Tobler, Steno and Geologic Maps

Waldo Tobler is a geographer at my alma mater, UC Santa Barbara. He is known for Tobler’s Law or the “first law of geography” which states “Everything is related to everything else, but near things are more related to each other than distant things.”

My classmate Sunil Bharuchi recently published a discussion of Tobler’s Law on his blog, GIS 295 Web GIS. He included this image, which explains spatial auto correlation.

Spatial autocorrelation measures how well a set of spatial features and their values are clustered together in space. A spatial feature is a point, line or polygon that identifies the geographic location of a real world object; this object could be a building, a forest, a rock unit or a lake.

According to Tobler’s law, spatial features will be clustered next to more similar spatial features – this is illustrated in the first image above. But, is this always true? Sunil’s post got me thinking.

Here is a geologic map of Yosemite National Park. Which of the images above does it look like?

Map of Yosemite National Park.svg
Map of Yosemite National Park” by General_geologic_map_of_Yosemite_area.png: en:United States Geological Survey derivative work: Grandiose – This file was derived from  General geologic map of Yosemite area.png: . Licensed under CC BY-SA 3.0 via Commons.

I’ve spent years looking at geologic maps, so I told Sunil “image three looks more like geology.” But, does that mean Tobler is wrong?

Not at all.

Nicolas Steno (Niels Stensen, 1638-1686) was a Danish scientist and bishop who made important contributions to the fields of anatomy, paleontology, crystallography and geology. Steno’s principles of statigraphy explain the formation of sedimentary rock and are still used by geologists to determine the history of a rock unit. There are three principles:

  1. The Principle of Superposition: When sediments are deposited, the sediment that is deposited first is at the bottom while sediment that is deposited later is at the top. Therefore, the lower sediments are older.
  2. The Principle of Original Horizontality: Sediment is originally deposited in horizontal layers.
  3. The Principle of Original Continuity: Sediment is deposited in continuous sheets that only stop when they meet an obstacle or taper off because of distance from the source.

Doesn’t the Principle of Original Horizontality sound a lot like Tobler’s Law? Then why don’t geological maps look like the first picture on Sunil’s image?

First of all, sedimentary rock isn’t the only type of rock on Earth.Steno’s principles do not apply to igneous and metamorphic rock.

Second, the Earth is an active planet. Plate tectonics causes sedimentary layers to bend, break and even overturn. Igneous rocks intrude into existing rock from below the Earth’s surface or erupt from above. These processes mean that geologic units are often very complex and the resulting spatial patterns reflect that complexity.

Yosemite USA.JPG
Yosemite USA” by GuyFrancisOwn work. Licensed under CC BY-SA 3.0 via Commons.

James Hutton (1726-1997) was a Scottish physician and geologist who is known as the founder of modern geology. He was the first to suggest that the Earth is continually being formed and that based on the rates of geologic processes, the Earth must be much,much older than the accepted estimate of a few thousand years. He is also known for the Law of Cross-cutting Relationships.

Law of Cross-cutting Relationships: If a fault or other body of rock cuts through another body of rock, then that intrusion must be younger in age than the rock that it cuts or displaces.

It is this Law of Cross-cutting Relationships that helps us interpret geological units and create geological maps.

Can you figure out the temporal relationships in this cross section?

geology
From Earth: Portrait of a Planet, 4th Edition (2011) by Stephen Marshak.

So, how does Tobler’s Law fit in? It depends on scale. If you are standing on an outcrop of sandstone, chances are good that the rock surrounding you will also be sandstone – especially if you are in the tectonically quieter center of a continent. But, If you are mapping Yosemite park using one kilometer pixels, you will find a lot more variation in neighboring areas.

 

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200 Years of Geological Mapping

This is a geologic map of Britain. It is a screen shot of the British Geologic Survey’s “Geology of Britain” viewer.

Brit1

I chose to show bedrock and surface geology because that’s what William Smith showed when he produced the first geologic map of Britain two hundred years ago in 1815.

Unlike many of the English men who made great scientific contributions, William Smith was not nobility – or even well off. He was the son of a farmer. As a young man, he became an apprentice to a surveyor. He eventually went to work for the Somersetshire Coal Canal Company.

While working in the mines, Smith noticed that individual layers of rock on the sides of the pit were  always arranged in the same recognizable relative order. He also noticed that some layers were identifiable by the fossils they contained, and that these fossils were also always in a predictable order.  He was inspired to see if the relationship between the layers of rock or strata, their positions and the fossils they contain was consistent throughout Britain.

As William Smith studied the rocks of England, he drew cross-sections showing relationships and maps showing location. Eventually his work evolved into the first national geologic map. It measured 6 feet by 8.5 feet and showed the rocks of Britain at the a scale of 5 miles per inch.

Smith’s map isn’t so different from the BGS map created using GPS units and satellite data.

627px-Geological_map_Britain_William_Smith_1815
By William Smith (1769-1839) {Public Domain], via Wikimedia Commons

Two hundred years ago, one man created a map by walking through Britain. Since then, geologic maps have been created for every part of the Earth. Thanks to William Smith, mapping is an intergal part of the training of every geologist.

As a geology student, I learned to map in the field by carefully measuring and plotting geologic contacts, folds and faults on a topographic base map.  It wasn’t always easy to distinguish between the greyish-brown of one unit and the brownish-grey of another or determine my location based on map contours. Yet, I eventually learned to make a map that could be interpreted to tell the geologic history of a small area. William Smith didn’t have a topographic base map. How did he do it?

Smith’s map is more than the distribution of rocks. It is a first edition volume of Britain’s geologic history. Since 1815, that volume has been edited and revised hundreds of times, but William Smith is remembered and honored as the original author.

You learn more about William Smith and his maps  and play with an interactive William Smith mapping app here.

Edited some typos (12/7/15)

 

All Maps are Not Created Equal: Blogging About Maps

The assignment is to identify two web maps and two static maps and determine the appropriateness of the medium for internet use.

Geological maps often start as topographic maps.  Topographic maps are available for download from the USGS. There is a fee for most of the maps.

My Geology 111 students use the Fredericksburg quadrangle to practice their map skills. That map can be viewed here. You can see in the image below, that this is not an ideal map for the web.

There is a lot of detail on this map, but I can’t see that detail on my monitor. The contours are barely visible. I ask my students to count contours to estimate change in elevation. This would be impossible if they had to do it on a laptop screen.

fredericksburgquad

When I was a student, I used topographic maps to make geologic maps – maps that show rock units. This is an image of a paper geologic map of Virginia stolen from VirginiaPlaces.org.

geologyva

I can see the entire map on my laptop screen. I can interpret and understand the information. But, it could be much, much better.

The USGS has created an interactive geological map of the U.S. With this map, it is possible to zoom in to a state or county and see the geology of an area in increasing detail. This is the Fredericksburg area. I was able to add County names and information from Google Earth, so I could determine where the rocks are located. fburggeo

This is great and very easy to use, but it only shows one type of information. What if I want to know about rocks and climate? One of the benefits of using a computer to view maps is that multiple types of information can be stored and viewed on one map.

The USGS and esri worked together to create the “Ecological Tapestry of the World“. This interactive map shows rock type, but it also shows bioclimates, landforms,and land cover – all at a 250 meter resolution.

Here’s Fredericksburg.ecomap

The information is also available as a layer in ArcGIS online.