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uncertainties.py
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'''
A fault class dealing with uncertainties in the forward model (fault geometry, crustal elastic properties)
Written by T. Ragon September 2018
'''
# Externals
import numpy as np
import os
from scipy.stats import linregress
# Personals
from .multifaultsolve import multifaultsolve as multiflt
class uncertainties(object):
# ----------------------------------------------------------------------
# Initialize class
def __init__(self, name, faults, datasets, export=None, verbose=True):
'''
Class calculating the covariance matrix of the predictions.
Args:
* name : Name of the object
* faults : Prior fault geometry, can be a list of several faults
* datasets : List of data objects
ex: dataset=[gps]+[insar1,insar2]
* export : None by default
or string with path to directory
'''
self.verbose = verbose
if self.verbose:
print ("---------------------------------")
print ("---------------------------------")
print ("Initializing uncertainties object")
# Store things into self
self.name = name
self.faults = faults
self.datasets = datasets
self.export = export
# check the utm zone
if np.shape(self.faults)!=():
self.utmzone = faults[0].utmzone
for fault in faults:
if fault.utmzone is not self.utmzone:
print("UTM zones are not equivalent, this is a problem")
self.ready = False
return
self.putm = faults[0].putm
else:
self.utmzone = faults.utmzone
# check that Cd have been assembled prior to initialization
if np.shape(self.faults)!=():
for fault in faults:
# if fault.dassembled is None:
# print("d has not been assembled in fault structure {}".format(fault.name))
if fault.Cd is None:
print("Cd has not been assembled in fault structure {}".format(fault.name))
else:
self.Cd = fault.Cd
else:
if self.faults.Cd is None:
print("Cd has not been assembled in fault structure {}".format(self.faults.name))
else:
self.Cd = self.faults.Cd
# Set the kernels and covariance matrices as empty arrays
self.KDip = []
self.KStrike = []
self.KPosition = []
self.KElastic = []
self.KernelsFull = []
self.CovDip = []
self.CovStrike = []
self.CovPosition = []
self.CovElastic = []
self.CovFull = []
self.CpDip = []
self.CpStrike = []
self.CpPosition = []
self.CpElastic = []
self.CpFull = []
self.CdFull = []
return
# ----------------------------------------------------------------------
# ----------------------------------------------------------------------
# Calculate uncertainties related to the fault dip
def calcCpDip(self, dip_range, sigma, mprior, edks=False, **edks_params):
'''
Calculate the uncertainties of the predictions deriving from uncertainties in the fault dip.
From Ragon et al. (2018) GJI
Args:
* dip_range : array, dip values (in degrees) to test around the prior fault dip (of Fault)
ex: dip_range = [-1,2]
If there are several fault segments (e.g. several faults in fault), len(dip_range) must be equal to len(fault)
ex: dip_range = [[-1,2],[-2,3],[-4,1],[0,5]] for a fault with 4 segments
* sigma : prior uncertainty (standard deviation) in the dip parameter (in degrees)
ex: sigma = 5
If there are several fault segments (e.g. several faults in fault), len(sigma) must be equal to len(fault)
ex: sigma = [5,7,2,3] for a fault with 4 segments
* mprior : initial model used to calculate Cp
length must be equal to two times the number of patches
can be uniform and derived from Mo, ex: meanslip = -Mo*10**(-7)/(3*10**10*length*width)
OR derived from a first inversion without accounting for uncertainties
Kwargs:
* edks : If True, GFs calculated using a layered Earth model calculated with EDKS.
If False, GFs with Okada
If edks is True, please specify in **edks_params:
ex: Cp_dip(fault,datasets,[40,50],sigma,mprior,edks=True,edksdir='path/to/kernels',modelname='CIA',sourceSpacing=0.5)
* edksdir : path of the edks kernels
* modelname : Filename of the EDKS kernels
* sourceSpacing : source spacing to calculate the Green's Functions
OR sourceNumber : Number of sources per patches.
OR sourceArea : Maximum Area of the sources.
Returns:
* CpDip
/!\ To save you from having to recalculate a new fault geometry for each new dip parameter,
each fault patches are rotated along the fault tip. When Equivalent Rectangles are
calculated, fault patches are approximated and it may bias slighly (0 to 5% -?)
the value of Cp. To avoid this effect, you could instead recalculate your fault geometry.
