How to calculate the occurrence_rate for a rupture?

[Aulia Khalqillah]

Hi,

I just simulate the hazard calculation by using event based. In the hdf5 file, there is rupture dataset. In this file, each rup_id has its own occurrence_rate. How to calculate this occurrence_rate for each rup_id? Is the Gutenberg-Richter relationship used for occurrence_rate calculation?

I hope anyone can help answer these questions. Thanks

Aulia K

[Peter Pažák]

Hi,

all these calculations are done by the engine in the background and the output is saved to hdf5 during the runs,

if you want to understand in more detail, you can study the code and/or calculate the rates using a sample script:

from openquake.hazardlib.source import PointSource
from openquake.hazardlib.mfd import TruncatedGRMFD
from openquake.hazardlib.scalerel import WC1994
from openquake.hazardlib.geo import Point, NodalPlane
from openquake.hazardlib.pmf import PMF
from openquake.hazardlib.tom import PoissonTOM

src = PointSource(
    source_id='1',
    name='point',
    tectonic_region_type='Active Shallow Crust',
    mfd=TruncatedGRMFD(min_mag=5., max_mag=6.5, bin_width=0.1, a_val=0.01, b_val=0.98),
    rupture_mesh_spacing=2,
    magnitude_scaling_relationship=WC1994(),
    rupture_aspect_ratio=1,
    temporal_occurrence_model=PoissonTOM(50.), #50 years investigation time
    upper_seismogenic_depth=2.,
    lower_seismogenic_depth=12.,
    location=Point(9.1500, 45.1833,30),
    nodal_plane_distribution=PMF([(1., NodalPlane(strike=45, dip=50, rake=0))]),
    hypocenter_distribution=PMF([(1, 10.)]) #depth 10 km
)

ruptures = [r for r in src.iter_ruptures()] #sample the ruptures in 50 years

print(ruptures[0].mag) #gives 5.05 as magnitude of the first rupture

print(ruptures[0].occurrence_rate) #gives 2.6023325356665764e-06 as a corresponding occurrence rate

which is indeed the occurrence rate for magnitude 5.5:

print(TruncatedGRMFD(min_mag=5., max_mag=6.5, bin_width=0.1, a_val=0.01, b_val=0.98).get_annual_occurrence_rates()) #gives among others 5.05, 2.6023325356665764e-06

Hope this helps

Peter

Dátum: utorok 18. júla 2023, čas: 10:14:04 UTC+2, odosielateľ: auliakhalq...@gmail.com

[Aulia Khalqillah]

Thank you for your response. This is very helpful information.

Based on the script that you showed, we need the parameters of a-value and b-value in truncated GR MFD. How do we calculate these parameters for the simple fault source. Do we need the earthquake distribution around the correspond fault ?

Thank you for the attention.

Aulia K

[Aulia Khalqillah]

Hi Peter and everyone.

I came back to this thread because I want to get the confirmation about the occurrence rate that I have calculated through the event-based mode for the single source model (subduction interface). I applied the TruncatedGRMFD to calculate the occurrence rate where the a-value = 5.9, b-value = 0.79, bin_width = 0.1, min_mag = 6.5, and max_mag = 9.1.

I have tried to calculate this through the OpenQuake engine, then produced the ruptrue file corresponding to each magnitude and its occurrence rate. Also, I have tried to calculcate the occurrence rate directly using TruncatedGRMFD module in a Python script (attached) by using the above parameters.

Both method gives different results for the occurrence rate given each magnitude. Example,

Mag | Occurrence Rate OQ-engine | Occurrence Rate Direct Calculation

6.55 | 0.00269678886979818 | 0.968147176087502

Is my Python code correct to calculate the occurrence rate? I attach the corresponding files.

Many thanks for the attention.

Aulia K

[Peter Pažák]

Hi Aulia,

the calculation in the notebook, essentially setting up a truncated GR MFD which calculates the rates per magnitude bin is correct.
The output in the excel: the occurrence rates are per each location, so if you for example sum all the frequencies in the excel for M 6.55, it gives 0.7281.

Some of the ruptures are most probably missing, because they are too far from the exposure/hazard sites.

I believe if you would have sites covering the whole source zone densely, you would get exactly the total rate of 0.9681 as from the MFD, the main reason for

the observed difference is that the rate is divided into all discretized points in the (area) source.

Peter

Dátum: streda 2. júla 2025, čas: 7:22:45 UTC+2, odosielateľ: auliakhalq...@gmail.com

[Aulia Khalqillah]

Dear Peter,

Thank you for your explanation.

Best regards,
Aulia K

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