diff --git a/src/main/java/gov/usgs/earthquake/nshmp/gmm/Gmm.java b/src/main/java/gov/usgs/earthquake/nshmp/gmm/Gmm.java index 9c5fdee03e1662f70c037f5a9fb9c482b54094d8..d749ab0cd0a8f4e89b732a56f9b59273704efede 100644 --- a/src/main/java/gov/usgs/earthquake/nshmp/gmm/Gmm.java +++ b/src/main/java/gov/usgs/earthquake/nshmp/gmm/Gmm.java @@ -250,6 +250,13 @@ public enum Gmm { SadighEtAl_1997.COEFFS_BC_HI, SadighEtAl_1997.CONSTRAINTS), + // /** @see Grazier_2018 */ + // GRAIZER_2018( + // Graizer_2018.class, + // Graizer_2018.NAME, + // Graizer_2018.COEFFS, + // Graizer_2018.CONSTRAINTS), + /* Subduction Interface and Slab WUS 2008 2014 2018, AK 2007 */ /** @see AtkinsonBoore_2003 */ diff --git a/src/main/java/gov/usgs/earthquake/nshmp/gmm/Graizer_2018.java b/src/main/java/gov/usgs/earthquake/nshmp/gmm/Graizer_2018.java new file mode 100644 index 0000000000000000000000000000000000000000..481c1b371100ded629b133036c049f85683d5044 --- /dev/null +++ b/src/main/java/gov/usgs/earthquake/nshmp/gmm/Graizer_2018.java @@ -0,0 +1,348 @@ +/** + * + */ +package gov.usgs.earthquake.nshmp.gmm; + +import static gov.usgs.earthquake.nshmp.gmm.FaultStyle.REVERSE; +import static gov.usgs.earthquake.nshmp.gmm.FaultStyle.REVERSE_OBLIQUE; +import static gov.usgs.earthquake.nshmp.gmm.GmmInput.Field.MW; +import static gov.usgs.earthquake.nshmp.gmm.GmmInput.Field.RAKE; +import static gov.usgs.earthquake.nshmp.gmm.GmmInput.Field.RRUP; +import static gov.usgs.earthquake.nshmp.gmm.GmmInput.Field.VS30; +import static java.lang.Math.abs; +import static java.lang.Math.atan; +import static java.lang.Math.cos; +import static java.lang.Math.exp; +import static java.lang.Math.log; +import static java.lang.Math.max; +import static java.lang.Math.min; +import static java.lang.Math.pow; +import static java.lang.Math.sqrt; + +import java.util.Map; + +import com.google.common.annotations.Beta; +import com.google.common.collect.Range; + +import gov.usgs.earthquake.nshmp.Faults; +import gov.usgs.earthquake.nshmp.gmm.GmmInput.Constraints; +import gov.usgs.earthquake.nshmp.tree.LogicTree; + +/** + * TODO: + * + * * is Q_SA, for G3, defined by Eq. 8? + * + * * coefficients c21 and c22 are not defined in G18 or GK16 papers. + * coefficients b1, b2, b3, and λ are not defined in G18 or GK16 papers, + * inferred from matlab script + * + * * Do we want basin and non-basin flavors? + * + * * Better to interpolate GM instead of coefficients (since they may not be + * monotonic), so use the set of 16 periods in Table 1 and Matlab + * + * * Attempt to compute values in Table S1 and/or S2 using the manual regression + * code blocks in Matlab (so far, the matlab code does not reproduce the tables) + * + * + * Implementation of the GK17 ground motion model for shallow crustal + * continental earthquakes by Grazier (2018). This model computes the average + * (RotD50) horizontal components of PGA and 5% damped PSA at periods from 0.01 + * to 10 s. The model includes a number of significant changes from the previous + * GK15 (Graizer and Kalkan, 2016). + * + * <p><b>References:</b><ul> + * + * <li>Graizer, V., 2018, GK17 Ground-Motion prediction equation for horizontal + * PGA and 5% damped PSA from shallow crustal continental earthquakes: Bulletin + * of the Seismological Society of America, v. 108, n. 1, p. 380-398. + * <b>doi:</b> <a href="http://dx.doi.org/10.1785/0120170158"> + * 10.1785/0120170158</a></li> + * + * <li>Graizer, V., and