def fitCCC(f,
amp,
phi,
eRho=0.01,
ePhi=0.001,
lam=1000.,
mstart=None,
taupar=(1e-2, 1e-5, 100),
cpar=(0.5, 0, 1)):
"""Fit complex spectrum by Cole-Cole model."""
fCC = ColeColeComplex(f)
tLog = pg.RTransLog()
fCC.region(0).setStartValue(max(amp))
if mstart is None: # compute from amplitude decay
mstart = 1. - min(amp) / max(amp)
fCC.region(1).setParameters(mstart, 0, 1) # m (start,lower,upper)
fCC.region(2).setParameters(*taupar) # tau
fCC.region(3).setParameters(*cpar) # c
data = pg.cat(amp, phi)
ICC = pg.RInversion(data, fCC, False) # set up inversion class
ICC.setTransModel(tLog)
error = pg.cat(eRho * amp, pg.RVector(len(f), ePhi))
ICC.setAbsoluteError(error) # perr + ePhi/data)
ICC.setLambda(lam) # start with large damping and cool later
ICC.setMarquardtScheme(0.8) # lower lambda by 20%/it., no stop chi=1
model = np.asarray(ICC.run()) # run inversion
ICC.echoStatus()
response = np.asarray(ICC.response())
return model, response[:len(f)], response[len(f):]
def setData(self, data):
"""TODO."""
if isinstance(data, list):
if len(data) == len(self.managers):
self.tD.clear()
self.dataVals.clear()
self.dataErrs.clear()
self.fop.setData(data)
for i, mgr in enumerate(self.managers):
t = mgr.tD
self.tD.add(t, data[i].size())
self.dataVals = pg.cat(self.dataVals,
data[i](mgr.dataToken()))
if mgr.errIsAbsolute:
self.dataErrs = pg.cat(
self.dataErrs,
data[i]('err') / data[i](mgr.dataToken()))
else:
self.dataErrs = pg.cat(self.dataErrs, data[i]('err'))
self.data = data
self.inv.setTransData(self.tD)
self.inv.setTransModel(self.tM)
else:
raise BaseException("To few datacontainer given")
def block1dInversionNew(self, nlay=2, lam=100.0, verbose=True):
"""invert all data together by a 1D model (more general solution)"""
data, error = pg.RVector(), pg.RVector()
for mrs in self.mrs:
data = pg.cat(data, mrs.data)
error = pg.cat(error, mrs.error)
f = JointMRSModelling(self.mrs, nlay)
mrsobj = self.mrs[0]
for i in range(3):
f.region(i).setParameters(mrsobj.startval[i], mrsobj.lowerBound[i], mrsobj.upperBound[i])
# f.region(0).setStartValue(mrsobj.startval[0])
# f.region(1).setStartValue(mrsobj.startval[1])
# f.region(2).setStartValue(mrsobj.startval[2])
# # Model transformation instances saved in class
# transTH = pg.RTransLogLU(mrsobj.lowerBound[0], mrsobj.upperBound[0])
# transWC = pg.RTransLogLU(mrsobj.lowerBound[1], mrsobj.upperBound[1])
# transT2 = pg.RTransLogLU(mrsobj.lowerBound[2], mrsobj.upperBound[2])
# f.region(0).setTransModel(transTH)
# f.region(1).setTransModel(transWC)
# f.region(2).setTransModel(transT2)
INV = pg.RInversion(data, f, verbose)
INV.setLambda(lam)
INV.setMarquardtScheme(0.8)
INV.stopAtChi1(False) # now in MarquardtScheme
INV.setDeltaPhiAbortPercent(0.5)
INV.setAbsoluteError(error)
model = INV.run()
return model
def setData(self, data):
"""
"""
if type(data) is list:
if len(data) == len(self.managers):
self.tD.clear()
self.dataVals.clear()
self.dataErrs.clear()
self.fop.setData(data)
for i, mgr in enumerate(self.managers):
t = mgr.tD
self.tD.add(t, data[i].size())
self.dataVals = pg.cat(self.dataVals, data[i](mgr.dataToken()))
if mgr.errIsAbsolute:
self.dataErrs = pg.cat(self.dataErrs, data[i]('err')/data[i](mgr.dataToken()))
else:
self.dataErrs = pg.cat(self.dataErrs, data[i]('err'))
self.data = data
self.inv.setTransData(self.tD)
self.inv.setTransModel(self.tM)
else:
raise BaseException("To few datacontainer given")
def runEA(self,nlay=None,type='GA',pop_size=100,max_evaluations=10000,**kwargs):
import inspyred
import random
def mygenerate( random, args ):
""" generate a random vector of model size """
return [random.random() for i in range( nlay*3 - 1 )]
def my_observer(population, num_generations, num_evaluations, args):
best = min(population)
print('{0:6} -- {1}'.format(num_generations,best.fitness))
@inspyred.ec.evaluators.evaluator
def datafit( individual, args ):
misfit = (self.data-self.f.response(self.genMod(individual)))/self.error
return np.mean(misfit**2)
# prepare forward operator
if self.f is None or (nlay is not None and nlay is not self.nlay): self.createFOP(nlay)
lowerBound = pg.cat( pg.cat( pg.RVector(self.nlay-1,self.lowerBound[0]),
pg.RVector(self.nlay,self.lowerBound[1])), pg.RVector(self.nlay,self.lowerBound[2]) )
upperBound = pg.cat( pg.cat( pg.RVector(self.nlay-1,self.upperBound[0]),
pg.RVector(self.nlay,self.upperBound[1])), pg.RVector(self.nlay,self.upperBound[2]) )
if self.logpar:
self.lLB, self.lUB = pg.log(lowerBound), pg.log(upperBound) # ready mapping functions
else:
self.lLB, self.lUB = lowerBound, upperBound
# self.f = MRS1dBlockQTModelling(nlay, self.K, self.z, self.t)
# setup random generator
rand = random.Random()
rand.seed(int(time.time()))
# choose among different evolution algorithms
if type == 'GA':
ea = inspyred.ec.GA(rand)
ea.variator = [inspyred.ec.variators.blend_crossover, inspyred.ec.variators.gaussian_mutation]
ea.selector = inspyred.ec.selectors.tournament_selection
ea.replacer = inspyred.ec.replacers.generational_replacement
if type == 'SA': ea = inspyred.ec.SA(rand)
if type == 'DEA': ea = inspyred.ec.DEA(rand)
if type == 'PSO': ea = inspyred.swarm.PSO(rand)
if type == 'ACS': ea = inspyred.swarm.ACS(rand,[])
if type == 'ES':
ea = inspyred.ec.ES(rand)
ea.terminator = [inspyred.ec.terminators.evaluation_termination,
inspyred.ec.terminators.diversity_termination]
else:
ea.terminator = inspyred.ec.terminators.evaluation_termination
#ea.observer = my_observer
ea.observer = [inspyred.ec.observers.stats_observer, inspyred.ec.observers.file_observer]
self.pop = ea.evolve(evaluator=datafit,generator=mygenerate,maximize=False,
pop_size=pop_size,max_evaluations=max_evaluations,num_elites=1,
bounder=inspyred.ec.Bounder(0.,1.),**kwargs)
self.pop.sort(reverse=True)
self.fits=[ind.fitness for ind in self.pop]
def test_VESManager(showProgress=False):
"""
run from console with: python -c 'import pygimli.physics.ert.ves as pg; pg.test_VESManager(1)'
"""
thicks = [2., 10.]
res = [100., 5., 30]
phi = [0., 20., 0.]
