5.2.8.1.2. eqcorrscan.utils.mag_calc.calc_b_value

eqcorrscan.utils.mag_calc.calc_b_value(magnitudes, completeness, max_mag=None, plotvar=True)[source]

Calculate the b-value for a range of completeness magnitudes.

Calculates a power-law fit to given magnitudes for each completeness magnitude. Plots the b-values and residuals for the fitted catalogue against the completeness values. Computes fits using numpy.polyfit, which uses a least-squares technique.

Parameters:

  • magnitudes (list) – Magnitudes to compute the b-value for.

  • completeness (list) – list of completeness values to compute b-values for.

  • max_mag (float) – Maximum magnitude to attempt to fit in magnitudes.

  • plotvar (bool) – Turn plotting on or off.

Return type:

list

Returns:

List of tuples of (completeness, b-value, residual, number of magnitudes used)

Note

High “residuals” indicate better fit. Residuals are calculated according to the Wiemer & Wyss 2000, Minimum Magnitude of Completeness in Earthquake Catalogs: Examples from Alaska, the Western United States, and Japan, BSSA.

Example

>>> from obspy.clients.fdsn import Client
>>> from obspy import UTCDateTime
>>> from eqcorrscan.utils.mag_calc import calc_b_value
>>> client = Client('IRIS')
>>> t1 = UTCDateTime('2012-03-26T00:00:00')
>>> t2 = t1 + (3 * 86400)
>>> catalog = client.get_events(starttime=t1, endtime=t2, minmagnitude=3)
>>> magnitudes = [event.magnitudes[0].mag for event in catalog]
>>> b_values = calc_b_value(magnitudes, completeness=np.arange(3, 7, 0.2),
...                         plotvar=False)
>>> round(b_values[4][1], 1)
1.0
>>> # We can set a maximum magnitude:
>>> b_values = calc_b_value(magnitudes, completeness=np.arange(3, 7, 0.2),
...                         plotvar=False, max_mag=5)
>>> round(b_values[4][1], 1)
1.0