'''
# For a fault with one segment
if np.shape(self.faults)==() or np.shape(self.faults)[0]==1 :
if np.shape(self.faults)==():
fault = self.faults
else:
fault = self.faults[0]
# Define the range on which calculate Kernels
dip_rg = np.linspace(dip_range[0],dip_range[1],6)
# Calculate the Green's functions for the various dips in dip_rg
gfs = []
for d in dip_rg:
print('---------------------------------')
print('---------------------------------')
print('Calculating new Fault Geometry and Greens Functions')
print('For dip = dip_prior + %.2f degrees' % (d))
# Modify the fault geometry
p_axis1 = np.array([fault.xf[-1],fault.yf[-1],fault.top])
p_axis2 = np.array([fault.xf[0],fault.yf[0],fault.top])
# Copy the fault
Fg = fault.duplicateFault()
# Rotate the patches
for p in range(len(fault.patch)):
Fg.rotatePatch(p,d, p_axis1, p_axis2)
Fg.computeEquivRectangle()
if edks is True:
os.chdir(modelname=edks_params['edksdir'])
if 'Spacing' in str(edks_params.items()[1][0]):
gfs.append(Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceSpacing=edks_params.items()[1][1]))
elif 'Number' in str(edks_params.items()[1][0]):
gfs.append(Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceNumber=edks_params.items()[1][1]))
else:
gfs.append(Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceArea=edks_params.items()[1][1]))
else:
gfs.append(Fg.calcGFsCp(self.datasets, edks=False))
# Calculate the sensitivity Kernels of the Green's Functions (the derivatives) by linearizing their variation
slope = np.empty(gfs[0].shape)
rvalue = np.empty(gfs[0].shape)
pvalue = np.empty(gfs[0].shape)
stderr = np.empty(gfs[0].shape)
inter = np.empty(gfs[0].shape)
for i in range(gfs[0].shape[0]):
for j in range(gfs[0].shape[1]):
# Do a linear regression for each couple parameter/data, along the dip range
slope[i,j], inter[i,j], rvalue[i,j], pvalue[i,j], stderr[i,j] = linregress(dip_rg,[gfs[k][i,j] for k in range(len(dip_rg))])
Kdip= slope
K = []
K.append(Kdip)
kernels = np.asarray(K)
k = np.transpose(np.matmul(kernels, mprior))
C1 = np.matmul(k, [[np.float(sigma)**2]])
CpDip = np.matmul(C1, np.transpose(k))
self.KDip = kernels
self.CovDip = np.array([[np.float(sigma)**2]])
if self.KernelsFull==[]:
self.KernelsFull = self.KDip
else:
self.KernelsFull = np.concatenate((self.KernelsFull,self.KDip))
if self.CovFull==[]:
self.CovFull = self.CovDip
else:
Z = np.zeros((np.shape(self.CovFull)[0],np.shape(self.CovDip)[0]),dtype=int)
self.CovFull = np.asarray(np.bmat([[self.CovFull, Z], [Z, self.CovDip]]))
self.CpDip = CpDip
if self.CpFull==[]:
self.CpFull = self.CpDip
else:
self.CpFull = np.add(self.CpFull, self.CpDip)
self.CdFull = np.add(self.Cd, self.CpFull)
if self.export is not None:
self.CdFull.astype('f').tofile(os.path.join(self.export,self.name+'CdFull.bin'))
self.KernelsFull.astype('f').tofile(os.path.join(self.export,self.name+'KernelsFull.bin'))
self.CovFull.astype('f').tofile(os.path.join(self.export,self.name+'CovFull.bin'))
self.KDip.astype('f').tofile(os.path.join(self.export,self.name+'KDip.bin'))
self.CovDip.astype('f').tofile(os.path.join(self.export,self.name+'CovDip.bin'))
print('---------------------------------')
print('---------------------------------')
print('CdFull successfully updated with CpDip')
# For a multi-segmented fault
else:
Kdip = []
# Initialize the faults
Faults = []
for f in range(len(self.faults)):
fault = self.faults[f]
dip = dip_range[f][0]
p_axis1 = np.array([fault.xf[0],fault.yf[0],fault.top])
p_axis2 = np.array([fault.xf[-1],fault.yf[-1],fault.top])
Fg = fault.duplicateFault()
for p in range(len(fault.patch)):
Fg.rotatePatch(p,dip, p_axis1, p_axis2)
Fg.computeEquivRectangle()
# Calculate GFs
if edks is True:
os.chdir(modelname=edks_params['edksdir'])
if 'Spacing' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceSpacing=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