# model fails
thicks = [2., 6., 10.]
res = [100., 500., 20., 800.]
phi = [0., 20., 50., 0]
synthModel = pg.cat(thicks, res)
ab2 = np.logspace(np.log10(1.5), np.log10(100.), 25)
mgr = VESManager(verbose=True, debug=False)
mgr.fop.setRegionProperties(0, limits=[0.5, 200], trans='log')
ra, err = mgr.simulate(synthModel, ab2=ab2, mn2=1.0, noiseLevel=0.01)
mgr.exportData('synth.ves', ra, err)
mgr.invert(ra, err, nLayer=4, lam=100,
showProgress=showProgress)
pg.wait()
### Test -- reinit with new parameter count
mgr.invert(ra, err, nLayer=3,
showProgress=showProgress)
#np.testing.assert_array_less(mgr.inv.inv.chi2(), 1)
### Test -- reinit with new data basis
ab2 = np.logspace(np.log10(1.5), np.log10(50.), 10)
ra, err = mgr.simulate(synthModel, ab2=ab2, mn2=1.0, noiseLevel=0.01)
mgr2 = VESManager(verbose=False, debug=False)
mgr2.invert(ra, err, nLayer=3, ab2=ab2, mn2=1.0,
showProgress=showProgress)
#np.testing.assert_array_less(mgr2.inv.inv.chi2(), 1)
pg.wait()
### Test -- reinit with complex resistivies
mgr.complex = True
synthModel = pg.cat(synthModel, phi)
ra, err = mgr.simulate(synthModel, ab2=ab2, mn2=1.0, noiseLevel=0.01)
mgr.exportData('synthc.ves', ra, err)
mgr.invert(ra, err,
showProgress=showProgress)
np.testing.assert_array_less(mgr.inv.inv.chi2(), 1)
if showProgress:
print("test done");
pg.wait()
def test_VESManager(showProgress=False):
"""
run from console with: python -c 'import pygimli.physics.ert.ves as pg; pg.test_VESManager(1)'
"""
thicks = [2., 10.]
res = [100., 5., 30]
phi = [0., 20., 0.]
# model fails
thicks = [2., 6., 10.]
res = [100., 500., 20., 800.]
phi = [0., 20., 50., 0]
synthModel = pg.cat(thicks, res)
ab2 = np.logspace(np.log10(1.5), np.log10(100.), 25)
mgr = VESManager(verbose=True, debug=False)
mgr.fop.setRegionProperties(0, limits=[0.5, 200], trans='log')
ra, err = mgr.simulate(synthModel, ab2=ab2, mn2=1.0, noiseLevel=0.01)
mgr.exportData('synth.ves', ra, err)
mgr.invert(ra, err, nLayer=4, lam=100,
showProgress=showProgress)
pg.wait()
### Test -- reinit with new parameter count
mgr.invert(ra, err, nLayer=3,
showProgress=showProgress)
#np.testing.assert_array_less(mgr.inv.inv.chi2(), 1)
### Test -- reinit with new data basis
ab2 = np.logspace(np.log10(1.5), np.log10(50.), 10)
ra, err = mgr.simulate(synthModel, ab2=ab2, mn2=1.0, noiseLevel=0.01)
mgr2 = VESManager(verbose=False, debug=False)
mgr2.invert(ra, err, nLayer=3, ab2=ab2, mn2=1.0,
showProgress=showProgress)
#np.testing.assert_array_less(mgr2.inv.inv.chi2(), 1)
pg.wait()
### Test -- reinit with complex resistivies
mgr.complex = True
synthModel = pg.cat(synthModel, phi)
ra, err = mgr.simulate(synthModel, ab2=ab2, mn2=1.0, noiseLevel=0.01)
mgr.exportData('synthc.ves', ra, err)
mgr.invert(ra, err,
showProgress=showProgress)
np.testing.assert_array_less(mgr.inv.inv.chi2(), 1)
if showProgress:
print("test done");
pg.wait()
def setData(self, data):
self.fop.setData(data)
self.dataVals = pg.Vector(0)
self.dataErrs = pg.Vector(0)
for i, mgr in enumerate(self.mgrs):
self.tD.add(mgr.tD, data[i].size())
self.dataVals = pg.cat(self.dataVals, mgr.dataVals(data[i]))
self.dataErrs = pg.cat(self.dataErrs, mgr.relErrorVals(data[i]))
self.inv.setTransData(self.tD)
def setData(self, data):
self.fop.setData(data)
self.dataVals = pg.Vector(0)
self.dataErrs = pg.Vector(0)
for i, mgr in enumerate(self.mgrs):
self.tD.add(mgr.tD, data[i].size())
self.dataVals = pg.cat(self.dataVals, mgr.dataVals(data[i]))
self.dataErrs = pg.cat(self.dataErrs, mgr.relErrorVals(data[i]))
self.inv.setTransData(self.tD)
def loadData(self, fileName, **kwargs):
mat = np.loadtxt(fileName)
if len(mat[0]) == 4:
self.fop.setDataBasis(ab2=mat[:, 0], mn2=mat[:, 1])
return mat.T
if len(mat[0]) == 6:
self.complex = True
self.fop.setDataBasis(ab2=mat[:, 0], mn2=mat[:, 1])
return mat[:, 0], mat[:, 1], np.array(pg.cat(
mat[:, 2], mat[:, 4])), np.array(pg.cat(mat[:, 3], mat[:, 5]))
def loadData(self, fileName, **kwargs):
""" Load simple data matrix
"""
mat = np.loadtxt(fileName)
if len(mat[0]) == 4:
self.fop.setDataSpace(ab2=mat[:, 0], mn2=mat[:, 1])
return mat.T
if len(mat[0]) == 6:
self.complex = True
self.fop.setDataSpace(ab2=mat[:, 0], mn2=mat[:, 1])
return (mat[:, 0], mat[:,
1], np.array(pg.cat(mat[:, 2], mat[:, 4])),
np.array(pg.cat(mat[:, 3], mat[:, 5])))
def fitCCCC(f,
amp,
phi,
error=0.01,
lam=10.,
taupar=(1e-2, 1e-5, 100),
cpar=(0.25, 0, 1),
mpar=(0, 0, 1)):
"""Fit complex spectrum by Cole-Cole model based on sigma."""
fCC = ColeColeComplexSigma(f)
tLog = pg.RTransLog()
fCC.region(0).setStartValue(1. / max(amp))
if mpar[0] == 0:
mpar[0] = 1. - min(amp) / max(amp)
fCC.region(1).setParameters(*mpar) # m (start,lower,upper)
fCC.region(2).setParameters(*taupar) # tau
fCC.region(3).setParameters(*cpar) # c
data = pg.cat(1. / amp * np.cos(phi), 1. / amp * np.sin(phi))
ICC = pg.RInversion(data, fCC, False) # set up inversion class
ICC.setTransModel(tLog)
ICC.setAbsoluteError(data * error +
max(data) * 0.0001) # perr + ePhi/data)
ICC.setLambda(lam) # start with large damping and cool later
ICC.setMarquardtScheme(0.8) # lower lambda by 20%/it., no stop chi=1
model = np.asarray(ICC.run()) # run inversion
ICC.echoStatus()
response = np.asarray(ICC.response())
rRe, rIm = response[:len(f)], response[len(f):]
rAmp = 1. / np.sqrt(rRe**2 + rIm**2)
return model, rAmp, np.arctan(rIm / rRe)
def createERTData(elecs, schemeName='none', **kwargs):
""" Simple data creator for compatibility (advanced version in BERT).
