Lab 8: Mapping - Contouring - Methods - Computer




Now that you understand contouring, we move to an introduction to modern (computer age) methods of working with geological data. On the maps we've looked at for learning contouring, you recall that observations made in the real world by scientists are not usually done in a spatially regular way - x,y locations of data observations tend to be scattered about. This is natural. Consider these examples of data taken at places located here and there, and not on a regular pattern:


Weather Stations


Weather stations are located at airports. You've probably noticed this when checking for weather reports on the Internet, or checking weather radar. Cities (and airports) are not located on a regular grid pattern; they were founded by pioneers who, for various reasons, settled in this area or that.


Oil and Water well locations


Oil and water wells are drilled on an irregular spacing for the most part, wherever it is thought that water or oil will be found. In some areas, well locations can be very close to one another, while large gaps are typical too. In some oil fields oil wells are drilled on a regular grid, but this is the exception. This type of data is very important in geology. Data for the tops and bottoms of sedimentary strata drilled through are the main type of data for each well. So, there will be an x, y location for the well itself, and there will be z values (depth) for the tops and bottoms of rock layers drilled through.


Stars and Galaxies


Astronomers work with data that is scattered, as you can see when looking at the night sky. The data is in three dimensions, of course, in true fashion, with stars scattered in the universe, some closer to us, some farther away. Objects include planets, stars, dust clouds, and whole galaxies. In many uses, two-dimensional maps are made, for which grids and contour maps are done.


Constructing a Grid


It is better for scientific work, for the mathematics and calculations involved, if data is somehow regularly spaced. One very common way of handling irregularly spaced data is to build grids (grid models) whose values are based on the real data -- the scattered real data. First, lets look at the original data and a grid of locations for which values need to be calculated:


The black dots show the x,y locations of the original data (could be weather stations, oil wells, stars, etc.) and the red dots show the x,y locations of the regular grid locations. When you build a grid, you choose how many rows and columns for the grid. There are 9 rows and 9 columns in this grid, for a total of 81 grid locations. The original data (black dots) contains 27 locations, so you see that usually we increase the density of point locations, plus the grid is regular and easier to work with in later calculations.


Now that we have set up a 9 x 9 grid with 81 x,y locations, we need to calculate the z values for each grid location. Grid locations are often called grid nodes. For each grid node, the z value calculation is based on a number of surrounding points in the original (scattered) data, found within a search radius around each grid node:


This illustration shows the calculation for the first grid node, shown by the X, along with the search circle to find points in the original data to use in the calculation. For this grid node, two points in the original data, outlined by squares, are found in the search radius around the grid node. A larger search radius would circumscribe more original data points, but it is best to keep the search radius fairly small, so that grid node calculations represent original z values in the local area of the grid node. Gridding of each of the 81 grid nodes will individually happen. Computers are fast, so it wouldn't take long to make a 9x9, 81 node grid, but for large grids involving thousands of grid nodes, the process take a lot of computer horsepower -- but modern-day computers are fast!


This illustration shows the calculation for another node. For this grid node, there are four points in the original data that fall within the search radius.


The calculation is done by one of many mathematical methods, or algorithms, that have been developed for computer mapping. Some of the calculations are very simple, involving only arithmetic. For instance, the z values of the original points falling within the search radius for a grid node could be averaged to get a z value for the grid node. Other gridding methods are fairly simple, involving algebra and trigonometry, but the most popular methods involve the use of calculus. For users of computer mapping software, just like the users of computer games, it isn't necessary to understand these calculations to make grids. For scientists doing real work it helps to learn the characteristics of the various gridding algorithms and how each perform.


Contour maps are easily made from grids, and are the most common way of visualizing the range of z values calculated. With the same data, different gridding methods provide unique treatment of the calculation problem, and the contour maps show it . The algorithm used to produce the grids in the examples in this lab is natural neighbor gridding . Natural neighbor gridding uses a technique to select which original data points within the search radius will be weighted more in the calculation, based on their distribution around the grid node.


Modern-day science involves computers and computer software of many types, but gridding and contouring software is very important in the disciplines like geology, which involve mapping of surfaces -- the land surface, and the surfaces of underground layers, faults, and rock bodies.


The following contour map was drawn with a computer program (matplotlib python library). First the original, scattered x,y,z data was gridded with a program called, imaginatively enough, griddata, which produced a regular grid like the one show above with the red dots. This regular grid, with interpolated z values for all grid nodes, was then sent to the matplotlib contour program, which produced the following color-filled contour map. That's one of the good things about computer mapping -- it would take forever to color a map like this by hand, but a computer program can do it in seconds.


For descriptions of commonly encountered map features on contour maps, continue on to the landforms section.