frequency period (as seen in Figure 13), which makes it an excellent reconnaissance tool.  A good quality first pass map can be made in minutes in areas where detailed mapping can take days.  An excellent example is Figure 16 in the original paper [1].  More details can be found in the last two paragraphs of the paper:  Reservoir-scale structural data from seismic terrain and Fast 3-D screening. 


[1] Beyer, L. (2001). – Rapid 3-D screening with seismic terrain: deepwater Gulf of Mexico examplesThe Leading Edge, 20 (4), 386–395.

[2] Duff, B.A., and Mason, D.J. (1989) – The instantaneous-phase time slice: A crucial display for enhancing 3-D interpretationExploration Geophysics 20 (2) 213 – 217

Visualization tips for geoscientists: Matlab, part III


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)),...
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)),...
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(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:


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)));


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:


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)));


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.


[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).


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

Related posts (MyCarta)

Visualization tips for geoscientists: Surfer

Visualization tips for geoscientists: Matlab

Visualization tips for geoscientists: Matlab, part II

Image Processing Tips for Geoscientists – part 1

The rainbow is dead…long live the rainbow! – Perceptual palettes, part 1


This is the first  post in a series on the rainbow and similar color palettes. My goal is to demonstrate it is not a good idea to use these palettes to display scientific data, and then answer these two questions: (1) is there anything we can do to “fix” the rainbow, and (2) if not, can we design a new one from scratch.

The rainbow is dead…some examples

In a previous post I showed a pseudo-3D rendering of my left hand x-ray using intensity (which is a measure of bone thickness) as the elevation. I mapped the rendering to both grayscale and rainbow color palettes, and here I reproduced the two images side by side:

I used this example to argue (briefly) that the rainbow obscures some details and confuses images by introducing artifacts. Notice that in this case it clearly reduces the effectiveness of the pseudo-3D rendering in general. It also introduces inversions in the perception of elevation. The thick part in the head of the radius bone, indicated by the arrow, looks like a depression, whereas it is clearly (and correctly) a high in the grayscale version.

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Visualization tips for geoscientists: Matlab, part II


In my previous post on this topic I left two loose ends: one in the main text about shading in 3D, and one in the comment section to follow-up on a couple of points in Evan’s feedback. I finally managed to go back and spend some time on those and that is what I am posting about today.

Part 1 – apply shading with transparency in 3D with the surf command

I was trying to write some code to apply the shading with transparency and the surf command. In fact, I’ve been trying, and asking around in the Matlab community for more than one year. But to no avail. I think it is not possible to create the shading directly that way. But I did find a workaround. The breakthrough came when I asked myself this question: can I find a way to capture in a variable the color and the shading associated with each pixel in one of the final 2D maps from the previous post? If I could do that, then it would be possible to assign the colors and shading in that variable using this syntax for the surf command:


where data is the gravity matrix and c is the color and shading matrix. To do it in practice I started from a suggestion by Walter Robertson on the Matlab community in his answer to my question on this topic.

The full code to do that is below here, followed by an explanation including 3 figures. As for the other post, since the data set I use is from my unpublished thesis in Geology, I am not able to share it, and you will have to use your own data, but the Matlab code is simply adapted.

%% cell 1
shadedpcolor(x,y,data,(1-normalise(slope)),[-5.9834 2.9969],[0 1],0.45,cube1,0);
axis equal; axis off; axis tight
shadedcolorbar([-5.9834 2.9969],0.55,cube1);

In cell 1 using again shadedpcolor.mnormalise.m, and cube1 color palette I create the 2D shaded image, which I show here in Figure 1.

Figure 1

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Visualization tips for geoscientists – Matlab


In my last post I described how to create a powerful, nondirectional shading for a geophysical surface using the slope of the data to assign the shading intensity (i.e. areas of greater slope are assigned darker shading). Today I will show hot to create a similar effect in Matlab.

