{
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"\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",
"----"
]
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{
"cell_type": "markdown",
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"## 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: $\\text{weight} = m \\times g$.)"
]
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"### 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."
]
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"id": "d74b36fd-e51c-46ad-ba8d-ecb07c436e47",
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"source": [
"**Answer**"
]
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"cell_type": "markdown",
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"metadata": {},
"source": [
"
\n",
"
"
]
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"cell_type": "markdown",
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"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?"
]
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"cell_type": "markdown",
"id": "255304d7-8593-481a-bffd-adcedb1c595a",
"metadata": {},
"source": [
"**Answer**"
]
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"cell_type": "markdown",
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"source": [
"
\n",
"
"
]
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"### 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}"
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"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."
]
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{
"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": {},
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"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"
]
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---|---|---|---|---|---|---|---|---|---|---|
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750 rows × 10 columns
\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", "