Parameters
----------
sounding : bool [False]
Create a 1D VES Schlumberger configuration.
elecs need to be an array with elecs[0] = mn/2 and elecs[1:] = ab/2.
"""
if kwargs.pop('sounding', False):
data = pg.DataContainerERT()
data.setSensors(pg.cat(-elecs[::-1], elecs))
nElecs = len(elecs)
for i in range(nElecs - 1):
data.createFourPointData(i, i, 2 * nElecs - i - 1, nElecs - 1,
nElecs)
return data
if schemeName != "dd":
import pybert as pb # that's bad!!! TODO: remove pybert deps
return pb.createData(elecs, schemeName, **kwargs)
isClosed = kwargs.pop('closed', False)
data = pg.DataContainerERT()
data.setSensors(elecs)
nElecs = len(elecs)
a = []
b = []
m = []
n = []
eb = 0
for i in range(nElecs):
for j in range(eb + 2, nElecs):
ea = i
eb = ea + 1
em = j
en = em + 1
if isClosed:
en = en % nElecs
if en < nElecs and en != ea:
a.append(ea)
b.append(eb)
m.append(em)
n.append(en)
data.resize(len(a))
data.add('a', a)
data.add('b', b)
data.add('m', m)
data.add('n', n)
data.set('valid', np.ones(len(a)))
return data
def response_mt(self, model, i=0):
model = np.nan_to_num(model)
fw, fi, fa, fr = self.fractions(model)
rho = self.fpm.rho(fw, fi, fa, fr)
s = self.fpm.slowness(fw, fi, fa, fr)
print("=" * 30)
print(" Min. | Max.")
print("-" * 30)
print(" Water: %.2f | %.2f" % (np.min(fw), np.max(fw)))
print(" Ice: %.2f | %.2f" % (np.min(fi), np.max(fi)))
print(" Air: %.2f | %.2f" % (np.min(fa), np.max(fa)))
print(" Rock: %.2f | %.2f" % (np.min(fr), np.max(fr)))
print("-" * 30)
print(" SUM: %.2f | %.2f" % (np.min(fa + fw + fi + fr),
np.max(fa + fw + fi + fr)))
print("=" * 30)
print(" Rho: %.2e | %.2e" % (np.min(rho), np.max(rho)))
print(" Vel: %d | %d" % (np.min(1 / s), np.max(1 / s)))
t = self.RST.fop.response(s)
rhoa = self.ERT.fop.response(rho)
return pg.cat(t, rhoa)
def drawSeismogramm(axes, mesh, u, ids, dt, i=None):
r"""Extract and show time series from wave field
Parameters
----------
"""
axes.set_xlim(-20., 20.)
axes.set_ylim(0., dt*len(u)*1000)
axes.set_aspect(1)
axes.set_ylabel('Time in ms')
if i is None:
i = len(u)-1
t = np.linspace(0, i*dt*1000, i+1)
for iw, n in enumerate(ids):
pos = mesh.node(n).pos()
print(pos)
axes.plot(pos[0], 0.05, '^', color='black')
trace = pg.cat(pg.RVector(0), u[:(i+1), n])
# print(i+1, n)
# print(trace, (max(pg.abs(trace))))
# if max(pg.abs(trace)) > 1e-8:
trace *= np.exp(0.5*t)
trace /= (max(pg.abs(trace))*1.5)
drawWiggle(axes, trace, t=t, xoffset=pos[0])
axes.invert_yaxis()
def drawModel(self, ax, model):
nLay = (len(model)+1) // 3
super(VESCModelling, self).drawModel(ax, model[0:nLay*2-1])
pg.mplviewer.drawModel1D(ax=ax,
model=pg.cat(model[0:nLay-1], model[nLay*2-1::]),
plot='plot',
xlabel='Phase [mrad]')
def response(self, par):
"""Response vector as combined in-phase and out-phase data."""
thk = np.asarray(par[:self.nlay-1], dtype=np.float)
res = np.asarray(par[self.nlay-1:2*self.nlay-1], dtype=np.float)
mur = np.asarray(par[2*self.nlay-1:3*self.nlay-1], dtype=np.float) + 1
ip, op = self.vmd_hem(self.height, rho=res, d=thk, mur=mur)
return pg.cat(ip, op)
def drawModel(self, ax, model):
nLay = (len(model)+1) // 3
super(VESCModelling, self).drawModel(ax, model[0:nLay*2-1])
pg.mplviewer.drawModel1D(ax=ax,
model=pg.cat(model[0:nLay-1], model[nLay*2-1::]),
plot='plot',
xlabel='Phase [mrad]')
def checkErrors(self, err, dataVals):
"""Return relative error. Default we assume 'err' are relative vales.
"""
if isinstance(err, pg.DataContainer):
rae = None
if not err.allNonZero('err'):
pg.warn(
"Datacontainer have no 'err' values. "
"Fallback of 1mV + 3% using ERTManager.estimateError(...) "
)
rae = self.estimateError(err,
absoluteError=0.001,
relativeError=0.03)
else:
rae = err['err']
if self.fop.complex():
ipe = None
if err.haveData('iperr'):
amp, phi = pg.utils.toPolar(dataVals)
# assuming ipErr are absolute dPhi in mrad
ipe = err['iperr'] / abs((phi * 1000))
else:
pg.warn("Datacontainer have no 'iperr' values. "
"Fallback set to 0.01")
ipe = np.ones(err.size()) * 0.01
# pg._y("err", min(rae), max(rae), rae)
# pg._y("iperr", min(ipe), max(ipe), ipe)
return pg.cat(rae, ipe)
return rae
def drawSeismogramm(axes, mesh, u, ids, dt, i=None):
r"""Extract and show time series from wave field
Parameters
----------
"""
axes.set_xlim(-20., 20.)
