From d01e0d91e0ee0676431b6393bdf850e055df5b8a Mon Sep 17 00:00:00 2001
From: Peter Powers <pmpowers@usgs.gov>
Date: Wed, 15 Jun 2022 14:09:30 -0600
Subject: [PATCH] added m9 adjustments
---
.../nshmp/gmm/AbrahamsonGulerce_2020.java | 61 +++++++++++++------
.../earthquake/nshmp/gmm/KuehnEtAl_2020.java | 39 ++++++++++--
.../earthquake/nshmp/gmm/ParkerEtAl_2020.java | 59 ++++++++++++++----
3 files changed, 126 insertions(+), 33 deletions(-)
diff --git a/src/main/java/gov/usgs/earthquake/nshmp/gmm/AbrahamsonGulerce_2020.java b/src/main/java/gov/usgs/earthquake/nshmp/gmm/AbrahamsonGulerce_2020.java
index 23bd5c54..b2e632f0 100644
--- a/src/main/java/gov/usgs/earthquake/nshmp/gmm/AbrahamsonGulerce_2020.java
+++ b/src/main/java/gov/usgs/earthquake/nshmp/gmm/AbrahamsonGulerce_2020.java
@@ -91,6 +91,7 @@ public abstract class AbrahamsonGulerce_2020 implements GroundMotionModel {
private static final double VSS_MAX = 1000.0; // Errata 2021/7/12
private static final double VS30_ROCK = 1000.0;
+ private static final double Z2P5_REF_AG = 1998.0;
private static final double D0 = 0.47;
@@ -177,10 +178,10 @@ public abstract class AbrahamsonGulerce_2020 implements GroundMotionModel {
double pgaRock = 0.0;
if (in.vs30 < coeffs.vlin) {
- pgaRock = exp(calcMean(coeffsPGA, slab(), basin(), adjust(), 0.0,
+ pgaRock = exp(calcMean(coeffsPGA, slab(), basin(), seattle(), adjust(), 0.0,
in.Mw, in.rRup, in.zTor, VS30_ROCK, in.z2p5));
}
- double μ = calcMean(coeffs, slab(), basin(), adjust(), pgaRock,
+ double μ = calcMean(coeffs, slab(), basin(), seattle(), adjust(), pgaRock,
in.Mw, in.rRup, in.zTor, in.vs30, in.z2p5);
double σ = calcSigma(coeffs, coeffsPGA, pgaRock, in.rRup, in.vs30);
@@ -192,12 +193,15 @@ public abstract class AbrahamsonGulerce_2020 implements GroundMotionModel {
abstract boolean basin();
+ abstract boolean seattle();
+
abstract boolean adjust();
private static double calcMean(
Coefficients c,
boolean slab,
boolean basin,
+ boolean seattle,
boolean adjust,
double pgaRock,
double Mw,
@@ -229,7 +233,7 @@ public abstract class AbrahamsonGulerce_2020 implements GroundMotionModel {
}
/* Eq. 3.7, 3.8 - Site-response scaling */
- double vsS = getVsStar(vs30);
+ double vsS = calcVsStar(vs30);
double fSite = c.a12 * log(vsS / c.vlin);
if (vsS < c.vlin) {
fSite += -c.b * log(pgaRock + C) + c.b * log(pgaRock + C * pow((vsS / c.vlin), N));
@@ -241,20 +245,23 @@ public abstract class AbrahamsonGulerce_2020 implements GroundMotionModel {
double fBasin = 0.0;
if (basin && !Double.isNaN(z2p5)) {
double z2p5m = z2p5 * 1000.0;
- /*
- * Note: PEER report (and xlsx) uses factor rounded to 0.88, fortran code
- * uses the calculated value. Using 0.878 would improve the match of
- * lnZ2p5ref to the fortran code (within 0.01%).
