{ "cells": [ { "cell_type": "markdown", "id": "737d9695-0324-4212-8e87-c7d068dcf809", "metadata": { "tags": [] }, "source": [ "\n", "# Pressure, Plate Motion, and Earthquake Size\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", "----" ] }, { "cell_type": "markdown", "id": "a868fe76-d62f-4548-b9e1-c8ecc745fd11", "metadata": {}, "source": [ "## Part I: Pressure variations on and within a terrestrial planet\n", "\n", "Pressure, force per unit area, plays an important role in making a habitable planet. Atmospheric pressure controls the living condition on the planet's surface while the pressure deep inside the planet dictate which materials at which states exist in the planet. We study pressure on Earth and other planets to understand the dynamic of the planets and find the condition that life may prosper.\n", "\n", "### Section A: pressure at the surface\n", "\n", "Pressure at the surface mostly comes from the atmosphere layer on top of the rocky planet. The surface pressure dictates whether liquid water can exist on the planet. The variation of the pressure in space and time causes the circulation of air and more importantly, weather.\n", "\n", "The air pressure at the Earth’s surface is $1.013 \\times 10^5 \\text{ N/m}^2$. This pressure supports the weight of the Earth’s\n", "atmosphere. (Weight is the gravitational force: $\\text{weight} = m \\times g$.)" ] }, { "cell_type": "markdown", "id": "aced84bc-1efb-4369-9524-ad4b736ce9b9", "metadata": {}, "source": [ "### TO DO\n", "\n", "**Question 1** What is the mass of Earth's atmosphere? The radius of the Earth: $6371 \\text{ km}$. The gravitational acceleration $g: 9.8 \\text{ m/s}^2$. You assume that weight of the Earth's atmosphere acts equally on Earth's surface." ] }, { "cell_type": "markdown", "id": "d74b36fd-e51c-46ad-ba8d-ecb07c436e47", "metadata": {}, "source": [ "**Answer**" ] }, { "cell_type": "markdown", "id": "f5cd3a16-f4d9-4473-922a-823309a71ddc", "metadata": {}, "source": [ "

\n", "

" ] }, { "cell_type": "markdown", "id": "3732eb07-cc5e-445b-ab9d-414f4af74181", "metadata": {}, "source": [ "**Question 2** The planets closest to us, Mars and Venus, are in many ways similar to Earth, but their atmospheres are quite different.\n", "\n", "| Planet | Venus | Mars |\n", "| ---------------------------- | ----------------------- | ----------------------- |\n", "| Radius | 6052 km | 3397 km |\n", "| Gravitational acceleration | 9.1 m/s$^2$ | 3.8 m/s$^2$ |\n", "| Mass of atmosphere | 4.5 x 10$^{20}$ kg | 2.2 x 10$^{16}$ kg |\n", "\n", "What is the atmospheric pressure on the surface of Mars and Venus?" ] }, { "cell_type": "markdown", "id": "255304d7-8593-481a-bffd-adcedb1c595a", "metadata": {}, "source": [ "**Answer**" ] }, { "cell_type": "markdown", "id": "8d66f29f-279c-4a83-88f8-4337e5d26d1c", "metadata": {}, "source": [ "

\n", "

" ] }, { "cell_type": "markdown", "id": "9c93baf9-72cf-4d3f-837e-ca55be5fb8e0", "metadata": {}, "source": [ "### Section B: pressure inside the rocky interior\n", "\n", "While measuring pressure on the surface is easy, measuring deep inside the interior is challenging if possible, because we may not directly access the environment down below. Instead, we determine the pressure from other physical properties including planet's density which can be determined from seismological observations and astronomical observations. \n", "\n", "Dziewonski and Anderson (1980) made the Preliminary Reference Earth Model (PREM) from normal mode observations (mode of the Earth's vibrations), travel time observations for seismic waves and astronomic and geodetic data. PREM contains physical properties such as density, seismic wave velocities, and other elastic properties at specific depths including major boundaries such as Mohorovičić discontinuity and core-mantle bounary.\n", "\n", "\n", "\n", "*Image: Seismic velocities ($\\alpha$ and $\\beta$) and density ($\\rho$) for the Preliminary Reference Earth Model (PREM).*\n", "\n", "In this problem set, we will use PREM to calculate the mass of the Earth, gravitational acceleration, and pressure at any given depth. We have demonstrated how to calculate the pressure inside a planet $P(r)$ from the planet's mass density $\\rho = \\rho(r)$ and the pressure at the planet's surface $P(R)$.\n", "\n", "\\begin{equation}\n", "P(r) = P(R) + \\int_r^R \\rho(a) g(a) da\n", "\\end{equation}\n", "\n", " The gravitational acceration $g(r)$ inside a planet can be determined using Newton's law of gravitation with mass inside the sphere of radius $r$:\n", "\n", "\\begin{equation}\n", "g(r) = \\frac{GM_{\\text{inside}}}{r^2} = \\frac{G}{r^2} \\int_0^r 4\\pi a^2 \\rho(a) da\n", "\\end{equation}" ] }, { "cell_type": "markdown", "id": "5e4d9a3a-828f-4c2e-8465-9ff052b82ce7", "metadata": {}, "source": [ "Note that the density must satisfy the equation\n", "\n", "\\begin{equation}\n", "M_E = \\int_0^R 4\\pi r^2 \\rho(r) dr\n", "\\end{equation}\n", "\n", "where $M_E$ is the planet's mass and $R$ is the planet radius. If you wonder about this equation, it is essentially $\\text{mass} = \\text{density} \\times \\text{volume}$ integrated over the entire sphere." ] }, { "cell_type": "code", "execution_count": 1, "id": "0932a449-d7d2-4cd8-a97f-2c6730a0564a", "metadata": {}, "outputs": [], "source": [ "import pint\n", "import pandas as pd\n", "import pint_pandas\n", "\n", "def read_mineos_cards(file,header = 3, R = None):\n", " \"\"\"\n", " Read a card deck file of physical properties in mineos format\n", " \n", " Input Parameters:\n", " ----------------\n", " \n", " file: mineos card file containing columns with various properties\n", " \n", " header: number of lines in the header\n", " \n", " R: Mean radius of the planet\n", " \"\"\"\n", "\n", " # Get the default unit registry e.g. MKS units\n", " ureg = pint.get_application_registry()\n", " \n", " # set default radius as Earth\n", " if R is None: R = 6371000.0 * ureg.meter\n", "\n", " names=['radius','rho','vpv','vsv','qkappa','qmu','vph','vsh','eta']\n", " units =['m','kg/m^3','m/s','m/s','dimensionless','dimensionless','m/s','m/s','dimensionless']\n", " fields=list(zip(names,units))\n", " #formats=[np.float for ii in range(len(fields))]\n", " # modelarr = np.genfromtxt(file,dtype=None,comments='#',skip_header=3,names=fields)\n", " modelarr = pd.read_csv(file,skiprows=header,comment='#',sep='\\s+',names=fields)\n", "\n", " # read the units from last header\n", " modelarr_ = modelarr.pint.quantify(level=-1)\n", " \n", " # Get the depths based on subtracting radius from R\n", " modelarr_['depth'] = R - modelarr_['radius'].pint.to(R.units)\n", " \n", " return modelarr_" ] }, { "cell_type": "code", "execution_count": 2, "id": "ff6f23f1-a90d-4606-a459-3afae58f91b3", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/opt/export/course/geo203/anaconda3/envs/fall2022/lib/python3.9/site-packages/pint_pandas/pint_array.py:648: UnitStrippedWarning: The unit of the quantity is stripped when downcasting to ndarray.\n", " return np.array(qtys, dtype=\"object\", copy=copy)\n", "/opt/export/course/geo203/anaconda3/envs/fall2022/lib/python3.9/site-packages/pint_pandas/pint_array.py:648: UnitStrippedWarning: The unit of the quantity is stripped when downcasting to ndarray.\n", " return np.array(qtys, dtype=\"object\", copy=copy)\n" ] }, { "data": { "text/html": [ "
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radiusrhovpvvsvqkappaqmuvphvshetadepth
00.013088.4811262.213667.81327.684.611262.213667.81.06371000.0
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.................................
7456369800.01020.01450.00.057822.50.01450.00.01.01200.0
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7496371000.01020.01450.00.057822.50.01450.00.01.00.0
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750 rows × 10 columns

