Plots and Logs Plots and Stuff 1. A plot is a two-dimensional display (it fits on a sheet of paper) of points or curves or regions. Plots and Stuff 2.

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Presentation transcript:

Plots and Logs Plots and Stuff 1

A plot is a two-dimensional display (it fits on a sheet of paper) of points or curves or regions. Plots and Stuff 2

3 (5,8) x y (8,22) points

Plots and Stuff 4 x y curves

Plots and Stuff 5 x y regions

Plots and Stuff 6 Some ways to make plots

Plots and Stuff 7 helicorder using thermal paper

Plots and Stuff 8

9 there is no shame in plotting by hand

Plots and Stuff 10

Problems with plots A frequent problem with visible plots is dynamic range Plots and Stuff 11

dynamic range tells us about the largest and smallest things we can usefully plot at the same time the dynamic range of a plot is related to the number of pixels on a side Plots and Stuff 12

an earthquake example Plots and Stuff 13

Plots and Stuff 14 ground motion (uM) vs. magnitude

Plots and Stuff 15 ground motion (uM) vs. magnitude

Exponential (Geometric) Change Plots and Stuff 16

Example: hearing Nature produces sounds that routinely vary over a range of 100,000 in amplitude: rustle of leaves in the brush lightning and thunder Evolution accommodated our need to hear this wide range by developing hearing that is geometric in sensitivity. Plots and Stuff 17

The usual way we accommodate exponential or geometric change is to take the logarithm() of the quantity that varies most rapidly. There are many flavors of logarithm (you knew that was coming). The most common ones are natural logarithms decimal or common logarithms binary logarithms Plots and Stuff 18 Greek: ratios of numbers

Plots and Stuff 19

Plots and Stuff 20 ground motion (uM) vs. magnitude

Plots and Stuff 21 common logarithm of ground motion (uM) vs. magnitude

Special log-plotting paper Plots and Stuff 22 not going to pursue this log-log is often too much of a good thing

Earthquake Applications ground motion versus magnitude example: Richter magnitude earthquake number versus magnitude example: Gutenberg-Richter law stress release versus magnitude aftershock occurrence versus time Omori’s law Plots and Stuff 23

Gutenberg-Richter Law Plots and Stuff 24

Plots and Stuff 25