- */
- double lnZ2p5ref = (vs30 >= 570)
- ? 7.6
- : (vs30 > 200)
- ? 8.52 - 0.88 * log(vs30 / 200.0)
- : 8.52;
+ double lnZ2p5ref = 8.52;
+ if (vs30 >= 570) {
+ lnZ2p5ref = 7.6;
+ } else if (vs30 > 200) {
+ lnZ2p5ref = 8.52 - 0.88 * log(vs30 / 200.0);
+ }
/* Eq. 3.9, 3.11 - Cascadia basin scaling (Errata 2021/7/12) */
- double zPrime = (z2p5m + 50.0) / (exp(lnZ2p5ref) + 50.0);
- fBasin = (log(zPrime) > 0) ? c.a39 * log(zPrime) : 0.0;
+ double lnzPrime = calcLnzPrime(z2p5m, exp(lnZ2p5ref));
+ if (lnzPrime > 0) {
+ fBasin = c.a39 * lnzPrime;
+ if (seattle && z2p5 > 6.0 & c.imt.period() > 1.9) {
+ double lnzPrimeAdj = calcLnzPrime(z2p5m, Z2P5_REF_AG);
+ double m9adj = log(2.0) - c.a39 * lnzPrimeAdj;
+ fBasin += m9adj;
+ }
+ }
}
/* Eq. 3.1 */
@@ -271,7 +278,12 @@ public abstract class AbrahamsonGulerce_2020 implements GroundMotionModel {
return μ;
}
- private static double getVsStar(double vs30) {
+ /* Args in meters. */
+ private static double calcLnzPrime(double z2p5, double z2p5ref) {
+ return log((z2p5 + 50.0) / (z2p5ref + 50.0));
+ }
+
+ private static double calcVsStar(double vs30) {
return min(vs30, VSS_MAX);
}
@@ -287,7 +299,7 @@ public abstract class AbrahamsonGulerce_2020 implements GroundMotionModel {
double φSq = φlinSq(c.d1, c.d2, rRup);
- double vsS = getVsStar(vs30);
+ double vsS = calcVsStar(vs30);
/* Add nonlinear effects. */
if (vsS < c.vlin) {
@@ -341,6 +353,11 @@ public abstract class AbrahamsonGulerce_2020 implements GroundMotionModel {
return false;
}
+ @Override
+ boolean seattle() {
+ return false;
+ }
+
@Override
boolean adjust() {
return false;
@@ -365,6 +382,11 @@ public abstract class AbrahamsonGulerce_2020 implements GroundMotionModel {
return false;
}
+ @Override
+ boolean seattle() {
+ return false;
+ }
+
@Override
boolean adjust() {
return true;
@@ -389,6 +411,11 @@ public abstract class AbrahamsonGulerce_2020 implements GroundMotionModel {
return false;
}
+ @Override
+ boolean seattle() {
+ return false;
+ }
+
@Override
boolean adjust() {
return true;
diff --git a/src/main/java/gov/usgs/earthquake/nshmp/gmm/KuehnEtAl_2020.java b/src/main/java/gov/usgs/earthquake/nshmp/gmm/KuehnEtAl_2020.java
index 352ec391..90fd24b2 100644
--- a/src/main/java/gov/usgs/earthquake/nshmp/gmm/KuehnEtAl_2020.java
+++ b/src/main/java/gov/usgs/earthquake/nshmp/gmm/KuehnEtAl_2020.java
@@ -117,6 +117,7 @@ public abstract class KuehnEtAl_2020 implements GroundMotionModel {
private static final double C = 1.88; // p. 22 !!! Value from python code
private static final double N = 1.18; // p. 22 !!! Value from python code
private static final double VSROCK = 1100;
+ private static final double LN_Z2P5_REF_KUEHN = log(200.0);
private static final class Coefficients {
final Imt imt;
@@ -244,15 +245,19 @@ public abstract class KuehnEtAl_2020 implements GroundMotionModel {
abstract boolean basin();
+ abstract boolean seattle();
+
@Override
public LogicTree<GroundMotion> calc(GmmInput in) {
double pgaRef = exp(calcPgaRef(coeffsPGA, in.Mw, in.rRup, in.zTor));
- double μ = calcMean(coeffs, basin(), in.Mw, in.rRup, in.zTor, in.vs30, in.z2p5, pgaRef);
+ double μ = calcMean(coeffs, basin(), seattle(),
+ in.Mw, in.rRup, in.zTor, in.vs30, in.z2p5, pgaRef);
