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 gibson:teaching:spring-2018:math445:lab3 [2018/02/05 17:27]gibson gibson:teaching:spring-2018:math445:lab3 [2018/02/05 17:30] (current)gibson Both sides previous revision Previous revision 2018/02/05 17:30 gibson 2018/02/05 17:27 gibson 2018/02/05 17:25 gibson 2018/02/05 17:21 gibson created 2018/02/05 17:30 gibson 2018/02/05 17:27 gibson 2018/02/05 17:25 gibson 2018/02/05 17:21 gibson created Line 51: Line 51: 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. 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. + 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.  Your final answer should be an explicit formula for //N(M)//. **Problem 6: 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 more energy than an earthquake of magnitude //M//. The following dataset gives the number //N// of earthquakes in a given **Problem 6: 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 more energy than an earthquake of magnitude //M//. The following dataset gives the number //N// of earthquakes in a given Line 68: Line 68: Deduce the form of the functional relation //E(N)// using Matlab plotting, then estimate ​ 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. + and fine-tune the constants in the relation, ​and provide an explicit formula for //E(N)//. **Problem 7: World population.** The following data set provides the human population //P// of the earth at a given time //t//, measured in years A.D. **Problem 7: World population.** The following data set provides the human population //P// of the earth at a given time //t//, measured in years A.D. 