Since the data set I use is from my unpublished thesis in Geology, 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 snippets below assume you have a geophysical surface already imported in the workspace and stored in a variable called “data”, as well as the derivative in a variable called “data_slope”.

Method 1 – with a slope mask and transparency

Some time ago I read this interesting Image Processing blog post by Steve Eddins at Mathworks on overlaying images using transparency. I encourage readers to take a look at this and other posts by Steve, he’s great! That particular blog post gave me the idea to use transparency and the slope to create my favorite shading in Matlab.

In addition to the code below you will need normalise.m from Peter Kovesi‘s website, and to import the color palette cube1.

%% alpha transparency code snippet
black = cat(3, zeros(size(data)), zeros(size(data)), ...
    zeros(size(data)));             % make a truecolor all-black image
gray=black+0.2;                     % make a truecolor all-gray image
alphaI=normalise(data_slope);       % create transparency weight matrix
                                    % using data_slope

imagesc(data);colormap(cube1);      % display data
hold on
h = imagesc(gray);                  % overlay gray image on data
hold off
set(h, 'AlphaData', alphaI);        % set transparency of gray layer using
axis equal;                         % weight matrix
axis tight;
axis off;

And here is the result in Figure 1 below – not bad!

Figure 1. Shaded using transparency

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Visualization tips for geoscientists: Surfer

I have been thinking for a while about writing on visualization of geophysical data. I finally got to it, and I am now pleased  to show you a technique I use often.  This tutorial has shaped up into 2 independent posts: in the first post I will show how to implement the technique with Surfer, in the second one with Matlab (you will need access to a license of Surfer 8.08 or later, and Matlab 2007a or later to replicate the work done in the tutorial).

I will illustrate the technique using gravity data since it is the data I developed it for. In an upcoming series of gravity exploration tutorials I will discuss in depth the acquisition, processing, enhancement, and interpretation of gravity data (see [1] and [4]). For now, suffice it to say that gravity prospecting is useful in areas where rocks with different density are laterally in contact, either stratigraphic or tectonic, producing a measurable local variation of the gravitational field. This was the case for the study area (in the Monti Romani of Southern Tuscany) from my thesis in Geology at the University of Rome [2].

In this part of the Apennine belt, a Paleozoic metamorphic basement (density ~2.7 g/cm3) is overlain by a thick sequence of clastic near-shore units of the Triassic-Oligocene Tuscany Nappe (density ~2.3 g/cm3). The Tuscan Nappe is in turn covered by the Cretaceous-Eocene flish units of the Liguride Complex (density ~2.1 g/cm3).

During the deformation of the Apennines, NE verging compressive thrusts caused doubling of the basement. The tectonic setting was later complicated by tensional block faulting with formation of horst-graben structures generally extend along NW-SE and N-S trends which were further disrupted by later and still active NE-SW normal faulting (see [2], and reference therein, for example [3]).

This complex tectonic history placed the basement in lateral contact with the less dense rocks of the younger formations and this is reflected in the residual anomaly map [4] of Figure 1. Roughly speaking, there is a high in the SE quadrant of ~3.0 mgal corresponding to the location of the largest basement outcrop, an NW-SE elongated high of ~0.5 mgal in the centre bound by lows on both the SW and NE (~-6.0 and ~-5.0 mgal, respectively), and finally a local high in the N.W. quadrant of ~-0.5 mGal. From this we can infer that in this area can infer that the systems of normal faults caused differential sinking of the top of basement in different blocks leaving an isolated high in the middle, which is consistent with the described tectonic history [2]. Notice that grayscale representation is smoothly varying, reflecting (and honoring) the structure inherent in the data. It does not allow good visual discrimination and comparison of differences, but from the interpretation standpoint I recommend to always start out with it: once a first impression is formed it is difficult to go back. There is time later to start changing the dispaly.

 Figure 1 – Grayscale residual anomalies in milligals. This version of the map was generate using the IMAGE MAP option in Surfer.