elif 'Number' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceNumber=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceArea=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=False)
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
Faults.append(Fg)
for f in range(len(self.faults)):
Faults_cp = Faults
fault = self.faults[f]
gfs = []
# Define the range on which calculate Kernels
dip_rg = np.linspace(dip_range[f][0],dip_range[f][1],6)
p_axis1 = np.array([fault.xf[0],fault.yf[0],fault.top])
p_axis2 = np.array([fault.xf[-1],fault.yf[-1],fault.top])
# Calculate the Green's functions for the various dips in dip_rg
for d in dip_rg:
print('---------------------------------')
print('---------------------------------')
print('Calculating new Fault Geometry and Greens Functions')
print('For dip = dip_prior + %.2f degrees' % (d))
# Modify the fault geometry
Fg = fault.duplicateFault()
for p in range(len(fault.patch)):
Fg.rotatePatch(p,d, p_axis1, p_axis2)
Fg.computeEquivRectangle()
# Calculate GFs for each different fault geometry
if edks is True:
os.chdir(modelname=edks_params['edksdir'])
if 'Spacing' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceSpacing=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
elif 'Number' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceNumber=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceArea=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=False)
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
Faults_cp[f] = Fg
slv = multiflt('Multi-seg fault', Faults_cp)
slv.assembleGFs()
gfs.append(slv.G)
# Calculate the sensitivity Kernels of the Green's Functions (the derivatives) by linearizing their variation
slope = np.empty(gfs[0].shape)
rvalue = np.empty(gfs[0].shape)
pvalue = np.empty(gfs[0].shape)
stderr = np.empty(gfs[0].shape)
inter = np.empty(gfs[0].shape)
for i in range(gfs[0].shape[0]):
for j in range(gfs[0].shape[1]):
# Do a linear regression for each couple parameter/data, along the dip range
slope[i,j], inter[i,j], rvalue[i,j], pvalue[i,j], stderr[i,j] = linregress(dip_rg,[gfs[k][i,j] for k in range(len(dip_rg))])
Kdip.append(slope)
kernels = np.asarray(Kdip)
k = np.transpose(np.matmul(kernels, mprior))
Covdip = np.zeros((len(self.faults),len(self.faults)))
for f in range(len(self.faults)):
Covdip[f,f] = sigma[f]**2
C1 = np.matmul(k, Covdip)
CpDip = np.matmul(C1, np.transpose(k))
self.KDip = kernels
self.CovDip = Covdip
if self.KernelsFull==[]:
self.KernelsFull = self.KDip
else:
self.KernelsFull = np.concatenate((self.KernelsFull,self.KDip))
if self.CovFull==[]:
self.CovFull = self.CovDip
else:
Z = np.zeros((np.shape(self.CovFull)[0],np.shape(self.CovDip)[0]),dtype=int)
self.CovFull = np.asarray(np.bmat([[self.CovFull, Z], [Z, self.CovDip]]))
self.CpDip = CpDip
if self.CpFull==[]:
self.CpFull = self.CpDip
else:
self.CpFull = np.add(self.CpFull, self.CpDip)
self.CdFull = np.add(self.Cd, self.CpFull)
if self.export is not None:
self.CdFull.astype('f').tofile(os.path.join(self.export,self.name+'CdFull.bin'))
self.KernelsFull.astype('f').tofile(os.path.join(self.export,self.name+'KernelsFull.bin'))
self.CovFull.astype('f').tofile(os.path.join(self.export,self.name+'CovFull.bin'))
self.KDip.astype('f').tofile(os.path.join(self.export,self.name+'KDip.bin'))
self.CovDip.astype('f').tofile(os.path.join(self.export,self.name+'CovDip.bin'))
print('---------------------------------')
print('---------------------------------')
print('CdFull successfully updated with CpDip')
return
# ----------------------------------------------------------------------
# ----------------------------------------------------------------------
# Calculate uncertainties related to the fault strike
def calcCpStrike(self, strike_range, rotation_axis, sigma, mprior, whole_fault=True, edks=False, **edks_params):
'''
Calculate the uncertainties of the predictions deriving from uncertainties in the fault strike.
