Electronic Supplement to
Distance and Azimuthal Dependence of Ground-Motion Variability for Unilateral Strike-Slip Ruptures

by Jagdish Chandra Vyas, Paul Martin Mai, and Martin Galis

This electronic supplement contains figures of slip distributions, residuals to ground-motion prediction equations (GMPEs) with and without directivity correction, distance and azimuthal dependence of ground-motion variability for different source models. It documents the intermediate steps that lead to the final results, as well as providing an additional analysis performed to better support our key findings.

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Figures

Figure S1. Original slip distributions of the five kinematic sources of the 1992 Landers earthquake. The rupture models are Cotton (Cotton and Campillo, 1995), Hernandez (Hernandez et al., 1999), Zeng (Zeng and Anderson, 2000), Wald (Wald and Heaton; 1994), and Cohee (Cohee and Beroza, 1994). (Red star, hypocenter; EW, east–west direction; NS, north–south direction).

Figure S2. Distance dependence (Joyner–Boore distance, R_JB) of μ_ln(PGV) and ϕ_ln(PGV) for the five source models of the 1992 Landers earthquake with (a) bin width = 15 km and (b) bin width = 25 km. The circle size represents the number of stations in each bin. The solid black circles indicate the average ϕ_ln(PGV) that decreases with increasing distance R_JB as power law ($\alpha R_{\mathrm{JB}}^k$). The dashed lines represent the power law fit to the corresponding ϕ_ln(PGV) values for the different source models. Constant variability is depicted for ground-motion prediction equations (GMPEs): BA, Boore and Atkinson (2008); CB, Campbell and Bozorgnia (2008); AS, Abrahamson and Silva (2008); and CY, Chiou and Youngs (2008).

Figure S3. Azimuthal dependence of μ_ln(PGV) and ϕ_ln(PGV) for the five source models of the 1992 Landers earthquake (bin width = 30°). The circle size represents the number of stations in each bin. The black circles and black line indicate the average μ_ln(PGV) and average ϕ_ln(PGV) of the five source models. The coefficients I, γ, x₀, and C of the Lorentz function are obtained from nonlinear optimization for average μ_ln(PGV). Note that 0° azimuth represents the average strike direction.

Figure S4. Directivity predictor f_D in natural log scale for T = 5 s and T = 10 s periods computed from Spudich and Chiou (2008) for the five source models of the 1992 Landers earthquake. Tiny triangles indicate the stations within 1–71 km R_JB distance, and colors depict the f_D value for that station. The parameter f_D is positive in the both forward and backward directivity regions but shows negative values in the direction almost perpendicular to the plane. The general spatial distribution of the f_D-values is similar to the S-wave radiation pattern, because f_D is computed from the isochrone directivity predictor, a variable based on isochrone theory. Values of f_D for T = 10 s period are higher than those for T = 5 s, indicating that stronger corrections are needed for longer periods.

Figure S5. Residuals (natural-log scale) between simulations for the five rupture models of the 1992 Landers earthquake and predictions from (a) Boore and Atkinson (2008) GMPE and (b) the Spudich and Chiou (2008) directivity-corrected Boore and Atkinson (2008) GMPE. The pseudospectral acceleration residuals are computed at periods of T = 5 s and T = 10 s for neglecting and including the directivity correction to the GMPE. Each black line and black star, respectively, marks the fault trace and epicenter of the rupture model. Residuals are high positive in the forward-directivity region as well as in the fault-perpendicular direction, regardless of whether or not the directivity effect is included in the GMPE. In the backward-directivity region, the residuals are close to zero or negative for both cases. This spatial pattern of residuals is consistent for both periods considered (T = 5 s and T = 10 s). The differences between the residuals for both cases (with and without directivity correction) are generally insignificant, aside from small differences very near the fault. Although the f_D-value is meant to account for complex fault geometry and rupture-propagation direction, it has only a small effect.

Figure S6. Azimuthal dependence of μ_ln(PGV) for seven source models obtained from rupture-parameter combinations of Cotton (m1–m7; see main article for details) and Cotton’s model (bin width = 15°). The circle size represents the number of stations in each bin. The coefficients I, γ, x₀, and C of the Lorentz function (depicted by dashed black lines) are obtained from nonlinear optimization for μ_ln(PGV). The Lorentz function fit to the Cotton model (depicted by gray line) and its residual sum of squares (RSS) are given as reference to facilitate the comparison. Note that 0° azimuth represents the average strike direction.

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