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.



~t