lec3 - 1 Common relationships between geologic variables...

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Unformatted text preview: 1 Common relationships between geologic variables. What kind of mathematical model can you use to Recall that chapters 1 &2 have been posted on class web page We discussed this simple linear relationship last time Depth x k Age This is a linear represent different processes? relationship Whether it represents the geologic process adequately is an assumption we make? The previous equation assumes that the age of the sediments at depth =0 are always 0. Thus the intercept is 0 and we ignore it. 70000 10000 10000 20000 30000 40000 AGE (years) 50000 60000 What are the -10000 20 40 60 80 100 Depth (meters) These lines represent cases where the age at 0 depth is different from 0 intercepts? 2 A D k A Should we expect age … we would guess that the increased weight of the overburden would squeeze water from the formation and actually cause grains depth relationships to be linear? would squeeze water from the formation and actually cause grains to be packed together more closely. Thus meter thick intervals would not correspond to the same interval of time. Meter-thick intervals at greater depths would correspond to greater intervals of time. We might also guess that at greater and greater depths the grains themselves would deform in response to the large weight of the overburden pushing down on each grain. 3 These compaction effects make the age-depth relationship non-linear. The same interval of depth D at large depths will include sediments deposited over a much longer period of time than will a shallower interval of the same thickness. The relationship becomes non-linear. The line y=mx+b really isn’t a very good approximation of this age depth relationship. To characterize it more accurately we need to use different kinds of functions - non-linear functions. Quadratic vs. Linear Behavior 50000 100000 150000 Age Here are two different possible representations of age depth data 15,000- D 1000 A and (in red ) 15 000 D 1000 3 2 D A For positive depth-50 50 100 Depth (meters)-100000-50000 15,000- D 1000 3 2 D A What kind of equation is this? 4 Quadratics The general form of a quadratic equation is c bx ax y 2 25 75 125 Y Quadratics 2 2 2 x y 20 10 2 2 x x y-6-4-2 2 4 6 X-75-25 2 3 6 y x Similar examples are presented in the text. Recall the answer to the questions - What are the roots? 2 4 b b 2 4 2 b b ac x a Remember what the significance of the roots is? Tom Wilson, Department of Geology and Geography 5 The increase of temperature with depth beneath the earth’s surface (taken as a whole) is a non-linear process. Waltham presents the 5000 Depth (km) Temperature ( o C) 0 10 100 1150 400 1500 700 1900 2800 3700 510 430 following table 1000 2000 3000 4000 T 5100 4300 6360 4300 1000 2000 3000 4000 5000 6000 7000 Depth (km) See http://www.ucl.ac.uk/Mathematics/geomath/powcontext/poly.html We see that the variations of T with Depth are nearly linear in certain regions of the subsurface. In the upper 100 km in certain regions of the subsurface....
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lec3 - 1 Common relationships between geologic variables...

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