ShakeMap vs. GMPE Comparison

Why Compare at All

ShakeMap interpolation (see Intensity Information & Examples) is an observation-driven estimate — it reflects what instruments actually recorded, interpolated across the network. A Ground Motion Prediction Equation (GMPE) is the opposite kind of estimate: a physics- and statistics-informed model of what shaking should look like, computed independently of any particular recording. For significant events, Intensity Lab runs both and presents an engineering comparison — a residual plot (observed − predicted vs. distance) and a scatter plot (predicted vs. observed) on the event page's engineering panel — so a reader can see where the two agree and where they diverge.

GMPEs are empirical equations fit to large databases of recorded ground motions. They predict PGA (and other parameters) as a function of earthquake magnitude, source-to-site distance, and site conditions. Intensity Lab computes four NGA-West2 models through the GEM OpenQuake engine (openquake.hazardlib):

The Four Models

Key	Authors	OpenQuake Class
ask14	Abrahamson, Silva & Kamai (2014)	AbrahamsonEtAl2014
bssa14	Boore, Stewart, Seyhan & Atkinson (2014)	BooreEtAl2014
cb14	Campbell & Bozorgnia (2014)	CampbellBozorgnia2014
cy14	Chiou & Youngs (2014)	ChiouYoungs2014

GMPE PGA output is converted to MMI using the same Worden et al. (2012) GMICE described in Intensity Information & Examples, so a GMPE-derived MMI and a ShakeMap-derived MMI are directly comparable numbers.

Required Input Parameters

Each GMPE requires earthquake source parameters, distance metrics, and site characterization. Many of these are not directly reported by USGS for smaller events; the table below documents every parameter, the value used, and the source or justification.

Parameter	Symbol	Value Used	Source / Rationale
Moment magnitude	M	Event magnitude	USGS ComCat
Fault rake	λ	0° (strike-slip)	Default for uncharacterized Western US faults
Fault dip	δ	90° (vertical)	Conservative for uncharacterized faults
Hypocentral depth	h	Event depth, or 10 km	USGS ComCat; 10 km default if unknown
Rupture width	W	10^{(0.32M − 1.01)}	Wells & Coppersmith (1994) all-mechanism scaling
Top of rupture depth	Z_tor	max(0, h − W/2)	Estimated from depth and rupture half-width
Joyner-Boore distance	R_jb	Epicentral distance	Point-source approximation (haversine)
Rupture distance	R_rup	√(R_jb² + h²)	Hypocentral distance (3-D Pythagorean)
Horizontal distances	R_x, R_y0	0.0	Not applicable; no rupture-plane geometry available
Shear-wave velocity	V_s30	Site-specific	See Vs30 section below
V_s30 measured flag	—	False	All values are model estimates, not field measurements
Depth to V_s = 1000 m/s	Z_1.0	ASK14 regression from V_s30	Abrahamson et al. (2014), Eq. 31
Depth to V_s = 2500 m/s	Z_2.5	CB14 regression from V_s30	Campbell & Bozorgnia (2014), Eq. 33

Fault Geometry: Rake and Dip

The NGA-West2 models require fault rake (slip direction) and dip (fault plane angle). For most Western US events, focal mechanism data is not available in real time. Intensity Lab assumes rake = 0° (pure strike-slip) and dip = 90° (vertical fault plane). Strike-slip faulting is the dominant mechanism in California's transform plate boundary setting. For thrust or normal events this will introduce some error; the GMPEs are relatively insensitive to rake for sites at distances greater than ~20 km from the rupture.

Distance Metrics: R_jb and R_rup

NGA-West2 models use two distance measures: the Joyner-Boore distance (R_jb), the closest horizontal distance to the surface projection of the rupture, and R_rup, the closest 3-D distance to the rupture plane. Because rupture geometry is not available for most M3–5 events, Intensity Lab approximates R_jb as the epicentral distance and R_rup as the hypocentral distance (√(R_epi² + depth²)). For sites more than ~20 km from the epicenter — the majority of all 2,002 gazetteer sites for any given event — this point-source approximation introduces less than 5% error in predicted PGA.

Basin Depth Parameters: Z_1.0 and Z_2.5

Several NGA-West2 models require the depth to the V_s = 1000 m/s horizon (Z_1.0) and depth to V_s = 2500 m/s (Z_2.5), which describe sedimentary basin depth. These are estimated from site V_s30 using published regression equations rather than measured. Sites in deep basins (e.g., Los Angeles Basin) may have basin depths significantly larger than these estimates.

Regional caution: The NGA-West2 models were developed primarily from California strong-motion recordings. Estimates for regions with different crustal properties — such as Oregon, Nevada, or central Mexico — should be interpreted with caution and treated as approximate.

V_s30: Site-Specific Soil Conditions

V_s30 is the time-averaged shear-wave velocity in the upper 30 meters of the Earth's surface, measured in m/s. It is the primary proxy for local site amplification in GMPE calculations: softer soils (low V_s30) amplify shaking; hard rock (high V_s30) attenuates it. The same site-specific V_s30 used for GMPEs also parameterizes site response in the BBP physics-based simulations — see Physics-Based Simulation (BBP).

The primary source is the SCEC Unified Community Velocity Model (UCVM), queried per site; the USGS global raster and a rock-site default are fallbacks. Data source priority for each site:

CGS Geology — California Geological Survey geology-based V_s30 map accessed via SCEC UCVM (California sites only)
Wald & Allen / UCVM — Topographic slope proxy (Wald & Allen 2007) computed from UCVM's statewide DEM, which covers California and extends into western Nevada, Oregon, and northern Mexico via a rotated 1,800 × 900 km grid centered on California
Wald & Allen / USGS — Topographic slope proxy (Wald & Allen 2007) from the USGS ShakeMap global V_s30 raster, used for locations outside the UCVM grid coverage (e.g., eastern Nevada, Idaho)
Default (760 m/s) — Rock-site reference value used when neither source returns a valid result

The API exposes site-specific V_s30 for any location in the supported region: GET /api/v1/vs30?lat={lat}&lon={lon}