axes.set_ylim(0., dt * len(u) * 1000)
axes.set_aspect(1)
axes.set_ylabel('Time in ms')
if i is None:
i = len(u) - 1
t = np.linspace(0, i * dt * 1000, i + 1)
for iw, n in enumerate(ids):
pos = mesh.node(n).pos()
print(pos)
axes.plot(pos[0], 0.05, '^', color='black')
trace = pg.cat(pg.RVector(0), u[:(i + 1), n])
# print(i+1, n)
# print(trace, (max(pg.abs(trace))))
# if max(pg.abs(trace)) > 1e-8:
trace *= np.exp(0.5 * t)
trace /= (max(pg.abs(trace)) * 1.5)
drawWiggle(axes, trace, t=t, xoffset=pos[0])
axes.invert_yaxis()
def __init__(self,
fop,
data,
error,
startmodel,
lam=20,
beta=10000,
maxIter=50,
fwmin=0,
fwmax=1,
fimin=0,
fimax=1,
famin=0,
famax=1,
frmin=0,
frmax=1):
LSQRInversion.__init__(self, data, fop, verbose=True, dosave=True)
self._error = pg.Vector(error)
# Set data transformations
self.logtrans = pg.trans.TransLog()
self.trans = pg.trans.Trans()
self.dcumtrans = pg.trans.TransCumulative()
self.dcumtrans.add(self.trans, fop.RST.data.size())
self.dcumtrans.add(self.logtrans, fop.ERT.data.size())
self.setTransData(self.dcumtrans)
# Set model transformation
n = fop.cellCount
self.mcumtrans = pg.trans.TransCumulative()
self.transforms = []
phase_limits = [[fwmin, fwmax], [fimin, fimax], [famin, famax],
[frmin, frmax]]
for i, (lower, upper) in enumerate(phase_limits):
if lower == 0:
lower = 0.001
self.transforms.append(pg.trans.TransLogLU(lower, upper))
self.mcumtrans.add(self.transforms[i], n)
self.setTransModel(self.mcumtrans)
# Set error
self.setRelativeError(self._error)
# Set some defaults
# Set maximum number of iterations (default is 20)
self.setMaxIter(maxIter)
# Regularization strength
self.setLambda(lam)
self.setDeltaPhiAbortPercent(0.25)
# fop = self.forwardOperator()
fop.createConstraints() # Important!
ones = pg.Vector(fop._I.rows(), 1.0)
phiVec = pg.cat(ones, startmodel)
self.setParameterConstraints(fop._G, phiVec, beta)
self.setModel(startmodel)
def inv2D(self,
nlay,
lam=100.,
resL=1.,
resU=1000.,
thkL=1.,
thkU=100.,
minErr=1.0):
"""2d LCI inversion class."""
if isinstance(nlay, int):
modVec = pg.RVector(nlay * 2 - 1, 30.)
cType = 0 # no reference model
else:
modVec = nlay
cType = 10 # use this as referencemodel
nlay = (len(modVec) + 1) / 2
# init forward operator
self.f2d = self.FOP2d(nlay)
# transformations
self.transData = pg.RTrans()
self.transThk = pg.RTransLogLU(thkL, thkU)
self.transRes = pg.RTransLogLU(resL, resU)
for i in range(nlay - 1):
self.f2d.region(i).setTransModel(self.transThk)
for i in range(nlay - 1, nlay * 2 - 1):
self.f2d.region(i).setTransModel(self.transRes)
# set constraints
self.f2d.region(0).setConstraintType(cType)
self.f2d.region(1).setConstraintType(cType)
# collect data vector
datvec = pg.RVector(0)
for i in range(len(self.x)):
datvec = pg.cat(datvec, self.datavec(i))
# collect error vector
if self.ERR is None:
error = 1.0
else:
error = []
for i in range(len(self.x)):
err = np.maximum(self.ERR[i][self.activeFreq] * 0.701, minErr)
error.extend(err)
# generate starting model by repetition
model = pg.asvector(np.repeat(modVec, len(self.x)))
INV = pg.RInversion(datvec, self.f2d, self.transData)
INV.setAbsoluteError(error)
INV.setLambda(lam)
INV.setModel(model)
INV.setReferenceModel(model)
return INV
def response(self, model):
""" cut-together forward responses of all soundings """
modA = np.reshape(model, (self.nx, self.nlay*2-1))
resp = pg.RVector(0)
for i, modi in enumerate(modA):
resp = pg.cat(resp, self.FOP1d[i].response(modi))
return resp
def response(self, model):
""" yields forward model response """
modA = np.asarray(model).reshape((self.nlay * 2 - 1, self.nx)).T
resp = pg.RVector(0)
for modi in modA:
resp = pg.cat(resp, self.FOP1d.response(modi))
return resp
def response(self, model):
""" cut-together forward responses of all soundings """
modA = np.asarray(model).reshape((self.nlay * 2 - 1, self.nx)).T
resp = pg.RVector(0)
for modi in modA:
resp = pg.cat(resp, self.FOP.response(modi))
return resp
def response(self, model):
"""Response as pasted forward responses from all soundings."""
modA = np.reshape(model, (self.nx, self.nlay*2-1))
resp = pg.RVector(0)
for i, modi in enumerate(modA):
resp = pg.cat(resp, self.FOP1d[i].response(modi))
return resp
def block1dInversion(self,
nlay=2,
lam=100.,
show=False,
verbose=True,
uncertainty=False):
"""Invert all data together by a 1D model (more general solution)."""
data, error = pg.Vector(), pg.Vector()
for mrs in self.mrs:
data = pg.cat(data, mrs.data)
error = pg.cat(error, np.real(mrs.error))
# f = JointMRSModelling(self.mrs, nlay)
f = MultiFOP(self.mrs, nlay)
mrsobj = self.mrs[0]
for i in range(3):
f.region(i).setParameters(mrsobj.startval[i], mrsobj.lowerBound[i],
mrsobj.upperBound[i])
INV = pg.Inversion(data, f, verbose)
INV.setLambda(lam)
INV.setMarquardtScheme(0.8)
# INV.stopAtChi1(False) # should be already in MarquardtScheme
INV.setDeltaPhiAbortPercent(0.5)
INV.setAbsoluteError(error)
model = INV.run()
m0 = self.mrs[0]
m0.model = np.asarray(model)
if uncertainty:
from pygimli.utils import iterateBounds
m0.modelL, m0.modelU = iterateBounds(INV,
dchi2=INV.chi2() / 2,
change=1.2)
if show:
self.show1dModel()
# %% fill up 2D model (for display only)
self.WMOD, self.TMOD = [], []
thk = model[0:nlay - 1]
wc = model[nlay - 1:2 * nlay - 1]
t2 = model[2 * nlay - 1:3 * nlay - 1]
for i in range(len(self.mrs)):
self.WMOD.append(np.hstack((thk, wc)))
self.TMOD.append(np.hstack((thk, t2)))
return model
def response(self, par):
ip, op = self.vmd_hem(self.height,
np.asarray(par)[self.nlay-1:self.nlay*2-1],
np.asarray(par)[:self.nlay-1])
# ip, op = self.vmd_hem(self.height,
# np.asarray(par(self.nlay-1, self.nlay*2-1)),
# np.asarray(par(0, self.nlay-1)))
return pg.cat(ip, op)
def createDefaultStartModel(self):
"""
"""
res = pb.getComplexData(self.data())
parCount = self.regionManager().parameterCount()
re = pg.Vector(parCount, pg.mean(pg.math.real(res)))
im = pg.Vector(parCount, -pg.mean(pg.math.imag(res)))
return pg.cat(re, im)
def createDefaultStartModel(self):
"""
"""
res = pb.getComplexData(self.data())
parCount = self.regionManager().parameterCount()
re = pg.RVector(parCount, pg.mean(pg.real(res)))
im = pg.RVector(parCount, -pg.mean(pg.imag(res)))
return pg.cat(re, im)
def squeezeComplex(z, polar=False, conj=False):
"""Squeeze complex valued array into [real, imag] or [amp, phase(rad)]"""
if isinstance(z, (pg.matrix.CSparseMapMatrix, pg.matrix.CSparseMatrix,
pg.matrix.CMatrix)):
return toRealMatrix(z, conj=conj)
if isComplex(z):
vals = np.array(z)
if conj:
vals = np.conj(vals)
if polar is True:
vals = pg.cat(*toPolar(z))
else:
vals = pg.cat(vals.real, vals.imag)
return vals
return z
def response(self, model):
"""Cut together forward responses of all soundings."""