// short periods can't be lower than PGA
if (coeffs.imt.isSA() && coeffs.imt.period() <= 0.1) {
- double μPga = calcMean(coeffsPGA, basin(), in.Mw, in.rRup, in.zTor, in.vs30, in.z2p5, pgaRef);
+ double μPga = calcMean(coeffsPGA, basin(), seattle(),
+ in.Mw, in.rRup, in.zTor, in.vs30, in.z2p5, pgaRef);
μ = max(μ, μPga);
}
@@ -283,6 +288,7 @@ public abstract class KuehnEtAl_2020 implements GroundMotionModel {
private static double calcMean(
Coefficients c,
boolean basin,
+ boolean seattle,
double Mw,
double rRup,
double zTor,
@@ -295,7 +301,7 @@ public abstract class KuehnEtAl_2020 implements GroundMotionModel {
double fDepth = depthTerm(c, zTor);
double fAtten = arcCrossingTerm(c, rRup);
double fSite = siteAmpTerm(c, vs30, pgaRef);
- double fBasin = basin ? basinTerm(c, vs30, z2p5) : 0.0;
+ double fBasin = basin ? basinTerm(c, vs30, z2p5, seattle) : 0.0;
return c.θ1 + fMag + fGeom + fDepth + fAtten + fSite + fBasin;
}
@@ -367,7 +373,8 @@ public abstract class KuehnEtAl_2020 implements GroundMotionModel {
private static double basinTerm(
Coefficients c,
double vs30,
- double z2p5) {
+ double z2p5,
+ boolean seattle) {
// TODO add Seattle flag
@@ -378,8 +385,15 @@ public abstract class KuehnEtAl_2020 implements GroundMotionModel {
double z2p5m = z2p5 * 1000.0;
double δlnZ = log(z2p5m) - basinZref(vs30);
double fb = c.θ11 + c.θ12 * δlnZ;
+ fb = Math.min(fb, c.θ11S); // Seattle cap
+
+ if (seattle && z2p5 > 6.0 & c.imt.period() > 1.9) {
+ double δz2p5adj = log(z2p5m) - LN_Z2P5_REF_KUEHN;
+ double m9adj = log(2.0) - (c.θ11 + c.θ12 * δz2p5adj);
+ fb += m9adj;
+ }
- return Math.min(fb, c.θ11S); // Seattle cap
+ return fb;
// switch (region) {
// case Region.CASCADIA:
@@ -431,6 +445,11 @@ public abstract class KuehnEtAl_2020 implements GroundMotionModel {
boolean basin() {
return false;
}
+
+ @Override
+ boolean seattle() {
+ return false;
+ }
}
private static abstract class Cascadia extends KuehnEtAl_2020 {
@@ -450,6 +469,11 @@ public abstract class KuehnEtAl_2020 implements GroundMotionModel {
boolean basin() {
return false;
}
+
+ @Override
+ boolean seattle() {
+ return false;
+ }
}
private static abstract class Alaska extends KuehnEtAl_2020 {
@@ -469,6 +493,11 @@ public abstract class KuehnEtAl_2020 implements GroundMotionModel {
boolean basin() {
return false;
}
+
+ @Override
+ boolean seattle() {
+ return false;
+ }
}
static class GlobalInterface extends Global {
diff --git a/src/main/java/gov/usgs/earthquake/nshmp/gmm/ParkerEtAl_2020.java b/src/main/java/gov/usgs/earthquake/nshmp/gmm/ParkerEtAl_2020.java
index 8b289b6a..a3e5b737 100644
--- a/src/main/java/gov/usgs/earthquake/nshmp/gmm/ParkerEtAl_2020.java
+++ b/src/main/java/gov/usgs/earthquake/nshmp/gmm/ParkerEtAl_2020.java
@@ -38,6 +38,11 @@ import gov.usgs.earthquake.nshmp.tree.LogicTree;
* authors recommend {@code zHyp}.
*
* <li>The basin depth scaling model is that developed for Cascadia.
+ * Implementations include USGS developed depth tapering and restriction to long
+ * periods ({@code T ≥ 1 s}), as well as a Seattle-specific basin
+ * implementation that makes further adjustments based on M9 simulations for
+ * sites over the deepest depths ({@code Z2.5 > 6 km}) and for long periods
+ * ({@code T &qeq; 2 s}).
