Thursday, March 14, 2013

Mathematica Strat Column

Update 3/25/2013

In my new life as the only geophysicist in a geology/geography department, one of my first jobs is to figure out the local stratigraphy.  These are the rocks we plan to investigate by outcrop and near surface studies, ultimately building a 3D digital geomodel.  The formation of interest just now is the Mississippian Lime, a hot oil target in Oklahoma and Kansas.  Now there have been stratigraphers working around NW Arkansas for over a century, may of them still alive and kicking.  I am the new kid on the block and sure to step on some toes as I try to understand the stratigraphic section.

First I scanned all available digital theses from U Arkansas geology students, then checked the state Geological Survey and recent guidebooks.  Lots of general agreement, but differences in detail.  Then I found this amazing 1970 report from the Picher mine district in far NE Oklahoma. This summarized 130 years of mine geology experience and analysis.  Those miners were working the area like an ant farm and gaining an intimate knowledge of the Boone (Miss Lime) formation.  Surface geologists over the same time have subdivided the Boone into 'upper' and 'lower' with an thin oolitic limestone in there somewhere.  The mine team subdivided the Boone into 6 lithostratigraphic units, which no one ever brought up to the surface.

But my plan is to take a fresh look at the Boone/Miss with modern technology and tools.  The 6 subdivision are useful as a starting point to divide the sections into units that someone might see in well logs and core, sections that someone might care about in the petroleum exploration business.  Note my use of the word 'unit', that avoids the uber-defined terms 'member' and 'facies'.  Surface geologist are very strict with nomenclature.

Anyway, I made a column in excel first.  The nature of a spreadsheet was perfect for this, each member was a couple of cells high and the hierarchy of stratigraphy could build up across columns.  Figure 1 shows this stratigraphic column.

Figure 1. Excel stratigraphic column for NW Arkansas with members having equal height.

Next I went into Adobe Illustrator and laboriously (think 13 hours) converted this to a depth column.  It is shown in Figure 2. 

Figure 2. Same column with members shown in true thickness.

Beautiful, but what happens when some experienced stratigrapher says: "No way, the Batesville is way thinner than that!" Another 12 hours? Not for this cowboy. So I thought about this and concluded that a strat column is just a bunch of rectangles in columns, all linked up.  It occurred to me that Mathematica's manipulate function could be used to build an interactive stratigraphic column.  The finest subdivision of the column is the member, everything else is made up from aggregation of members into formations, series, and systems.  So I spend some time (think 5 hours) building the widget with each member having a thickness sliding bar.  The default values represent the rock column beneath Old Main, except for the Bloyd formation that is missing.  Bloyd thicknesses are given as average values around NW Arkansas (Figure 3)

Figure 3. Interactive stratigraphic column coded in Mathematica with thickness (feet) slider bars.

To show how the whole thing adjusts, if the Chattanooga is much thinner we get Figure 4.

Figure 4. Mathematica stratigraphic column automatically adjusted for Chattanooga Shale thickness of 10 ft rather than the default 60 ft shown in Figure 3

It may not be quite as pretty as the hand-drawn version, but changes take an instant.  And as the stratigraphers beat on me, the code can be modified to my current understanding of the stratigraphy.  

Of course, I am only the latest to try and correlate rock units between regions.  There are some sacred documents that have to be considered.  First is the North American Stratigraphic Code (AAPG, 2005), which actually is some pretty interesting reading in places.  But even to summarize it here is out of the question, the minutiae of stratigraphy is here.  Read it if you want to know what all the arguing is about around the next geology field trip campfire. 

Every state in the USA has a geologic map, carefully prepared over many decades from legions of field workers.  These describe surface rocks, but the state maps rarely fit together.  Infamous 'state line faults' are more common than one would think; places where a geologic unit changes name or assigned age across a state boundary, standing as mute testimony to intellectual battles fought long ago. But progress is being made on this venerable and cantankerous problem. An effort is well underway to stitch together surface geology maps, not just across the United States, but the entire world (OneGeology, 2013). It is wildly ambitious, their motto "making geological map data for the Earth accessible" says it all.  But, in fact, the web site is a bit difficult to navigate, somewhat buggy, and quite slow.  Strange as it may seem, the best way to get at this treasure trove of global geological information, and more, is an iPad app called EarthObserver developed by the Lamont-Doherty Earth Observatory at Columbia University (LDO, 2010).  This amazing App draws on the OneGeology database to give you global geology maps, gravity, magnetics, tectonic plates and boundaries, spreading rates, and more.  Anyone teaching introductory tectonics could build the entire course from EarthObserver.  One could complain it needs better referencing; state and country outlines, latitude and longitude, that sort of thing.  But this is quibbling, it is fantastic.

For example, suppose you are up one night wondering what is the fastest plate boundary velocity on earth, and where is it?  The EarthObserver image in Figure 5 shows a good candidate not far from Samoa.  Maybe I should go there sometime and check it out with the money I saved buying the EarthObserver App.  It costs 99 cents.

Figure 5. EarthObserver screen shot of some fast-moving plates (24 cm/yr) near Samoa.  How fast is 24 cm/yr? It is about the speed as human hair growth, or about 6 times faster than the moon is receding from the earth due to tidal friction.

References cited:

AAPG, 2005, North American stratigraphic code, AAPG Bulletin, v. 89, no. 11, pp. 1547–1591
north american stratigraphic code - USGS National Geologic Map ...

OneGeology, 2013, Making Geological Map Data for the Earth Accessible

LDO, 2010, EarthObserver App: The whole world in your hand

1 comment:

Matt Hall said...

Excellent stuff, Chris... I love it when geophysicists look at geologists' problems (and vice versa!). No doubt an engineer would have solved your problem with Excel.

You might like Timescale Creator too, if you don't already know about it. It's calibrated to time, however, and I don't think it 'understands' depth. You could hack it though, since it has a way to make custom columns (I described the method in this blog post, and their help is pretty good).

One of its nicest feature is the ability to export to SVG, which is an editable vector graphics format. So you can add your own stuff (like your nice grain size log) afterwards.