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" ], "text/plain": [ " radius rho vpv vsv qkappa qmu vph vsh \\\n", "0 0.0 13088.48 11262.21 3667.8 1327.6 84.6 11262.21 3667.8 \n", "1 6824.0 13088.47 11262.2 3667.79 1327.6 84.6 11262.2 3667.79 \n", "2 13648.0 13088.44 11262.18 3667.78 1327.6 84.6 11262.18 3667.78 \n", "3 20472.0 13088.39 11262.14 3667.75 1327.6 84.6 11262.14 3667.75 \n", "4 27296.0 13088.32 11262.09 3667.72 1327.6 84.6 11262.09 3667.72 \n", ".. ... ... ... ... ... ... ... ... \n", "745 6369800.0 1020.0 1450.0 0.0 57822.5 0.0 1450.0 0.0 \n", "746 6370100.0 1020.0 1450.0 0.0 57822.5 0.0 1450.0 0.0 \n", "747 6370400.0 1020.0 1450.0 0.0 57822.5 0.0 1450.0 0.0 \n", "748 6370700.0 1020.0 1450.0 0.0 57822.5 0.0 1450.0 0.0 \n", "749 6371000.0 1020.0 1450.0 0.0 57822.5 0.0 1450.0 0.0 \n", "\n", " eta depth \n", "0 1.0 6371000.0 \n", "1 1.0 6364176.0 \n", "2 1.0 6357352.0 \n", "3 1.0 6350528.0 \n", "4 1.0 6343704.0 \n", ".. ... ... \n", "745 1.0 1200.0 \n", "746 1.0 900.0 \n", "747 1.0 600.0 \n", "748 1.0 300.0 \n", "749 1.0 0.0 \n", "\n", "[750 rows x 10 columns]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "PREM = read_mineos_cards('Files/PREM750_CARDS')\n", "\n", "PREM" ] }, { "cell_type": "code", "execution_count": 3, "id": "ffa56537-d32e-4b1a-98d8-cddab8e81ba7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0 13.088480000000002\n", "1 13.088470000000003\n", "2 13.088440000000004\n", "3 13.088390000000002\n", "4 13.088320000000003\n", " ... \n", "745 1.0200000000000002\n", "746 1.0200000000000002\n", "747 1.0200000000000002\n", "748 1.0200000000000002\n", "749 1.0200000000000002\n", "Name: rho, Length: 750, dtype: pint[gram / cubic_centimeter]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# grabbing values in 'g/cc' as a pandas series\n", "PREM.rho.pint.to('g/cc')" ] }, { "cell_type": "code", "execution_count": 4, "id": "ca170c60-63ca-4735-bd47-558be4789da0", "metadata": { "scrolled": true, "tags": [] }, "outputs": [ { "data": { "text/plain": [ "array([13.08848, 13.08847, 13.08844, 13.08839, 13.08832, 13.08822,\n", " 13.08811, 13.08798, 13.08783, 13.08766, 13.08746, 13.08725,\n", " 13.08702, 13.08676, 13.08649, 13.0862 , 13.08588, 13.08555,\n", " 13.08519, 13.08482, 13.08442, 13.08401, 13.08357, 13.08311,\n", " 13.08264, 13.08214, 13.08162, 13.08109, 13.08053, 13.07995,\n", " 13.07935, 13.07873, 13.07809, 13.07744, 13.07676, 13.07606,\n", " 13.07534, 13.0746 , 13.07384, 13.07306, 13.07225, 13.07143,\n", " 13.07059, 13.06973, 13.06885, 13.06795, 13.06702, 13.06608,\n", " 13.06512, 13.06413, 13.06313, 13.0621 , 13.06106, 13.06 ,\n", " 13.05891, 13.05781, 13.05668, 13.05553, 13.05437, 13.05318,\n", " 13.05198, 13.05075, 13.0495 , 13.04823, 13.04695, 13.04564,\n", " 13.04431, 13.04296, 13.04159, 13.0402 , 13.03879, 13.03736,\n", " 13.03591, 13.03444, 13.03295, 13.03144, 13.02991, 13.02836,\n", " 13.02679, 13.0252 , 13.02358, 13.02195, 13.0203 , 13.01863,\n", " 13.01693, 13.01522, 13.01349, 13.01173, 13.00996, 13.00816,\n", " 13.00635, 13.00451, 13.00266, 13.00078, 12.99888, 12.99697,\n", " 12.99503, 12.99307, 12.9911 , 12.9891 , 12.98708, 12.98504,\n", " 12.98299, 12.98091, 12.97881, 12.97669, 12.97455, 12.97239,\n", " 12.97021, 12.96801, 12.96579, 12.96355, 12.96129, 12.95901,\n", " 12.9567 , 12.95438, 12.95204, 12.94968, 12.94729, 12.94489,\n", " 12.94247, 12.94002, 12.93756, 12.93508, 12.93257, 12.93005,\n", " 12.9275 , 12.92494, 12.92235, 12.91975, 12.91712, 12.91447,\n", " 12.91181, 12.90912, 12.90641, 12.90368, 12.90094, 12.89817,\n", " 12.89538, 12.89257, 12.88974, 12.88689, 12.88402, 12.88113,\n", " 12.87822, 12.87529, 12.87234, 12.86937, 12.86638, 12.86337,\n", " 12.86034, 12.85729, 12.85421, 12.85112, 12.84801, 12.84488,\n", " 12.84172, 12.83855, 12.83535, 12.83214, 12.82891, 12.82565,\n", " 12.82238, 12.81908, 12.81576, 12.81243, 12.80907, 12.8057 ,\n", " 12.8023 , 12.79888, 12.79545, 12.79199, 12.78851, 12.78501,\n", " 12.78149, 12.77795, 12.7744 , 12.77082, 12.76722, 12.7636 ,\n", " 12.16635, 12.15977, 12.15314, 12.14645, 12.13971, 12.13291,\n", " 12.12605, 12.11914, 12.11218, 12.10515, 12.09807, 12.09093,\n", " 12.08373, 12.07648, 12.06917, 12.06179, 12.05437, 12.04688,\n", " 12.03933, 12.03172, 12.02405, 12.01633, 12.00854, 12.00069,\n", " 11.99278, 11.98481, 11.97678, 11.96868, 11.96053, 11.95231,\n", " 11.94403, 11.93569, 11.92728, 11.91881, 11.91028, 11.90168,\n", " 11.89302, 11.8843 , 11.87551, 11.86666, 11.85774, 11.84875,\n", " 11.8397 , 11.83058, 11.8214 , 11.81215, 11.80284, 11.79346,\n", " 11.784 , 11.77449, 11.7649 , 11.75525, 11.74553, 11.73574,\n", " 11.72588, 11.71595, 11.70595, 11.69589, 11.68575, 11.67554,\n", " 11.66526, 11.65492, 11.6445 , 11.634 , 11.62344, 11.61281,\n", " 11.6021 , 11.59132, 11.58047, 11.56955, 11.55855, 11.54748,\n", " 11.53634, 11.52512, 11.51383, 11.50246, 11.49102, 11.4795 ,\n", " 11.46791, 11.45625, 11.4445 , 11.43269, 11.42079, 11.40882,\n", " 11.39677, 11.38464, 11.37244, 11.36016, 11.3478 , 11.33537,\n", " 11.32285, 11.31026, 11.29758, 11.28483, 11.272 , 11.25909,\n", " 11.2461 , 11.23303, 