analysis.estimate_a#

seismostats.analysis.estimate_a(magnitudes: ~numpy.ndarray, mc: float, delta_m: float, scaling_factor: float | None = None, m_ref: float | None = None, b_value: float | None = None, method: ~seismostats.analysis.avalue.base.AValueEstimator = <class 'seismostats.analysis.avalue.classic.ClassicAValueEstimator'>, **kwargs) → float#

Returns the a-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.

  • scaling_factor – Scaling factor. If given, this is used to normalize the number of observed events. For example: Volume or area of the region considered or length of the time interval, given in the unit of interest.

  • m_ref – Reference magnitude for which the a-value is estimated.

  • b_value – b-value of the Gutenberg-Richter law. Only relevant when m_ref is not None.

  • method – AValueEstimator class to use for calculation.

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

Returns:

a – a-value of the Gutenberg-Richter law.

Examples

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

>>> magnitudes = np.array([2.1, 2.3, 2.0, 2.0, 2.1, 2.2, 2.1, 2.3, 2.0, 2.0])
>>> mc = 2.0
>>> delta_m = 0.1
>>> a = estimate_a(magnitudes, mc, delta_m)
>>> a

1.0

>>> from seismostats.analysis import APositiveAValueEstimator

>>> times = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
>>> a = estimate_a(magnitudes, mc, delta_m, times=times, method=APositiveAValueEstimator)
>>> a

0.9542425094393249
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