gibson:teaching:fall-2013:math445:lab8
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gibson:teaching:fall-2013:math445:lab8 [2013/11/04 13:39] gibson created |
gibson:teaching:fall-2013:math445:lab8 [2013/11/04 19:04] (current) gibson |
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| - Cut & paste the data set to a text file with an appropriate name, e.g. ''earthquakes.asc'' for problem 1. | - Cut & paste the data set to a text file with an appropriate name, e.g. ''earthquakes.asc'' for problem 1. | ||
| - | - Load the dataset to Matlab with ''load earthquakes.asc''. | + | - Load the dataset to Matlab with ''load''. |
| - | - Set //x// to the first column of ''earthquakes'', ''y'' to the second. | + | - Extract the two columns of the loaded data into two appropriately named vectors, e.g. //R// and //N// for problem 1. For the remaining generic instructions I'll use the names ''x'' and ''y''. |
| - | - Experiment with ''plot'', ''semilogy'', ''semilogx'', and ''loglog'' to determine the form of log-linear relationship ''x'' and ''y''. | + | - Experiment with ''plot'', ''semilogy'', ''semilogx'', and ''loglog'' to determine the functional relationship between ''y'' and ''x''. |
| - | - Estimate the constants in the log-linear relationship graphically to determine ''y'' as a function of ''x'', e.g. ''y = 3.2 x - 4''. | + | - Estimate the constants in the log-linear relationship graphically to determine the function. |
| - Plot the estimated function and the data together, and fine-tune your function by adjusting the constants until there is a good fit between the function and the data. | - Plot the estimated function and the data together, and fine-tune your function by adjusting the constants until there is a good fit between the function and the data. | ||
| Line 21: | Line 21: | ||
| For each data set, turn in your plots and your estimate of the function //y(x)//. | For each data set, turn in your plots and your estimate of the function //y(x)//. | ||
| - | **Problem 1: The distribution of earthquake magnitudes.** Big earthquakes are rare, and little earthquakes are frequent. In fact, there is a very | + | **Problem 1: The distribution of earthquake magnitudes, by Moment Magnitude scale.** Big earthquakes are rare, and |
| - | clean empirical law that governs how many earthquakes of a given magnitude typically occur world-wide in a given year. Your job is to deduce | + | little earthquakes are frequent. In fact, there is a very clean empirical law that governs how many earthquakes of a |
| - | that law from the following historical data. | + | given magnitude typically occur world-wide in a given year. Your job is to deduce that law from the following |
| + | historical data. | ||
| <code> | <code> | ||
| - | % magnitude number/year | + | % M N |
| 8 2 | 8 2 | ||
| 7 18 | 7 18 | ||
| Line 37: | Line 38: | ||
| </code> | </code> | ||
| - | The first column is the Richter magnitude //R//, and the second column is the number of earthquakes //N// of that magnitude that occur, on average, in a year. The last two entries are estimates. Derive a | + | The first column is the [[http://en.wikipedia.org/wiki/Moment_magnitude_scale | moment magnitude]] //M//, and the second column is the number of earthquakes //N// of that magnitude that occur, on average, in a year. The last two entries are estimates, since it's impossible to detect every small earthquake around the world. The data are obtained from [[http://www.earthquake.ethz.ch/education/NDK/NDK|Earthquake Statistics and Earthquake Prediction Research]] by Stefan Wiemer, Institute of Geophysics, Zurich. |
| + | |||
| + | Using Matlab plotting commands, deduce the form of the functional relationship //N(M)//. Estimate the constants in the relationship by estimating the slope and the //y//-intercept, and then fine-tuning by matching the plot of your estimate against the plot of the data. | ||
| + | |||
| + | **Problem 2: The distribution of earthquake magnitudes, by energy.** The moment magnitude scale is logarithmic, in that an earthquake of magnitude //M+1// releases about 32 times energy than an earthquake of magnitude //M//. The following data | ||
| + | set gives the number //N// of earthquakes in a given year of energy //E// measured in Joules. | ||
| + | |||
| + | <code> | ||
| + | % E N | ||
| + | 6e16 2 | ||
| + | 2e15 18 | ||
| + | 6e13 120 | ||
| + | 2e12 800 | ||
| + | 6e10 6200 | ||
| + | 2e09 49000 | ||
| + | 6e07 365000 | ||
| + | 1e06 2920000 | ||
| + | </code> | ||
| + | |||
| + | Deduce the form of the functional relation //E(N)// using Matlab plotting, then estimate and fine-tune the constants | ||
| + | in the relation, just as in problem 1. | ||
| + | |||
| + | **Problem 3: World population.** The following data set provides the human population //P// of the earth at a given | ||
| + | time //t//, measured in years A.D. | ||
| + | |||
| + | <code> | ||
| + | % t P | ||
| + | 1927 2e09 | ||
| + | 1960 3e09 | ||
| + | 1974 4e09 | ||
| + | 1987 5e09 | ||
| + | 1999 6e09 | ||
| + | 2011 7e09 | ||
| + | </code> | ||
| + | |||
| + | Deduce the form of the functional relation //P(t)// and determine the constants graphically. | ||
| + | |||
| + | Assume that the formula you derived for //P(t)// is valid indefinitely into the future and the past. What year will | ||
| + | the population of the earth reach one trillion? What year were the first humans born? Do you believe these answers? | ||
| + | If not, why not? | ||
gibson/teaching/fall-2013/math445/lab8.1383601192.txt.gz · Last modified: 2013/11/04 13:39 by gibson
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