If the fault is multi-segmented, you have two options:
- investigate the variation of strike for each segment independently
option whole_fault = False
- investigate the variation of strike for the whole fault (whole_fault is True by default)
From Ragon et al. (2018) GJI
Args:
* strike_range : array, strike values (in degrees) to test around the prior fault strike (of Fault)
Positive angles are counter-clockwise looking toward the center of the Earth
ex: strike_range = [-1,2]
If whole_fault is False (multi-segmented fault), len(strike_range) must be equal to len(fault)
ex: strike_range = [[-1,2],[-2,3],[-4,1],[0,5]] for a fault with 4 segments
* rotation_axis : can be 'center', 'first', 'second' or an had-oc position [X,Y]
define the axis around which the fault will rotate
'center' : the center of the fault
'first' : the first point of the fault trace (Fault.xf[0],Fault.yf[0])
'last' : the last point of the fault trace (Fault.xf[-1],Fault.yf[-1])
[X,Y] : ad-hoc coordinates
* sigma : prior uncertainty (standard deviation) in the strike parameter (in degrees)
ex: sigma = 5
If whole_fault is False (multi-segmented fault), len(sigma) must be equal to len(fault)
ex: sigma = [5,7,2,3] for a fault with 4 segments
* mprior : initial model used to calculate Cp
length must be equal to two times the number of patches
can be uniform and derived from Mo, ex: meanslip = -Mo*10**(-7)/(3*10**10*length*width)
OR derived from a first inversion without accounting for uncertainties
* whole_fault : True by default.
if True for a multi-segmented fault, the strike variation for the whole fault will be investigated
the first strike_range value (strike_range[0]) will be assumed as rotation angles for the whole fault
around the center or the whole fault, the first point of the first segment or the last point of the last segment
if False for a multi-segmented fault, the strike variation of each segment will be investigated independently
for either the center, first or last point of each fault segment
Kwargs:
* edks : If True, GFs calculated using a layered Earth model calculated with EDKS.
If False, GFs with Okada
If edks is True, please specify in **edks_params:
ex: Cp_strike(fault,datasets,[40,50],'center',sigma,mprior,edks=True,edksdir='path/to/kernels',modelname='CIA',sourceSpacing=0.5)
* edksdir : path of the edks kernels
* modelname : Filename of the EDKS kernels
* sourceSpacing : source spacing to calculate the Green's Functions
OR sourceNumber : Number of sources per patches.
OR sourceArea : Maximum Area of the sources.
Returns:
* CpStrike
'''
# For a fault with one segment
if np.shape(self.faults)==() or np.shape(self.faults)[0]==1 :
if np.shape(self.faults)==():
fault = self.faults
else:
fault = self.faults[0]
# Define the range on which calculate Kernels
stk_rg = np.linspace(strike_range[0],strike_range[1],6)
# Calculate the Green's functions for the various strike values in stk_rg
gfs = []
# Define the rotation axis
if rotation_axis == 'center':
p_axis1 = np.array([(fault.xf[0]+fault.xf[-1])/2,(fault.yf[0]+fault.yf[-1])/2,fault.top])
p_axis2 = np.array([(fault.xf[0]+fault.xf[-1])/2,(fault.yf[0]+fault.yf[-1])/2,fault.top+10])
elif rotation_axis == 'first':
p_axis1 = np.array([fault.xf[0],fault.yf[0],fault.top])
p_axis2 = np.array([fault.xf[0],fault.yf[0],fault.top+10])
elif rotation_axis == 'last':
p_axis1 = np.array([fault.xf[-1],fault.yf[-1],fault.top])
p_axis2 = np.array([fault.xf[-1],fault.yf[-1],fault.top+10])
else:
p_axis1 = np.array([rotation_axis[0],rotation_axis[1],fault.top])
p_axis2 = np.array([rotation_axis[0],rotation_axis[1],fault.top+10])
for s in stk_rg:
print('---------------------------------')
print('---------------------------------')
print('Calculating new Fault Geometry and Greens Functions')
print('For strike = strike_prior + %.2f degrees' % (s))
# Modify the fault geometry
Fg = fault.duplicateFault()
# rotate the patches
for p in range(len(fault.patch)):
Fg.rotatePatch(p,s, p_axis1, p_axis2)
Fg.computeEquivRectangle()
if edks is True:
os.chdir(modelname=edks_params['edksdir'])
if 'Spacing' in str(edks_params.items()[1][0]):
gfs.append(Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceSpacing=edks_params.items()[1][1]))
elif 'Number' in str(edks_params.items()[1][0]):
