# 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.

Hint

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.uses the defined Vs30 grid

measure of distance: Joyner-Boore distance.

AkkarEtAl2014_Repi (Akkar

*et al.*[12])uses the defined Vs30 grid

measure of distance: epicentral distance.

AkkarEtAl2014_Rjb (Akkar

*et al.*[12])uses the defined Vs30 grid

measure of distance: Joyner-Boore distance.

BEA2014 ()

uses the defined Vs30 grid

measure of distance: epicentral distance.

CEA2014 (Cauzzi

*et al.*[15])uses the defined Vs30 grid

measure of distance: epicentral distance.

Dost2004 (Dost

*et al.*[16])does not use a Vs30 grid

measure of distance: epicentral distance.

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

where

*M*: is the local magnitude for Iceland,does not use a Vs30 grid

KowsariEtAl2020_Y1 (Kowsari

*et al.*[17]),does not use a Vs30 grid

measure of distance: Joyner-Boore distance.

KowsariEtAl2020_Y2 (Kowsari

*et al.*[17]),does not use a Vs30 grid

measure of distance: Joyner-Boore distance.

UICE-K20A (Kowsari

*et al.*[17]) specifically developed for south Iceland seismic zone:where

: the moment magnitude,

: coefficients,

*S*: soil factor (0 or 1),does not use a Vs30 grid.

UICE-K20C (Kowsari

*et al.*[17]) specifically developed for south Iceland seismic zone:where

: the moment magnitude,

: coefficients,

*S*: soil factor (0 or 1),does not use a Vs30 grid.

## 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/oq-sm.py`

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.