The Fundamentals of Coordinate Systems in Digital Outcrop Modelling

Introduction

Digital Outcrop Models (DOMs) have revolutionised the way geologists study and understand Earth's ancient environments. By creating digital representations of real-world geological outcrops, DOM allows scientists to conduct in-depth analyses without the physical limitations traditionally associated with fieldwork. One fundamental component in creating these models is the implementation of a suitable coordinate system. This plays a crucial role in accurately representing geological features and facilitating precise measurements and analyses.

The coordinate system acts as a standardised framework for locating each point in the digital outcrop model. Without a suitable coordinate system, features within the model may not be represented accurately, leading to potentially incorrect conclusions. Therefore, understanding how to effectively use and navigate coordinate systems in DOM is vital.

In this blog post, we will delve into the details of what coordinate systems are, how they function within DOMs, and practical tips on using them effectively. We will also introduce the concepts of Well-Known Text (WKT) and European Petroleum Survey Group (EPSG) codes, which are essential for standardising coordinate systems across different platforms and software. By the end of this post, you'll have a basic understanding of how to use coordinate systems in DOM, enhancing your accuracy and efficiency in geological modelling.

Understanding Coordinate Systems

Coordinate systems are integral to virtually every aspect of spatial data management and analysis. Essentially, a coordinate system provides a standardised method for defining a point in space. In two dimensions, this is typically achieved through a pair of numerical values which correlate to a point on a flat plane. In three dimensions, an additional value is added to account for depth or height.

These coordinate systems can be categorised into three main types: Cartesian, cylindrical, and spherical.

• Cartesian Coordinate System: This is likely the most intuitive and widely used system. It utilises a series of perpendicular lines (or axes) to define a point in space. In 3D, these axes are commonly referred to as the X, Y, and Z (depth) axes. In geospatial systems, there is a geocentric coordinate system (EPSG:4978) which uses a cartesian system with its origin in the centre of the earth. This has applications in building virtual earth systems. The UTM system is commonly used in geospatial data and uses cartesian coordinates, but UTM is in fact a cylindrical system.
• Cylindrical Coordinate System: This system is based on a circular cylinder, with a point defined by its distance from a central axis (radius), the angle around that axis (azimuth), and the height above or below a reference plane. Examples of these are the Mercator projections used for most modern maps of the world, with the cylinder axis through the poles. The UTM system is also a cylindrical system, but with a transverse cylinder (axis through the equator) rotated for each zone. Most online map systems use a Web Mercator projection.
• Spherical Coordinate System: Based on a sphere, a point in this system is defined by the distance from a central point (radius), the angle from a reference direction (azimuth), and the angle from a reference plane (inclination or polar angle). WGS84 (EPSG:4326) is the latitude-longitude system we are all familiar where the coordinates are defined in degrees, minutes and seconds rather than in Metres.

The choice of a coordinate system is significant as it can greatly affect the accuracy of the model, particularly when interpreting complex geological structures. There are several ways of defining coordinate systems, but commonly EPSG codes and WKT are used. We have already mentioned a couple of EPSG codes (EPSG:4978, and EPSG:4326), but will look at these in the next section.

An Introduction to WKT and EPSG Codes

Well-Known Text (WKT) and European Petroleum Survey Group (EPSG) codes are standardised notations used in the geospatial industry for representing coordinate reference systems. Both WKT and EPSG are instrumental in ensuring the interoperability and accuracy of spatial data, particularly in GIS and other geoscience-related fields.

WKT includes two major variations: one for describing geometric objects and another for describing coordinate reference systems, commonly known as WKT for CRS (Coordinate Reference Systems). In the context of coordinate reference systems, WKT provides a structured textual representation for CRS components, including datums, spheroids, units of measure, and projection methods, among others. This format is known as WKT for CRS and is standardised in documents like ISO 19162 (also known as "WKT 2").

Here is an example WKT for CRS describing the WGS 84 coordinate reference system:

GEOGCRS["WGS 84",  DATUM["World Geodetic System 1984",    ELLIPSOID["WGS 84", 6378137, 298.257223563,      LENGTHUNIT["metre", 1]]],
  PRIMEM["Greenwich", 0, ANGLEUNIT["degree", 0.0174532925199433]],
  CS[ellipsoidal, 2],
    AXIS["longitude", east, ORDER[1], ANGLEUNIT["degree", 0.0174532925199433]],
    AXIS["latitude", north, ORDER[2], ANGLEUNIT["degree", 0.0174532925199433]],
  USAGE[    SCOPE["unknown"],
    AREA["World"],
    BBOX[-90, -180, 90, 180]],
  ID["EPSG", 4326]]

An EPSG code is a numeric identifier that corresponds to a specific spatial reference system (SRS). EPSG stands for "European Petroleum Survey Group," which was an organisation involved in the standardisation of geodetic and coordinate reference systems within the petroleum industry. Each EPSG code serves as a shorthand label that encapsulates the parameters required to define a particular spatial reference system. These parameters often include the datum, projection method, unit of measure, and axis orientation, among other factors. For example, the EPSG code "4326" is widely recognised as representing the WGS 84 coordinate system, which is a geographic coordinate system based on the WGS 84 datum.

There are numerous resources on the internet where you can look up EPSG codes and get the equivalent WKT, for example:

WGS 84 - WGS84 - World Geodetic System 1984, used in GPS - EPSG:4326

Understanding WKT and EPSG codes is especially important when transferring spatial data between different platforms or software, as it ensures the coordinate system information is correctly retained. This is critical in DOM where maintaining spatial accuracy is key for effective analysis.