modA = np.reshape(model, (self.nx, self.np))
resp = pg.RVector(0)
for i, modi in enumerate(modA):
resp = pg.cat(resp, self.FOP1d[i].response(modi))
return resp
def response(self, par):
"""Response vector as combined in-phase and out-phase data."""
thk = np.asarray(par[:self.nlay - 1], dtype=np.float)
res = np.asarray(par[self.nlay - 1:2 * self.nlay - 1], dtype=np.float)
mur = np.asarray(par[2 * self.nlay - 1:3 * self.nlay - 1],
dtype=np.float) + 1
ip, op = self.vmd_hem(self.height, rho=res, d=thk, mur=mur)
return pg.cat(ip, op)
def response(self, model):
"""Response as pasted forward responses from all soundings."""
modA = np.reshape(model, (self.nx, self.nlay * 2 - 1))
resp = pg.RVector(0)
for i, modi in enumerate(modA):
resp = pg.cat(resp, self.FOP1d[i].response(modi))
return resp
def response(self, model):
"""Cut together forward responses of all soundings."""
modA = np.asarray(model).reshape((self.nlay * 2 - 1, self.nx)).T
resp = pg.Vector(0)
for modi in modA:
resp = pg.cat(resp, self.FOP.response(modi))
return resp
def response(self, model):
"""Yields forward model response."""
modA = np.asarray(model).reshape((self.nlay * 2 - 1, self.nx)).T
resp = pg.Vector(0)
for modi in modA:
resp = pg.cat(resp, self.FOP1d.response(modi))
return resp
def getIntegrationWeights(self, rMin, rMax):
"""Retrieve Gauss-Legende/Laguerre integration weights."""
nGauLegendre = max(int((6.0 * np.log10(rMax / rMin))), 4)
nGauLaguerre = 4
k = pg.RVector()
w = pg.RVector()
k0 = 1.0 / (2.0 * rMin)
pg.GaussLegendre(0.0, 1.0, nGauLegendre, k, w)
kLeg = k0 * k * k
wLeg = 2.0 * k0 * k * w / np.pi
pg.GaussLaguerre(nGauLaguerre, k, w)
kLag = k0 * (k + 1.0)
wLag = k0 * np.exp(k) * w / np.pi
return pg.cat(kLeg, kLag), pg.cat(wLeg, wLag)
def createInv(self, nlay, lam=100., errVES=3, verbose=True):
"""Create Marquardt type inversion instance with data transformatio"""
self.createFOP(nlay)
self.tMod = pg.RTransLog()
self.tMRS = pg.RTrans()
self.tVES = pg.RTransLog()
self.transData = pg.RTransCumulative()
self.transData.push_back(self.tMRS, len(self.data))
self.transData.push_back(self.tVES, len(self.rhoa))
data = pg.cat(self.data, self.rhoa)
self.INV = pg.RInversion(data, self.f, self.transData, verbose)
self.INV.setLambda(lam)
self.INV.setMarquardtScheme(0.8)
self.INV.stopAtChi1(False) # now in MarquardtScheme
self.INV.setDeltaPhiAbortPercent(0.5)
# self.INV.setMaxIter(1)
error = pg.cat(self.error, self.rhoa * errVES / 100.)
self.INV.setAbsoluteError(error)
def loadData(self, fileName, **kwargs):
mat = np.loadtxt(fileName)
if len(mat[0]) == 4:
self.fop.setDataBasis(ab2=mat[:,0], mn2=mat[:,1])
return mat.T
if len(mat[0]) == 6:
self.complex = True
self.fop.setDataBasis(ab2=mat[:,0], mn2=mat[:,1])
return mat[:,0], mat[:,1], np.array(pg.cat(mat[:,2], mat[:,4])), np.array(pg.cat(mat[:,3], mat[:,5]))
def createInv(self,nlay,lam=100.,errVES=3,verbose=True):
""" create marquardt type inversion instance with data transformation """
self.createFOP(nlay)
self.tMod = pg.RTransLog()
self.tMRS = pg.RTrans()
self.tVES = pg.RTransLog()
self.transData = pg.RTransCumulative()
self.transData.push_back( self.tMRS, len(self.data) )
self.transData.push_back( self.tVES, len(self.rhoa) )
data = pg.cat(self.data, self.rhoa)
self.INV = pg.RInversion(data, self.f, self.transData, verbose)
self.INV.setLambda(lam)
self.INV.setMarquardtScheme(0.8)
self.INV.stopAtChi1(False) # now in MarquardtScheme
self.INV.setDeltaPhiAbortPercent(0.5)
# self.INV.setMaxIter(1)
error = pg.cat(self.error, self.rhoa*errVES/100.)
self.INV.setAbsoluteError(error)
def genMods( individual ):
""" generate MRS and VES models from unit vector """
model = pg.asvector( individual ) * ( self.lUB - self.lLB ) + self.lLB
if self.logpar:
model = pg.exp( model )
modMRS = model(0,nlay*3-1)
modVES = pg.cat(model(0,nlay-1),model(nlay*3-1,nlay*4-1))
return modMRS, modVES
def response(self, model):
"""
"""
modA = np.asarray(model).reshape((self.nlay_*2-1,self.nx_)).T
resp = pg.RVector(0)
for modi in modA:
resp = pg.cat(resp, self.FOP_.response(modi))
return resp
def response(self, par):
"""Compute response vector by pasting in-phase and out-phase data."""
ip, op = self.vmd_hem(self.height,
np.asarray(par)[self.nlay-1:self.nlay*2-1],
np.asarray(par)[:self.nlay-1])
# ip, op = self.vmd_hem(self.height,
# np.asarray(par(self.nlay-1, self.nlay*2-1)),
# np.asarray(par(0, self.nlay-1)))
return pg.cat(ip, op)
def response(self, par):
"""Compute response vector by pasting in-phase and out-phase data."""
ip, op = self.vmd_hem(self.height,
np.asarray(par)[self.nlay - 1:self.nlay * 2 - 1],
np.asarray(par)[:self.nlay - 1])
# ip, op = self.vmd_hem(self.height,
# np.asarray(par(self.nlay-1, self.nlay*2-1)),
# np.asarray(par(0, self.nlay-1)))
return pg.cat(ip, op)
def getIntegrationWeights(self, rMin, rMax):
"""Retrieve Gauss-Legende/Laguerre integration weights."""
