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FittingLab - Geology 351 - Geomath Estimating the...

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Geology 351 - Geomath Estimating the coefficients of various Mathematical relationships in Geology Throughout the semester you’ve encountered a variety of mathematical relationships between various geologic variables such as age vs. depth, porosity vs. depth, earthquake magnitude and fault plane area, for example. Very often our data are derived from observations and the parameters defining these various relationships are useful to us as predictors in other situations. Geologists often deal with empirical data and must form quantitative models of geologic behavior based on these observations. The objective of the current lab is to provide you with experience in the use of spreadsheet functions to derive coefficients defining straight lines, exponential functions, power laws and polynomials of the sort we have been studying. Example 1: GET INTO EXCEL Let's start with a simple linear relationship such as the one suggested between age and sediment thickness. Recall the data we worked with in an earlier lab that was taken from problem 2.11 in Waltham's text. In this problem, data shown in the table below * were given for the Troll 3.1 well in the Norwegian North Sea. This is data you used before and should have on your G:\Drive. Depth Age 19.75 1490 407 10510 545 11160 825 11730 1158 12410 1454 12585 2060 13445 2263 14685 * Data taken from Lehman, S., and Keigwin, L., (1992), Sudden changes in North Atlantic circulation during the last deglaciation, Nature, 386, 757-762. You can place column titles Depth and Age in columns A and B, cells A1 and B1. Generate a plot of the data 45
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Your plot should look like that shown at right. Now this plot clearly demonstrates that the relationship between depth and age is non-linear. Earlier we recognized that two straight lines are needed to explain these data: one curve for depths less than 500cm and another curve for depths greater than 500 cm. The graph shows us that sedimentation rate decreased abruptly about 10500 years ago. In our previous analysis of this data we estimated the rate of change of age with change of depth from two points in each area. Depth Age Δ Δ was computed from data points with depths extending from 19.75cm to 407cm and ages from 1490years to 10510 years. This yielded Depth Age Δ Δ = cm years 29 . 23 25 . 387 9020 = . We did a similar analysis of the deeper data and obtained a more gradual age/depth relationship of _________________(Remember how? Refer to your earlier work). L a s t 1 0 y e r 0 500 1000 1500 2000 2500 Depth (cm) 0 2000 4000 6000 8000 10000 12000 14000 16000 Age (years) Recent Sedimentation Record - North Sea P re c d in g 5 rs What we want to do now is use Excel to determine the slope of these data for us, and we’ll limit our analysis to the deeper data since the shallow data consisting of only two points is a trivial case – (there's only one possible answer!). Excel will compute a trendline through the data. The computation assumes that the deviations of Age from the computed line are minimized. The line that Excel computes is the "best fit" line – trendline. But when Excel computes a trendline, it considers all the data points, whereas in our earlier lab we considered only the two end points and thus assumed that the other values fell along the general trend defined by those two points. This may
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FittingLab - Geology 351 - Geomath Estimating the...

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