Coordinate Systems in Digital Outcrop Modelling

Within Digital Outcrop Modelling, coordinate systems serve as the foundation upon which models are built. They provide a mathematical framework to accurately represent the spatial relationships and orientations of geological features.

When building a model, the choice of the coordinate system is dependent on the scale and complexity of the geological structure being represented. For large-scale models or those spanning significant geographical distances, a geographic coordinate system like WGS 84 may be suitable. For smaller-scale, more localised models, a Cartesian coordinate system may be appropriate.

Within VRGS you need to be able to work in Metres, so a projected coordinate system is necessary. The most commonly used coordinate system for this is UTM, though other coordinate systems are available such as the Ordinance Survey of Great Britain OSGB (EPSG:27700).

Practical Tips for Using Coordinate Systems in Digital Outcrop Modelling

• Understanding the Project Needs: Every geological project is unique, with varying scales and complexities so you should select the coordinate system that best suits the nature of your project.
• Knowledge of WKT and EPSG Codes: Always maintain an accurate representation of your chosen coordinate system when importing or exporting data between different platforms. WKT and EPSG codes ensure consistency and avoid misinterpretations.
• Software Familiarity: Each software application handles coordinate systems differently. It's crucial to understand how your preferred software interprets and applies the coordinate system you've chosen.
• Double-Check Your Setup: Errors in setting up your coordinate system can lead to significant issues later. Always double-check your initial setup for accuracy.

Challenges and Solutions in Using Coordinate Systems

Applying coordinate systems in DOMs is not without its challenges. However, understanding these issues can lead to solutions that enhance the accuracy of your models.

• Distortion: Depending on the scale and complexity of your model, distortion can occur when a coordinate system isn't appropriate for the structure being modelled. If faced with this issue, it may be beneficial to explore alternative coordinate systems that better suit the nature of your project.
• Transformation Issues: Problems can arise when converting or transforming between coordinate systems, potentially causing inaccuracies in your model.
• Datum Mismatch: This can occur when combining data that utilise different datums. Always ensure that you're using the correct datum and applying necessary transformations to harmonise data.

These challenges underline the importance of understanding the coordinate system you're working with and being familiar with coordinate systems. By tackling these challenges head-on, you can create more accurate and reliable digital outcrop models.

Troubleshooting Tips for Coordinate Systems in Digital Outcrop Modelling

• Inaccurate Modelling Result: If your modelling result doesn't look as expected, it might be due to incorrect use of the coordinate system. Make sure to double-check the coordinate system used and whether it's appropriate for your specific case.
• Issues with Importing/Exporting Data: If you're facing issues while importing or exporting data between different software, there could be a discrepancy in the coordinate systems being used. Always check that the WKT or EPSG codes are accurately represented during this transfer process.
• Conversion Errors: When transforming from one coordinate system to another, errors may arise due to differences in scale, rotation, or translation parameters. Ensure you fully understand these transformations and have the correct parameters.
• Geographic vs Projected Coordinate Systems: Remember, geographic coordinate systems are based on a 3D model of the Earth, while projected systems are 2D. If you import data into VRGS using a Geographic system (eg WGS84) then when displayed the data will usually have a very small spatial extent, and look very spikey. In this case, set the project coordinate system in VRGS to an appropriate UTM zone, then transform the data.
• Handling Z coordinates: Not all software handles Z coordinates (elevation) in the same way. Be sure to understand how your software deals with this third coordinate to avoid misinterpretation of data. One notable issue is that some subsurface modelling applications use depth as positive numbers, and elevation as negative, while in GIS and geospatial work, elevation is positive and depth is negative. This can lead to your data and/or models being upside down.
• Datum Mismatch: A common issue is using two datasets with different geodetic datums without proper transformation. Always verify the datum and use appropriate transformation when necessary.
• Always update to the latest software version: Sometimes, issues might arise from bugs in the software that have been resolved in newer versions. So, always keep your software up to date.
• You cannot usually convert between coordinate systems using a simple translation even if your datasets are all in metres. If you take a dataset in UTM Zone 30N (EPSG:32630), and try and simply translate it to match data in OSGB (EPSG:27700) you will find they are rotated with respect to each other.

Remember, when you face a problem, the first step in troubleshooting is always to understand the problem clearly. Break it down into smaller parts and tackle each part one by one.

Conclusion

The role of coordinate systems in Digital Outcrop Modelling cannot be understated. By providing a consistent and standardised mathematical framework, coordinate systems enable the accurate representation and analysis of complex geological structures. Understanding how to effectively implement and navigate these systems is critical for any geologist working in the digital realm.

The introduction of standardisation tools such as WKT and EPSG codes further enhances the utility and accuracy of coordinate systems in DOM. By maintaining consistency across different platforms and software, these codes allow for more precise data interpretation and model creation.

While the process can be intricate and challenges may arise, the rewards of correctly utilising coordinate systems are immense. Greater model accuracy, improved data interpretation, and more meaningful geological insights are just some of the benefits that can be gained.

As the field of Digital Outcrop Modelling continues to evolve, the importance of understanding and effectively using coordinate systems will only grow. So, we encourage you to keep learning, exploring, and refining your skills in this area. The path to greater understanding and discovery in geology lies in your hands, and the right tools will ensure your success.