# Source code for openquake.hmtk.plotting.seismicity.max_magnitude.cumulative_moment

```
#!/usr/bin/env python
# LICENSE
#
# Copyright (c) 2010-2017, GEM Foundation, G. Weatherill, M. Pagani, D. Monelli
#
# The Hazard Modeller's Toolkit (openquake.hmtk) is free software: you can redistribute
# it and/or modify it under the terms of the GNU Affero General Public License
# as published by the Free Software Foundation, either version 3 of the
# License, or (at your option) any later version.
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# along with OpenQuake. If not, see <http://www.gnu.org/licenses/>
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# DISCLAIMER
#
# The software Hazard Modeller's Toolkit (openquake.hmtk) provided herein is released as
# a prototype implementation on behalf of scientists and engineers working
# within the GEM Foundation (Global Earthquake Model).
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# It is distributed for the purpose of open collaboration and in the hope that
# it will be useful to the scientific, engineering, disaster risk and software
# design communities.
#
# The software is NOT distributed as part of GEM's OpenQuake suite
# (http://www.globalquakemodel.org/openquake) and must be considered as a
# separate entity. The software provided herein is designed and implemented
# by scientific staff. It is not developed to the design standards, nor
# subject to same level of critical review by professional software developers,
# as GEM's OpenQuake software suite.
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# Feedback and contribution to the software is welcome, and can be directed to
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# (hazard@globalquakemodel.org).
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'''
Module to produce cumulative moment plot
'''
import numpy as np
import matplotlib.pyplot as plt
[docs]def plot_cumulative_moment(year, mag):
'''Calculation of Mmax using aCumulative Moment approach, adapted from
the cumulative strain energy method of Makropoulos & Burton (1983)
:param year: Year of Earthquake
:type year: numpy.ndarray
:param mag: Magnitude of Earthquake
:type mag: numpy.ndarray
:keyword iplot: Include cumulative moment plot
:type iplot: Boolean
:return mmax: Returns Maximum Magnitude
:rtype mmax: Float
'''
# Calculate seismic moment
m_o = 10. ** (9.05 + 1.5 * mag)
year_range = np.arange(np.min(year), np.max(year) + 1, 1)
nyr = np.int(np.shape(year_range)[0])
morate = np.zeros(nyr, dtype=float)
# Get moment release per year
for loc, tyr in enumerate(year_range):
idx = np.abs(year - tyr) < 1E-5
if np.sum(idx) > 0:
# Some moment release in that year
morate[loc] = np.sum(m_o[idx])
ave_morate = np.sum(morate) / float(nyr)
# Average moment rate vector
exp_morate = np.cumsum(ave_morate * np.ones(nyr))
plt.step(year_range, np.cumsum(morate), 'b-', linewidth=2)
plt.plot(year_range, exp_morate, 'r-', linewidth=2)
# Get offsets
upper_morate = exp_morate + (np.max(np.cumsum(morate) - exp_morate))
lower_morate = exp_morate + (np.min(np.cumsum(morate) - exp_morate))
plt.plot(year_range, upper_morate, 'r--', linewidth=1)
plt.plot(year_range, lower_morate, 'r--', linewidth=1)
plt.axis([np.min(year), np.max(year), 0.0, np.sum(morate)])
```