gfs.append(Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceNumber=edks_params.items()[1][1]))
else:
gfs.append(Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceArea=edks_params.items()[1][1]))
else:
gfs.append(Fg.calcGFsCp(self.datasets,edks=False))
# Calculate the sensitivity Kernels of the Green's Functions (the derivatives) by linearizing their variation
slope = np.empty(gfs[0].shape)
rvalue = np.empty(gfs[0].shape)
pvalue = np.empty(gfs[0].shape)
stderr = np.empty(gfs[0].shape)
inter = np.empty(gfs[0].shape)
for i in range(gfs[0].shape[0]):
for j in range(gfs[0].shape[1]):
# Do a linear regression for each couple parameter/data, along the range of strike values
slope[i,j], inter[i,j], rvalue[i,j], pvalue[i,j], stderr[i,j] = linregress(stk_rg,[gfs[k][i,j] for k in range(len(stk_rg))])
Kstk= slope
K = []
K.append(Kstk)
kernels = np.asarray(K)
k = np.transpose(np.matmul(kernels, mprior))
C1 = np.matmul(k, [[np.float(sigma)**2]])
CpStrike = np.matmul(C1, np.transpose(k))
self.KStrike = kernels
self.CovStrike = np.array([[np.float(sigma)**2]])
if self.KernelsFull==[]:
self.KernelsFull = self.KStrike
else:
self.KernelsFull = np.concatenate((self.KernelsFull,self.KStrike))
if self.CovFull==[]:
self.CovFull = self.CovStrike
else:
Z = np.zeros((np.shape(self.CovFull)[0],np.shape(self.CovStrike)[0]),dtype=int)
self.CovFull = np.asarray(np.bmat([[self.CovFull, Z], [Z, self.CovStrike]]))
self.CpStrike = CpStrike
if self.CpFull==[]:
self.CpFull = self.CpStrike
else:
self.CpFull = np.add(self.CpFull, self.CpStrike)
self.CdFull = np.add(self.Cd, self.CpFull)
if self.export is not None:
self.CdFull.astype('f').tofile(os.path.join(self.export,self.name+'CdFull.bin'))
self.KernelsFull.astype('f').tofile(os.path.join(self.export,self.name+'KernelsFull.bin'))
self.CovFull.astype('f').tofile(os.path.join(self.export,self.name+'CovFull.bin'))
self.KStrike.astype('f').tofile(os.path.join(self.export,self.name+'KStrike.bin'))
self.CovStrike.astype('f').tofile(os.path.join(self.export,self.name+'CovStrike.bin'))
print('---------------------------------')
print('---------------------------------')
print('CdFull successfully updated with Cpstrike')
# For a multi-segmented fault
elif np.shape(self.faults)!=() and whole_fault==False:
Kstk = []
# Initialize the faults
Faults = []
for f in range(len(self.faults)):
fault = self.faults[f]
strike = strike_range[f][0]
# Define the rotation axis
if rotation_axis == 'center':
p_axis1 = np.array([(fault.xf[0]+fault.xf[-1])/2,(fault.yf[0]+fault.yf[-1])/2,fault.top])
p_axis2 = np.array([(fault.xf[0]+fault.xf[-1])/2,(fault.yf[0]+fault.yf[-1])/2,fault.top+10])
elif rotation_axis == 'first':
p_axis1 = np.array([fault.xf[0],fault.yf[0],fault.top])
p_axis2 = np.array([fault.xf[0],fault.yf[0],fault.top+10])
elif rotation_axis == 'last':
p_axis1 = np.array([fault.xf[-1],fault.yf[-1],fault.top])
p_axis2 = np.array([fault.xf[-1],fault.yf[-1],fault.top+10])
else:
p_axis1 = np.array([rotation_axis[0],rotation_axis[1],fault.top])
p_axis2 = np.array([rotation_axis[0],rotation_axis[1],fault.top+10])
Fg = fault.duplicateFault()
for p in range(len(fault.patch)):
Fg.rotatePatch(p,strike, p_axis1, p_axis2)
Fg.computeEquivRectangle()
# Calculate GFs
if edks is True:
os.chdir(modelname=edks_params['edksdir'])
if 'Spacing' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceSpacing=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
elif 'Number' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceNumber=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceArea=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=False)
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
Faults.append(Fg)
for f in range(len(self.faults)):
Faults_cp = Faults
fault = self.faults[f]
gfs = []
# Define the range on which calculate Kernels
stk_rg = np.linspace(strike_range[f][0],strike_range[f][1],6)
# Define the rotation axis
if rotation_axis == 'center':
p_axis1 = np.array([(fault.xf[0]+fault.xf[-1])/2,(fault.yf[0]+fault.yf[-1])/2,fault.top])
p_axis2 = np.array([(fault.xf[0]+fault.xf[-1])/2,(fault.yf[0]+fault.yf[-1])/2,fault.top+10])
elif rotation_axis == 'first':
p_axis1 = np.array([fault.xf[0],fault.yf[0],fault.top])
p_axis2 = np.array([fault.xf[0],fault.yf[0],fault.top+10])
elif rotation_axis == 'last':
p_axis1 = np.array([fault.xf[-1],fault.yf[-1],fault.top])
