This electronic supplement comprises text and figures supporting the conclusions made in the main article. Text includes description of seismic-velocity model and wave propagation and interpretation of directivity effects, and figures include fault geometry, Z1 and Z2.5 depths, effects of rupture speed variations on directivity effects and amplifications.
Calculations of seismic-wave propagation employed the seismic velocities and densities of the Wasatch Front Community Velocity Model (WFCVM), v.3c (Magistrale et al., 2008), with minor modifications to the seismic-velocity structure of the shallow subsurface described in Moschetti and Ramírez-Guzmán (2011). The parameterization of the WFCVM follows the methodology developed for the Southern California Earthquake Center’s (SCEC) CVM-S (Magistrale et al., 2000), whereby higher resolution basin models are embedded in a regional seismic-velocity model, and seismic wavespeeds in the sedimentary basins are specified from separate data sources.
The WFCVM is composed of the following primary components: (1) basin surfaces derived from gravity inversion, seismic refraction, borehole basement depths, and geologic contacts; (2) seismic velocities within the sedimentary basins from a range of sources, including geophysical measurements, borehole observations, and empirical relations (Faust, 1951); and (3) a regional seismic-velocity model. The basins important to our earthquake scenarios are the Salt Lake, Weber, and Utah basins (Fig. 1 in the main article and Fig. S2). The WFCVM does not include other known basins (e.g., Tooele and Rush basins). Previous studies found good agreement at frequencies up to about 0.5 Hz between observed and synthetic seismograms for several small, local earthquakes (Magistrale et al., 2008; Moschetti and Ramírez-Guzmán, 2011), indicating that the WFCVM includes the main 3D seismic structures required for accurate ground-motion modeling.
The quality factors describing seismic attenuation from Brocher (2006) are given by
(S1)
(S2)
(S3)
and were implemented with Rayleigh damping, which is a frequency-dependent viscous damping that is unique in the current implementation in not distinguishing between its effects on the P and S waves:Q(f)−1=aK+bM, in which K and M are the stiffness- and mass-element matrices, respectively. Magistrale et al. (2008) also employed the attenuation model of Brocher (2006) in a validation exercise for the WFCVM. Though recent research has demonstrated the importance of considering the frequency dependence of attenuation in ground-motion modeling (Raoof et al., 1999; Withers et al., 2015), our wave propagation code employs a frequency-independent implementation of the seismic quality factors. Nevertheless, the effects of frequency-dependent attenuation are less pronounced at the lower frequencies of our simulations, and the effect on our results is expected to be small (Liu et al., 1976).
Simulations employed the Hercules finite-element toolchain (Tu et al., 2006), which meshes the simulation domain of the WFCVM, partitions the mesh, and solves the elastodynamic equations. The Hercules solver is second-order in time and in space. Meshing employs an octree-based methodology, which adapts the model resolution to the local shear wavespeed. Code verification has been carried out for simulations in southern California (Bielak et al., 2010) and in the New Madrid seismic zone (Ramírez-Guzmán et al., 2015) and found good agreement with other, widely used wave-propagation codes (Graves, 1996; Olsen and Archuleta, 1996). Studies employing the ground-motion simulations from Hercules have been carried out for various regions, including southern California (Taborda and Bielak, 2013); the Santa Clara and Livermore Valleys, California (Hartzell et al., 2010, 2014, 2016); the New Madrid seismic zone (Ramírez-Guzmán et al., 2015); and the Wasatch fault zone (Moschetti and Ramírez-Guzmán, 2011; Taborda et al., 2012).
In constructing the mean model for comparison with the simulations, we used only those ground-motion prediction equations (GMPEs) that are defined for the low VS30 values found at sites within the sedimentary basins of the Wasatch Front (Abrahamson et al., 2014, hereafter, ASK14; Boore et al., 2014, hereafter, BSSA14; Campbell and Bozorgnia, 2014, hereafter, CB14; Chiou and Youngs, 2014, hereafter, CY14). The VS30 and basin depth parameters were obtained from the WFCVM for each recording site (Magistrale et al., 2008). The average predicted ground motion from the four GMPEs was computed from the mean, logarithmized spectral accelerations from these four GMPEs (μASK14, μBSSA14, μCB14, μCY14):
(S4)
The average predicted ground-motion variability from the four GMPEs was computed from the total standard deviations associated with these four GMPEs (σASK14, σBSSA14, σCB14, σCY14):
(S5)
Ben-Menahem (1961, 1962) identified a directivity factor AD for surface and body waves, with the analytical form:
(S6)
in which b is the length of the seismic source (or asperity), T is the wave period, θ is the angle between along-strike axis of the rupture direction and the site of interest, and Vrup is the rupture speed. For surface waves, Va represents the phase speed; for body waves, Va represents the apparent velocity. Although interpretation of directivity effects from earthquakes on the Salt Lake City segment of the Wasatch fault zone (SLCSWFZ) is complicated from the case described by equation (S6) because the SLCSWFZ is a normal fault and directivity effects result from contributions of surface waves, as well as from SH- and SV body waves, we interpret the resulting patterns in terms of the Ben-Menahem amplifications (equation S6). For the long-period results investigated here, the use of harmonic period to understand variation of the response spectral results as a function of oscillator period is a reasonable assumption (Bora et al., 2016).
Equation (S6) defines the directivity factor, which is a function of azimuth, rupture velocity, and the ratio of the source dimension to wave period b/T. We plot the effects of changing the rupture speed and changing b/T in Figures S3a–c and S4a. The corresponding amplification factors are plotted in Figures S3d and S4b and exhibited symmetry about θ = 0, with amplitudes and azimuthal dependence that are a function of b/T.
Figure S1. Fault geometry employed for the ground-motion simulations. The 3D fault representation comprised two segments, one consisting of the Cottonwood and East Bench faults and one segment for the Warm Springs fault, meeting at depth. The surface traces, plotted on the lower map and the upper fault representation, were taken from Bruhn et al. (1992).
Figure S2. The Z1 and Z2.5 depths from the seismic-velocity model are plotted. The surface trace of the SLCSWFZ is plotted for reference. Points in (a) indicate locations where simulated ground motions were saved. Grid spacing of recorded points was significantly higher in the east–west direction.
Figure S3. Effect of rupture speed variations on the directivity factor (equation S6) and the amplifications predicted by these directivity factors. Directivity factors for varying rupture speeds, for (a) b/T = 0.5, (b) b/T = 3, and (c) b/T = 6. (d) Amplifications predicted by equation (S6) for increasing rupture speed.
Figure S4. Effect of changing b/T on (a) the directivity factor (equation S6) for a fixed rupture speed and (b) the amplifications predicted for modifying the b/T ratio.
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