11.21987, 11.20664, 11.19333, 11.17993,\n", " 11.16645, 11.15289, 11.13925, 11.12553, 11.11172, 11.09783,\n", " 11.08386, 11.0698 , 11.05566, 11.04144, 11.02713, 11.01274,\n", " 10.99826, 10.9837 , 10.96905, 10.95432, 10.9395 , 10.92459,\n", " 10.9096 , 10.89452, 10.87935, 10.8641 , 10.84876, 10.83333,\n", " 10.81781, 10.80221, 10.78651, 10.77073, 10.75486, 10.7389 ,\n", " 10.72285, 10.70671, 10.69048, 10.67416, 10.65775, 10.64124,\n", " 10.62465, 10.60796, 10.59119, 10.57432, 10.55736, 10.5403 ,\n", " 10.52316, 10.50592, 10.48858, 10.47116, 10.45363, 10.43602,\n", " 10.41831, 10.40051, 10.38261, 10.36461, 10.34652, 10.32834,\n", " 10.31005, 10.29168, 10.2732 , 10.25463, 10.23596, 10.2172 ,\n", " 10.19833, 10.17937, 10.16031, 10.14115, 10.1219 , 10.10254,\n", " 10.08309, 10.06353, 10.04388, 10.02412, 10.00427, 9.98432,\n", " 9.96426, 9.9441 , 9.92384, 9.90348, 5.56645, 5.56175,\n", " 5.55705, 5.55236, 5.54766, 5.54297, 5.53828, 5.53359,\n", " 5.5289 , 5.52421, 5.51953, 5.51485, 5.51016, 5.50548,\n", " 5.50081, 5.49613, 5.49145, 5.49145, 5.48673, 5.48201,\n", " 5.47729, 5.47257, 5.46785, 5.46313, 5.45842, 5.4537 ,\n", " 5.44899, 5.44427, 5.43956, 5.43485, 5.43013, 5.42542,\n", " 5.42071, 5.416 , 5.41129, 5.40657, 5.40186, 5.39715,\n", " 5.39244, 5.38773, 5.38302, 5.3783 , 5.37359, 5.36888,\n", " 5.36417, 5.35945, 5.35474, 5.35002, 5.34531, 5.34059,\n", " 5.33587, 5.33116, 5.32644, 5.32172, 5.317 , 5.31228,\n", " 5.30755, 5.30283, 5.2981 , 5.29338, 5.28865, 5.28392,\n", " 5.27919, 5.27446, 5.26972, 5.26498, 5.26025, 5.25551,\n", " 5.25077, 5.24602, 5.24128, 5.23653, 5.23178, 5.22703,\n", " 5.22227, 5.21752, 5.21276, 5.208 , 5.20323, 5.19847,\n", " 5.1937 , 5.18893, 5.18415, 5.17938, 5.1746 , 5.16982,\n", " 5.16503, 5.16024, 5.15545, 5.15065, 5.14586, 5.14106,\n", " 5.13625, 5.13144, 5.12663, 5.12182, 5.117 , 5.11217,\n", " 5.10735, 5.10252, 5.09769, 5.09285, 5.08801, 5.08316,\n", " 5.07831, 5.07346, 5.0686 , 5.06374, 5.05887, 5.054 ,\n", " 5.04913, 5.04425, 5.03936, 5.03447, 5.02958, 5.02468,\n", " 5.01978, 5.01487, 5.00996, 5.00504, 5.00012, 4.99519,\n", " 4.99026, 4.98532, 4.98038, 4.97543, 4.97047, 4.96551,\n", " 4.96055, 4.95558, 4.9506 , 4.94562, 4.94063, 4.93564,\n", " 4.93064, 4.92563, 4.92062, 4.9156 , 4.91058, 4.90555,\n", " 4.90051, 4.89547, 4.89042, 4.88537, 4.88031, 4.87524,\n", " 4.87016, 4.86508, 4.85999, 4.8549 , 4.8498 , 4.84469,\n", " 4.83957, 4.83445, 4.82932, 4.82418, 4.81904, 4.81388,\n", " 4.80873, 4.80356, 4.79839, 4.7932 , 4.78802, 4.78282,\n", " 4.77761, 4.7724 , 4.76718, 4.76195, 4.75672, 4.75148,\n", " 4.74622, 4.74096, 4.73569, 4.73042, 4.72513, 4.71984,\n", " 4.71454, 4.70923, 4.70391, 4.69858, 4.69325, 4.6879 ,\n", " 4.68255, 4.67719, 4.67182, 4.66644, 4.66105, 4.65565,\n", " 4.65024, 4.64482, 4.6394 , 4.63396, 4.62852, 4.62306,\n", " 4.6176 , 4.61213, 4.60664, 4.60115, 4.59565, 4.59014,\n", " 4.58461, 4.57908, 4.57354, 4.56799, 4.56242, 4.55685,\n", " 4.55127, 4.54568, 4.54007, 4.53446, 4.52883, 4.5232 ,\n", " 4.51755, 4.5119 , 4.50623, 4.50055, 4.49486, 4.48916,\n", " 4.48345, 4.47773, 4.472 , 4.46625, 4.4605 , 4.45473,\n", " 4.44895, 4.44317, 4.44317, 4.4393 , 4.43543, 4.43156,\n", " 4.42767, 4.42379, 4.4199 , 4.416 , 4.4121 , 4.4082 ,\n", " 4.40428, 4.40037, 4.39644, 4.39252, 4.38858, 4.38465,\n", " 4.3807 , 3.99214, 3.99097, 3.98981, 3.98864, 3.98748,\n", " 3.98632, 3.98515, 3.98399, 3.98282, 3.98166, 3.98049,\n", " 3.97933, 3.97817, 3.977 , 3.97584, 3.97584, 3.96744,\n", " 3.95903, 3.95063, 3.94223, 3.93383, 3.92542, 3.91702,\n", " 3.90862, 3.90022, 3.89181, 3.88341, 3.87501, 3.86661,\n", " 3.8582 , 3.8498 , 3.8414 , 3.833 , 3.82459, 3.81619,\n", " 3.80779, 3.79939, 3.79098, 3.78258, 3.77418, 3.76578,\n", " 3.75737, 3.74897, 3.74057, 3.73217, 3.72376, 3.54326,\n", " 3.53968, 3.53609, 3.53251, 3.52893, 3.52534, 3.52176,\n", " 3.51818, 3.51459, 3.51101, 3.50743, 3.50385, 3.50026,\n", " 3.49668, 3.4931 , 3.48951, 3.48593, 3.48235, 3.47877,\n", " 3.47518, 3.4716 , 3.46802, 3.46443, 3.46085, 3.45727,\n", " 3.45368, 3.4501 , 3.44652, 3.44294, 3.43935, 3.43577,\n", " 3.35949, 3.36016, 3.36082, 3.36148, 3.36214, 3.3628 ,\n", " 3.36346, 3.36413, 3.36479, 3.36545, 3.36611, 3.36677,\n", " 3.36743, 3.36809, 3.36876, 3.36942, 3.37008, 3.37074,\n", " 3.3714 , 3.37206, 3.37273, 3.37339, 3.37405, 3.37471,\n", " 3.37471, 3.37514, 3.37557, 3.37601, 3.37644, 3.37687,\n", " 3.3773 , 3.37773, 3.37817, 3.3786 , 3.37903, 3.37946,\n", " 3.37989, 3.38032, 3.38076, 2.9 , 2.9 , 2.9 ,\n", " 2.9 , 2.9 , 2.9 , 2.9 , 2.9 , 2.9 ,\n", " 2.9 , 2.9 , 2.6 , 2.6 , 2.6 , 2.6 ,\n", " 2.6 , 2.6 , 2.6 , 2.6 , 2.6 , 2.6 ,\n", " 2.6 , 1.02 , 1.02 , 1.02 , 1.02 , 1.02 ,\n", " 1.02 , 1.02 , 1.02 , 1.02 , 1.02 , 1.02 ])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# grabbing value in 'g/cc' as a numpy array\n", "PREM.rho.pint.to('g/cc').values.data" ] }, { "cell_type": "markdown", "id": "2eb5ee2b-5c97-43dd-ac95-6359de6c9e58", "metadata": { "tags": [] }, "source": [ "### Mini-tutorial\n", "\n", "- **Integration with scipy**\n", "\n", "[SciPy](https://docs.scipy.org/doc/scipy/tutorial/general.html) is a collection of mathematical algorithms and convenience functions built on the [NumPy](https://numpy.org/doc/stable/user/whatisnumpy.html) extension of Python. SciPy allows us to optimize functions, find roots of functions, interpolate, and integrate. It also provides mathematical and physical constants\n", "\n", "Since PREM provided the density at specific depths, and we do not know the analytical form of density, we will use the trapezoidal rule to integrate.