nGauLegendre = max(int((6.0 * np.log10(rMax / rMin))), 4)
nGauLaguerre = 4
k = pg.RVector()
w = pg.RVector()
k0 = 1.0 / (2.0 * rMin)
pg.GaussLegendre(0.0, 1.0, nGauLegendre, k, w)
kLeg = k0 * k * k
wLeg = 2.0 * k0 * k * w / np.pi
pg.GaussLaguerre(nGauLaguerre, k, w)
kLag = k0 * (k + 1.0)
wLag = k0 * np.exp(k) * w / np.pi
return pg.cat(kLeg, kLag), pg.cat(wLeg, wLag)
def inv2D(self, nlay, lam=100., resL=1., resU=1000., thkL=1.,
thkU=100., minErr=1.0):
"""
2d LCI inversion class
"""
if isinstance(nlay, int):
modVec = pg.RVector(nlay * 2 - 1, 30.)
cType = 0 # no reference model
else:
modVec = nlay
cType = 10 # use this as referencemodel
nlay = (len(modVec) + 1) / 2
# init forward operator
self.f2d = self.FOP2d(nlay)
# transformations
self.tD = pg.RTrans()
self.tThk = pg.RTransLogLU(thkL, thkU)
self.tRes = pg.RTransLogLU(resL, resU)
for i in range(nlay - 1):
self.f2d.region(i).setTransModel(self.tThk)
for i in range(nlay - 1, nlay * 2 - 1):
self.f2d.region(i).setTransModel(self.tRes)
# set constraints
self.f2d.region(0).setConstraintType(cType)
self.f2d.region(1).setConstraintType(cType)
# collect data vector
datvec = pg.RVector(0)
for i in range(len(self.x)):
datvec = pg.cat(datvec, self.datavec(i))
# collect error vector
if self.ERR is None:
error = 1.0
else:
error = []
for i in range(len(self.x)):
err = np.maximum(self.ERR[i][self.activeFreq] * 0.701, minErr)
error.extend(err)
# generate starting model by repetition
model = pg.asvector(np.repeat(modVec, len(self.x)))
INV = pg.RInversion(datvec, self.f2d, self.tD)
INV.setAbsoluteError(error)
INV.setLambda(lam)
INV.setModel(model)
INV.setReferenceModel(model)
return INV
def fitDebyeModel(self, ePhi=0.001, lam=1e3, lamFactor=0.8,
mint=None, maxt=None, nt=None, new=True,
showFit=False, cType=1):
"""fit a (smooth) continuous Debye model (Debye decomposition)"""
nf = len(self.f)
if mint is None:
mint = .1 / max(self.f)
if maxt is None:
maxt = .5 / min(self.f)
if nt is None:
nt = nf*2
# %% discretize tau, setup DD and perform DD inversion
self.tau = np.logspace(log10(mint), log10(maxt), nt)
phi = self.phi
tLin, tLog, tM = pg.RTrans(), pg.RTransLog(), pg.RTransLogLU(0., 1.)
if new:
reNorm, imNorm = self.zNorm()
fDD = DebyeComplex(self.f, self.tau)
Znorm = pg.cat(reNorm, imNorm)
IDD = pg.RInversion(Znorm, fDD, tLog, tM, False)
IDD.setAbsoluteError(max(Znorm)*0.003+0.01)
else:
fDD = DebyePhi(self.f, self.tau)
IDD = pg.RInversion(phi, fDD, tLin, tM, True)
IDD.setAbsoluteError(ePhi) # 1 mrad
fDD.regionManager().setConstraintType(cType)
IDD.stopAtChi1(False)
startModel = pg.RVector(nt, 0.01)
IDD.setModel(startModel)
IDD.setLambda(lam)
IDD.setLambdaFactor(lamFactor)
self.mDD = IDD.run()
IDD.echoStatus()
if new:
resp = np.array(IDD.response())
respRe = resp[:nf]
respIm = resp[nf:]
respC = ((1 - respRe) + respIm * 1j) * max(self.amp)
self.phiDD = np.angle(respC)
self.ampDD = np.abs(respC)
if showFit:
fig, ax = self.showData(znorm=True, nrows=3)
ax[0].plot(self.f, respRe, 'r-')
ax[1].plot(self.f, respIm, 'r-')
ax[2].semilogx(self.tau, self.mDD, 'r-')
ax[2].set_xlim(max(self.tau), min(self.tau))
ax[2].set_ylim(0., max(self.mDD))
ax[2].grid(True)
ax[2].set_xlabel(r'$\tau$ [s]')
ax[2].set_xlabel('$m$ [-]')
else:
self.phiDD = IDD.response()
if showFit:
fig, ax = self.showData(nrows=3)
ax[2].semilogx(self.tau, self.mDD, 'r-')
def blockLCInversion(self, nlay=2, startModel=None, **kwargs):
"""Laterally constrained (piece-wise 1D) block inversion."""
data, error, self.nData = pg.Vector(), pg.Vector(), []
for mrs in self.mrs:
data = pg.cat(data, mrs.data)
error = pg.cat(error, mrs.error)
self.nData.append(len(mrs.data))
fop = MRSLCI(self.mrs, nlay=nlay)
fop.region(0).setZWeight(kwargs.pop('zWeight', 0))
fop.region(0).setConstraintType(kwargs.pop('cType', 1))
transData, transMod = pg.trans.Trans(), pg.trans.TransLog(
) # LU(1., 500.)
if startModel is None:
startModel = self.block1dInversion(nlay, verbose=False)
model = kwargs.pop('startvec', np.tile(startModel, len(self.mrs)))
INV = pg.Inversion(data, fop, transData, transMod, True, False)
INV.setModel(model)
INV.setReferenceModel(model)
INV.setAbsoluteError(error)
INV.setLambda(kwargs.pop('lam', 100))
INV.setMaxIter(kwargs.pop('maxIter', 20))
# INV.stopAtChi1(False)
INV.setLambdaFactor(0.9)
INV.setDeltaPhiAbortPercent(0.1)
model = INV.run()
self.WMOD, self.TMOD = [], []
for par in np.reshape(model, (len(self.mrs), 3 * nlay - 1)):
thk = par[0:nlay - 1]
self.WMOD.append(np.hstack((thk, par[nlay - 1:2 * nlay - 1])))
self.TMOD.append(np.hstack((thk, par[2 * nlay - 1:3 * nlay - 1])))
ind = np.hstack((0, np.cumsum(self.nData)))
resp = INV.response()
misfit = data - resp
emisfit = misfit / error
misfit *= 1e9
self.totalChi2 = INV.chi2()
self.totalRMS = INV.absrms() * 1e9
self.RMSvec, self.Chi2vec = [], []
for i in range(len(self.mrs)):
self.RMSvec.append(np.sqrt(np.mean(misfit[ind[i]:ind[i + 1]]**2)))
self.Chi2vec.append(np.mean(emisfit[ind[i]:ind[i + 1]]**2))
def blockLCInversion(self, nlay=2, startModel=None, **kwargs):
"""Laterally constrained (piece-wise 1D) block inversion."""
data, error, self.nData = pg.RVector(), pg.RVector(), []
for mrs in self.mrs:
data = pg.cat(data, mrs.data)
error = pg.cat(error, mrs.error)
self.nData.append(len(mrs.data))
fop = MRSLCI(self.mrs, nlay=nlay)
fop.region(0).setZWeight(kwargs.pop('zWeight', 0))
fop.region(0).setConstraintType(kwargs.pop('cType', 1))
transData, transMod = pg.RTrans(), pg.RTransLog() # LU(1., 500.)