*
* <li>Implementations are provided for the global model as well as Cascadia and
* Alaska regionalized models.</ul>
@@ -113,6 +118,7 @@ public abstract class ParkerEtAl_2020 implements GroundMotionModel {
private static final double B4 = 0.1;
private static final double V1 = 270.0; // m/s
private static final double VREF = 760.0; // m/s
+ private static final double LN_Z2P5_REF_PARKER = log(1279.0);
private static final double DB1 = 20.0; // km
private static final double DB2 = 67.0; // km
@@ -244,12 +250,12 @@ public abstract class ParkerEtAl_2020 implements GroundMotionModel {
double pgaRef = exp(calcMean(coeffsPGA, slab(), in.Mw, in.rRup, in.zTor));
double μ = calcMean(
- coeffs, slab(), basin(),
+ coeffs, slab(), basin(), seattle(),
in.Mw, in.rRup, in.zTor, pgaRef, in.vs30, in.z2p5);
double Ï•Total = phiTotal(coeffs, in.rRup, in.vs30);
double σ = Maths.hypot(coeffs.τ, ϕTotal);
- double σε = getσε(coeffs);
+ double σε = calcσε(coeffs);
double[] μs = new double[] { μ + σε, μ, μ - σε };
@@ -260,6 +266,8 @@ public abstract class ParkerEtAl_2020 implements GroundMotionModel {
abstract boolean basin();
+ abstract boolean seattle();
+
/* Calc median at 760 reference condition */
private static double calcMean(
Coefficients c,
@@ -280,6 +288,7 @@ public abstract class ParkerEtAl_2020 implements GroundMotionModel {
Coefficients c,
boolean slab,
boolean basin,
+ boolean seattle,
double Mw,
double rRup,
double zHyp,
@@ -295,7 +304,7 @@ public abstract class ParkerEtAl_2020 implements GroundMotionModel {
/* Equation 7 */
double Fslin = siteTermLinear(c, vs30);
double Fsnl = siteTermNonLinear(c, pgaRef, vs30);
- double Fsb = basin ? getSiteBasinTerm(c, vs30, z2p5) : 0.0;
+ double Fsb = basin ? siteBasinTerm(c, vs30, z2p5, seattle) : 0.0;
double Fs = Fslin + Fsnl + Fsb;
return c.c0 + Fp + Fm + Fd + Fs;
@@ -365,7 +374,11 @@ public abstract class ParkerEtAl_2020 implements GroundMotionModel {
}
/* Equation 11, 12, 13 */
- private static double getSiteBasinTerm(Coefficients c, double vs30, double z2p5) {
+ private static double siteBasinTerm(
+ Coefficients c,
+ double vs30,
+ double z2p5,
+ boolean seattle) {
if (Double.isNaN(z2p5)) {
return 0.0;
@@ -383,15 +396,24 @@ public abstract class ParkerEtAl_2020 implements GroundMotionModel {
(θ1 * (1 + Maths.erf((log10(vs30) - log10(νμ)) / νσ / sqrt(2))) + θ0);
double δz2p5 = log(z2p5m) - lnμz2p5;
- double Fb;
+ double Fb = calcFb(c, δz2p5);
+
+ if (seattle && z2p5 > 6.0 & c.imt.period() > 1.9) {
+ double δz2p5adj = log(z2p5m) - LN_Z2P5_REF_PARKER;
+ double m9adj = log(2.0) - calcFb(c, δz2p5adj);
+ Fb += m9adj;
+ }
+
+ return Fb;
+ }
+
+ private static double calcFb(Coefficients c, double δz2p5) {
if (δz2p5 <= (c.c_e1 / c.c_e3)) {
- Fb = c.c_e1;
+ return c.c_e1;
} else if (δz2p5 >= (c.c_e2 / c.c_e3)) {
- Fb = c.c_e2;
- } else {
- Fb = c.c_e3 * δz2p5;
+ return c.c_e2;
}
- return Fb;
+ return c.c_e3 * δz2p5;
}
/* Eqsuation 18, 19, 20 */
@@ -422,7 +444,7 @@ public abstract class ParkerEtAl_2020 implements GroundMotionModel {
}
/* Equation 27 */
- private static double getσε(Coefficients c) {
+ private static double calcσε(Coefficients c) {
double σε;
if (c.imt == Imt.PGA || c.imt == Imt.PGV || c.imt.period() < c.t1) {
σε = c.σε1;
@@ -451,6 +473,11 @@ public abstract class ParkerEtAl_2020 implements GroundMotionModel {
boolean basin() {
return false;
}
+
+ @Override
+ boolean seattle() {
+ return false;
+ }
}
private static abstract class Cascadia extends ParkerEtAl_2020 {
@@ -470,6 +497,11 @@ public abstract class ParkerEtAl_2020 implements GroundMotionModel {
boolean basin() {
return false;
}
+
+ @Override
+ boolean seattle() {
+ return false;
+ }
}
private static abstract class Alaska extends ParkerEtAl_2020 {
@@ -489,6 +521,11 @@ public abstract class ParkerEtAl_2020 implements GroundMotionModel {
boolean basin() {
return false;
}
+
+ @Override
+ boolean seattle() {
+ return false;
+ }
}
static final class GlobalInterface extends Global {
--
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