# Ground-motion models

## Definitions

In this section we review ground motion models that are appropriate for the prediction of strong ground motions at the sites. Ground-motion models, also called ground motion prediction equations (GMPE) are most commonly derived from strong ground motion recordings. For a given event of magnitude $$m^*$$ located at some distance $$r^*$$, the strong motion intensity $$i^*=f(m^*,r^*,{\theta})$$ can be estimated in terms of its conditional mean $$\eta_{(I|M,R)}$$ and its error term $$\varepsilon_I$$. The expected seismic intensity at the project site is a conditional random variable $$I/M,R$$ and the ground-motion models provide an estimate of the median and the error term of ground-motion intensity in terms of earthquake magnitude, distance and site and geologic conditions. The conditional mean $$\eta_{(I|M,R)}=f(m^*,r^*,{\theta})+\varepsilon$$ is an empirical regression model of earthquake magnitude $$(m^*)$$, source-to-site distance $$(r^*)$$ and geological/geotechnical site conditions $$(\theta)$$. The error term $$\varepsilon$$, is a random variable with a log-normal distribution with mean $$\mathrm{E}[\varepsilon]=0$$ and variance $$\mathrm{Var}[\varepsilon] \approx \sigma_{lnI|M,R}^2$$

Most GMPEs are defined in terms of finite fault distance metrics assuming a planar rupture geometry. The trace of the rupture is defined as the projection of the top edge of the rupture on the ground surface. The rupture plane, trace and the surface projection allow to define four finite fault distance metrics: $$R_{RUP}$$, $$R_{JB}$$ ,$$R_{X}$$ and $$R_{Y0}$$. The rupture distance $$R_{RUP}$$ is the distance from the site to the closest point of the rupture plane. The Joyner-Boore distance $$R_{JB}$$ is the closest distance between the site and the surface projection of the rupture plane and the auxiliary parameters $$R_X$$, $$R_{Y0}$$ and $$Z_{TOR}$$ are the coordinates from the site to the closest point of the top of the rupture.

Figure 15 illustrates these distances between a site and the rupture plane. A full description of these finite fault metrics can be found in Kaklamanos et al..73

## Logic tree

A minimum number of independent GMPEs are selected to capture the expected range of possible ground-motions in the target region. They are weighted in a logic tree to address their relative confidence based on the available information. The chosen set represents the composite distribution of epistemic uncertainty in the ground motion model for the site.

A region-specific ground-motion model is one of the weighted branches of the modeled logic tree (under certain guidelines).75 One or more of these models are complemented with GMPEs developed for similar seismic regions or suited for global analysis.76

The GMPE models selected for a site in a cratonic terrain and their inputs are summarised in Table 6. The GGM area is located in the east of the Yilgarn craton. This set and their weights (Figure 16) are a result of an expert workshop77 to assess the applicability of these models for use in the 2018 National Seismic Hazard Assessment of Australia (NSHA 18). Other tectonic regimes are present in the Australian seismic hazard but they do not contribute to this site.

Table 6 summarizes each model tectonic region and rupture, distances and site context required for each model. The site parameters $$V_{s30}$$ and $$Z_{1.0}$$ are the average shear-wave velocity in the top 30 m and the depth to engineering rock ($$V_s=1000\,\mathrm{m/s}$$) respectively. For the models developed specifically for Australia Somerville et al.78 and Switzerland79 the average shear-wave velocity is constrained to the targeted areas.

 Model Code Tectonic Rupture context Distance context Site context Allen 2012 Al12 SCC Mw, Zhyp Rrup 820 Atkinson Boore 2006 AB06 SCC Mw Rrup Vs30 Atkinson Boore 2006 Modified 2011 AB11 SCC Mw Rrup Vs30 Boore et al. 2014 Bo14 ASC Mw, rake Rjb Vs30 Chiou Youngs 2014 CY14 ASC Mw, rake, Ztor, dip Rrup, Rjb, Rx Vs30, z1.0 Somerville et al. 2009 (Yilgarn Craton) So09 SCC Mw Rjb 865 Zhao et al. 2006 Swiss 05 Zh06 ASC Mw, rake, Zhyp Rrup 700

1. “Estimating Unknown Input Parameters When Implementing the NGA Ground-Motion Prediction Equations in Engineering Practice.”↩︎

2. Kaklamanos, Baise, and Boore.↩︎

3. J. Bommer and F. Scherbaum, “The Use and Misuse of Logic Trees in Probabilistic Seismic Hazard Analysis,” Earthquake Spectra 24 (2008): 997–1009.↩︎

4. Jonathan Stewart et al., “GEM-PEER Task 3 Project: Selection of a Global Set of Ground Motion Prediction Equations” (Pacific Earthquake Enginnering Research Center, 2013).↩︎

5. Griffin et al., “Expert Elicitation of Model Parameters for the 2018 National Seismic Hazard Assessment.”↩︎

6. “Source and Ground Motion Models for Australian Earthquakes.”↩︎

7. B. Edwards et al., “Region‐specific Assessment, Adjustment, and Weighting of Ground‐motion Prediction Models: Application to the 2015 Swiss Seismic‐hazard Maps,” Bulletin of the Seismological Society of America 106 (2016): 1.↩︎