Magnitude-Scaling relationships

[ariascr...@gmail.com]

Hello,

I wonder why in a PSHA simulation if I use a discrete incremental magnitude frequency distribution and if I use a double truncated Gutenberg-Richter distribution, assuming both represent the same magnitude frequency distribution, I am obtaining bigger PGA's in the first case than the second one. I think I must to have the same results in both cases.

To give a context I am using the following data.

• <truncGutenbergRichterMFD aValue="2.688350" bValue="0.635628" maxMag="8.7" minMag="6.0"/>
  
  
• <incrementalMFD minMag="6" binWidth="0.1">
                    <occurRates>0.074917279795517
  0.064717122631906
  0.055905739946577
  0.048294046951857
  0.041718703181764
  0.036038607344361
  0.031131869407887
  0.026893194944209
  0.023231625599843
  0.020068587206946
  0.017336203648424
  0.014975840294109
  0.012936845751408
  0.011175464929441
  0.009653900091958
  0.008339499750027
  0.007204057988816
  0.00622320919262
  0.005375905179447
  0.004643963524909
  0.004011677382841
  0.003465478429724
  0.002993645699988
  0.002586054064048
  0.002233956951621
  0.00192979865776
  0.001667052203845
  0.001440079274161
                    </occurRates>

Thanks regards.

[Marco Pagani]

Because your MFDs are not exactly the same. From OQ manual page 38 “A discrete incremental magnitude-frequency distribution: It is the simplest distribution supported. It is defined by the minimum value of magnitude (representing the mid point of the first bin)”. On the contrary the mmin for a double truncated is the lowest magnitude i.e. when you discretise it the mmin corresponds to the lower limit of the first bin (see also Fig. 2.5 and 2.6)

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MARCO PAGANI | Seismic Hazard Team Lead | Skype mm.pagani | +39-0382-5169863

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[UWIDUHAYE Jean d'Amour]

Dear Sir/Madam,

I have a problem with my plugin when once tried to download or once tried to connect to openquake platform.

Your assistance is highly appreciated.

I am using Qgis 3.16 long release.

Kind regards,

Jean d'Amour U.

[ariascr...@gmail.com]

Hi Marco,

Thanks a lot, with your help I could did what I wanted. My problem was that I was using the calculated value for the "lambda" = 10^(a-b*M), but when we want to use the incremental MFD or arbitrary MFD, the values in the occurRates must to be the difference between each value of lambda (i.e. in my example lambda1 = 0.0749, lambda 2 = 0.0647 and the occurRate for the minmag (6.05)  is 0.0102).