Electronic Supplement to
The Case for Mean Rupture Distance in Ground-Motion Estimation

by Eric M. Thompson and Annemarie S. Baltay

This electronic supplement contains plots of ground-motion residuals, a table of the coefficients needed to evaluate the model, and a table of the ground-motion amplitudes used in the regression analysis, input parameters, and the evaluated model. Note that Table S2 is derived from Ancheta et al. (2014), with the addition of new columns.

Figures S1–S4 are residuals (for peak ground acceleration [PGA], or response spectra [SA]) plotted against various input parameters for the ground-motion model presented in the article. Each figure is identical, except for the intensity-measure type. The figures plot the interevent residual ($\delta E_e$) against the following event-specific parameters: magnitude, rake, and depth to top of rupture ($Z_{\mathrm{TOR}}$). The intraevent residuals ($\delta W_{es}$) are plotted against the following record-specific parameters: time-averaged shear-wave velocity to 30 m depth ($V_{S30}$), rupture distance ($R_{\mathrm{RUP}}$), Joyner–Boore distance ($R_{\mathrm{JB}}$), mean distance ($R_P$), with the power determined from equation (10) in the main article. Gray circles are the individual residuals (either $\delta W_{es}$ or $\delta E_e$); blue dots are the binned mean residuals; and blue lines are 95% confidence intervals on the binned mean residuals.

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Tables

Table S1. Model coefficients. Column names are either a coefficient for evaluating the ground-motion model or the following:

• IMT, intensity measure type. This is either PGA, PGV, or a number indicating the response spectra oscillator period.

• Power, the generalized mean power, evaluated from equation (10) in the main article and rounded to one decimal place.

Table S2. Selected ground-motion amplitudes input parameters used to develop the model in this article as well as the evaluated model results. The column names are as follow:

• RSN, record sequence number that matches the RSN in Ancheta et al. (2014);

• station name, unique station name;

• station lon, station longitude;

• station lat, station latitude;

• Vs30, time-averaged shear-wave velocity to 30 m depth. This is the preferred V_S30 in the Next Generation Attenuation-West2 (NGA-W2) database, including measured values and inferred values;

• z1pt0_H11, depth to the shear-wave velocity of 1.0 km/s, using the Harvard model (3D Southern California Earthquake Center [SCEC] Community Velocity Model) in southern California;

• z1pt0_S4, depth to the shear-wave velocity of 1.0 km/s, using the SCEC Community Velocity Model, MEA00, Version 2.2b in southern California;

• EQID, earthquake ID;

• earthquake lon, earthquake longitude;

• earthquake lat, earthquake latitude;

• earthquake depth, earthquake depth (km);

• rake, rake (°);

• Ztor, depth to top of rupture (km);

• magnitude, earthquake moment magnitude;

• dip, dip (°);

• Rhyp, hypocentral distance (km);

• Rjb, Joyner–Boore distance (km);

• Rrup, rupture distance (km);

• Rx, strike-normal distance (km);

• Rp X, power mean distance with power X;

• Rph X, horizontal power mean distance with power X;

• XiPrime, the Rowshandel (2013) directivity parameter ${\xi }^{\prime }$;

• LD, the Rowshandel (2013) directivity parameter LD;

• WP_X, the Rowshandel (2013) directivity parameter LD for period X;

• DT_X, Rowshandel’s directivity parameter DT for period X;

• PGV, peak ground velocity (cm/s);

• PGA, peak ground acceleration (g);

• TX, response spectra (g) at oscillator period X (the decimal is replaced with the letter ‘p’);

• TB17_rock_X, the model developed in this article for intensity measure type X, for reference rock (V_S30 = 760 m/s);

• Fs_X, the site term, as computed from Boore et al. (2014);

• BSSAregion_code, an integer indicating the regionalization of the anelastic attenuation term in Boore et al. (2014).

○  0, average Q

○  1, high Q

○  3, low Q

• basin_code, an integer indicating the following regionalization that we use to select the basin depth model to use.

○  0, N/A

○  1, California

○  2, Nevada

○  3, Alaska

○  4, Idaho

○  5, Canada

○  6, Mexico

○  7, El Salvador

○  8, Nicaragua

○  9, Japan

○  10, New Zealand

○  11, Taiwan

○  12, China

○  13, Bosnia

○  14, Croatia

○  15, Macedonia

○  16, Montenegro

○  17, Georgia

○  18, Armenia

○  19, Turkey

○  20, Greece

○  21, Italy

○  22, Israel

○  23, Iran

○  24, Uzbekistan

○  25, Germany

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Figures

Figure S1. Residual plots for PGA.

Figure S2. Residual plots for SA at T = 0.3 s.

Figure S3. Residual plots for SA at T = 1.0 s.

Figure S4. Residual plots for SA at T = 3.0 s.

Figure S5. Theoretical distance scaling of geometrical spreading and anelastic attenuation for both Fourier and response acceleration spectra. (a) Input Fourier acceleration spectra (FAS), shaded by magnitude, with frequency- and magnitude-independent anelastic attenuation Q = 500. (b) 5% damped oscillator transfer function for four periods. (c) Integrated product of (a,b) at each period to represent an approximate response spectra ($m_0^{1/2}$), shown for two different magnitudes, with filled circles on spectra representing the four periods of the shown oscillators and open circles for periods not explicitly shown. (d) Observed distance decay (assuming 1/R distance decay) of response spectra at four periods, normalized such that the amplitudes at R = 1 km are the same for given frequency for FAS and approximate SA $m_0^{1/2}$. Because there is no magnitude scaling of FAS attenuation, all magnitudes are plotted as a solid black line; line shading indicates the magnitude for the approximate SA $m_0^{1/2}$. (e) Same as (d) but using a finite-fault term h throughout the simulation, following equation (1) in the main article, so that the distance scaling is $(R^2+h^2{)}^{-\frac{1}{2}}$. A magnitude-dependent $h={10}^{-0.405+0.235\mathit{M}}$ (Yenier and Atkinson, 2015) is used. For simplicity, we include only magnitudes 4, 6, and 8 with FAS in thicker lines and the approximate SA $m_0^{1/2}$ in thinner lines. Greater magnitude dependence on the distance decay is obvious compared to (d).

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