# incrementalMFD and G-R occurrence rate

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### Paolo Zimmaro

Feb 8, 2015, 4:56:01 PM2/8/15
Dear all,
I'm performing calculations using some element of the SHARE PSHA model. In the OQ implementation of this model, I'm noticing that the Magnitude-Frequency distribution of the so-called Area Sources, is given using the "IncrementalMFD". The input of this MFD are: MinMag, binWidth and the occurrence rates.
In my understanding, these occurrence rates represent the list of incremental values for the annual occurrence rates. Is it true?
Below there is the incrementalMFD for a generic source of the SHARE model that I'm using:

<incrementalMFD binWidth="0.2" minMag="4.7">
<occurRates>0.156146154488 0.103164741202 0.0681602685775 0.0450330428636 0.0297530363638 0.0196576361839 0.01298767143 0.00858086941869 0.00566932420314 0.00374568535564 0.00247474977277 0.00163505096033 0.00108026745665 0.000713725630703 0.000471553847881 0.000311552537677</occurRates>
</incrementalMFD>

How can I calculate the correspondant (cumulative values for M>0) values (a and b) of the Gutenberg-Richter recurrence law, the Min and Max values that I have to use in OQ?
How can I obtain the same results using the truncGutenbergRichterMFD instead of the incrementalMFD  in OQ?

Hopefully someone can help me!

Paolo Zimmaro

### Laurentiu

Feb 9, 2015, 3:14:59 AM2/9/15
Dear Paolo,
Yes, the incremental MFD represents the annual occurence rates as described in OQ's manual section 2.1.4: Supported magnitude-frequency distributions.

First of all, your example is a summed MFD resulted from GR activity parameters combined with several maximum magnitudes, as defined in SHARE-area source logic tree, hence not trivial to re-built it. If you need the activity rates parameters (aGR-value,and b-GR value), together with the maximum magnitude, they are available in a shape file format, available to download here:

However, if you want to recompute the aGR cumulative value you need to use the following:

aGRVal = log10( N(low_mag) / (10^(-bGRval* low_mag)-10^(-bGR*upper_mag) )

I hope this helps, and for further questions related to the 2013 European seismic hazard model, please use the following contact address: share[at] sed.ethz.ch

Cheers, Laurentiu

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### Paolo Zimmaro

Feb 9, 2015, 5:57:42 AM2/9/15
Thank you so much Laurentiu for the useful information. Please notice that the incremental occurrence rates that I pasted are relative to magnitude values from Mmin (4.7) to MMax (7.7), so I'm not using the higher values of MMax for which the logic tree approach with different weights is used in the SHARE model.
In this connection, I'd like to understand how  I can derive the same occurrence rates with OQ using a different MFD (e.g. the truncGutenbergRichterMFD that is differently defined).

I applied the equation aGRVal = log10( N(low_mag) / (10^(-bGRval* low_mag)-10^(-bGR*upper_mag) )
using b=-0.9 and N(low_mag)=0.4595 (Cumulative number of eqks for M>low_mag), and I obtained for this distribution a cumulative a value = 3.8932.

Using b=0.9; a=3.8932, Mmin=4.6 and Mmax=7.8 for the truncGutenbergRichterMFD in OQ, I should obtain the same results of the model with incrementalMFD. But the results for a single site with a single source in terms of UHS and hazard curves are different.
Can you (or other usrers/developers) explain me why? Am I using wrong parameters?

Cheers,

Paolo

### Laurentiu

Feb 9, 2015, 9:52:03 AM2/9/15
Dear Paolo,

On Mon, Feb 9, 2015 at 11:57 AM, Paolo Zimmaro wrote:
Thank you so much Laurentiu for the useful information. Please notice that the incremental occurrence rates that I pasted are relative to magnitude values from Mmin (4.7) to MMax (7.7), so I'm not using the higher values of MMax for which the logic tree approach with different weights is used in the SHARE model.
In this connection, I'd like to understand how  I can derive the same occurrence rates with OQ using a different MFD (e.g. the truncGutenbergRichterMFD that is differently defined).

You don't derive occurence rates with OQ. You can define different type of recurrence models to characterize the seismic activity of a seismic source. The truncated GR MFD, as is defined by the OQ manual requires a pair of activity parameters (a-value, b-value and the minimum and the maximum magnitude).

