analysis.estimate_b#

seismostats.analysis.estimate_b(magnitudes: ~numpy.ndarray, mc: float, delta_m: float, weights: list | None = None, b_parameter: ~typing.Literal['b_value', 'beta'] = 'b_value', return_std: bool = False, method: ~seismostats.analysis.bvalue.base.BValueEstimator = <class 'seismostats.analysis.bvalue.classic.ClassicBValueEstimator'>, return_n: bool = False, **kwargs) → float | tuple[float, float] | tuple[float, float, float]#

Returns the b-value 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.

Parameters:

  • magnitudes – Array of magnitudes.

  • mc – Completeness magnitude.

  • delta_m – Bin size of discretized magnitudes.

  • weights – Array of weights for the magnitudes.

  • b_parameter – If ‘b_value’, the b-value is returned. If ‘beta’, the beta-value is returned. beta is the analogous value to b, but when formulating the GR law with base e.

  • return_std – If True, the standard deviation of the b-value is also returned.

  • method – BValueEstimator class to use for calculation.

  • return_n – If True, the number of events used for the estimation is also returned.

  • **kwargs – Additional parameters to be passed to the calculate() method.

Returns:

  • b – b-value or beta of the Gutenberg-Richter law.

  • std – Standard deviation of the b-value or beta. Only returned if return_std is True.

  • n – Number of events used for the estimation. Only returned if return_n is True.

Examples

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

>>> 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])
>>> mc = 2.0
>>> delta_m = 0.1

>>> b = estimate_b(magnitudes=magnitudes,
...                mc=mc,
...                delta_m=delta_m)
>>> b

1.114920128810535

>>> from seismostats.analysis import BPositiveBValueEstimator

>>> times = np.arange(len(magnitudes))
>>> b = estimate_b(magnitudes,
...                mc,
...                delta_m,
...                times=times,
...                method=BPositiveBValueEstimator)
>>> b

1.5490195998574323
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