Geology 351 - Geomath Segment II Introduction tom.h.wilson tom.wilson@mail.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV

Your Text for This Segment -- Mathematics: A simple tool for Geologists by David Waltham This text will take you through a lot of basic math and carry you through some differential and integral calculus. Most importantly math usage is illustrated using geologic examples.

Please add reading of Chapters 1& 2 to your class effort for this week. Today – I will go over some of the introductory materials in Chapter 1 as we shift gears, and then quickly into Chapter 2. It’s all very basic, but it make you think about math applications in geology

Computer Basics and Book Resources Time to Log In Ctrl Alt Del

http://www.geo.wvu.edu/ ~wilson/geo351.htm Have a look at the class web page Bring up Explorer and go to http://www.geo.wvu.edu/ ~wilson/geo351.htm

Intro.xls Exp.xls Integ.xls

Any general questions about segment 2? Compaction A common geological process

Age versus depth relationship (s) How thick was it originally? Over what length of time was it deposited? ~12,200 years What would an age versus depth plot look like for this coal? In this slide we’re looking at a coal about 4-5 feet thick. At the base of the coal lies an underclay. So you’re beginning to form swamp like conditions, but the pH is too high to preserve organics. The WT is probably right at the surface. At the time these swamps were formed, this area was in the subtropical locations 20 degrees N Lat. The peat begins to accumulate as the pH decreases to 2-3. At this point, the organics are preserved. Not all of them but a large percentage. The low pH knocks out the microbes. Now you’ll see within the coal, there are some non-coaly partings of ash. Basically as the pH ncreases, the organics are removed and you basically get what’s left in the fireplace when you burn your logs. This can happen by a change in climate or by local incursion of ground water which is generally neutral pH. Now as we get up toward the top, you can see there’s a very sharp boundary. Most likely what you have here is distributary channel deposits. Streams probably swept across the area and also probably eroded some of the swampy material. This shale might grade into a sand some distance left or right. Deposition rates of the peat are about 1-2 mm per year, but this 4-5 foot section has been compacted. The percent compaction for peats is about 90 %, do the original thickness was about 40 to 50 feet. SO we’re looking at an age difference from the top to base of the layer of (about 12,00 to 15,000 years at 2mm per year) as much as 24,000 to 30,000 years.

Consider another depositional environment Any ideas where this is? ? It's cold there

Troughs Layered Deposits of?

Variations induced by Astronomical Cycles? 510,000 years 0.5 to 2.1 million years ago 2.1 to 2.7 million years ago Variations induced by Astronomical Cycles?

Mathematics as a tool for solvig geological problems Chapter 1 Mathematics as a tool for solvig geological problems The example presented on page 3 illustrates a simple age-depth relationship for unlithified sediments This equation is a quantitative statement of what we all have an intuitive understanding of - increased depth of burial translates into increased age of sediments. But as Waltham suggests - this is an approximation of reality. What does this equation assume about the burial process? Is it a good assumption?

Age is linearly related to depth where a=age, z=depth Example - if k = 1500 years/m calculate sediment age at depths of 1m, 2m and 5.3m. Repeat for k =3000 years/m 1m 2m 5.3m Age = 1500 years Age = 3000 years Age = 7950 years Age is linearly related to depth For k = 3000years/m? Age = 3000 years Age = 6000 years Age = 15900 years

Subscripts ............ Superscripts - powers Exponential notation Units conversion See text, handout for additional details.

Bring up Excel Computer Lab ... We’ll take a few minutes today to get everyone logged on and take a look at some basic math ideas using some examples illustrated in excel

Nothing due for Thursday For Next Time Finish reading Chapters 1 and 2 (pages 1 through 38) of Waltham Look over the slides in today’s handout, work through the intro problems, and bring your questions to class this Thursday. Otherwise . . . . Nothing due for Thursday

? The stratigraphy is consistent over long distances Separated by about 62 miles

View of the scarp-like wall of one of the polar troughs cutting through the northern polar ice cap of Mars

Here’s another view. Note the sand dunes formed from the lag deposits eroded from the lower, siltier intervals of the cap.