\n", "\n", "In this mini-tutorial, we will compute a definite integral of $y = f(x) = 10 - x^2$ from $x=0$ to $x=3$. This integral can be evaluated easily the value by hand:\n", "\\begin{equation}\n", "\\int_{-3}^3 (10 - x^2) dx = \\left(10x - \\frac{x^3}{3}\\right) \\Big|_{x=-3}^{x=3} = 42\n", "\\end{equation}\n", "\n", "We will use `scipy.integrate.trapezoid` to integrate the function with given (x,y) using Trapezoidal rule.\n", "\n", "Focus on the following lines:\n", "\n", "`from scipy import integrate`\n", "\n", "`integral = integrate.trapezoid(y_trap, x_trap)`\n", "\n", "Run the next two cells below and then adjust the slider on the figure. Notice the area approaches 42 when the number of trapezoids increases." ] }, { "cell_type": "code", "execution_count": 5, "id": "8c3e7b9c-7402-4f2a-9f5f-d8abdca57aee", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from scipy import integrate\n", "\n", "import plotly.graph_objects as go\n", "from plotly.offline import init_notebook_mode, iplot\n", "init_notebook_mode()" ] }, { "cell_type": "code", "execution_count": 6, "id": "25981545-8ab6-4cf6-9514-5df9f630b83f", "metadata": { "tags": [] }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "line": { "color": "#000000", "width": 2 }, "mode": "lines", "name": "$y = 10 - x^2$", "type": "scatter", "visible": true, "x": [ -4, -3.99, -3.98, -3.97, -3.96, -3.95, -3.94, -3.93, -3.92, -3.91, 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Create figure\n", "fig = go.Figure()\n", "\n", "# actual curve\n", "x_true = np.linspace(-4,4,801)\n", "y_true = 10 - x_true ** 2\n", "\n", "num_steps = 21\n", "\n", "# True_curve\n", "trace_list1 = []\n", "\n", "# Outline of Trapezoids + shades\n", "trace_list2 = []\n", "\n", "# divides of Trapezoids\n", "trace_list3 = []\n", "\n", "# Add traces, one for each slider step\n", "for number_of_trapezoids in range(1,1+num_steps):\n", " trace_list1 += [go.Scatter(x=x_true, y=y_true, \n", " visible=True,\n", " line=dict(color=\"#000000\", width=2),\n", " mode=\"lines\",\n", " name=r\"$y = 10 - x^2$\")]\n", " \n", " # integrate y = f(x) from x=0 to x=3\n", " x_trap = np.linspace(-3,3,number_of_trapezoids+1)\n", " y_trap = 10 - x_trap ** 2\n", "\n", " # integration takes place here\n", " integral = integrate.trapezoid(y_trap, x_trap)\\\n", "\n", " trace_list2 += [go.Scatter(\n", " visible=False,\n", " line=dict(color=\"#E00000\", width=2),\n", " name=str(number_of_trapezoids) + \" trapezoids\",\n", " fill='tozeroy',\n", " x=x_trap,\n", " y=y_trap)]\n", " \n", " x_plot = x_trap\n", " y_plot = 0 * y_trap\n", " \n", " for jj in range(number_of_trapezoids+1):\n", " x_plot = np.concatenate((x_plot, [np.nan], [x_trap[jj], x_trap[jj]]))\n", " y_plot = np.concatenate((y_plot, [np.nan], [0, y_trap[jj]]))\n", " \n", " trace_list3 += [go.Scatter(\n", " visible=False,\n", " line=dict(color=\"#E00000\", width=2),\n", " name=\"area = %.3f\"%integral,\n", " x=x_plot,\n", " y=y_plot)]\n", " \n", "\n", "fig = go.Figure(data=trace_list1+trace_list2+trace_list3)\n", "\n", "# Make 10th trace visible\n", "fig.data[10-1].visible = True\n", "fig.data[10-1+num_steps].visible = True\n", "fig.data[10-1+2*num_steps].visible = True\n", "\n", "steps = []\n", "for i in range(num_steps):\n", " # Hide all traces\n", " step = dict(\n", " method = 'restyle',\n", " args = ['visible', [False] * len(fig.data)],\n", " label = str(i + 1)\n", " )\n", " # Enable the two traces we want to see\n", " step['args'][1][i] = True\n", " step['args'][1][i+num_steps] = True\n", " step['args'][1][i+2*num_steps] = True\n", " \n", " # Add step to step list\n", " steps.append(step)\n", "\n", "sliders = [dict(\n", " active=9,\n", " steps = steps,\n", " currentvalue={\"prefix\": \"Number of trapezoids: \"}\n", ")]\n", "\n", "fig.layout.sliders = sliders\n", "\n", "iplot(fig, show_link=False)" ] }, { "cell_type": "markdown", "id": "42fe1530-470c-4434-ae69-e37ea316fc76", "metadata": {}, "source": [ "### TO DO\n", "\n", "**Question 3** Plot the density profile. Include the location of the inner core boundary (radius = 1221.5 km) and the core-mantle boundary (3480 km). Comment on relative distribution of lighter versus heavier material inside the Earth between the regions-mantle, inner and outer core. Calculate the mass of the Earth by integration. Does the calculated value of the entire Earth's mass match the actual Earth's mass?" ] }, { "cell_type": "markdown", "id": "c0c073eb-3203-4052-b57d-c1ac255bfebe", "metadata": {}, "source": [ "**Answer**" ] }, { "cell_type": "markdown", "id": "4bc26095-44f9-4e5a-8199-d6a5aa084a87", "metadata": {}, "source": [ "

