.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/seismicity_rate.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_examples_seismicity_rate.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_seismicity_rate.py:


Modeling of seismicity
======================

This example shows how to translate stressing rate to seismicity rate using the function :func:`bruces.modeling.seismicity_rate`. Modeled seismicity rate can then be used to generate a magnitude-time distribution using the function :func:`bruces.modeling.magnitude_time`.

This example starts by generating a synthetic stressing rate with an instantaneous 1000 fold increase after 2 years followed by a 10 fold decrease after another 2 years.

The free parameter :math:`a \sigma` of the rate-and-state model is arbitrarily set to 0.15. Note that :func:`bruces.modeling.seismicity_rate` outputs the seismicity rate :math:`r` relative to the background seismicity rate :math:`r_0`. Modeling the magnitude-time distribution requires the actual seismicity rate :math:`r \times r_0`. Here, we assume that :math:`r_0` = 1 event/year.

.. GENERATED FROM PYTHON SOURCE LINES 12-55



.. image-sg:: /examples/images/sphx_glr_seismicity_rate_001.png
   :alt: seismicity rate
   :srcset: /examples/images/sphx_glr_seismicity_rate_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    (0.0, 10.0)





|

.. code-block:: default


    import bruces
    import numpy as np
    import matplotlib.pyplot as plt

    # Define stressing rate
    stress_ini = 1.0e-3
    times = np.linspace(0.0, 10.0, 201)
    stress = np.ones(201) * stress_ini
    stress[times > 2.0] = stress_ini * 1.0e3
    stress[times > 4.0] = stress_ini * 1.0e2

    # Model relative seismicity rate
    rates = bruces.modeling.seismicity_rate(
        times=times,
        stress=stress,
        stress_ini=stress_ini,
        asigma=0.15,
    )

    # Model magnitude-time distribution
    magnitudes = bruces.modeling.magnitude_time(
        times=times,
        rates=rates,
        m_bounds=[0.0, 2.0],
        seed=0,
    )

    # Plot
    fig, ax = plt.subplots(2, 1, sharex=True)

    ax[0].semilogy(times, stress / stress_ini, label="Stress")
    ax[0].semilogy(times, rates, label="Seismicity")
    ax[0].set_ylabel("Rate")
    ax[0].legend(frameon=False)

    for t, m in zip(times, magnitudes):
        if len(m):
            ax[1].scatter([t] * len(m), m, color="black", alpha=0.2)

    ax[1].set_xlabel("Time (year)")
    ax[1].set_ylabel("Magnitude")
    ax[1].set_xlim(times.min(), times.max())


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  6.178 seconds)


.. _sphx_glr_download_examples_seismicity_rate.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example


    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: seismicity_rate.py <seismicity_rate.py>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: seismicity_rate.ipynb <seismicity_rate.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_