OQ implementation of BCHydro equation

[Chris Van Houtte]

Hi there,

I was using your ground-motion model test tables to check my independent code of the BCHydro subduction equation (abrahamson2015.py). I could be wrong but there might be an error in the OQ implementation, particularly equation 4 (the forearc/backarc flag).

I could only match the model prediction tables at https://github.com/gem/oq-hazardlib/blob/master/openquake/hazardlib/tests/gsim/data/BCHYDRO/ for sites_backarc = 1, but not for sites_backarc = 0 (i.e. for forearc sites). The equation in the Earthquake Spectra preprint is

      theta15 + theta16 * log( max(Rrup,100) / 40) * F_faba

where F_faba =0 for sites on the forearc. I don't know python but it appears the abrahamson2015.py script instead does

      { theta15 + theta16 * log( max(Rrup,100) / 40) } * F_faba

i.e. including theta15 in the brackets.  Can you please verify which equation is the correct one? I can match the table with the second equation, but not the first.

Additionally the values for theta15 at PGA and SA(0.02s) are 0.9996 in the paper but 0.9969 in the abrahamson2015.py coefficient table.

Apologies if I have missed something and it is actually correct.

Thanks
Chris

[Graeme Weatherill]

Dear Chris,

Thank you for raising these points, but unfortunately in both cases I got conflicting information from different independent sources. Given the importance of this GMPE the lack of consistency has been an enormous cause of frustration.

For the Sa (0.02) theta15 coefficient. We were supplied separately with a digital version of the coefficients in an Excel spreadsheet by two independent sources, neither of which was Norm or Nick, but both of whom had participated in the BCHydro project. In the digital version the coefficient was 0.9969 and not 0.9996 as printed in the paper. The actual test tables were generated from a third version of the GMPE implemented by Shrey Shahi (on his github repo). This implementation also used the coefficient 0.9969. Finally, we have a copy of HAZ43b (which is one of Norm's own codes) and it too says 0.9969. Only the USGS NSHMP fortran code uses the value 0.9996. I am happy to concede the possibility if the printed values in Earthquake Spectra are correct and the other versions contain perhaps an old error that has propagated. On the other hand, experience has shown that, perversely, the coefficients actually printed in the publication are often the least reliable!

Regarding the forearc/backarc scaling term. Here I encounter more consensus. The implementation by Shahi adopts the same as OpenQuake (actually, in reality it is vice-versa). However, the USGS NSHMP also adopts this approach, so too does the digital implementation in the Excel file we were given. As another point of reference we look at the Montalva et al. (2015) GMPE, which uses the same functional form as BC Hydro but with a local calibration of the coefficients for Chile. From the matlab code provided by the author we see that the functional form of the forearc/backarc scaling is the same as that of OpenQuake. Finally, checking in with HAZ43b we see that it agrees with the OpenQuake way and not with the manuscript. Again, I cannot say for certain that we are correct, and it is entirely possible that the other sources are simply propagating an error from an earlier source and that we have added to the confusion. However, once again, experience tells us that the manuscripts are often the most error prone.

For the time being, the weight of evidence seems to agree with our implementations - as you can see we have done a lot of checking with this GMPE (and wasted a lot of time trying to resolve issues that should have been fixed by the authors themselves). So I would not change our implementation unless I get clarification from the authors. However, if you are still unsure I strongly recommend contacting the authors themselves to draw attention to this issue and please let us know what their response is. If it is a misprint in the paper then it is a critical one that requires an erratum.

Sorry for the long email. Hope it helps though.

Thanks,

Graeme

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[Chris Van Houtte]

Thanks very much for the detailed reply Graeme, it's a great help. Now that I think about it, the model appears to make more sense with the forearc/backarc scaling implemented in OpenQuake, rather than the one suggested in the paper. I'm happy to see some consensus, but will still try to seek some clarification from the authors. I'll be sure to inform you if I hear anything.

Best regards
Chris