Topographic contours are probably the most effective way to display height variations on maps.  Modern geologists have grown up with topographic contours (after all, we probably learnt how to read them in high school), so we never question their validity or usefulness.  Over the last several decades, colourised topographic maps have been introduced to aid topographic visualisation, but the way people use topographic data in GIS software has not changed drastically since hand-drawn topographic contours began to appear on paper maps in the 1800s.

When it comes to representing topography for 3D modelling of drillhole data that has sampled geological units exposed at the surface, I tell my clients to send me anything other than topographic contours and 2D topographic grids (also called digital terrain models, or DTM).  I only use these types of datasets as a last resort because I don’t find either of them all that illuminating as they are biased to work in a 2D representation of topographic data.

Notwithstanding the nearly 200-year history of topographic contours, in today’s post I’ll question the usefulness of topographic contours in the context of 3D modelling.  Some of you, who have grown up using maps and GIS software, might consider this idea to be blasphemous, but I’ve come to the conclusion that what is excellent for 2D analysis can be a hindrance for understanding geology in 3D.  After all, geology is 3D, not 2D.

Why would geologists want an accurate topographic surface?

Before discussing why geologists need an accurate topographic surface, I’ll summarise the two major benefits that I try to obtain from topographic data.

One important benefit is for resource estimations and open-pit design applications.  Accurate modelling of the topographic surface allows for more accurate volume computations, so this benefit to mining requires no further explanation.

The second benefit—and the main reason I’m interested in good quality topographic data—is to aid the geological interpretation and 3D geological modelling process for exploration and mining applications.  If the rocks that I’m trying to model are exposed at surface, the detailed geometry of the erosion surface can reveal important clues about the underlying fabric and geometry of the rocks, which in turn may tell me about the expected geometry of mineral deposits that are hosted within them.  In order to analyse this information, I want to generate the best quality topographic surface from the available raw data so that I can then incorporate the structural details I see on the topographic surface into my subsurface 3D geological model.

Topographic surface is a window to the subsurface geology

For example, in the topographic detail in Figure 1, a series of low dipping surfaces are seen as topographic features (arrowed), and these in turn are a perfect match to the interpreted low dipping nature of the subsurface felsic intrusions (modelled in pink).  In this case good quality structural information from the topography surface is used as an important clue to how to construct the 3D subsurface shape of this intrusion.
 

Figure 1.  Felsic intrusion body in pink is intruded into a well-layered metamorphic package. The tabular shapes of the intrusion are interpreted and modelled as intruding into metamorphic layering, which show up as topographic expressions (arrows).

Topography surface modelling is one of the initial steps that a geologist takes when building a 3D model from drillhole data in Leapfrog Mining or Geomodeller, yet it is something that geologists rarely pay much attention to.  Although this discussion may not be important if the rocks that host the mineralisation are buried under alluvium, it is an issue worth considering if the host rocks are exposed at the surface, or if structural controls can still be seen in the alluvium.

Topography contours = information loss!

A client provided a set of contours that represented the topographic surface from the area shown in Figure 1.  The contours’ data points are shown in Figure 2, and a straight triangulation of these points are shown in Figure 3.


Figure 2. 10 m contour data, with 22 252 points in the dataset; identical location to Figure 1. 
 

Figure 3. Triangulation surface from the 10 m contour point data shown in Figure 2.

The triangulation of the topography (Figure 3) reveals large flat areas, which is an artefact of triangulating contour data.  This surface has little value from the point of view of interpreting surface geology.
Topographic data in the form of contours is used by many mining and exploration companies, mainly because their default representation of topographic data is in 2D GIS software products.  However, if you stop and think about it, contour data is a highly biased sampling of topographic heights in certain X–Y planes, but is very sparsely sampled vertically (in the case of Figure 2, every 10 m, but the points are a fraction of a metre in spacing in the X–Y plane).  While this may have been a convenient form of topographic representation in the 2D map-centric world, it is poor quality 3D dataset for modelling.  Unless the sampling along the Z axis is as close as in the X–Y plane, you cannot generate a satisfactory surface when the points are triangulated (Figure 3).  Interpolating contour data also does not help because the sparse sampling in the Z-axis results in steps and bumps in the modelled topographic surface (Figure 4), which are artefacts of interpolating contour point data.


Figure 4.  Interpolated topography surface from contours shown in Figure 2 using default topography interpolation settings in Leapfrog Mining 2.4.5.17.  Resolution of the surface is 2 m.  Note the steps along topographic ridges (yellow arrows) and the localised bumps and dips (blue arrows), are both artefacts of interpolating topographic contour points using a smooth 3D interpolator.

The madness of throwing out great data 

The contour data shown in Figure 2 is derived from a far more detailed LIDAR dataset that contains interesting and useful geological details.  However, because most GIS and mining packages are not good at importing and using dense LIDAR data, the companies that process and clean LIDAR data convert this dense information into topographic contours and 2D grids (often requested by the clients), thereby throwing out useful information in the process of simplifying the data.  The original LIDAR data is still provided to mining and exploration companies, but most companies ignore this data and only use the simplified dataset (e.g. contours and 2D grids), even for their pit designs!  To me, this is madness—it gives data processing convenience a higher priority than extracting useful geological information and accurate volumes from LIDAR data.
Figure 5 shows the original cleaned up LIDAR data that the contours in Figure 2 were derived from.  I specifically asked for the source data from which the contours were derived from. 
 

Figure 5.  Cleaned up original LIDAR data showing the original points. The area shown is the same as Figure 2. The data comprises 197 500 points in this area, which is a subset of a LIDAR dataset that extends across over a much wider area and that comprises millions of points.

By modelling the LIDAR dataset (as shown in Figure 5) in Leapfrog software, the topographic surface shown in Figure 6 is generated, which contains very valuable structural geological information that can be integrated into the geological modelling process.
 

Figure 6. Topographic surface modelled from the LIDAR point data shown in Figure 5.  The processing was done in Leapfrog Mining 2.4.5.17.  Note that the surface shown in this figure is not a direct interpolation of the LIDAR data, as interpolation of all the points shown in Figure 5 would take too long to process using the default Leapfrog settings.

The topographic surface shown in Figure 6 lets a geologist preserve all the important geological details and also allows the topography surface to be modelled very rapidly, thus obtaining useful results without destroying good quality LIDAR data.  The surface shown in Figure 6 was used in the modelling process of the intrusion geometries shown in Figure 1.

Although I address topographic contours in this post, similar comments can also be made about 2D topographic grids (DTM), as X–Y gridding is essentially a 2D interpolation process and is not a true 3D interpolation method (often referred to as "2.5D", which is nothing more than jargon to impress the ill-informed).  In topographic gridding, the spacing of the X–Y grid is the same everywhere, and changes to rapid lateral topographic heights do not influence the grid spacing.  2D gridding effectiveness breaks down when steep topographic slopes are involved—however, structural geologists are most interested in the details of such rapid horizontal changes in topography.

Geologists should also investigate where the data used to create the 2D grid was derived from.  It may not have not been derived from the high quality LIDAR data, but derived from the gridding of topographic contour data, which makes the 2D grid a step further removed from the original data.

If you’re interested in the steps I took to model a topographic surface from LIDAR data that preserves the geological information (Figure 6), please email me at: jun.cowan@orefind.com.