Geomathematics GEOL 351
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This 12 page Class Notes was uploaded by Jessica Braun MD on Saturday September 12, 2015. The Class Notes belongs to GEOL 351 at West Virginia University taught by Thomas Wilson in Fall. Since its upload, it has received 41 views. For similar materials see /class/202715/geol-351-west-virginia-university in Geology at West Virginia University.
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Date Created: 09/12/15
i a Gamma7x7 Estimating the coefficients of linear exponential polynomial logarithmic and power law expressions tomhwilson tomwilsonmailwvuedu Department of Geology and Geography West Virginia University Morgantown WV Vnamwmui mm ln Show how the computer can be used to estimate the coefficients of various quantitative relationships in geology These include the linear age depth relationship discussed by Waltham the exponential porosity depth relationship polynomial relationship between temperature and depth and general power law relationships such as the Gutenberg Richter relation Vna mimmn luluNu IgquesTions To class may The raTe of accumulation p of ZZ carbonaTe sedimenTs on a reef is given p p06 approximately by PD is The iniTiaI accumulation raTe and Z W is The depTh aT which The accumuIaTion x raTe drops To 037 of iTs iniTiaI value mm wmluumn ma w muwly 4w 45 mm 271111me n m yxxwxmmmmg Vi The Thickness of a boTTomseT bed aT The ixX fooT a a deITa can often be well I toe approximaTed by Where T is The Thickness x is The disTance from The boTTomseT bed sTarT and T0 and X are consTarrTs medium llne rse home 2 mm mamn umumuc m a mm m munimwmm memu mm mgam Woduclm ma mm mm m A 7 mm r mm M proxy 2 water lopsevicresex co r d Ii e me um ne mm 29 mum manmq man m x mm mu Wb mnnUnmmgv specific frequzilcy magnifude dam to esf39mafe 39 he GutenbergRichter Relation logN bma we have the variables m vs N plotted where N is plotted on an axis that is logarithmically scaled b is the slope 5 6 7 8 9 andaistheintercept RichterMagnitude Number ofearthquakes peryear i1ivumnl mm ln a onship logN 0C 72blogA12 where r Am indicates that log N will also vary in proportion to the log of the fault surface area Hence we could also Log ofthe Number ofEanhquzkes per Year r m m mun Square Root of Fault Plane Area kilometers Characterisn e errear Drrrrerrsror Var amrrw muNn Tmqu Depmm m viiiwnul lmumy dogma Geognl w mg Depva LOGN Parameter a 7115559u55 Brewster 5 umuqaz calntv a u u uzqaas Uncercalntv db u usszaaslz 3 Sure um7933317 an v u u42347747 11qu 2 u ssausals Correlaclon in sssuzssl In today s lab we will calculate the bestfit line and calculate the slope and intercept for this line m In fhs example Slope b 116 intercept 606 VYbr1MnhUnm1 lxn e we know the slope and e GutenbergRichter relationship FrequencyMagnitudedatawestenZal Japan log N 116 m 6 06 we can estimate the probability or frequency of occurrence of an earthquake with magnitude 70 or greater by substituting m7 in the above equation log N 7812 606 Doing this yields the prediction that in this region of Japan there will be 1 earthquake with magnitude 7 or greater every 1 15 vears iwl nguml muhln log N 1167n 606 gN 7812 606 logN 7206 lologN 107206 or N 000371M year 1 years or 1148 A m7amp greater There39s about a one in a hundred chance of having a magnitude 7 or greater earthquake in any given year but over a 115 year time period the odds are close to 1 that a magnitude 7 earthquake will occur in this area TmnW39stutLDeymmmm wag ma 06 P11 V 1mm HunMu HZsfarea acfVfy in re surrounding area over fhe pasf 400 years reveals fhe presence of 3 earthuakes wfI magm39fua e 7 and greafer in fhs regan in good agreemenf wfI fhe predc ans from re ufenbeyRchfer reafan Yivlhulvuik urrzlr N CrD no er way 0 lock at this relationship is to say that it states that the number of breaks N is inversely proportional to fragment size r Power law fragmentation relationships have long been recognized in geologic applications YWHHMHML niwmu 70mm DepmmufGen Dsyzr lceognyhy Viliiunul nmhm sxcribed by power law s moo n i w Smc lwnglh of W th tax 5 2 3H1 Mumim nr sum emeran r l 2 L W s Numhef ul one on on me a gun Box counting is a method used to determine the fractal dimension The process begins by dividing an area into a few large oxes or square subdivisions and then counting the number of boxes that contain parts of the pattern One then decreases the box size and then counts again The process is repeated for successively smaller and smaller boxes and the results are plotted in a logN vs logr or log of number of boxes on a side as shown above The slope of that line is the fractal dimension iumlenlmwur 39djoes line fitting come r Basic pump test data Recovery Phase Wale Level Response m 725 72 722 LDOG39Ii39idagjs 12 J u m uzsLOG39Ic IliAT in N Original data showing Recovery phase data after drawdown during transformation which includes pumping and recovery a log transformation of the after pumping ceased observation times Vwmaxguml mm m mm mm mm mmmmmm mm I i A pilot carbon sequestration site 5 here in the Appalachians A V rquot 39 t wvu W 3 WM 4m 39 mm W e p 5 mm m Wm mm w 39 m vimn lKIINI39LI 399 7 mm mummm munda AllM I Dylanquotum 1quotquot Tam Wilsan Depnnrr memm mm 44 00400 4400200 4400000 7 4399800 4399600 4399400 4 00 Tam lesan Depn mem awalngyandegm y Vmxmut 1mm w w w w 538600 538800 539000 539200 539400 539600 539800 540000 Ph MH5 East Laheral Ith Suhsu ace fem 2mm 3mm ADD sun nusznmmmst 1m I m my nsxance mama MH5 u mu 2m 7m Hm sun 0mm mars T y memmumm 39 x 12mm 39 Before you leave today hand in the Take Home Isostacy problem Viilvumnl lmuh i Ine due dates Problems 310 and 311 computer part are due next Tuesday see instructions next page Problems 215 47 and 410 are due next Thursday bring questions on Tuesday We39ll go over them in class after you hand them in as part of the pretest review Vm miww luluNu 39 bproblem check off list Handn Tuesday The 24 I 310 Show your derivation for problem 310 Include all steps 5 points Comwter tasks 2 Hand in a Iplot of settling velocity versus particle radius 3 points IOn a separate sheet of paper or on the plot page itself IExplain how you will calculate lake depth 39 how your comwtations ot the lake depth 3 Hand in a Iplot of settling time versus particle radius for a I 00 meter deep lake 3 points IComment on how the plot of settling time compares to the plot of settling velocity 3 points 3 points Think about this in the context of comments in class about the relationship of Stokes equation for velocity compared to the expression modified to show how time varies with particle radius 3 points ixivuuu 1 mm Read over39 The fi r ring lab compu rer39 exercises We39ll ge r s rar red on Those nex r Tuesday Mid rer39m exam March 3rd waswan mumn
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