E. Kalkan, 2016, Summary of the GK15 ground-motion + * prediction equation for horizontal PGA and 5% damped PSA from shallow crustal + * continental earthquakes: Bulletin of the Seismological Society of America, v. + * 106, n. 2, p. 687-707. <b>doi:</b> <a + * href="http://dx.doi.org/10.1785/0120150194"> 10.1785/0120150194</a></li> + * + * </ul> + * + * <p><b>Component:</b> RotD50 average horizontal components + * + * @author U.S. Geological Survey + * @see Gmm#GRAIZER_2018 + */ +@Beta +public final class Graizer_2018 implements GroundMotionModel { + + public static void main(String[] args) { + for (Imt imt : Imt.mprsImts()) { + double t = (imt.equals(Imt.PGA)) ? 0.01 : imt.period(); + System.out.printf("%.3f, %.3f\n", t, imt.period()); + } + + } + + static final String NAME = "Graizer 2018 (GK17)"; + + static final CoefficientContainer COEFFS = new CoefficientContainer("GK17.csv"); + + static final Constraints CONSTRAINTS = Constraints.builder() + .set(MW, Range.closed(4.0, 8.5)) + .set(RRUP, Range.closed(0.0, 400.0)) + .set(RAKE, Faults.RAKE_RANGE) + .set(VS30, Range.closed(150.0, 1500.0)) + .build(); + + private static final class Coefficients { + final Imt imt; + final double σ; + final double τ; + final double φ; + + Coefficients(Imt imt, CoefficientContainer cc) { + this.imt = imt; + Map<String, Double> coeffs = cc.get(imt); + + this.σ = coeffs.get("sigma"); + this.τ = coeffs.get("tau"); + this.φ = coeffs.get("phi"); + } + } + + private final Imt imt; + private final double period; + private final Coefficients coeffs; + + public Graizer_2018(Imt imt) { + this.imt = imt; + this.period = imt.equals(Imt.PGA) ? 0.01 : imt.period(); + + coeffs = new Coefficients(imt, COEFFS); + } + + /** + * G18 provides table of sigmas at 16 periods that do not correspond exactly + * with USGS MPRS. The defined sigma values are interpolated in Matlab using + * the "shape-preserving piecewise cubic interpolation", and the resulting + * values are hard-coded here. + * + * The following Matlab code was used to compute sigma values at the MSRS + * periods: + * + * <pre> + * % From Table 3 in Graizer (2018) + * t = [0.010 0.020 0.040 0.075 0.100 0.150 0.200 0.400 0.500 0.750 1.000 2.000 3.000 4.000 5.000 8.000 10.0 ]; + * sigma = [0.631 0.633 0.653 0.713 0.734 0.720 0.693 0.673 0.693 0.732 0.738 0.783 0.774 0.733 0.746 0.789 0.736]; + * tau = [0.375 0.375 0.386 0.456 0.477 0.451 0.407 0.365 0.398 0.465 0.492 0.501 0.512 0.448 0.464 0.528 0.451]; + * phi = [0.507 0.511 0.527 0.549 0.557 0.562 0.560 0.565 0.568 0.565 0.549 0.601 0.580 0.581 0.584 0.587 0.582]; + * + * % MSRS periods + * t_nga = [0.01 0.02 0.03 0.05 0.075 0.1 0.15 0.2 0.25 0.3 0.4 0.5 0.75 1.0 1.5 2.0 3.0 4.0 5.0 7.5 10.0]; + * + * % interpolate at MSRS periods + * sigma_nga = interp1(t,sigma,t_nga,'pchip','extrap'); + * tau_nga = interp1(t,tau,t_nga,'pchip','extrap'); + * phi_nga = interp1(t,phi,t_nga,'pchip','extrap'); + * + * fprintf('%6s,%7s,%7s,%7s\n','T','sigma','tau','phi'); + * for i=1:length(t_nga) + * fprintf('%6.3f,%.5f,%.5f,%.5f\n',t_nga(i),sigma_nga(i),tau_nga(i),phi_nga(i)); + * end + * </pre> + */ + + @Override + public LogicTree<GroundMotion> calc(GmmInput in) { + /* Eq. 1 */ + // SA = G1 * G2 * G3 * G4 * G5 * SA_NORM * εγ + + var fault_style = GmmUtils.rakeToFaultStyle_NSHMP(in.rake); + + double sa_norm = spectralShape(period, in.Mw, in.rRup); + double G1 = filterG1(in.Mw, fault_style); // M-scaling + double G2 = filterG2(in.Mw, in.rRup); // R-scaling + + // PGA is apparently G1 * G2 ??? + + double G3 = filterG3(period, in.rRup); // Apparent attenuation scaling + double G4 = filterG4(period, in.Mw, in.rRup, fault_style); // Style of + // faulting style + double G5 = filterG5(period, in.vs30); // Site-scaling + + /** + * <pre> + * Questions: + * 1. Is a "G6" filter implied? To add the basin/deep sediment effects to the + * Vs30 amplification? No equation is provided but factors (relative to Vs30 + * amplification) are provided in Table S2 (as a function of Vs30 and T) + * + * But then use Eq. 16 to convert Z2.5 to effective Vs30 to look up the basin effect??? + * </pre> + */ + // "G6" for basin effect? look up from table? + + double μ = log(G1 * G2 * G3 * G4 * G5 * sa_norm); + double σ = coeffs.σ; + + return GroundMotions.createTree(μ, σ); + } + + /* Spectral shape constants (Figure 3) */ + private static final double m1 = -0.0012; + private static final double m2 = -0.38; + private static final double m3 = 4.08; + + private static final double a1 = 0.017; + private static final double a2 = 1.27; + private static final double a3 = 0.0001; + + private static final double Dsp = 0.75; + + private static final double t1 = 0.001; + private static final double t2 = 0.59; + private static final double t3 = -2.45; + + private static final double s1 = 0.0; + private static final double s2 = 0.077; + private static final double s3 = 0.3251; + + private static final double ζ = 2; + + /* 5% damped response spectral shape, SA_norm (Figure 3) */ + private static final double spectralShape(double T, double Mw, double rRup) { + double μ_mr = m1 * rRup + m2 * Mw + m3; + double I_mr = (a1 * Mw + a2) * exp(a3 * rRup); + double S_mr = s1 * rRup - (s2 * Mw + s3); + double Tsp0 = max(0.3, abs(t1 * rRup + t2 * Mw + t3)); + + double t_ratio = pow(T / Tsp0, ζ); + double t_μ_S = (log(T) + μ_mr) / S_mr; + return I_mr * exp(-0.5 * t_μ_S * t_μ_S) + + sqrt((1.0 - t_ratio) * (1.0 - t_ratio) + 4.0 * Dsp * Dsp * t_ratio); + } + + /* Model coefficients from Graizer & Kalkan (2016) Table 3 */ + private static final double c1 = 0.14; + private static final double c2 = -6.25; + private static final double c3 = 0.37; + private static final double c4 = 2.237; + private static final double c5 = -7.542; + private static final double c6 = -0.125; + private static final double c7 = 1.19; + private static final double c8 = -6.15; + private static final double c9 = 0.6; + + /* Constants from Graizer (2018) */ + private static final double β = 3.5; // defined p. 385 + private static final double b1 = 0.79; // inferred from matlab code + private static final double b2 = 0.27; // inferred from matlab code + private static final double b3 = 0.444; // inferred from matlab code + private static final double λ = 1.36; // inferred from matlab code + private static final double c21 = 0.000854; // inferred from matlab code + private static final double c22 = 1.0513; // inferred from matlab code + + /* Filter G1 - magnitude-scaling */ + private static final double filterG1(double Mw, FaultStyle fault_style) { + /* + * k_scale is style-of-faulting factor from Graizer and Kalkan (2016) Eq. 3 + */ + double k_scale = + (fault_style == REVERSE) ? 1.28 : (fault_style == REVERSE_OBLIQUE) ? 