b values & magnitude of completeness

Code from "ZMap" (written by Stefan Wiemer and others) has been added to Events to compute and plot b-values and the magnitude of completeness.

Definitions:

• b-value: the slope of a plot of the logarithm of the cumulative number of events against magnitude. A measure of the number of small earthquakes to larger earthquakes.

• magnitude of completeness (Mc): all events with magnitude>=Mc are in the catalog. Below Mc, not all events are detected, and below the magnitude detection threshold, no events are captured.

Let's use the Tohoku dataset we saved previously.

>> load tohoku_events_1day.mat

Use the bvalue method:

>> eventsObject.bvalue()

This will give a menu of techniques available to compute b-value (b) and magnitude of completeness (Mc):

`--------------------------------------------------------`
`Usage is: eventsObject.bvalue(mcType)`
`--------------------------------------------------------`
`mcType can be:`
`1: Maximum curvature`
`2: Fixed Mc = minimum magnitude (Mmin)`
`3: Mc90 (90% probability)`
`4: Mc95 (95% probability)`
`5: Best combination (Mc95 - Mc90 - maximum curvature)`

We will use the first menu option:

>> eventsObject.bvalue(1)

images/events.bvalue.png

In this particular example, the b-value is 0.6 and the magnitude of completeness is 4.2.