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 plugin cppgmpe 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.

We mainly discriminate the GMPEs based on their tectonic or geographical region:

• Tectonic regions

  • Active Shallow Crust

  • Geothermal

  • Induced

  • Stable Shallow Crust

  • Subduction IntraSlab

  • Subduction Interface

  • Volcanic

• Geographical Regions

  • Iceland

  • India

• Additional GMPEs

Tectonic regions

Active Shallow Crust	SA	PGA	PGV	Other IMTs	Component	Distances	Rupture Parameters	vs30	Other Site Parameters
AkkarBommer2010 [17]	✅	✅	✅		Avg. Horiz.	Rjb	Magnitude, Rake	✅
AkkarEtAl2014_Repi [18]	✅	✅	✅		Avg. Horiz.	Repi	Magnitude, Rake	✅
AkkarEtAl2014_Rhyp [18]	✅	✅	✅		Avg. Horiz.	Rhypo	Magnitude, Rake	✅
AkkarEtAl2014_Rjb [18]	✅	✅	✅		Avg. Horiz.	Rjb	Magnitude, Rake	✅
BooreAtkinson2008 [27]	✅	✅	✅		Avg. Horiz. (GMRotI50)	Rjb	Magnitude, Rake	✅
BooreAtkinson2011 [24]	✅	✅	✅		Avg. Horiz. (GMRotI50)	Rjb	Magnitude, Rake	✅
BooreEtAl2014 [29]	✅	✅	✅		Avg. Horiz. (RotD50)	Rjb	Magnitude, Rake	✅
BooreEtAl2014_HighQ [29]	✅	✅	✅		Avg. Horiz. (RotD50)	Rjb	Magnitude, Rake	✅
BooreEtAl2014_LowQ [29]	✅	✅	✅		Avg. Horiz. (RotD50)	Rjb	Magnitude, Rake	✅
BooreEtAl2020 [28]	✅	✅	✅		Avg. Horiz. (RotD50)	Rjb	Magnitude, Rake	✅
DerrasEtAl2014 [35]	✅	✅	✅		Avg. Horiz.	Rjb	Magnitude, Rake, HypoDepth	✅
DerrasEtAl2014_RhypoGermany [35]	✅	✅	✅		Avg. Horiz.	Rjb / Rhypo	Magnitude, Rake, HypoDepth, Width	✅
KaleEtAl2015_Iran [16]	✅	✅	✅		Avg. Horiz.	Rjb	Magnitude, Rake	✅
KaleEtAl2015_Turkey [16]	✅	✅	✅		Avg. Horiz.	Rjb	Magnitude, Rake	✅
KothaEtAl2020 [41]	✅	✅	✅		Avg. Horiz. (RotD50)	Rjb	Magnitude, HypoDepth
KothaEtAl2020_Site [41]	✅	✅	✅		Avg. Horiz. (RotD50)	Rjb	Magnitude, HypoDepth	✅
ZhaoEtAl2006_Asc [55]	✅	✅			Avg. Horiz.	Rrup	Magnitude, Rake, HypoDepth	✅
ZhaoEtAl2006_AscSGS [55]	✅	✅			Avg. Horiz.	Rrup	Magnitude, Rake, HypoDepth	✅

Geothermal	SA	PGA	PGV	Other IMTs	Component	Distances	Rupture Parameters	vs30	Other Site Parameters
ConvertitoEtAl2012_Geysers [34]		✅			Greater of two horizontal	Rhypo	Magnitude	✅

Induced	SA	PGA	PGV	Other IMTs	Component	Distances	Rupture Parameters	vs30	Other Site Parameters
Atkinson2015 [22]	✅	✅	✅		Avg. Horiz. (RotD50)	Rhypo	Magnitude
Atkinson2015_AltDistSat [22]	✅	✅	✅		Avg. Horiz. (RotD50)	Rhypo	Magnitude
DostEtAl2004 [36]		✅	✅		Avg. Horiz. (GMRotD100)	Rhypo	Magnitude
ZalachorisRathje2019 [54]	✅	✅	✅		Avg. Horiz. (RotD50)	Rjb, Rhypo	Magnitude, Rake	✅

Stable Shallow Crust	SA	PGA	PGV	Other IMTs	Component	Distances	Rupture Parameters	vs30	Other Site Parameters
Allen2012 [19]	✅	✅			Med. Horiz.	Rrup	Magnitude, HypoDepth
Allen2012_SS14 [19]	✅	✅			Med. Horiz.	Rrup	Magnitude, HypoDepth	✅
AtkinsonBoore2006 [23]	✅	✅	✅		Avg. Horiz.	Rrup	Magnitude	✅
BindiEtAl2017_Rhypo [25]	✅	✅			Avg. Horiz.	Rhypo	Magnitude	✅
BindiEtAl2017_Rjb [25]	✅	✅			Avg. Horiz.	Rjb	Magnitude	✅
RietbrockEtAl2013_MagDependent [47]	✅	✅	✅		Avg. Horiz.	Rjb	Magnitude
RietbrockEtAl2013_SelfSimilar [47]	✅	✅	✅		Avg. Horiz.	Rjb	Magnitude
RietbrockEdwards2019_Low [37]	✅	✅	✅		Avg. Horiz.	Rjb	Magnitude
RietbrockEdwards2019_Mean [37]	✅	✅	✅		Avg. Horiz.	Rjb	Magnitude
RietbrockEdwards2019_Up [37]	✅	✅	✅		Avg. Horiz.	Rjb	Magnitude