OK, now that we formed a first impression, what can we try to improve on this display? The first thing we can do to increase the perceptual contrast is to add color, as I have done in Figure 2. This is an improvement, now we are able to appreciate smaller changes, quickly assess differences, or conversely identify areas of similar anomaly. Adding the third dimension and perspective is a further improvement, as seen in figure 3. But there’s still something missing. Even though we’ve added color, relief, and perspective, the map looks a bit “flat”.

Figure 2 – Colored residual anomalies in milligals. This version of the map was generate using the IMAGE MAP option in Surfer.
Figure 3 – Colored 3D residual anomaly map in milligals. This version of the map was generate using the SURFACE MAP option in Surfer.

Adding contours is a good option to further bring out details in the data, and I like the flexibility of contours in Surfer. For example, for Figure 4 I assigned (in Contour Properties, Levels tab) a dashed line style to negative residual contours, and a solid line style to positive residual contours, with a thicker line for the zero contour. This can be done by modifying the style for each level individually, or by creating two separate contours, one for the positive data, one for the negative data, which is handy when several contour levels are present. The one drawback of using contours this way is that it is redundant. We used 3 weapons  – color, relief, and contours – to dispaly one dataset, and to characterize just one property, the shape of gravity anomaly. In geoscience it is often necessary, and desireable to show multiple (relevant) datasets in one view, so this is a bit of a waste. I would rather spare the contours, for example, to overlay and compare anomalous concentrations in gold pathfinder elements on this gravity anomaly map (one of the objectives of the study, being the Monti Romani an area of active gold exploration).

Figure 4 – Colored 3D residual anomaly map in milligals. Contours were added with the the CONTOUR MAP option in Surfer.  Figure 5 – Colored 3D residual anomaly map in milligals with lighting (3D Surface Properties menu). Illumination is generated by a point source with -135 deg azimuth and 60 deg elevation, plus an additional 80% gray ambient light, a 30% gray diffuse light, and a 10% gray specular light.

The alternative to contours is the use of illumination, or lighting, which I used in Figure 5. Lighting is doing a really good job: now we can recognize there is a high frequency texture in the data and we see some features both in the highs and lows. But there’s a catch:  we are now introducing perceptual artifacts, in the form of bright white highlight, which is obscuring some of the details where the surface is orthogonal to the point source light.

There is a way to illuminate the surface without introducing artifact – and that is really wanted to show you with this tutorial – which is to use a derivative of the data to assign the shading intensity (areas of greater gradient were assigned darker shading) [5]. In this case  I choose the terrain slope, which is the slope in the direction of steepest gradient at any point in the data (calculated in a running window). The result is a very powerful shading. Here is how you can do it in Surfer:


Result is shown in Figure 6 below:

Figure 6 – Terrain slope of residual anomaly. Black for low gradients, white for high gradients. Displayed using IMAGE MAP option.

2) CREATE COMPLEMENT OF TERRAIN SLOPE AND NORMALIZE TO [1 0] RANGE (to assign darker shading to areas of greater slope. This is done with 3 operations:

i)     GRID > MATH> B=A – min(A)

where min(A) is the minimum value, which you can read off the grid info (for example you would double click on the map above to open the Map Properties and there’s an info button next to the Input File field) .

ii)    GRID > MATH> C=B /max(B)

iii)   GRID > MATH> D= 1-C

Result is shown in Figure 7 below. This looks really good, see how now the data seems almost 3D? It would work very well just as it is. However, I do like color, so I added it back in Figure 8. This is done by draping the grayscale terrain slope complement IMAGE MAP as an overlay over the colored residual anomaly SURFACE MAP, and setting the Color Modulation to BLEND in the 3D Surface Properties in the Overlay tab. I really do like this display in Figure 8, I think it is terrific. Let me know if you like it best too.

Finally, in Figure 9, I added a contour of the anomaly in the Gold Pathfiners, to reiterate the point I made above that contours are best spared for a second dataset.