\n", "

" ] }, { "cell_type": "markdown", "id": "a7692fa9-c60c-4975-8881-d3891c7786a8", "metadata": {}, "source": [ "**Question 4** Compute the gravitational acceleration at any radii shown in PREM. Where inside the Earth is the gravitational acceleration maximum? Please explain the factors that might lead to this observation." ] }, { "cell_type": "markdown", "id": "84efbd3f-96c4-4a92-a0f4-6bc40bb72a60", "metadata": {}, "source": [ "**Answer**" ] }, { "cell_type": "markdown", "id": "c1c7e655-cbb0-48ce-bb70-4f525e63f01f", "metadata": {}, "source": [ "

\n", "

" ] }, { "cell_type": "markdown", "id": "cd51b606-f88c-4780-b549-aaabba5ff438", "metadata": {}, "source": [ "**Question 5** Compute the pressure based on the density profile of PREM. What are the pressures at the core-mantle boundary and the center of the Earth? How do these values compare to the atmospheric pressure on the Earth's surface?" ] }, { "cell_type": "markdown", "id": "abfe31aa-bf22-4d9a-ab51-4392b02929d9", "metadata": {}, "source": [ "**Answer**" ] }, { "cell_type": "markdown", "id": "7eb1002c-a313-4496-b2ab-ea3ed5b7509b", "metadata": {}, "source": [ "

\n", "

" ] }, { "cell_type": "markdown", "id": "14ceeb1a-0b3c-4e77-9db8-50f1d9eb8ff7", "metadata": {}, "source": [ "----\n", "## Part II: Plate Motion\n", "\n", "Below is a sketch that shows the (simplified) geometry of the lithospheric plates near the coast of Oregon and Washington. Three plates are present: the North America plate, the Pacific plate, and the Juan de Fuca plate.\n", "\n", "\n", "\n", "*Figure: Schematic of the plate configuration offshore Washington State and the Paciic Northwest.*\n", "\n", "Assume (1) that the spreading of the Juan de Fuca plate and Pacific plate is perpendicular to the\n", "ridge as drawn, and is 40 mm/yr, and (2) that the strike-slip motion between the North America\n", "plate and the Pacific plate is parallel to the North America—Pacific plate boundary and is 56 mm/yr.\n", "The orientation of the ridge is 10$^{\\circ}$ East of North. The orientation of the North America—Pacific\n", "plate boundary is 35$^{\\circ}$ West of North." ] }, { "cell_type": "code", "execution_count": 7, "id": "0fc7837c-40a1-40c8-8e2b-ee4960db12d7", "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "import json\n", "import numpy as np\n", "import plotly.express as px\n", "import plotly.graph_objects as go" ] }, { "cell_type": "code", "execution_count": 8, "id": "9e8ceb7b-5da9-451e-9917-13d37419b6b5", "metadata": {}, "outputs": [], "source": [ "def cutoff_track(lon, lat, cutoff_lon):\n", " \"\"\"\n", " Insert nan between two points that cross the cutoff lontitude. \n", " Avoid horizontal line when plot the track\n", " \n", " Input Parameters:\n", " ----------------\n", " \n", " lon: longitude array\n", " lat: latitude array\n", " cutoff_lon: divide the curve at this cutoff longitude\n", " \n", " Return:\n", " ------\n", " \n", " lon, lat: updated arrays\n", " \"\"\"\n", " xtrk = np.mod(lon - cutoff_lon, 360)\n", " is_cross = np.where(np.abs(xtrk[1:-1]-xtrk[0:-2]) > 90)[0]\n", " nans = np.empty(np.size(is_cross))\n", " nans[:] = np.nan\n", " lon = np.insert(lon, is_cross+1, nans)\n", " lat = np.insert(lat, is_cross+1, nans)\n", " return lon, lat\n", "\n", "def load_plate_boundaries(filename):\n", " \"\"\"\n", " Input Parameters:\n", " ----------------\n", " \n", " filename: input JSON file name containing the curve locations\n", " \"\"\" \n", "\n", " # Opening JSON file\n", " f = open(filename)\n", "\n", " # returns JSON object as a dictionary\n", " boundary = json.load(f)\n", " \n", " f.close()\n", "\n", " boundary = np.array(boundary[1])\n", " lons = boundary[:,0]\n", " lats = boundary[:,1]\n", "\n", " lons, lats = cutoff_track(lons, lats, 180)\n", " \n", " return lons, lats\n", "\n", "def add_arrow(fig, p0, p1, label_txt=\"\", c=\"black\"):\n", " \"\"\"\n", " Draw an arrow starting from p0 pointing at p1\n", " \n", " Input Parameters:\n", " -----------------\n", " \n", " fig: target figure object\n", " p0: [lon, lat] where the arrow starts\n", " p1: [lon, lat] where the arrow heads\n", " label_txt: label text [default: \"\"]\n", " c: arrow color [default: \"black\"]\n", " \"\"\"\n", " # vector of the arrow\n", " v = p1-p0\n", " # normalized vector\n", " w = v/np.linalg.norm(v)\n", " # orthogonal on v\n", " u =np.array([-v[1], v[0]])\n", "\n", " widh = 0.15\n", " l = 0.75\n", "\n", " P = p1-l*w\n", " S = P - widh*u\n", " T = P + widh*u\n", " fig.add_trace(\n", " go.Scattergeo(\n", " lon=[p0[0], p1[0], S[0], np.nan, p1[0], T[0]], \n", " lat=[p0[1], p1[1], S[1], np.nan, p1[1], T[1]],\n", " mode='lines',\n", " line_color=c,\n", " line_width=2,\n", " showlegend=False,\n", " text=label_txt\n", " )\n", " )\n", " \n", "def add_oval(fig, center, a, b, rot_angle, label_txt=\"\", c=\"black\"):\n", " \"\"\"\n", " Draw an oval\n", " \n", " Input Parameters:\n", " -----------------\n", " \n", " fig: target figure object\n", " center: [lon, lat] of the oval's center\n", " a: semi-major axis\n", " b: semi-minor axis\n", " rot_angle: rotation angle counter clockwise from horizontal