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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On Shaky Ground 2: How Earthquakes Teach Us About Geology

My first earthquake was the Loma Prieta earthquake on October 17, 1989. The 6.9 magnitude earthquake is also known as the World Series Quake because  millions saw the earthquake live on TV as they watched Game 3 at Candlestick Park.

The epicenter of the earthquake was located about 10 miles northeast of Santa Cruz on the Loma Prieta segment of the San Andreas fault system. I was on a commuter bus in Berkeley at the time; I didn’t feel a thing. But, many other people did.

More than 200 buildings were damaged in San Francisco’s Marina District. Forty-two people died when the upper level Cypress Street off-ramp of the Nimitz Freeway collapsed into the lower dock. Hundreds of Oakland residents were displaced when the buildings they lived in or worked in were closed because of structural damage.

Earthquakes are destructive. They cause property damage, injuries and loss of life. But, we can also learn a lot from earthquakes.

Earthquakes are caused by the interactions of tectonic plates. They generally occur at the boundaries where two or more plates meet. We can identify plate boundaries by mapping large amounts of earthquakes.

In this map, strong earthquakes from 2012-2014 are shown in red. Earthquakes from the last week are also shown.plateboundariesYou can see that most earthquakes occur in distinct bands. These bands outline the boundaries of Earth’s tectonic plates. The discovery that earthquakes occur in bands actually contributed to the idea of plate tectonics.

My students learn that there are three types of plate boundaries: divergent boundaries where plates move apart and new crust is formed; convergent boundaries where plates move together and oceanic crust is subducted or pushed down into the mantle; and, transform boundaries where plates move past each other. We can use earthquakes and volcanoes to determine the type of boundary at a map location.

When I added the Smithsonian Institutions Holocene volcanoes layer to the map, it looks like this. volcanoesThe yellow volcanoes are volcanoes that have been active over the last 10,000 years. As you can see, most of these volcanoes occur in the same area as earthquakes. There are some exceptions.

Volcanoes that occur far from plate boundaries are “hot spot” volcanoes. These form when crust travels over a mantle plume, an area in the mantle that is extra hot. Hawaii is a chain of hot spot volcanoes.Hawaii

There are also places where there are earthquakes an no volcanoes. The coast of California is one of those places.

CA

In California, the San Andreas fault marks a transform boundary where the Pacific Plate is moving past the North American plate. Volcanoes only occur at divergent and convergent boundaries. The volcanoes to the east are extinct leftovers from Basin-Range rifting (divergent boundary).

We can use earthquake depth to determine if a map boundary is convergent or divergent. In this map, depth is shown by the size of the circle. Deeper earthquakes appear larger.

deep

Shallow earthquakes (less than 75 km deep) often occur at mid-ocean ridges. These are long chains of underwater volcanoes where tectonic plates move apart and new crust is formed. Deep earthquakes occur at subduction zones where oceanic crust is being pushed under continental crust.

Oceanic-continental_convergence_Fig21oceancont

When this occurs, the subducting plate bumps and scrapes against the overriding plate. This causes deep earthquakes. When the subducting material reaches a depth of about 660 km, the rock becomes soft enough to flow and earthquakes stop.

Non-map images are from Creative Commons (Wikipedia). My map can be found here.