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Full tensor gradient (FTG) technology measures the second spatial derivative of Earth’s gravity potential. Efficient visualisation of this data containing five independent components will lead to more efficient interpretations of FTG surveys.

We present an algorithm for visualising FTG gravity datasets which displays local lateral orientations encoded in the FTG data. It uses a colour map to highlight geologically significant structures such as linear features and radially symmetric points by identifying different geological features and using colour components to represent different feature types. We demonstrate the applicability of the algorithm on two datasets: one synthetic dataset with various levels of noise, and one real-world dataset.

Our algorithm creates a cross-hatched texture where the texture fibres indicate the orientations of geological features embedded in the FTG tensor at that point. The fibre widths also indicate the magnitude of the feature in that direction. The density of the fibres also indicates the relative density of the underlying rock mass.

We apply a colourmap to the texture. Images comprise three colour channels, we use each colour channel for representing a different tensor invariant:

  • Red channel: produces large values for linear features, invariant to the choice of horizontal axes: 
    Equation for computing red colour channel
  • Green channel: produces large values for linear features, invariant to the choice of horizontal axes: 
    Equation for computing the green colour channel
  • Blue channel: produces large values for radially symmetric features invariant to the choice of horizontal axes: Equation for computing the blue colour channel

Therefore, red and green (or their combination, i.e. yellow) features represent lineaments, and blue features represent point masses. In this manner, all tensor components are represented in the final visualisation output.
Often, the different invariants produce responses simultaneously, so a combination of colours is seen. Note that the invariants do not use a common scale and so one invariant may drop off at a different rate to other invariants, creating colour rings around objects. 


We show the results of applying the algorithm to a synthetic dataset and a field FTG survey. The synthetic dataset contains five anomalies of various densities, depths and shapes, as shown in the following Gz image:

Gz image with masses labelled

Label Object shape Relative density Depth range
A Block +0.2g/cc 500–900m
B Sheet +0.15g/cc 0–1000m
C Sphere +0.3g/cc 50–350m
D Cone -0.4g/cc 150–350m
E Tunnel -2.7g/cc 3–7m

Firstly, we display the tensor components (click a component to enlarge it):

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Here is the visualisation produced from those components. We are currently developing an applet to allow you to interactively zoom and navigate the image, as different features become apparent at different scales. In the meantime, click to see the full-size image: 

Synthetic output


In this image, note the linear feature on the left has thick fibres running parallel to the feature, and thin fibres running across it. Also note that the texture surrounding the concentrated point-like features converges on the features. The very small tunnel feature E is visible due to the changes in fibre orientation around the mass anomaly, although it is barely visible in the original tensor data. The deep mass anomaly A is quite faint in the tensor component images due to its depth, but it is represented clearly in the visualisation above.

The effect of independently adding Gaussian noise (with standard deviations of 1E and 2E) to each tensor component is shown below. No noise removal process has been attempted, e.g. the tensor property that the tensor has zero trace is not enforced. These results may therefore be improved upon. 

Synthetic data with 1E noise Synthetic data with 2E noise
 With 1E noise  With 2E noise

Although the deep mass A is no longer visible in the noise-corrupted images, preliminary experiments with producing visualisations for different frequency bands of the FTG components have given good results for highlighting deep mass features. This is because the noise is isolated to the high-frequency bands only. In addition, as it's known that deeper masses produce longer wavelength responses, visualising anomalies corresponding to a specific frequency band can give a rough indication of the relative depths of anomalies.

The following images are based on low-pass filtered tensor components, where images on the left contain only low frequencies, and images on the right contain all frequencies, for data corrupted with 2E Gaussian noise. We are currently working on a tool to let you interactively switch between images and zoom in on finer details - come back soon to check it out! In the meantime, you can click on the images below to view them in full-size.

2E noise, scale 1 2E noise, scale 2 2E noise, scale 3 2E noise, scale 4 2E noise, scale 5 2E noise, scale 6

We have also developed an algorithm for estimating the depth of positive (denser) mass anomalies


Next we apply the algorithm to a field FTG survey:

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The resulting visualisation is shown below. Click on the image to enlarge it.
Field dataset visualisation

These results highlight not only the significant point mass anomalies horizontally centred in the image, but also brings out fainter geological structures to the left and right of the image, which are often visible in only a few of the original tensor components.

We are currently in the process of analysing other datasets and comparing our results with geological maps of the survey areas.