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groundShakingCalculation.py
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import math
import numpy as np
import time
from scipy.stats import truncnorm
from scipy import interpolate
def calculate_distance_matrix(exposureLocations):
noLocations = len(exposureLocations)
distanceMatrix = np.zeros((noLocations,noLocations))
for i in range(noLocations):
for j in range(noLocations):
distanceMatrix[i][j]=calculate_distance_2points(exposureLocations[i],exposureLocations[j])
return distanceMatrix
def calculate_single_spatial_correlation_matrix(distanceMatrix,IMT,correlationType):
noLocations = len(distanceMatrix)
correlationMatrix = np.zeros((noLocations,noLocations))
b = calculate_spatial_length_scale(IMT,'Vs30clustered')
for i in range(noLocations):
for j in range(noLocations):
if i == j:
correlationMatrix[i][j] = 1
else:
if correlationType == 'no correlation':
correlationMatrix[i][j] = 0
if correlationType == 'full correlation':
correlationMatrix[i][j] = 0.99999
if correlationType == 'spatial':
correlationMatrix[i][j]=math.exp(-3*distanceMatrix[i][j]/b)
return correlationMatrix
def calculate_spatial_correlation_matrices(distanceMatrix,IMTs,correlationType):
noLocations = len(distanceMatrix)
noIMTs = len(IMTs)
spatialCorrMatrices = []
for i in range(noIMTs):
spatialCorrMatrices.append(calculate_single_spatial_correlation_matrix(distanceMatrix,IMTs[i],correlationType))
return np.array(spatialCorrMatrices)
def calculate_spatial_covariance_matrices(closestGroundShaking,spatialCorrMatrices):
noIMT = len(spatialCorrMatrices)
noLocations = len(spatialCorrMatrices[0])
spatialCovMatrices = []
for i in range(noIMT):
tempCovMatrix = np.zeros((noLocations,noLocations))
for j in range(noLocations):
for k in range(noLocations):
tempCovMatrix[j][k]=spatialCorrMatrices[i][j][k]*closestGroundShaking[j][2+noIMT+i]*closestGroundShaking[k][2+noIMT+i]
spatialCovMatrices.append(tempCovMatrix)
return np.array(spatialCovMatrices)
def calculate_cross_correlation_matrix(listIMT,correlationType):
noIMT = len(listIMT)
crossCorrMatrix = np.zeros((noIMT,noIMT))
for i in range(noIMT):
if listIMT[i] == 'PGA':
T1 = 0.05
elif listIMT[i][0:2] == 'SA':
T1 = float(listIMT[i].replace("SA(","").replace(")",""))
for j in range(noIMT):
if listIMT[j] == 'PGA':
T2 = 0.05
elif listIMT[j][0:2] == 'SA':
T2 = float(listIMT[j].replace("SA(","").replace(")",""))
if i == j:
crossCorrMatrix[i][j] = 1
else:
Tmax = max([T1,T2]);
Tmin = min([T1,T2]);
if Tmin<0.189:
II = 1
else:
II = 0
if correlationType == 'no correlation':
crossCorrMatrix[i][j] = 0
if correlationType == 'full correlation':
crossCorrMatrix[i][j] = 0.99999
if correlationType == 'cross':
crossCorrMatrix[i][j] = 1-math.cos((math.pi/2)-(0.359+0.163*II*math.log(Tmin/0.189))*math.log(Tmax/Tmin))
return crossCorrMatrix
def generate_random_fields_ground_motion(IMTs,groundShaking,spatialCovMatrices,crossCorrMatrix,siteEffects,noSigmas,noGMFs):
noLocations = spatialCovMatrices.shape[1]
noIMT = crossCorrMatrix.shape[0]
L = []
LLT = []
Z = []
for i in range(noIMT):
L.append(np.linalg.cholesky(spatialCovMatrices[i]))
L=np.array(L)
for i in range(noIMT):
LLTrow = []
for j in range(noIMT):
LLTrow.append(np.dot(L[i],np.transpose(L[j]))*crossCorrMatrix[i][j])
for irow in range(len(LLTrow[0])):
singleLLTrow = np.zeros((int(len(LLTrow)*len(LLTrow[0]))))
for iL in range(len(LLTrow)):
singleLLTrow[iL*len(LLTrow[0]):(iL+1)*len(LLTrow[0])] = LLTrow[iL][irow]
LLT.append(singleLLTrow)
LLT=np.array(LLT)
mu = []
for i in range(noIMT):
for j in range(noLocations):
mu.append(np.ones(noGMFs)*groundShaking[j][i+2])
mu = np.array(mu)
L = (np.linalg.cholesky(LLT))
Z = truncnorm.rvs(-noSigmas, noSigmas, loc=0, scale=1, size=(noLocations*noIMT,noGMFs))
gmfs = np.exp(np.dot(L,Z)+mu)
if siteEffects:
gmfs = amplifyGMFs(IMTs,groundShaking[:,-1],gmfs)*0.8
return gmfs
def amplifyGMFs(IMTs,Vs30s,gmfs):
noLocations = len(Vs30s)
for i in range(4):
if IMTs[i] == 'PGA':
T = 0.0
elif IMTs[0:2] == 'SA':
IMT = IMTs[i]
T = float(IMT.replace("SA(","").replace(")",""))
for iloc in range(noLocations):
gmfs[i*noLocations+iloc] = amplify_ground_shaking(T,Vs30s[iloc],gmfs[i*noLocations+iloc])
return gmfs
def calculate_spatial_length_scale(IMT,Vs30Case):
if IMT == 'PGA':
T = 0.0
elif IMT[0:2] == 'SA':
T = float(IMT.replace("SA(","").replace(")",""))
if T < 1:
if Vs30Case != 'Vs30clustered':
b = 8.5+17.2*T
elif Vs30Case == 'Vs30clustered':
b = 40.7-15.0*T
elif T >= 1:
b = 22.0 + 3.7*T
return b
def calculate_distance_2points(point1,point2):
lon1 = point1[0]
lon2 = point2[0]
lat1 = point1[1]
lat2 = point2[1]
lon1, lat1, lon2, lat2 = map(math.radians, [lon1, lat1, lon2, lat2])
dlon = lon2 - lon1
dlat = lat2 - lat1
a = math.sin(dlat/2)**2 + math.cos(lat1) * math.cos(lat2) * math.sin(dlon/2)**2
distance = 6367*2*math.asin(math.sqrt(a))
return distance
def amplify_ground_shaking(T,Vs30,IMLs):
ampFactorsShort = [(760/Vs30)**0.35,(760/Vs30)**0.35,(760/Vs30)**0.25,(760/Vs30)**0.10,(760/Vs30)**-0.05,(760/Vs30)**-0.05]
ampFactorsMid = [(760/Vs30)**0.65,(760/Vs30)**0.65,(760/Vs30)**0.60,(760/Vs30)**0.53,(760/Vs30)**0.45,(760/Vs30)**0.45]
if T<=0.3:
interpolator = interpolate.interp1d([-1,0.1,0.2,0.3,0.4,100],ampFactorsShort, kind = 'linear')
if T>0.3:
interpolator = interpolate.interp1d([-1,0.1,0.2,0.3,0.4,100],ampFactorsMid, kind = 'linear')
return interpolator(IMLs)*IMLs