p_axis2 = np.array([fault.xf[-1],fault.yf[-1],fault.top+10])
else:
p_axis1 = np.array([rotation_axis[0],rotation_axis[1],fault.top])
p_axis2 = np.array([rotation_axis[0],rotation_axis[1],fault.top+10])
# Calculate the Green's functions for the various strike values in stk_rg
for s in stk_rg:
print('---------------------------------')
print('---------------------------------')
print('Calculating new Fault Geometry and Greens Functions')
print('For strike = strike_prior + %.2f degrees' % (s))
# Modify the fault geometry
Fg = fault.duplicateFault()
for p in range(len(fault.patch)):
Fg.rotatePatch(p,s, p_axis1, p_axis2)
Fg.computeEquivRectangle()
# Calculate GFs for each different fault geometry
if edks is True:
os.chdir(modelname=edks_params['edksdir'])
if 'Spacing' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceSpacing=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
elif 'Number' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceNumber=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceArea=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=False)
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
Faults_cp[f] = Fg
slv = multiflt('Multi-seg fault', Faults_cp)
slv.assembleGFs()
gfs.append(slv.G)
# Calculate the sensitivity Kernels of the Green's Functions (the derivatives) by linearizing their variation
slope = np.empty(gfs[0].shape)
rvalue = np.empty(gfs[0].shape)
pvalue = np.empty(gfs[0].shape)
stderr = np.empty(gfs[0].shape)
inter = np.empty(gfs[0].shape)
for i in range(gfs[0].shape[0]):
for j in range(gfs[0].shape[1]):
# Do a linear regression for each couple parameter/data, along the range of strike values
slope[i,j], inter[i,j], rvalue[i,j], pvalue[i,j], stderr[i,j] = linregress(stk_rg,[gfs[k][i,j] for k in range(len(stk_rg))])
Kstk.append(slope)
kernels = np.asarray(Kstk)
k = np.transpose(np.matmul(kernels, mprior))
Covstk = np.zeros((len(self.faults),len(self.faults)))
for f in range(len(self.faults)):
Covstk[f,f] = sigma[f]**2
C1 = np.matmul(k, Covstk)
CpStrike = np.matmul(C1, np.transpose(k))
self.KStrike = kernels
self.CovStrike = Covstk
if self.KernelsFull==[]:
self.KernelsFull = self.KStrike
else:
self.KernelsFull = np.concatenate((self.KernelsFull,self.KStrike))
if self.CovFull==[]:
self.CovFull = self.CovStrike
else:
Z = np.zeros((np.shape(self.CovFull)[0],np.shape(self.CovStrike)[0]),dtype=int)
self.CovFull = np.asarray(np.bmat([[self.CovFull, Z], [Z, self.CovStrike]]))
self.CpStrike = CpStrike
if self.CpFull==[]:
self.CpFull = self.CpStrike
else:
self.CpFull = np.add(self.CpFull, self.CpStrike)
self.CdFull = np.add(self.Cd, self.CpFull)
if self.export is not None:
self.CdFull.astype('f').tofile(os.path.join(self.export,self.name+'CdFull.bin'))
self.KernelsFull.astype('f').tofile(os.path.join(self.export,self.name+'KernelsFull.bin'))
self.CovFull.astype('f').tofile(os.path.join(self.export,self.name+'CovFull.bin'))
self.KStrike.astype('f').tofile(os.path.join(self.export,self.name+'KStrike.bin'))
self.CovStrike.astype('f').tofile(os.path.join(self.export,self.name+'CovStrike.bin'))
print('---------------------------------')
print('---------------------------------')
print('CdFull successfully updated with CpStrike')
else:
# Define the range on which calculate Kernels
stk_rg = np.linspace(strike_range[0][0],strike_range[0][1],6)
# Define the rotation axis
if rotation_axis == 'center':
p_axis1 = np.array([(self.faults[0].xf[0]+self.faults[-1].xf[-1])/2,(self.faults[0].yf[0]+self.faults[-1].yf[-1])/2,self.faults[0].top])
p_axis2 = np.array([(self.faults[0].xf[0]+self.faults[-1].xf[-1])/2,(self.faults[0].yf[0]+self.faults[-1].yf[-1])/2,self.faults[0].top+10])
elif rotation_axis == 'first':
p_axis1 = np.array([self.faults[0].xf[0],self.faults[0].yf[0],self.faults[0].top])
p_axis2 = np.array([self.faults[0].xf[0],self.faults[0].yf[0],self.faults[0].top+10])
elif rotation_axis == 'last':
p_axis1 = np.array([self.faults[-1].xf[-1],self.faults[-1].yf[-1],self.faults[-1].top])
p_axis2 = np.array([self.faults[-1].xf[-1],self.faults[-1].yf[-1],self.faults[-1].top+10])
else:
p_axis1 = np.array([rotation_axis[0],rotation_axis[1],self.faults.top[0]])
p_axis2 = np.array([rotation_axis[0],rotation_axis[1],self.faults.top[0]+10])
Kstk = []
# Initialize the faults
Faults = []
for f in range(len(self.faults)):