Subduction IntraSlab	SA	PGA	PGV	Other IMTs	Component	Distances	Rupture Parameters	vs30	Other Site Parameters
Allen2022 [20]	✅	✅	✅		Med. Horiz.	Rhypo	Magnitude, HypoDepth	✅
ZhaoEtAl2006_SSlab [55]	✅	✅			Avg. Horiz.	Rrup	Magnitude, HypoDepth	✅
ZhaoEtAl2006_SSlabCascadia [55]	✅	✅			Avg. Horiz.	Rrup	Magnitude, HypoDepth	✅
ZhaoEtAl2006_SSlabNSHMP2014 [55]	✅	✅			Avg. Horiz.	Rrup	Magnitude, HypoDepth	✅

Subduction Interface	SA	PGA	PGV	Other IMTs	Component	Distances	Rupture Parameters	vs30	Other Site Parameters
ZhaoEtAl2006_SInter [55]	✅	✅			Avg. Horiz.	Rrup	Magnitude, HypoDepth	✅
ZhaoEtAl2006_SInterCascadia [55]	✅	✅			Avg. Horiz.	Rrup	Magnitude, HypoDepth	✅
ZhaoEtAl2006_SInterNSHMP2008 [55]	✅	✅			Avg. Horiz.	Rrup	Magnitude	✅

Volcanic	SA	PGA	PGV	Other IMTs	Component	Distances	Rupture Parameters	vs30	Other Site Parameters
Atkinson2010_Hawaii [21]	✅	✅	✅		Avg. Horiz.	Rjb	Magnitude, Rake, HypoDepth	✅
LanzanoLuzi2019_Deep [43]	✅	✅	✅		Avg. Horiz.	Rhypo	Magnitude	✅
LanzanoLuzi2019_DeepScaled [43]	✅	✅	✅		Avg. Horiz.	Rhypo	Magnitude	✅
LanzanoLuzi2019_Shallow [43]	✅	✅	✅		Avg. Horiz.	Rhypo	Magnitude	✅
LanzanoLuzi2019_ShallowScaled [43]	✅	✅	✅		Avg. Horiz.	Rhypo	Magnitude	✅
TusaLanger2016_RepiBA08DE [50]	✅	✅			Greater of two horizontal	Repi	Magnitude	✅
TusaLanger2016_RepiBA08SE [50]	✅	✅			Greater of two horizontal	Repi	Magnitude	✅
TusaLanger2016_RepiSP87DE [50]	✅	✅			Greater of two horizontal	Repi	Magnitude	✅
TusaLanger2016_RepiSP87SE [50]	✅	✅			Greater of two horizontal	Repi	Magnitude	✅
TusaLanger2016_Rhypo [50]	✅	✅			Greater of two horizontal	Rhypo	Magnitude	✅

Geographical regions

Iceland	SA	PGA	PGV	Other IMTs	Component	Distances	Rupture Parameters	vs30	Other Site Parameters
IMO-PV09 [45]		✅	✅	MMI		Repi	Magnitude
KowsariEtAl2020_Y1 [42]	✅	✅				Rjb	Magnitude
KowsariEtAl2020_Y2 [42]	✅	✅				Rjb	Magnitude, Rake
UICE-K20A [42] specifically developed for south Iceland seismic zone		✅		MMI		Rjb	Magnitude		Soil factor (based on vs30)
UICE-K20C [42] specifically developed for south Iceland seismic zone		✅		MMI		Rjb	Magnitude		Soil factor (based on vs30)

India	SA	PGA	PGV	Other IMTs	Component	Distances	Rupture Parameters	vs30	Other Site Parameters
NathEtAl2012_Lower [44]	✅	✅	✅		Vertical	Rrup	Magnitude
NathEtAl2012_Upper [44]	✅	✅	✅		Vertical	Rrup	Magnitude
RaghukanthIyengar2007 [39]	✅	✅			Avg. Horiz.	Rhypo	Magnitude	✅
RaghukanthIyengar2007_KoynaWarna [39]	✅	✅			Avg. Horiz.	Rhypo	Magnitude	✅
RaghukanthIyengar2007_Southern [39]	✅	✅			Avg. Horiz.	Rhypo	Magnitude	✅
RaghukanthIyengar2007_WesternCentral [39]	✅	✅			Avg. Horiz.	Rhypo	Magnitude	✅
SharmaEtAl2019 [48]	✅	✅			Avg. Horiz.	Rjb	Magnitude, Rake	✅

Additional GMPEs

Additional models	SA	PGA	PGV	Other IMTs	Component	Distances	Rupture Parameters	vs30	Other Site Parameters
BEA2014 [26]	✅	✅	✅	DRS		Rhypo	Magnitude	✅
CEA2014 [33]	✅	✅	✅	DRS		Rrup / Rhypo	Magnitude	✅

• If not explicitly listed in ‘Other IMTs’, MMI is derived from PGA.

• Further, see SA, PGA, PGV, Vs30 grid

• For a detailed description of the implemented code and coefficients see also OpenQuake documentation.

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 plugin py3gmpe. Read the instructions for the configuration.

Modified Mercalli intensity (MMI)

Some GMPEs/GMMs such as IMO-PV09 provide estimates of Modified Mercalli intensity (MMI), others not, e.g., CEA2014. When not provided by a GMPE/GMM, MMI is estimated from PGA using formulas in Wald et al. [52]:

• : = 2.20 * log_{10}(PGA) + 1

• : = 3.66 * log_{10}(PGA) - 1.66

where PGA is given in .

The debug logging output tells how MMI is computed for a selected GMPE/GMM.