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I'm a consulting geologist for a small company in the Denver area. I study problems related to active tectonics, using geomorphology, structural geology and remote sensing.

Sunday, November 26, 2006

local airy isostacy

still working on that stupid problem. not because it's particularly impossible, but because i am still only nominally motivated to finish it. the deal is: local airy isostatic compensationally derived elevation as a function of variable thickness of mantle lithosphere under thermally driven expansion of mantle rock and correlated changes in material density in the presence of a steady-state geotherm. joy. it's an interesting problem actually, but since i lack the calculus skills of your average m.i.t. mathematics grad student, i am attacking the problem from a graphical / geometric standpoint. luckily, all the base assumptions i'm making allow me to look at the problem this way, since "steady-state conduction" generally means linear geothermal gradient... i.e. a straight line that is easy to assess with simple algebra. it's the feedback from variable thickness and multi-material (varying material properties) layering in the model that throw a wrench in the works. the equation i've derived has 20 terms at the moment. i'm sure if i'd attended a normal highschool that actually taught math worth a damn i could probably boil this down to a simple integral with something like 5-6 terms, but lo; the alternative community highschool was better at teaching things like comparative literature and global economic politics.

anyway, i need to go buy batteries for my calculator before i can really finish this thing. here's a quick pic of my scratching and scribbling.


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