if startModel is None:
startModel = self.block1dInversion(nlay, verbose=False)
model = kwargs.pop('startvec', np.tile(startModel, len(self.mrs)))
INV = pg.RInversion(data, fop, transData, transMod, True, False)
INV.setModel(model)
INV.setReferenceModel(model)
INV.setAbsoluteError(error)
INV.setLambda(kwargs.pop('lam', 100))
INV.setMaxIter(kwargs.pop('maxIter', 20))
# INV.stopAtChi1(False)
INV.setLambdaFactor(0.9)
INV.setDeltaPhiAbortPercent(0.1)
model = INV.run()
self.WMOD, self.TMOD = [], []
for par in np.reshape(model, (len(self.mrs), 3*nlay-1)):
thk = par[0:nlay-1]
self.WMOD.append(np.hstack((thk, par[nlay-1:2*nlay-1])))
self.TMOD.append(np.hstack((thk, par[2*nlay-1:3*nlay-1])))
ind = np.hstack((0, np.cumsum(self.nData)))
resp = INV.response()
misfit = data - resp
emisfit = misfit / error
misfit *= 1e9
self.totalChi2 = INV.chi2()
self.totalRMS = INV.absrms()*1e9
self.RMSvec, self.Chi2vec = [], []
for i in range(len(self.mrs)):
self.RMSvec.append(np.sqrt(np.mean(misfit[ind[i]:ind[i+1]]**2)))
self.Chi2vec.append(np.mean(emisfit[ind[i]:ind[i+1]]**2))
def checkError(self, err, data=None):
"""Collect error values."""
if len(err) != len(self.mgrs):
pg.critical("Please provide data for all managers")
vals = pg.Vector(0)
for i, mgr in enumerate(self.mgrs):
# we get the data values again or we have to split data
dataVals = mgr.checkData(self.fop._data[i])
vals = pg.cat(vals, mgr.checkError(err[i], dataVals))
return vals
def genMods(individual):
"""generate MRS and VES models from unit vector"""
model = individual * (self.lUB - self.lLB) + self.lLB
# model = pg.asvector(individual) * (self.lUB - self.lLB) + self.lLB
if self.logpar:
model = pg.exp(model)
modMRS = model(0, nlay * 3 - 1)
modVES = pg.cat(model(0, nlay - 1),
model(nlay * 3 - 1, nlay * 4 - 1))
return modMRS, modVES
def response(self, par):
"""Cut together forward responses of all soundings."""
mods = np.asarray(par).reshape(self._nSoundings, self._parPerSounding)
resp = pg.Vector(0)
for i in range(self._nSoundings):
r = self._fops1D[i].response(mods[i])
#print("i:", i, mods[i], r)
resp = pg.cat(resp, r)
return resp
def prepare(self, dataVals, errorVals, nLayers=4, **kwargs):
dataVec = pg.RVector()
for d in dataVals:
dataVec = pg.cat(dataVec, d)
errVec = pg.RVector()
for e in errorVals:
errVec = pg.cat(errVec, e)
self.fop.initJacobian(dataVals=dataVals,
nLayers=nLayers,
nPar=kwargs.pop('nPar', None))
### self.fop.initJacobian resets prior set startmodels
if self._startModel is not None:
self.fop.setStartModel(self._startModel)
rC = self.fop.regionManager().regionCount()
if kwargs.pop('disableLCI', False):
self.inv.setMarquardtScheme(0.7)
#self.inv.setLocalRegularization(True)
for r in self.fop.regionManager().regionIdxs():
self.fop.setRegionProperties(r, cType=0)
else:
#self.inv.stopAtChi1(False)
cType = kwargs.pop('cType', None)
if cType is None:
cType = [1] * rC
zWeight = kwargs.pop('zWeight', None)
if zWeight is None:
zWeight = [0.0] * rC
self.fop.setRegionProperties('*',
cType=cType,
zWeight=zWeight,
**kwargs)
self.inv.setReferenceModel(self.fop.startModel())
return dataVec, errVec
def block1dInversionNew(self, nlay=2, lam=100., verbose=True):
"""invert all data together by a 1D model (more general solution)"""
data, error = pg.RVector(), pg.RVector()
for mrs in self.mrs:
data = pg.cat(data, mrs.data)
error = pg.cat(error, mrs.error)
f = JointMRSModelling(self.mrs, nlay)
mrsobj = self.mrs[0]
for i in range(3):
f.region(i).setParameters(mrsobj.startval[i], mrsobj.lowerBound[i],
mrsobj.upperBound[i])
INV = pg.RInversion(data, f, verbose)
INV.setLambda(lam)
INV.setMarquardtScheme(0.8)
# INV.stopAtChi1(False) # should be already in MarquardtScheme
INV.setDeltaPhiAbortPercent(0.5)
INV.setAbsoluteError(error)
model = INV.run()
return model
def block1dInversion(self, nlay=2, lam=100., show=False, verbose=True,
uncertainty=False):
"""Invert all data together by a 1D model (more general solution)."""
data, error = pg.RVector(), pg.RVector()
for mrs in self.mrs:
data = pg.cat(data, mrs.data)
error = pg.cat(error, np.real(mrs.error))
# f = JointMRSModelling(self.mrs, nlay)
f = MultiFOP(self.mrs, nlay)
mrsobj = self.mrs[0]
for i in range(3):
f.region(i).setParameters(mrsobj.startval[i], mrsobj.lowerBound[i],
mrsobj.upperBound[i])
INV = pg.RInversion(data, f, verbose)
INV.setLambda(lam)
INV.setMarquardtScheme(0.8)
# INV.stopAtChi1(False) # should be already in MarquardtScheme
INV.setDeltaPhiAbortPercent(0.5)
INV.setAbsoluteError(error)
model = INV.run()
m0 = self.mrs[0]
m0.model = np.asarray(model)
if uncertainty:
from pygimli.utils import iterateBounds
m0.modelL, m0.modelU = iterateBounds(
INV, dchi2=INV.chi2() / 2, change=1.2)
if show:
self.show1dModel()
# %% fill up 2D model (for display only)
self.WMOD, self.TMOD = [], []
thk = model[0:nlay-1]
wc = model[nlay-1:2*nlay-1]
t2 = model[2*nlay-1:3*nlay-1]
for i in range(len(self.mrs)):
self.WMOD.append(np.hstack((thk, wc)))
self.TMOD.append(np.hstack((thk, t2)))
return model
def fitCCC(f, amp, phi, eRho=0.01, ePhi=0.001, lam=1000., mstart=None,
taupar=(1e-2, 1e-5, 100), cpar=(0.5, 0, 1)):
"""Fit complex spectrum by Cole-Cole model."""