fault = self.faults[f]
strike = stk_rg[0]
Fg = fault.duplicateFault()
for p in range(len(fault.patch)):
Fg.rotatePatch(p,strike, p_axis1, p_axis2)
Fg.computeEquivRectangle()
# Calculate GFs
if edks is True:
os.chdir(modelname=edks_params['edksdir'])
if 'Spacing' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceSpacing=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
elif 'Number' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceNumber=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceArea=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=False)
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
Faults.append(Fg)
for f in range(len(self.faults)):
Faults_cp = Faults
fault = self.faults[f]
gfs = []
# Calculate the Green's functions for the various strike values in stk_rg
for s in stk_rg:
print('---------------------------------')
print('---------------------------------')
print('Calculating new Fault Geometry and Greens Functions')
print('For strike = strike_prior + %.2f degrees' % (s))
# Modify the fault geometry
Fg = fault.duplicateFault()
for p in range(len(fault.patch)):
Fg.rotatePatch(p,s, p_axis1, p_axis2)
Fg.computeEquivRectangle()
# Calculate GFs for each different fault geometry
if edks is True:
os.chdir(modelname=edks_params['edksdir'])
if 'Spacing' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceSpacing=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
elif 'Number' in str(edks_params.items()[1][0]):
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceNumber=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceArea=edks_params.items()[1][1])
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
else:
Fg.calcGFsCp(self.datasets,edks=False)
Fg.assembleGFs(self.datasets)
Fg.assembled(self.datasets)
Fg.assembleCd(self.datasets)
Faults_cp[f] = Fg
slv = multiflt('Multi-seg fault', Faults_cp)
slv.assembleGFs()
gfs.append(slv.G)
# Calculate the sensitivity Kernels of the Green's Functions (the derivatives) by linearizing their variation
slope = np.empty(gfs[0].shape)
rvalue = np.empty(gfs[0].shape)
pvalue = np.empty(gfs[0].shape)
stderr = np.empty(gfs[0].shape)
inter = np.empty(gfs[0].shape)
for i in range(gfs[0].shape[0]):
for j in range(gfs[0].shape[1]):
# Do a linear regression for each couple parameter/data, along the range of strike values
slope[i,j], inter[i,j], rvalue[i,j], pvalue[i,j], stderr[i,j] = linregress(stk_rg,[gfs[k][i,j] for k in range(len(stk_rg))])
Kstk.append(slope)
kernels = np.asarray(Kstk)
k = np.transpose(np.matmul(kernels, mprior))
Covstk = np.zeros((len(self.faults),len(self.faults)))
for f in range(len(self.faults)):
Covstk[f,f] = sigma[f]**2
C1 = np.matmul(k, Covstk)
CpStrike = np.matmul(C1, np.transpose(k))
self.KStrike = kernels
self.CovStrike = Covstk
if self.KernelsFull==[]:
self.KernelsFull = self.KStrike
else:
self.KernelsFull = np.concatenate((self.KernelsFull,self.KStrike))
if self.CovFull==[]:
self.CovFull = self.CovStrike
else:
Z = np.zeros((np.shape(self.CovFull)[0],np.shape(self.CovStrike)[0]),dtype=int)
self.CovFull = np.asarray(np.bmat([[self.CovFull, Z], [Z, self.CovStrike]]))
self.CpStrike = CpStrike
if self.CpFull==[]:
self.CpFull = self.CpStrike
else:
self.CpFull = np.add(self.CpFull, self.CpStrike)
self.CdFull = np.add(self.Cd, self.CpFull)
if self.export is not None:
self.CdFull.astype('f').tofile(os.path.join(self.export,self.name+'CdFull.bin'))
self.KernelsFull.astype('f').tofile(os.path.join(self.export,self.name+'KernelsFull.bin'))
self.CovFull.astype('f').tofile(os.path.join(self.export,self.name+'CovFull.bin'))
self.KStrike.astype('f').tofile(os.path.join(self.export,self.name+'KStrike.bin'))
self.CovStrike.astype('f').tofile(os.path.join(self.export,self.name+'CovStrike.bin'))
print('---------------------------------')
print('---------------------------------')
print('CdFull successfully updated with CpStrike')
return CpStrike
# ----------------------------------------------------------------------
# ----------------------------------------------------------------------
# Calculate uncertainties related to the fault position
def calcCpPosition(self, position_range, sigma, mprior, whole_fault=True, edks=False, **edks_params):
'''
Calculate the uncertainties of the predictions deriving from uncertainties in the fault position.