1.14 : 1.0; + + return (Mw < 5.5) ? (c21 * exp(c22 * Mw) * k_scale) : (c1 * atan(Mw + c2) + c3) * k_scale; + } + + /* Filter G2 - distance scaling */ + private double filterG2(double Mw, double rRup) { + /* Eq. 4 */ + double R2 = c4 * Mw + c5; + double D2 = c6 * cos(c7 * (Mw + c8)) + c9; + + /* Eq. 3 */ + double w1 = (1 - sqrt(50 / R2)) * (1 - sqrt(50 / R2)); + double w2 = 4 * D2 * D2 * sqrt(50 / R2); + double w3 = (1 - (50 / R2)) * (1 - (50 / R2)); + double w4 = 4 * D2 * D2 * (50 / R2); + double w = sqrt((w1 + w2) / (w3 + w4)); + + /* Eq. 3 */ + double g1 = (1 - sqrt(rRup / R2)) * (1 - sqrt(rRup / R2)); + double g2 = 4 * D2 * D2 * (rRup / R2); + double g3 = 4 * D2 * D2 * sqrt(rRup / R2); + + return (rRup < 50.0) ? 1 / sqrt(g1 + g2) : w / sqrt(g1 + g3); + } + + /* Filter G3 - Apparent Attenuation of Spectral Accelerations */ + private double filterG3(double T, double rRup) { + double freq = 1.0 / T; + + // TODO: Is this the right formulation of QSA to use? + /* Qsa from Eq. 8 (as a function of freq) */ + double p = (freq < 1.0) ? 0.90 : (freq < 10.0) ? 0.91 : 0.95; + double Qsa = 120 * pow(freq, p); + + return exp(-freq * rRup / β / Qsa); + } + + /* Filter G4 - Fault-style scaling */ + private double filterG4(double T, double Mw, double rRup, FaultStyle fault_style) { + // coefficients b1, b2, b3, and λ inferred from matlab code + if ((fault_style != FaultStyle.REVERSE) || (Mw < 4.0)) { + return 1.0; + } + double dist = (rRup <= 90.0) ? rRup : 90; + + /* Eq. 12 */ + double CSoF0 = (b1 + b2 / (1 + (T / 7.0) * (T / 7.0))) * + (b3 + 1 / (1 + pow(dist / 100.0, λ))); + + return (Mw >= 5.5) ? CSoF0 : 1 + (CSoF0 - 1) * exp(Mw - 5.5); + } + + /* Filter G5 - Site-response term */ + private double filterG5(double T, double vs30) { + /** + * <pre> + * Questions: + * 1. is f in Eq. 15 frequency or something else that doesn't seem to be defined? + * + * 2. Should Eq. 15 reproduce Table S1: VS30 site amplification factors relative + * to the western hard rock of VS30 = 1100 m/s? (it doesn't seem to) + * + * </pre> + */ + double freq = 1.0 / T; + + /* + * amplification coefficient constant for vs30 below 180 m/s and above 1100 + * m/s + */ + double vs = max(180.0, min(1100.0, vs30)); + double vss = max(275.0, vs); + + /* Eq. 15 */ + double kvs = -0.5 * log(vs / 1100.0); + double fvs = vss / 120.0 - 2.0; + + return 1 + kvs / sqrt((1 - (fvs / freq)) * (1 - (fvs / freq)) + 1.96 * (fvs / freq)); + } + + /* Sediment thickness (Z2.5) */ + private double sedimentThickness(double vs30, double z2p5) { + // Eq. 16 is a Z2.5 - Vs30 relation + // ln(z2p5) = 7.108 - 1.145 * ln(vs30) + + // Matlab script has this relation: + // ln(z2p5) = 7.521 - 1.233 * ln(VS30) + + // No equations in the paper are a function of Z2.5. + // Paper refers to Table S2 for basin amplification (as a function of Vs30 + // and Vs30), which are specified as relative to the site amplification due + // Vs30 + + return 1.0; + } +} diff --git a/src/main/resources/gmm/coeffs/GK17.csv b/src/main/resources/gmm/coeffs/GK17.csv new file mode 100644 index 0000000000000000000000000000000000000000..7e65a8a2e365fc0bc5fa9e1585c58e6b7c2dc0dc --- /dev/null +++ b/src/main/resources/gmm/coeffs/GK17.csv @@ -0,0 +1,23 @@ + T, sigma, tau, phi + PGA,0.63100,0.37500,0.50700 + 0.010,0.63100,0.37500,0.50700 + 0.020,0.63300,0.37500,0.51100 + 0.030,0.64069,0.37845,0.51851 + 0.050,0.66893,0.40170,0.53414 + 0.075,0.71300,0.45600,0.54900 + 0.100,0.73400,0.47700,0.55700 + 0.150,0.72000,0.45100,0.56200 + 