position (in degrees)\n", " label_txt: label text [default: \"\"]\n", " c: arrow color [default: \"black\"]\n", " \"\"\"\n", " rot_angle = rot_angle * np.pi / 180\n", " \n", " theta = np.linspace(0, 2*np.pi, 101)\n", "\n", " x_oval_horizontal = a * np.cos(theta)\n", " y_oval_horizontal = b * np.sin(theta)\n", "\n", " # rotation\n", " lon_oval = center[0] + x_oval_horizontal * np.cos(rot_angle) - y_oval_horizontal * np.sin(rot_angle)\n", " lat_oval = center[1] + x_oval_horizontal * np.sin(rot_angle) + y_oval_horizontal * np.cos(rot_angle)\n", " \n", " fig.add_trace(\n", " go.Scattergeo(\n", " lon=lon_oval, \n", " lat=lat_oval,\n", " mode='lines',\n", " line_color=c,\n", " line_width=4,\n", " showlegend=False,\n", " text=label_txt\n", " )\n", " )\n", "\n", "\n", "def plot_earthquake_map(catalog):\n", " \"\"\"\n", " Input Parameters:\n", " ----------------\n", " \n", " catalog: dataframe containing earthquakes\n", " \"\"\" \n", " \n", " rlons, rlats = load_plate_boundaries('../PS_Plate_Tectonics/Files/ridge.json')\n", " tlons, tlats = load_plate_boundaries('../PS_Plate_Tectonics/Files/transform.json')\n", " hlons, hlats = load_plate_boundaries('../PS_Plate_Tectonics/Files/trench.json')\n", "\n", " fig1a = px.line_geo(lon=rlons, lat=rlats, width=1200, height=600)\n", " fig1a.update_traces(line={'color':'skyblue', 'width':3})\n", " \n", " fig1b = px.line_geo(lon=tlons, lat=tlats, width=1200, height=600)\n", " fig1b.update_traces(line={'color':'skyblue', 'width':3})\n", " \n", " fig1c = px.line_geo(lon=hlons, lat=hlats, width=1200, height=600)\n", " fig1c.update_traces(line={'color':'skyblue', 'width':3})\n", " \n", " fig2 = px.scatter_geo(catalog, lon=\"ep.lon\", lat=\"ep.lat\", size=\"centroid.MW\", color=\"ep.depth\", width=600, height=600, \n", " labels={\"ep.lon\":\"longitude (degrees)\", \"ep.lat\":\"latitude (degrees)\", \"centroid.MW\":\"Moment Magnitude\",\n", " \"ep.depth\":\"depth (km)\", \"ep.timestamp\":\"origin time\"}, \n", " hover_data=['ep.timestamp'], \n", " title=\" \")\n", " \n", " fig = go.Figure(data=fig2.data + fig1a.data + fig1b.data + fig1c.data, layout = fig2.layout)\n", " fig.update_geos(lataxis_showgrid=True, lonaxis_showgrid=True)\n", " fig.update_layout(\n", " geo = dict(\n", " lonaxis = dict(\n", " showgrid = True,\n", " gridwidth = 0.5,\n", " range= [ -138.0, -118.0 ],\n", " dtick = 5\n", " ),\n", " lataxis = dict (\n", " showgrid = True,\n", " gridwidth = 0.5,\n", " range= [ 37.0, 57.0 ],\n", " dtick = 5\n", " )\n", " )\n", " )\n", " \n", " # Adds arrows\n", " length_scale = 25\n", " \n", " # Juan de Fuca ridge: Juan de Fucca arrow\n", " p0 = np.array([-129.5, 46.4])\n", " length = 40 / length_scale\n", " direction = 100 * np.pi/180\n", " p1 = p0 + length * np.array([np.sin(direction), np.cos(direction)])\n", " add_arrow(fig, p0, p1, \"40 mm/yr\")\n", " \n", " # Juan de Fuca ridge: Pacific plate arrow\n", " p0 = np.array([-130.5, 46.6])\n", " length = 40 / length_scale\n", " direction = 280 * np.pi/180\n", " p1 = p0 + length * np.array([np.sin(direction), np.cos(direction)])\n", " add_arrow(fig, p0, p1, \"40 mm/yr\")\n", " \n", " # North American plate arrow\n", " p0 = np.array([-134, 57])\n", " length = 56 / length_scale\n", " direction = 145 * np.pi/180\n", " p1 = p0 + length * np.array([np.sin(direction), np.cos(direction)])\n", " add_arrow(fig, p0, p1, \"56 mm/yr\")\n", " \n", " # North American plate arrow\n", " p0 = np.array([-135, 53])\n", " length = 56 / length_scale\n", " direction = 325 * np.pi/180\n", " p1 = p0 + length * np.array([np.sin(direction), np.cos(direction)])\n", " add_arrow(fig, p0, p1, \"56 mm/yr\")\n", " \n", " # Juan de Fuca ridge: Juan de Fuca plate arrow\n", " p0 = np.array([-127, 41.4])\n", " length = 40 / length_scale\n", " direction = 100 * np.pi/180\n", " p1 = p0 + length * np.array([np.sin(direction), np.cos(direction)])\n", " add_arrow(fig, p0, p1, \"40 mm/yr\", \"white\")\n", " \n", " # Juan de Fuca ridge: Pacific plate arrow\n", " p0 = np.array([-128, 41.6])\n", " length = 40 / length_scale\n", " direction = 280 * np.pi/180\n", " p1 = p0 + length * np.array([np.sin(direction), np.cos(direction)])\n", " add_arrow(fig, p0, p1, \"40 mm/yr\")\n", " \n", " # Add oval\n", " add_oval(fig, [-128.7, 43.7], 2.5, 1.2, -20, \"\", \"limegreen\")\n", " fig.add_annotation(x=.25, y=.40,\n", " text=\"???\",\n", " font=dict(\n", " color=\"darkgreen\",\n", " size=20\n", " ),\n", " showarrow=False)\n", " \n", " fig.show()" ] }, { "cell_type": "code", "execution_count": 9, "id": "7cd93bb3-0062-4253-ab16-a500ab29b9e6", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/tmp/ipykernel_3220305/2244039337.py:2: DtypeWarning:\n", "\n", "Columns (15) have mixed types. Specify dtype option on import or set low_memory=False.\n", "\n" ] } ], "source": [ "# Read earthquake catalog\n", "cmt_cat = pd.read_table(\"../PS_Plate_Tectonics/Files/Global_CMT_1972_2018.csv\", delimiter=',')\n", "cmt_cat = cmt_cat.sort_values(by=['ep.depth', 'centroid.MW'])" ] }, { "cell_type": "markdown", "id": "b92f73fa-6f36-43f0-a481-b3b5b6892c8b", "metadata": {}, "source": [ "
\n", "