I applied the equation aGRVal = log10 (N (low_mag) / (10^ (-bGRval* low_mag) -10^(-bGR*upper_mag) )

using b=-0.9 and N(low_mag)=0.4595 (Cumulative number of eqks for M>low_mag), and I obtained for this distribution a cumulative a value = 3.8932.

That's the same as in the shape file: aGR=3.9 and bGR=0.90;
Using b=0.9; a=3.8932, Mmin=4.6 and Mmax=7.8 for the truncGutenbergRichterMFD in OQ, I should obtain the same results of the model with incrementalMFD. But the results for a single site with a single source in terms of UHS and hazard curves are different.

If I understand correctly, you are performing an exercise, computing the seismic hazard for a single source, but two different options for the recurrence models: an incremental MFD and a truncated GR MFD. Is this correct?
Could you send me the exact files you are running, please? It might be easier for me to review your source model files.

Can you (or other usrers/developers) explain me why? Am I using wrong parameters?

Cheers,

Paolo

Cheers, Laurentiu

On Sunday, February 8, 2015 at 10:56:01 PM UTC+1, Paolo Zimmaro wrote:
Dear all,
I'm performing calculations using some element of the SHARE PSHA model. In the OQ implementation of this model, I'm noticing that the Magnitude-Frequency distribution of the so-called Area Sources, is given using the "IncrementalMFD". The input of this MFD are: MinMag, binWidth and the occurrence rates.
In my understanding, these occurrence rates represent the list of incremental values for the annual occurrence rates. Is it true?
Below there is the incrementalMFD for a generic source of the SHARE model that I'm using:

<incrementalMFD binWidth="0.2" minMag="4.7">
<occurRates>0.156146154488 0.103164741202 0.0681602685775 0.0450330428636 0.0297530363638 0.0196576361839 0.01298767143 0.00858086941869 0.00566932420314 0.00374568535564 0.00247474977277 0.00163505096033 0.00108026745665 0.000713725630703 0.000471553847881 0.000311552537677</occurRates>
</incrementalMFD>

How can I calculate the correspondant (cumulative values for M>0) values (a and b) of the Gutenberg-Richter recurrence law, the Min and Max values that I have to use in OQ?
How can I obtain the same results using the truncGutenbergRichterMFD instead of the incrementalMFD  in OQ?

Hopefully someone can help me!

Paolo Zimmaro

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### Paolo Zimmaro

Feb 9, 2015, 10:23:49 AM2/9/15

Dear Laurentiu,
I'm trying, using an exercise, to obtain the same outputs (in terms of HC or UHS), using the incrementalMFD and the truncGutenbergRichterMFD.

The starting point is a known definition of the occurrence rates through an incrementalMFD (from the SHARE model).

Please notice that I'm using the values for source ITAS319, ID 352 for Mmin=4.7 with 16 values of the incremental occurrence rate (without Mmax+increments, in order to avoid the Mmax logic tree issue).

The cumulative a value that you're talkin about is the weighted average of the 3IDs for that source (351 w=30% SS, 352 w=65% NF, 353 w=5% RF), while the cumulative a value that I'm trying to back-calculate is only for ID 352.

The goal of these analyses is to derive the same outputs, using two different MFD, and so the correct a, b, Mmax and Mmin to put in the truncGutenbergRichterMFD.

Please find attached the files that I'm using to perform the analyses.

Cheers,
Paolo
MFD.rar

### Paolo Zimmaro

Mar 13, 2015, 7:32:22 AM3/13/15
Dear Laurentiu,
did you have the opportunity to take care about my question? In the previous message, I attached the files that I'm using to perform the analysis that we are talking about.

Cheers,

Paolo

### ariascr...@gmail.com

Jun 10, 2021, 8:28:49 PMJun 10
to OpenQuake Users
Hi Paolo and Laurentiu,

I am currently developing my master's project and I have the same error that Paolo was referring to. I know many years have passed since publication, but I wonder if some of you were able to solve the problem of different results with the same recurrence rates but defined in two different ways.

I appreciate a lot your help.

Best regards,
Cristian

### Laurentiu

Jun 11, 2021, 12:47:28 AMJun 11
Hello Christian,
the abGR-values of the ESHM13 model are given in the shape files of each seismogenic source model,
The shape file of the area source model contains attributes to re-implement it in OpenQuake.
The fields "A" and "B" correspond to the aGR- and bGR-values, whereas the fields MAXMAG01 to 04 are the maximum magnitude values. The weights of the maximum magnitudes are listed in the WMAXMAG01 to WMAXMAG04.
I hope this helps,
Laurentiu

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