Geology is a science rather than an engineering discipline because it models the real world instead of building structures. Models evolve with the collection of new data and the scientist’s improving understanding.

Geologists require tools that enable them to create and compare possible models quickly and efficiently, engineers need tools with a greater emphasis on precision because they form the basis for precise construction. In mining, the traditional engineering design approach of using sections, plans and elevations to define a structure in 3D is also used to specify natural geological structures, despite geological structures almost never being straight. The contrast is evident in Figure 1.

01

figure 1a

A comparison of engineering and geological structures.

figure 1b

Explicit modelling

Explicit modelling is essentially akin to an engineering drawing process. The modeller defines geological structures such as veins and faults by explicitly drawing them on regularly spaced sections and joining them. The data may constrain where they draw and tools may accelerate the process but fundamentally it is a drawing process.
However, geology doesn’t come in boxes, triangles, straight lines or even sophisticated Bezier curves, these are simply ways of representing the geology on a computer.

Implicit modelling

Implicit modelling is generated by computer algorithms directly from a combination of measured data and user interpretation. The modelling requires a geologist’s insight, but this is made in the form of trends, stratigraphic sequences and other geologically meaningful terms. This approach is faster, more flexible and fundamentally better suited to modelling geology.

Models can also satisfy important geological constraints, e.g. lithological units can fill the space under the ground with no gaps and spaces, cutting through any section at any position will always be consistent with other sections. Unlike explicit modelling where sections are created independently and fitted together to try and create a 3D model. In figure 2 they appear similar, however the explicit section (left) is an input used to create the model formed by manually joining contact points, whereas the implicit section (right) is an output created by slicing through a 3D model created directly from the data.

02

figure 2a

The explicit section in the first image is created by manually joining contact points, whereas the implicit section in the second image is created directly from the data.

figure 1b
When first created, implicit models were considered to be lacking detail and were mainly used in early exploration. However, implicit modelling algorithms have evolved rapidly and can now easily exceed the complexity and level of detail in hand-drawn models. This process of improvement continues.Modellers were much more familiar with wireframes, sections and block models than the concept of mathematical functions. For certain practical problems, these are entirely appropriate. E.g. modern computer graphics hardware is optimised to display wireframes, an axially-aligned section may succinctly explain the geology and a block model may map very closely to an open pit mining process.

03

figure3

A complex vein system

The critical advantage of an implicit model is that it allows the user to answer a simple question: If I went to a particular point under the ground, what would I expect to find based on the data? When we know this at a resolution determined by the data, we can:

The speed of implicit modelling means that models can incorporate the latest data and be kept up-to-date. But another significant benefit is that more than one geological interpretation can be considered and maintained. In future the principal benefit of implicit modelling will be that geological risk can finally be quantified in a usable manner.
The famous mathematical modeller George Box said:

“All models are wrong, but some are useful.”

In essence, implicit modelling allows geologists to produce useful models quickly and efficiently and then adapt them to the needs of the end user, be they engineers, managers or investors.

This web content is a summary of the article “Why implicit modelling”, originally published in the Unearthing 3D implicit modelling ebook. Download full ebook here.

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