GMPE/GMM: Ground Motion Prediction Equations and Models

The SIGMA packages provides GMPEs/GMMs which are internally defined. For greater flexibility externally defined custom GMPEs can by added.

Internal GMPE/GMM

The internally defined GMPE models and GMMs provide the fasted access to results. They are made available through the plug-in gmpeeewd and can be used without further software installations. Read the instructions for their configuration.


Some models require to define a focal mechanism and a finite fault, e.g. to compute distance measures. Read the section Defining rupture parameters for instructions on defining a focal mechanism and rupture geometry interactively.

The models are:

  • AkkarBommer2010 (Akkar and Bommer [11]) implements GMPE developed by Akkar and Bommer [11] and published as “Empirical Equations for the Prediction of PGA, PGV, and Spectral Accelerations in Europe, the Mediterranean Region, and the Middle East”. SA at 4 s (not supported by the original equations) has been added in the context of the SHARE project and assumed to be equal to SA at 3 s but scaled with proper factor. Equation coefficients for PGA and SA periods up to 0.05 seconds have been taken from updated model as described in Bommer et al. [13]. Coefficients for PGV and SA above 0.05 seconds are taken from the original 2010 publication.

  • AkkarEtAl2014_Repi (Akkar et al. [12])

  • AkkarEtAl2014_Rjb (Akkar et al. [12])

  • BEA2014 ()

  • CEA2014 (Cauzzi et al. [15])

  • Dost2004 (Dost et al. [16])

  • IMO-PV09 (Pétursson and Vogfjörð [18]) specifically developed for Iceland:

    log_{10}(PGV) &= -1.69 * log_{10}(r + 0.00299 * 10^{0.621*M}) + 1.05 * M - 4.96 \\
log_{10}(PGA) &= -2.26 * log_{10}(r + 0.0309 * 10^{0.569*M-0.0194*M^2}) - 0.0437*M^2 + 1.28 * M - 2.85 \\
MMI &= 1.6 * log_{10}(PGA) + 5.7


  • KowsariEtAl2020_Y1 (Kowsari et al. [17]),

  • KowsariEtAl2020_Y2 (Kowsari et al. [17]),

  • UICE-K20A (Kowsari et al. [17]) specifically developed for south Iceland seismic zone:

    log_{10}(PGA) = C_1 + C_2 * M_w   + C_3 * M^2 + (C_4 + C_5 * M_w) * log_{10}(\sqrt{C_6^2+R_{JB}^2}) + C_7*S


  • UICE-K20C (Kowsari et al. [17]) specifically developed for south Iceland seismic zone:

    log_{10}(PGA) = C_1 + C_2 * M_w + (C_3 + C_4 * M_w) * log_{10}(\sqrt{C_5^2+R_{JB}^2})+C_6*S


External custom GMPEs

In AUTOSIGMA and SIGMA you may use external custom GMPEs, e.g. by your own or other custom Python scripts. For example the modules can interface with the GMPEs provided by OpenQuake [6] and the Python script $SEISCOMP_ROOT/share/sigma/pygmpe/ of the SIGMA package. This unique feature allows to additionally implement their own GMPEs which may come from their own research and which may be tailored to specific regions. Check the list of models [4] provided by OpenQuake.

The interface to custom GMPEs is provided through the plug-in py3gmpe. Read the instructions for the configuration.