Display logarithmically distributed data in Surfer

Surfer can grid data using a logarithmic scale and display logarithmic contour levels and color scales. This is extremely useful for data with Z values that span several orders of magnitude, such as concentration data with very small values like 0.001 and very large values like those over 10000 (see sample file VOC_Concentration.xlsx for an example of a data file like this). In such cases, gridding with a linear scale smooths the extreme high and low values and biases the grid to the high Z values, thus looses detail in areas with the lower Z values. Gridding and displaying the data on a logarithmic scale allows you to better discern the variability in the lower and higher data ranges.

Gridding Data

If you have logarithmically distributed data, the first step is to grid the data with a logarithmic transform.

1. Click Home | Grid Data | Grid Data.
2. In the Grid Data - Select Data dialog,
   1. Select your data file from the Dataset 1 list on the right side of the dialog, or click the Browse button, select your data file, and click Open.
   2. Set the X, Y, and Z to the appropriate columns from the data file.
   3. Choose your desired Gridding Method from the list on the left.
   4. Click Skip to End.
3. In the Grid Data - <gridding method> - Output dialog,
   1. Set the desired grid limits and resolution in the Output Grid Geometry section.
   2. In the Grid Z Limits section, choose the appropriate Z Transform option. The logarithmic options are:
      • Log, save as log
        This will automatically take the log of the Z values in the data file, grid the log values, and save the grid. The Z of the grid is the log of the original data in the data file. Choose this option if your data spans several orders of magnitude and you want the resulting Z value in the grid file to be in logarithmic units.
      • Log, save as linear
        This will automatically take the log of the Z values in the data file, grid the log values, convert the log values in the grid back to linear values, and save the grid with the Z being in the original linear data units. Choose this option if your data spans several orders of magnitude and you want the resulting Z value in the grid file to be in the same units as your original data.
   3. Set the Output Grid name.
   4. Click Finish to create the grid file.

Displaying Data

Once the grid is created, you can create maps from it, such as contour, color relief or 3D surface maps. How you set the contour level method or the colormap properties will depend on the Z transform chosen when gridding the data.

Log, save as log

If you gridded the data with a Z Transform of Log, save as log, you do not need to do anything special to produce a map with logarithmic scaling. You can simply display contours with the Simple or Advanced level methods and display other grid-based maps (i.e. color relief, shaded relief, or 3D surfaces) with a linear colormap.

This linear contour map displayed with linear contours shows smoothing in the
areas with the very low data values and the areas with the very high data values.

This logarithmic contour map displays z values in log units, and closely honors very low and very high data values.
It was created from a grid with Z Transform set to Log, save as log, and using the Simple level method.

Log, save as linear

If you gridded the data with a Z Transform of Log, save as linear, you will want to use the Logarithmic level method for a contour map or a logarithmic colormap for another grid-based map. This will give you a map showing the logarithmic distribution of the data, but with the Z values of your original data.

Contour Map

Create a contour map with logarithmic contours by following these steps:

1. Click Home | New Map | Contour, select the grid file and click Open.
2. Select the Contours layer in the Contents window.
3. In the Properties window, on the Levels page, set the Level method to Logarithmic. The contour levels and the colormap are both automatically scaled logarithmically.

This contour map shows Z values in the original data units, but still closely honors the very low and very high data values.
It was created from a grid with Z Transform set to Log, save as linear.

Other Grid-Based Maps (i.e. Color Relief or 3D Surface Maps)

Create a non-contour grid-based map with a logarithmically-scaled colormap by following the steps below. These steps were created specifically for color relief maps, but apply to other grid-based map types as well.

1. Click Home | New Map | Color Relief, select the grid file, and click Open.
2. Select the Color Relief layer in the Contents window.
3. In the Properties window, on the General page, click the Custom colormap (...) button in the Colors field.
4. In the Colormap Editor dialog check the Logarithmic scaling check box. You will not see the nodes on the colormap change position, but if you select a node you will see that the Value for each node is now calculated on a log scale.

Check the Logarithmic scaling check box to create a logarithmically-distributed colormap.
The Data Value for each color node updates according to the new scale. For example, the yellow node initially
had a value of 1100.818075 on a linear scale, and it was converted to 12.77771601 on a logarithmic scale.

5. Click OK. The map is updated with the new color scale.

This color relief map with a logarithmic colormap was created from
a grid with Z Transform set to Log, save as linear.

For more information, see:

• Surfer sample file Logarithmic.srf
• Distribution of minor contours in Surfer when using Logarithmic contour levels
• Display logarithmic contour levels in Surfer for existing grid file
• Calculation of logarithmically-scaled Colormap nodes in Surfer
• Logarithmic color scale shows little-to-no color variation in Surfer
• Setting logarithmic contour levels/colormap scaling in Surfer when grid contains negative numbers
• Gridding data with negative or 0 values in Surfer with a log transform

Updated December 2, 2021