analysis.ClassicBValueEstimator#

class seismostats.analysis.ClassicBValueEstimator#

Estimator to calculate the b-value and other parameters of the Gutenberg-Richter (GR) law.

\[N(m) = 10 ^ {a - b \cdot (m - m_{ref})},\]

where \(N(m)\) is the number of events with magnitude larger than or equal to \(m\) that occurred in the timeframe of the catalog, \(a\) and \(b\) are the a- and b-value, and \(m_{ref}\) is the reference magnitude above which earthquakes are counted.

Source:

Aki 1965 (Bull. Earthquake research institute, vol 43, pp 237-239)
Tinti and Mulargia 1987 (Bulletin of the Seismological Society of America, 77(6), 2125-2134.)

Examples

>>> import numpy as np
>>> from seismostats.analysis import ClassicBValueEstimator

>>> magnitudes = np.array([2. , 2.5, 2.1, 2.2, 2.5, 2.2, 2.6, 2.3,
...                        2.7, 2.2, 2.4, 2. , 2.7, 2.2, 2.3, 2.1,
...                        2.4, 2.6, 2.2, 2.2, 2.7, 2.4, 2.2, 2.5])

>>> my_estimator = ClassicBValueEstimator()
>>> my_estimator.calculate(
...     magnitudes=magnitudes, mc=2.0, delta_m=0.1)

>>> my_estimator.b_value

1.114920128810535

Attributes

`b_value`	The b-value of the Gutenberg-Richter law.
`beta`	The beta value of the Gutenberg-Richter law.
`delta_m`	Bin size of the discretized magnitudes.
`magnitudes`	The magnitudes used to estimate the b-value.
`mc`	The completeness magnitude used to estimate the b-value.
`n`	Number of magnitudes used to estimate the b-value.
`std`	Shi and Bolt uncertainty of the b-value estimate.
`std_beta`	Shi and Bolt uncertainty of the beta estimate.
`value`	The b-value of the Gutenberg-Richter law.
`weights`	The weights used to estimate the b-value.

Methods

`calculate`	Calculates the b-value of the Gutenberg-Richter (GR) law.
`p_lilliefors`	p-value of the Lilliefors test.