In my next post I will show you how to do all of the above programmatically in Matlab (and share the code). Meanwhile, comments, suggestions, requests are welcome. Have fun mapping and visualizing!

Figure 7 – Complement of the terrain slope. White for low gradients, black for high gradients. Displayed using IMAGE MAP option.
Figure 8 – Complement of the terrain slope with color added back.
Figure 9 – Complement of the terrain slope with color added back and contour overlay of gold pathfinders in stream sediments.


Did you lie the colormap? In future series on perceptually balanced colormaps I will tell you how I created it. For now, if you’d like to try it on your data you can download it here:

cube1 – generic format with RGB triplets;

Cube1_Surfer – this is preformatted for Surfer with 100 RGB triplets and header line. Dowload the .doc file, open and save as plain text, then change extension to .clr;

Cube1_Surfer_inverse – the ability to flip color palette is not implemented in Surfer (at least not in version 8) so I am including the flipped version of above. Again, dowload the .doc file, open and save as plain text, then change extension to .clr.


Visualization tips for geoscientists: Matlab

Visualization tips for geoscientists: Matlab, part II

Visualization tips for geoscientists: Matlab, part III

Image Processing Tips for Geoscientists – part 1

Compare lists from text files using Matlab – an application for resource exploration


Basement structure in central and southern Alberta: insights from gravity and magnetic maps

Making seismic data come alive

Visual Crossplotting

Mapping multiple attributes to three- and four-component color models — A tutorial

Enhancing Fault Visibility Using Bump Mapped Seismic Attributes 


I would like to thank Michele di Filippo at the Department of Earth Science, University of Rome La Sapienza, to whom I owe a great deal. Michele, my first mentor and a friend, taught me everything I know about the planning and implementation of a geophysical field campaign. In the process I also learned from him a great deal about geology, mapping, Surfer, and problem solving. Michele will make a contribution to the gravity exploration series.


[1] If you would like to learn more about gravity data interpretation please check these excellent notes by Martin Unsworth Unsworth, Professor of Physics at the Earth and Atmospheric Sciences department, University of Alberta.

[2] Niccoli, M., 2000:  Gravity, magnetic, and geologic exploration in the Monti Romani of Southern Tuscany, unpublished field and research thesis, Department of Earth Science, University of Rome La Sapienza.

[3] Moretti A., Meletti C., Ottria G. (1990) – Studio stratigrafico e strutturale dei Monti Romani (GR-VT) – 1: dal Paleozoico all’Orogenesi Alpidica. Boll. Soc. Geol. It., 109, 557-581. In Italian.

[4] Typically reduction of the raw data is necessary before any interpretation can be attempted. The result of this process of reduction is a Bouguer anomaly map, which is conceptually equivalent to what we would measure if we stripped away everything above sea level, therefore observing the distribution of rock densities below a regular surface. It is standard practice to also detrend the Bouguer anomaly to separate the influence of basin or crustal scale effects, from local effects, as either one or the other is often the target of the survey. The result of this procedure is typically called Residuals anomaly and often shows subtler details that were not apparent due to the regional gradients. Reduction to rsiduals makes it easier to qualitatively separate mass excesses from mass deficits. For a more detailed review of gravity exploration method check again the notes in [1] and refer to this article on the CSEG Recorder and reference therein.

[5] Speaking in general, 3D maps without lighting often have a flat appearance, which is why light sources are added. The traditional choice is to use single or multiple directional light sources, but the result is that only linear features orthogonal to those orientations will be highlighted. This is useful when interpreting for lineaments or faults (when present), but not in all circumstances, and requires a lot of experimenting. in other cases, like this one , directional lighting introduces a bright highlight, which obscures some detail. A more generalist, and in my view more effective alternative, is to use information derived from the data itself for the shading. One way to do that is to use a high pass filtered version of the data. i will show you how to do that in matlab in the next tutorial. Another solution, which I favored in this example, is to use a first derivative of the data.