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"# GeoExchange Site Visit and Local Geology Field Trip\n",
"\n",
"IN THE SPACE BELOW, WRITE OUT IN FULL AND THEN SIGN THE HONOR PLEDGE:\n",
"\n",
"“I pledge my honor that I have not violated the honor code during this examination.”\n",
"\n",
"**PRINT NAME**: \n",
"\n",
"If a fellow student has contributed significantly to this work, please acknowledge them here:\n",
"\n",
"**Peer(s)**: \n",
"\n",
"*Contribution:*\n",
"\n",
"\n",
"By uploading this assignment through Canvas, I sign off on the document below electronically.\n",
"\n",
"----"
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"## Part I: Geotherm: Temperature within the Earth\n",
"\n",
"Conduction is the process by which heat is transferred from the *hotter* end to the *colder* end of an object. The ability of the object of dimension $z$ to conduct heat is known as its *thermal conductivity*, and is denoted $k$. Heat spontaneously flows along a temperature gradient $\\nabla$T = (T2-T1)/$z$, a physical quantity that describes in which direction and at what rate the temperature changes the most rapidly around a particular location. Fourier's Law of heat conduction is expresses the *flux* or the rate of heat flow ($Q$ in $mW/m^2$) as:\n",
"\n",
"$$ Q = k \\cdot A \\frac{T_2-T_1}{z}, $$\n",
"\n",
"where the symbols and their typical values are provided in the table below. \n",
"\n",
"\n",
"\n",
"\n",
"The expressions below is a *model* calculating an approximate conductive geothermal gradient for the lithosphere. Note that these have been derived by taking a cylinder rock of length $z$ and area $A$ and considering Fourier's Law. Also provided is a code snippet to plot the geotherm interactively. Your task is to experiment with and comment on this *model* by changing parameters (e.g. mantle heat flow, thermal conductivity). We explore this in the questions below. Note that the thermal conductivities are derived from samples at room temperature (refer [Pollack et al., *Journal of Geophysical Research*, 1993](Files/Pollack_etal_1993_Rev_Geophys.pdf)). In the *real* Earth, some of these properties can vary both with depth (e.g. $k$) and location on the surface (e.f. T$_s$). \n",
"\n",
"$$\n",
"\\mathrm{T}(z) = \\begin{cases}\n",
" \\frac{Qz}{K}+\\frac{A_\\mathrm{o}z(b-z/2)}{K} +T_s & \\text{if } z < b \\\\ % & is your \"\\tab\"-like command (it's a tab alignment character)\n",
" \\frac{Qz}{K}+\\frac{A_\\mathrm{o}b^2}{2K} +T_s & \\text{b $\\leq$ z $\\leq$ L, where L = 100 km }\n",
"\\end{cases}\n",
"$$\n",
"\n",
"| Parameter | Symbol | Typical Value | Units |\n",
"| ---------------------------- | ----------------------- | ----------------------- | ------------ |\n",
"| Temperature at the surface | T$_s$ | 15 | $^{\\circ}$C |\n",
"| Heat flow in continents | Q | 65 | mW/m$^2$ |\n",
"| Heat flow in oceans | Q | 101 | mW/m$^2$ |\n",
"| Thermal conductivity of Granite | k | 3.1 | W/m/deg |\n",
"| Thermal conductiity of Basalt | k | 1.5 | W/m/deg |\n",
"| Heat production | A$_\\mathrm{o}$ = $\\rho$H$_s$ | 2.0 | $\\mu$W/m$^3$ |\n",
"| Characteristic depth of A$_\\mathrm{o}$| b | 10 | km |\n",
"| Depth | z | Variable | km |\n"
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2 | \n", "2020-07-01 02:00:00 | \n", "6240.119 | \n", "69.600 | \n", "36930.052 | \n", "12195.363 | \n", "14.876885 | \n", "
3 | \n", "2020-07-01 03:00:00 | \n", "6126.111 | \n", "69.286 | \n", "36897.495 | \n", "12146.217 | \n", "14.004767 | \n", "
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