fCC = ColeColeComplex(f)
tLog = pg.RTransLog()
fCC.region(0).setStartValue(max(amp))
if mstart is None: # compute from amplitude decay
mstart = 1. - min(amp) / max(amp)
fCC.region(1).setParameters(mstart, 0, 1) # m (start,lower,upper)
fCC.region(2).setParameters(*taupar) # tau
fCC.region(3).setParameters(*cpar) # c
data = pg.cat(amp, phi)
ICC = pg.RInversion(data, fCC, False) # set up inversion class
ICC.setTransModel(tLog)
error = pg.cat(eRho*amp, pg.RVector(len(f), ePhi))
ICC.setAbsoluteError(error) # perr + ePhi/data)
ICC.setLambda(lam) # start with large damping and cool later
ICC.setMarquardtScheme(0.8) # lower lambda by 20%/it., no stop chi=1
model = np.asarray(ICC.run()) # run inversion
ICC.echoStatus()
response = np.asarray(ICC.response())
return model, response[:len(f)], response[len(f):]
def blockLCInversion(self, nlay=2, startModel=None, lam=100.0, cType=1):
"""laterally constrained (piece-wise 1D) block inversion"""
data, error, self.nData = pg.RVector(), pg.RVector(), []
for mrs in self.mrs:
data = pg.cat(data, mrs.data)
error = pg.cat(error, mrs.error)
self.nData.append(len(mrs.data))
fop = MRSLCI(self.mrs, nlay=nlay)
fop.region(0).setZWeight(0.01)
fop.region(0).setConstraintType(cType)
transData, transMod = pg.RTrans(), pg.RTransLog() # LU(1., 500.)
if startModel is None:
startModel = self.block1dInversion(nlay, verbose=False)
model = np.tile(startModel, len(self.mrs))
INV = pg.RInversion(data, fop, transData, transMod, True, False)
INV.setModel(model)
INV.setReferenceModel(model)
INV.setAbsoluteError(error)
INV.setLambda(lam)
INV.stopAtChi1(False)
model = INV.run()
self.WMOD, self.TMOD = [], []
for par in np.reshape(model, (len(self.mrs), nlay * 3 - 1)):
thk = par[0 : nlay - 1]
self.WMOD.append(np.hstack((thk, par[nlay - 1 : 2 * nlay - 1])))
self.TMOD.append(np.hstack((thk, par[2 * nlay - 1 : 3 * nlay - 1])))
ind = np.hstack((0, np.cumsum(self.nData)))
resp = INV.response()
misfit = data - resp
emisfit = misfit / error
misfit *= 1e9
self.RMSvec, self.Chi2vec = [], []
for i in range(len(self.mrs)):
self.RMSvec.append(np.sqrt(np.mean(misfit[ind[i] : ind[i + 1]] ** 2)))
self.Chi2vec.append(np.mean(emisfit[ind[i] : ind[i + 1]] ** 2))
def createStartModel(self, rhoa, nLayer, thickness=None):
r"""Create suitable starting model.
Create suitable starting model based on median apparent resistivity
values and skin depth approximation.
"""
res = np.ones(nLayer) * pg.median(rhoa)
if thickness is None:
skinDepth = np.sqrt(max(self.t) * pg.median(rhoa)) * 500
thk = np.arange(nLayer) / sum(np.arange(nLayer)) * skinDepth / 2.
thk = thk[1:]
else:
thk = np.ones(nLayer-1) * thickness
self.setStartModel(pg.cat(thk, res))
return self.startModel()
def runEMO(self,nlay=5,pop_size=100,max_generations=100):
""" run evolutionary multi-objective optimization (EMO) using inspyred
for now fixed to NSGA-II algorithm after Deb (2002)
(non-dominated sorting genetic algorithm) """
import inspyred
def genMods( individual ):
""" generate MRS and VES models from unit vector """
model = pg.asvector( individual ) * ( self.lUB - self.lLB ) + self.lLB
if self.logpar:
model = pg.exp( model )
modMRS = model(0,nlay*3-1)
modVES = pg.cat(model(0,nlay-1),model(nlay*3-1,nlay*4-1))
return modMRS, modVES
def mygenerate( random, args ):
""" generate a random vector of model size """
return [random.random() for i in range( nlay*4 - 1 )]
@inspyred.ec.evaluators.evaluator
def datafit( individual, args ):
""" return data fits for MRS and VES as Pareto object """
modMRS, modVES = genMods(individual)
MRSmisfit = ( self.data - self.f(modMRS) ) / self.error
VESmisfit = ( np.log(self.rhoa) - np.log(self.fVES(modVES)) ) / np.log(1.02)
return inspyred.ec.emo.Pareto([np.mean(MRSmisfit**2),np.mean(VESmisfit**2)])
self.createFOP(nlay)
self.fVES = pg.DC1dModelling(nlay,self.ab2,self.mn2)
lowerBound = pg.cat(
pg.cat( pg.RVector(nlay-1,self.lowerBound[0]), pg.RVector(nlay,self.lowerBound[1])),
pg.cat( pg.RVector(nlay,self.lowerBound[2]), pg.RVector(nlay,self.lowerBound[3]) ) )
upperBound = pg.cat(
pg.cat( pg.RVector(nlay-1,self.upperBound[0]), pg.RVector(nlay,self.upperBound[1])),
pg.cat( pg.RVector(nlay,self.upperBound[2]), pg.RVector(nlay,self.upperBound[3]) ) )
if self.logpar:
self.lLB, self.lUB = pg.log(lowerBound), pg.log(upperBound) # ready mapping functions
else:
self.lLB, self.lUB = lowerBound, upperBound
rand = random.Random()
rand.seed(int(time.time()))
ea = inspyred.ec.emo.NSGA2(rand)
ea.variator = [inspyred.ec.variators.blend_crossover, inspyred.ec.variators.gaussian_mutation]
ea.terminator = inspyred.ec.terminators.generation_termination
ea.observer = [inspyred.ec.observers.stats_observer, inspyred.ec.observers.file_observer]
self.pop = ea.evolve(evaluator=datafit,
generator=mygenerate,
maximize=False,
bounder=inspyred.ec.Bounder(0.,1.),
pop_size=pop_size,
max_generations=max_generations)
def drawSeismogramm(ax, mesh, u, dt, ids=None, pos=None, i=None):
r"""Extract and show time series from wave field
Parameters
----------
ids: list
List of node ids for the given mesh.
pos : list
List of positions for the given mesh. We will look for the nearest node.
"""
ax.set_xlim(mesh.xmin(), mesh.xmax())
ax.set_ylim(0., dt*len(u)*1000)
ax.set_aspect(1)
ax.set_ylabel('Time (ms)')
ax.set_xlabel('Distance (m)')
if i is None:
i = len(u)-1
t = np.linspace(0, i*dt*1000, i+1)
if ids is None and pos is not None:
ids = []
for p in pos:
ids.append(mesh.findNearestNode(p))
xDist = mesh.node(0).pos().distance(mesh.node(1).pos())
for iw, n in enumerate(ids):
pos = mesh.node(n).pos()
ax.plot(pos[0], 0.05, '^', color='black')
trace = pg.cat(pg.RVector(0), u[:(i+1), n])
# print(i+1, n)
# print(trace, (max(pg.abs(trace))))
# if max(pg.abs(trace)) > 1e-8:
trace *= np.exp(1/1000 * t)
trace /= (max(pg.abs(trace)))
trace *= 10
drawWiggle(ax, trace, t=t, xoffset=pos[0])
ax.invert_yaxis()