Review

\n", "

Feel free to adjust the filter parameters in the cell below to have more or less earthquakes on the map. You may hover the dots to get the information of the earthquakes. The colors of the lines indicate the type of plate boundaries: Red is a Trench, Green is a Transform, and Blue is a Ridge boundary.

\n", "
" ] }, { "cell_type": "code", "execution_count": 10, "id": "36c8a668-814d-4f1f-a3fc-7c2d094f9ccf", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/tmp/ipykernel_3220305/2372063229.py:18: RuntimeWarning:\n", "\n", "invalid value encountered in remainder\n", "\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "customdata": [ [ "2007-02-26 12:19:54.500000" ], [ "2007-05-09 07:50:03.800000" ], [ "2008-04-26 06:40:10.600000" ], [ "2016-12-14 16:41:05.500000" ], [ "1990-01-16 20:08:22.000000" ], [ "2008-01-19 23:13:05.400000" ], [ "1993-03-25 13:34:35.400000" ], [ "2009-11-17 15:30:45.400000" ], [ "2007-06-25 02:32:24.600000" ], [ "1980-08-01 16:38:56.300000" ], [ "2001-11-30 07:46:58.300000" ], [ "2013-01-14 14:55:51.900000" ], [ "1980-05-18 15:32:11.400000" ], [ "2016-12-28 08:18:01.000000" ], [ "2013-03-30 21:43:28.200000" ], [ "1997-10-26 10:44:08.100000" ], [ "1989-05-04 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"text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Filter to improve readablility\n", "Mw_min = 5 # Moment magnitude\n", "Mw_max = 10 # Moment magnitude\n", "depth_min = 0 # minimum depth in km\n", "depth_max = 6400 # maximum depth in km\n", "datetime_min = '1000-01-01 00:00:00.000000' # 'yyyy-mm-dd hh:mm:ss.SSSSSS'\n", "datetime_max = '2050-01-01 00:00:00.000000' # 'yyyy-mm-dd hh:mm:ss.SSSSSS'\n", "lon_min = -138\n", "lon_max = -118\n", "lat_min = 37\n", "lat_max = 57\n", "\n", "# Don't change these two statements\n", "mask = (cmt_cat['centroid.MW'] >= Mw_min) & (cmt_cat['centroid.MW'] <= Mw_max) & (cmt_cat['ep.depth'] >= depth_min) & (cmt_cat['ep.depth'] <= depth_max) & (cmt_cat['ep.timestamp'] >= datetime_min) & (cmt_cat['ep.timestamp'] <= datetime_max)\n", "mask = mask & (cmt_cat['ep.lon'] >= lon_min) & (cmt_cat['ep.lon'] <= lon_max) & (cmt_cat['ep.lat'] >= lat_min) & (cmt_cat['ep.lat'] <= lat_max)\n", "plot_earthquake_map(cmt_cat[mask])" ] }, { "cell_type": "markdown", "id": "6cf3c189-de4d-40b4-b9b9-e55b0652c0d9", "metadata": {}, "source": [ "### Mini-tutorial\n", "\n", " - **Scalars and Vectors in Python**" ] }, { "cell_type": "markdown", "id": "40b0ddf8-888e-47e5-a12a-044d5e82ceb8", "metadata": {}, "source": [ "scalars are quantities having only a magnitude (e.g. a temperature of 300 K). It is nonsense to ask for direction of a scalar. On the other hand, vectors are quantities having a magnitude as well as a direction (e.g. a velocity with a magnitude of 10 m/s and a direction of 30$^{\\circ}$ East of North). Vectors can be represent as an array of numbers specifying the quantity for each direction. For example, a velocity with a magnitude of 10 m/s and a direction of 30$^{\\circ}$ East of North can be represented as $v = \\begin{pmatrix} 5 \\\\ 5\\sqrt{3} \\end{pmatrix}$ m/s where the first number is the velocity in the east direction and the second number is the velocity in the north direction. This is similar to \"vector\" object in programming language. In Python, this means you can use `numpy.array` to represent vectors. The conversion of the magnitude and the (azimuthal) direction to the values in east and north direction can be done as follow:" ] }, { "cell_type": "code", "execution_count": 11, "id": "257d6d07-9417-43b0-98ef-5aa572c52a20", "metadata": {}, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "code", "execution_count": 12, "id": "e172f5a6-9048-4df1-8526-c2a428bdce4e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([5. , 8.66025404])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "magnitude = 10\n", "direction = 30 # in degrees\n", "\n", "direction_radian = direction * np.pi / 180 # convert to radians\n", "\n", "# vector\n", "v_east = magnitude * np.sin(direction_radian)\n", "v_north = magnitude * np.cos(direction_radian)\n", "v = np.array([v_east, v_north])\n", "\n", "# display a vector\n", "v" ] }, { "cell_type": "markdown", "id": "8b3617e4-e195-4ae4-ada7-e5479363f5a9", "metadata": {}, "source": [ "\n", "\n", "*Figure: Horizontal and Vertical components of a vector.*" ] }, { "cell_type": "markdown", "id": "883770d4-df5e-4377-85f0-45b401b5edc1", "metadata": {}, "source": [ "You may add two vectors by adding up element-wise from the two vectors. For `numpy.array`, you may simply add two vectors together like `w = u + v` where `u` and `v` are two vectors." ] }, { "cell_type": "code", "execution_count": 13, "id": "00fefe61-5ec2-4810-adde-1bf2904a5bff", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 5, -1])" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# vector addition\n", "u = np.array([3, -2])\n", "v = np.array([2, 1])\n", "\n", "# the result of vector addition\n", "w = u + v\n", "\n", "# display the result vector\n", "w" ] }, { "cell_type": "markdown", "id": "a2502890-4735-4cc6-88e7-98f8549ee41b", "metadata": {}, "source": [ "\n", "\n", "*Figure: Example of an addition of two vectors.*" ] }, { "cell_type": "markdown", "id": "fbb58775-0eb8-45f2-b8d3-35d5d575da99", "metadata": {}, "source": [ "### TO DO\n", "\n", "**Question 6** What is the motion (the direction with respect to North in degrees, and the magnitude in mm/yr) of the Juan de Fuca plate with respect to the North America plate? Draw an arrow showing this direction on the map. \n", "\n", "**Hint**: Because the Juan de Fuca plate is small, you can consider this a ‘flat Earth’ problem. Also, recall that if three plates interact, and the velocity vector of plate $A$ with respect to plate $B$ is $_B\\textbf{V}_A$, and that of plate $B$ with respect to plate $C$ is $_C\\textbf{V}_B$, then $_C\\textbf{V}_A= _C\\textbf{V}_B + _B\\textbf{V}_A$" ] }, { "cell_type": "markdown", "id": "16dd0b0b-3868-4e30-a5d4-1e326aa9f0a0", "metadata": {}, "source": [ "**Answer**" ] }, { "cell_type": "markdown", "id": "959cfd23-ebd9-450b-bafb-34508645bc6a", "metadata": {}, "source": [ "

\n", "

" ] }, { "cell_type": "markdown", "id": "20db7852-e6b1-4eee-aa86-46ecd3c5d79b", "metadata": {}, "source": [ "**Question 7.1** Based on the relative plate motion, what type of plate boundary is this? (Reminder: there are three types of plate boundaries: convergent or collision boundaries, divergent or spreading boundaries, and transform boundaries.)" ] }, { "cell_type": "markdown", "id": "05c61696-a8e4-43ed-afbd-ac4feb12a7d1", "metadata": {}, "source": [ "**Answer**" ] }, { "cell_type": "markdown", "id": "e7de1dbb-5c1c-4b48-82c1-529519ffc826", "metadata": {}, "source": [ "

\n", "

" ] }, { "cell_type": "markdown", "id": "80399ddf-b053-4b5d-bca1-4dadcb815af6", "metadata": {}, "source": [ "**Question 7.2** Based on plate motions, figure out what kind of boundary is denoted by the oval in the interactive figure above. What type of fault (strike-slip, normal, or reverse) is giving rise to these earthquakes?" ] }, { "cell_type": "markdown", "id": "a9ac0dfd-e705-4f37-a404-78976f00f26d", "metadata": {}, "source": [ "**Answer**" ] }, { "cell_type": "markdown", "id": "7150cfd8-7fc5-4e97-ac74-a8f8d8631dbe", "metadata": {}, "source": [ "

\n", "

