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

```
# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# LICENSE
#
# Copyright (C) 2010-2023 GEM Foundation, G. Weatherill, M. Pagani,
# D. Monelli.
#
# The Hazard Modeller's Toolkit 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.
#
# You should have received a copy of the GNU Affero General Public License
# along with OpenQuake. If not, see <http://www.gnu.org/licenses/>
#
# 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).
#
# 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
# (https://www.globalquakemodel.org/tools-products) 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.
#
# Feedback and contribution to the software is welcome, and can be
# directed to the hazard scientific staff of the GEM Model Facility
# (hazard@globalquakemodel.org).
#
# The Hazard Modeller's Toolkit (openquake.hmtk) is therefore distributed WITHOUT
# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
# FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
# for more details.
#
# The GEM Foundation, and the authors of the software, assume no
# liability for use of the software.
"""
Module to produce cumulative moment plot
"""
import numpy as np
import matplotlib.pyplot as plt
from openquake.hmtk.plotting.seismicity.catalogue_plots import _save_image
[docs]def plot_cumulative_moment(
year,
mag,
figure_size=(8, 6),
filename=None,
filetype="png",
dpi=300,
ax=None,
):
"""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 = 10.0 ** (9.05 + 1.5 * mag)
year_range = np.arange(np.min(year), np.max(year) + 1, 1)
nyr = 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))
if ax is None:
fig, ax = plt.subplots(figsize=figure_size)
else:
fig = ax.get_figure()
ax.step(year_range, np.cumsum(morate), "b-", linewidth=2)
ax.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))
ax.plot(year_range, upper_morate, "r--", linewidth=1)
ax.plot(year_range, lower_morate, "r--", linewidth=1)
ax.axis([np.min(year), np.max(year), 0.0, np.sum(morate)])
_save_image(fig, filename, filetype, dpi)
```