For a one-segment fault, will vary the position perpendicularly to the strike
For a multi-segmented fault, you have two options:
- investigate the variation of the position for each segment independently (may have offset between segments)
the position will vary perpendicularly to the strike of each segment
option whole_fault = False
- investigate the variation of the position for the whole fault (whole_fault is True by default)
the position will vary perpendicularly to the global strike of the fault
From Ragon et al. (2018) GJI
Args:
* position_range : array, position values (in km) to test around the prior fault position (of Fault)
Positive values are +90 degrees from the prior strike
ex: position_range = [-1,2]
If there are several fault segments (e.g. several faults in fault), len(position_range) must be equal to len(fault)
ex: position_range = [[-1,2],[-2,1],[-0.5,0.2],[0,0.5]] for a fault with 4 segments
* sigma : prior uncertainty (standard deviation) in the fault position (in km)
ex: sigma = 5
If there are several fault segments (e.g. several faults in fault), len(sigma) must be equal to len(fault)
ex: sigma = [1,0.5,1,0.5] for a fault with 4 segments
* mprior : initial model used to calculate Cp
length must be equal to two times the number of patches
can be uniform and derived from Mo, ex: meanslip = -Mo*10**(-7)/(3*10**10*length*width)
OR derived from a first inversion without accounting for uncertainties
* whole_fault : True by default.
if True for a multi-segmented fault, the position of the whole fault will be investigated
if False for a multi-segmented fault, the position of each segment will be investigated independently
Kwargs:
* edks : If True, GFs calculated using a layered Earth model calculated with EDKS.
If False, GFs with Okada
If edks is True, please specify in **edks_params:
ex: Cp_strike(fault,datasets,[40,50],'center',sigma,mprior,edks=True,edksdir='path/to/kernels',modelname='CIA',sourceSpacing=0.5)
* edksdir : path of the edks kernels
* modelname : Filename of the EDKS kernels
* sourceSpacing : source spacing to calculate the Green's Functions
OR sourceNumber : Number of sources per patches.
OR sourceArea : Maximum Area of the sources.
Returns:
* CpPosition
'''
# For a fault with one segment
if np.shape(self.faults)==() or np.shape(self.faults)[0]==1 :
if np.shape(self.faults)==():
fault = self.faults
else:
fault = self.faults[0]
# Define the range on which calculate Kernels
pos_rg = np.linspace(position_range[0],position_range[1],6)
# Calculate the Green's functions for the various strike values in stk_rg
gfs = []
for r in pos_rg:
print('---------------------------------')
print('---------------------------------')
print('Calculating new Fault Geometry and Greens Functions')
print('For position = position_prior + %.2f km' % (r))
# Get the fault strike (in radians)
strike = np.arccos( (fault.yf[-1]-fault.yf[0]) /
np.sqrt( (fault.xf[-1]-fault.xf[0])**2
+ (fault.yf[-1]-fault.yf[0])**2 ))
# Calculate the translation vector
x_translation = np.sin(np.pi/2 - strike)* r
y_translation = np.cos(np.pi/2 - strike)* r
z_translation = 0
vector = [x_translation, y_translation, z_translation]
# Modify the fault geometry
Fg = fault.duplicateFault()
for p in range(len(fault.patch)):
Fg.translatePatch(p,vector)
Fg.computeEquivRectangle()
if edks is True:
os.chdir(modelname=edks_params['edksdir'])
if 'Spacing' in str(edks_params.items()[1][0]):
gfs.append(Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceSpacing=edks_params.items()[1][1]))
elif 'Number' in str(edks_params.items()[1][0]):
gfs.append(Fg.calcGFsCp(self.datasets,edks=True,
modelname=edks_params['edksdir']+edks_params['modelname'],
sourceNumber=edks_params.items()[1][1]))
else:
gfs.append(Fg.calcGFsCp(self.datasets,edks=True,