Evenly Discretised Magnitude-Frequency Distribution (MFD)

The typologies of Magnitude-Frequency Distribution (MFD) supported by the OQ Engine are available in this folder. A description of these distributions is available here.

The main models supported are:

• Double Truncated MFD

• Evenly Spaced MFD

• Arbitrary MFD

• Tapered MFD

• Youngs and Coppersmith MFD

In this notebook, we briefly show how you can utilize evenly discretised MFD as an example.

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from openquake.hazardlib.mfd import EvenlyDiscretizedMFD

For EvenlyDiscretizedMFD, you need magnitudes, magnitude step, and rates for each magnitude as requirements.

magnitude_step = 0.2
magnitudes = np.arange(4.1, 7.0, magnitude_step)
rates = np.random.rand(magnitudes.size)

# Histogram plot
_ = plt.bar(magnitudes, rates, width=magnitude_step, fc='none', ec='blue')
_ = plt.xlabel('Magnitude, m')
_ = plt.ylabel('Rates [ev/yr]')

# Create the Evenly Discretised MFD
mfd = EvenlyDiscretizedMFD(min(magnitudes), magnitude_step, rates)

Each magnitude-frequency available in the OQ Engine offers a number of default methods including:

• check_constraints: controls the instantiation of the MFD based on the information provided,

• get_annual_occurrence_rates: returns a list of tuples, each one containing a magnitude and the corresponding rate,

• get_min_max_mag: returns the minimum and maximum magnitudes,

• modify_set_mfd: applies absolute modification of the MFD from the min_mag, bin_width, and occurrence_rates modification.

mocc = mfd.get_annual_occurrence_rates()

mags = np.array([m[0] for m in mocc])
rtes = np.array([m[1] for m in mocc])

df_mocc = pd.DataFrame({
    "Magnitudes": mags,
    "Rates": rtes
})
display(df_mocc)

	Magnitudes	Rates
0	4.1	0.102031
1	4.3	0.826247
2	4.5	0.812529
3	4.7	0.441247
4	4.9	0.181112
5	5.1	0.238289
6	5.3	0.034432
7	5.5	0.537567
8	5.7	0.882729
9	5.9	0.660822
10	6.1	0.719110
11	6.3	0.861916
12	6.5	0.905983
13	6.7	0.408337
14	6.9	0.977984