0.200,0.69300,0.40700,0.56000 + 0.250,0.68437,0.38956,0.56052 + 0.300,0.67811,0.37633,0.56181 + 0.400,0.67300,0.36500,0.56500 + 0.500,0.69300,0.39800,0.56800 + 0.750,0.73200,0.46500,0.56500 + 1.000,0.73800,0.49200,0.54900 + 1.500,0.76419,0.49776,0.57500 + 2.000,0.78300,0.50100,0.60100 + 3.000,0.77400,0.51200,0.58000 + 4.000,0.73300,0.44800,0.58100 + 5.000,0.74600,0.46400,0.58400 + 7.500,0.78675,0.52450,0.58689 +10.000,0.73600,0.45100,0.58200 diff --git a/src/test/java/gov/usgs/earthquake/nshmp/gmm/Graizer18Test.java b/src/test/java/gov/usgs/earthquake/nshmp/gmm/Graizer18Test.java new file mode 100644 index 0000000000000000000000000000000000000000..30285325936c6e145fe5897a45e7d5d6ae8828d8 --- /dev/null +++ b/src/test/java/gov/usgs/earthquake/nshmp/gmm/Graizer18Test.java @@ -0,0 +1,39 @@ +// package gov.usgs.earthquake.nshmp.gmm; +// +// import static gov.usgs.earthquake.nshmp.gmm.Gmm.GRAIZER_2018; +// +// import java.io.IOException; +// import java.util.EnumSet; +// import java.util.Set; +// import java.util.stream.Stream; +// +// import org.junit.jupiter.api.extension.ExtensionContext; +// import org.junit.jupiter.params.provider.Arguments; +// import org.junit.jupiter.params.provider.ArgumentsProvider; +// +// public class Graizer18Test implements ArgumentsProvider { +// +// private static String GMM_INPUTS = "/gmm/graizer_2018_inputs.csv"; +// private static String GMM_RESULTS = "/gmm/graizer_2018_results.csv"; +// +// // @ParameterizedTest(name = "({index}) {0} {2} {1}") +// // @ArgumentsSource(Graizer18Test.class) +// // void test(int index, Gmm gmm, Imt imt, double exMedian, double exSigma, +// // String inputs) { +// // GmmTest.test(index, gmm, imt, exMedian, exSigma, inputs); +// // } +// +// @Override +// public Stream<? extends Arguments> provideArguments(ExtensionContext context) +// throws Exception { +// return GmmTest.loadResults(GMM_RESULTS, GMM_INPUTS); +// } +// +// /* Result generation sets */ +// private static Set<Gmm> gmms = EnumSet.of(GRAIZER_2018); +// +// public static void main(String[] args) throws IOException { +// GmmTest.generateResults(gmms, Imt.mprsImts(), GMM_INPUTS, GMM_RESULTS); +// } +// +// } diff --git a/src/test/resources/gmm/graizer_2018_inputs.csv b/src/test/resources/gmm/graizer_2018_inputs.csv new file mode 100644 index 0000000000000000000000000000000000000000..e369c0a4097d54f8d63b035aff38c83db4cde0fc --- /dev/null +++ b/src/test/resources/gmm/graizer_2018_inputs.csv @@ -0,0 +1,102 @@ +#Mw,rjB,rRup,rX,dip,width,zTor,zHyp,rake,vs30,vsInf,z1p0,z2p5 +4.5,5,6.4,-5,45,2.4,4,5,90,760,1,NaN,NaN +4.5,0,4,0,45,2.4,4,5,90,760,1,NaN,NaN +4.5,2.6,6.2,5,45,2.4,4,5,90,760,1,NaN,NaN +4.5,12.6,13.8,15,45,2.4,4,5,90,760,1,NaN,NaN +5,5,5.8,-5,45,5,3,4.5,90,760,1,NaN,NaN +5,0,3,0,45,5,3,4.5,90,760,1,NaN,NaN +5,1.5,5.7,5,45,5,3,4.5,90,760,1,NaN,NaN +5,11.5,13.2,15,45,5,3,4.5,90,760,1,NaN,NaN +5,26.5,27.3,30,45,5,3,4.5,90,760,1,NaN,NaN +5.5,5,5.8,-5,45,5,3,4.5,90,760,1,NaN,NaN +5.5,0,3,0,45,5,3,4.5,90,760,1,NaN,NaN +5.5,1.5,5.7,5,45,5,3,4.5,90,760,1,NaN,NaN +5.5,11.5,13.2,15,45,5,3,4.5,90,760,1,NaN,NaN +5.5,26.5,27.3,30,45,5,3,4.5,90,760,1,NaN,NaN +6,5,5.4,-5,45,10,2,5.5,90,760,1,NaN,NaN +6,0,2,0,45,10,2,5.5,90,760,1,NaN,NaN +6,0,5,5,45,10,2,5.5,90,760,1,NaN,NaN +6,8,12.1,15,45,10,2,5.5,90,760,1,NaN,NaN +6,23,24.7,30,45,10,2,5.5,90,760,1,NaN,NaN +6,93,93.4,100,45,10,2,5.5,90,760,1,NaN,NaN 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