" ] }, { "cell_type": "markdown", "id": "f53dac7f-9f78-4486-aa41-7b65c3a94e4a", "metadata": {}, "source": [ "----\n", "## Part III: Quake Magnitude" ] }, { "cell_type": "markdown", "id": "6b93ba28-9de3-4629-990b-287e5a03af77", "metadata": {}, "source": [ "Seismologists were for a long time content to use the intensity scale and the magnitude scale to measure and compare the sizes of earthquakes. Both of these scales are empirical, even though determining a magnitude involves making a measurement on a seismogram. Neither measure depends directly on the size of the earthquake fault or the amount of slip that occurred on it. These scales can be contrasted against the seismic moment (or scalar moment), usually denoted by $M_0$. This quantity can be routinely and accurately determined from seismograms. To do so is more complicated than measuring a magnitude, but the advantage of the seismic moment is that it is directly related to physical quantities. The seismic moment is\n", "\n", "$$ M_0 =\\mu \\times A \\times u, $$\n", "\n", "where $A$ is the area of the fault that slipped, $u$ is the average amount of slip on the fault, and $\\mu$ is the shear modulus, which is a property of the rocks surrounding the fault. The shear modulus describes how much force is necessary to elastically bend the rock – a typical value for rocks in the Earth’s crust is $\\mu= 3.3 \\times 10^{10} \\text{N}/\\text{m}^2$.\n", "\n", "\n", "\n", "*Figure: Comparison of moment, magnitudes, fault area, and fault slip for four earthquakes. Sizes of rectangles indicate the areas of the faults that slip. $M_s$, the magnitude obtained from amplitudes of surface-wave vibrations, saturates for events with $M_w > 8$ and so is no longer a useful measurement of earthquake size (Modified from Figure 4.6-3 of Stein and Wysession, Introduction to Seismology, Earthquakes and Earth Structure).*\n", "\n", "\n", "We can calculate the seismic moment of the greatest known earthquake, the 1960 Chile earthquake, by using estimates of the fault dimensions and slip: the length of the fault $L∼1000$ km, the width $W∼200$ km and the total slip $u∼20$ meters: $M_0 = 1000 \\times 10^3 \\times 200 \\times 10^3 \\times 20 \\times 3 \\times 10^{10} = 1.2 \\times 10^{23} \\text{Nm}$ (Newton $\\times$ meter). Physically this is not an *energy* but a *moment*, i.e. a force times a length of lever arm." ] }, { "cell_type": "markdown", "id": "0e955129-fbe0-45a9-997b-af2de7fff19d", "metadata": {}, "source": [ "\n", "\n", "\n", "\n", "*Figures: (top) Histogram of earthquakes of various moment magnitudes, (middle) fraction of the cumulative moment released by various earthquakes, (bottom) cumulative moment with time since modern recordings of earthquakes. Data Source: [Global CMT Project](globalcmt.org)*\n", "\n", "\n", "**Take away message**: Most earthquakes are small, so the total moment (or energy) released is dominated by a small number of large earthquakes. " ] }, { "cell_type": "markdown", "id": "0d737386-5757-4bfb-b8d3-816fd0d185e4", "metadata": { "tags": [] }, "source": [ "### TO DO\n", "\n", "**Question 8** The seismic moment of the 1994 Northridge (L.A.) earthquake was $2 \\times 10^{19}$ Nm. The slip appears to have been 1.3 meters. How big was the fault area that slipped?" ] }, { "cell_type": "markdown", "id": "f892fe23-0cf6-46ee-b801-3c54b9e26105", "metadata": {}, "source": [ "**Answer**" ] }, { "cell_type": "markdown", "id": "9cf67174-1bfd-4973-968c-69d17ad517e4", "metadata": {}, "source": [ "

\n", "

" ] }, { "cell_type": "markdown", "id": "1e3cd39d-3ef5-4538-b3bf-e43a0fe5ed6d", "metadata": {}, "source": [ "**Question 9** If the 20 meters of slip that occurred in the 1960 Chile earthquake corresponded to the accumulated plate motions between the Nazca and South America plates since the previous great earthquake in this region — when would that earthquake have occurred? [**Useful fact**: Approximately 8 km of the Nazca plate has subducted beneath South America in the last 100,000 years.]" ] }, { "cell_type": "markdown", "id": "9b7e7fee-7caf-436c-a962-506abf4a3884", "metadata": {}, "source": [ "**Answer**" ] }, { "cell_type": "markdown", "id": "3472ffd7-7a03-4e43-9be7-d167530abce3", "metadata": {}, "source": [ "

\n", "

" ] }, { "cell_type": "markdown", "id": "168c7f3b-bf25-4e5f-a9a6-5ac74e9ca92f", "metadata": {}, "source": [ "**Question 10** When an earthquake happens, the energy stored in the elastically deformed plates is converted into other energy forms, primarily frictional heat and elastic wave energy (most of which turns into heat, too). It turns out that it is very difficult to measure the amount of energy $E$ released in an earthquake accurately but, to within a factor of 5, it appears to be proportional to the seismic moment. A relationship which seems to be on average correct is $E= M_0 \\times 5 \\times 10^{-5}$. The energy $E$ is measured in newton-meters (Nm) or joules (J)" ] }, { "cell_type": "markdown", "id": "0b7f7bde-c511-4a37-b494-624cd52e1364", "metadata": {}, "source": [ "Estimate the energy released in the 1994 Northridge (L.A.) earthquake. Compare the value you get with U.S. total daily energy consumption ($~5 \\times 10^{17}$ J)." ] }, { "cell_type": "markdown", "id": "30a0dc08-697c-4d54-8439-b766f9d8d495", "metadata": {}, "source": [ "**Answer**" ] }, { "cell_type": "markdown", "id": "3d1a618b-079c-4cde-923f-add91c5919d0", "metadata": {}, "source": [ "

\n", "

" ] }, { "cell_type": "markdown", "id": "30f6d036-ace6-47f4-b9ff-e68b534f923f", "metadata": {}, "source": [ "**Question 11** Instead of getting rid of the magnitude scale, seismologists decided to create a new magnitude based on the seismic moment. This was done so as not to confuse the public (and themselves), to avoid dealing with very large numbers like $10^{20}$, and to be able to compare old magnitude estimates with modern seismic moments, and so on. From the seismic moment ($M_0$ measured in Nm) one can calculate a magnitude $M_W$ called the moment magnitude using the equation\n", "\n", "$$ M_W = \\frac{2}{3} (\\log_{10}M_0 - 9.05) $$\n", "\n", "The constants in this equation were chosen so that the new scale coincides with Richter’s traditional magnitude scale. That is, an earthquake that is measured with traditional means to have a Richter magnitude of 6.5 will typically also have a seismic moment that corresponds to a moment magnitude of 6.5. However, for an individual earthquake, it is not uncommon for the the traditional magnitude to be wrong by half a magnitude unit. It is particularly difficult to measure the magnitudes of very large earthquakes using the ‘old-fashioned’ approach." ] }, { "cell_type": "markdown", "id": "41a798c7-7ad8-4e3c-80cb-5e7e1a5d3007", "metadata": {}, "source": [ "What is the moment magnitude of the 1960 Chile earthquake?" ] }, { "cell_type": "markdown", "id": "e13d80f4-ad77-48e4-8697-2694e8190c5f", "metadata": {}, "source": [ "**Answer**" ] }, { "cell_type": "markdown", "id": "a67e2b3a-e20a-4517-a14d-ff27366ca4cb", "metadata": {}, "source": [ "

\n", "

" ] }, { "cell_type": "markdown", "id": "7fb10029-cf0d-4688-8414-0467ffd7b17a", "metadata": {}, "source": [ "**Question 12** From these relationships, calculate how much more energy is released in a $M_W=7$ than in a $M_W=6$ earthquake (**Note**: Express this as a fraction or a ratio). " ] }, { "cell_type": "markdown", "id": "bb8078bb-3562-4cfc-a392-0741f0ab679d", "metadata": {}, "source": [ "**Answer**" ] }, { "cell_type": "markdown", "id": "56f53bda-446f-42f2-a1c8-a8ec0a2626ab", "metadata": {}, "source": [ "

\n", "

" ] }, { "cell_type": "markdown", "id": "78775f17-ac50-4efc-95c0-338a987fbc4a", "metadata": {}, "source": [ "**Question 13** Why do we tend to have large earthquakes ($M_W > 7.5$) in the subduction zones? Think about the factors that contibute to the scalar moment based on the equations above. " ] }, { "cell_type": "markdown", "id": "f09c46fd-5de4-441f-96d5-c7b61e3ed630", "metadata": {}, "source": [ "**Answer**" ] }, { "cell_type": "markdown", "id": "99ff58e4-558a-4db7-a986-01cc2635ae02", "metadata": {}, "source": [ "

\n", "

" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.12" } }, "nbformat": 4, "nbformat_minor": 5 }