def createStartModel(self, rhoa, nLayer):
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)
skinDepth = np.sqrt(max(self.t) * pg.median(rhoa)) * 500
thk = np.arange(nLayer) / sum(np.arange(nLayer)) * skinDepth / 2.
thk = thk[1:]
self.setStartModel(pg.cat(thk, res))
return self.startModel()
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 invert(self, data, mesh, lam=20, limits=None):
self.setData(data)
self.setMesh(mesh)
if limits is not None:
if hasattr(self.tM, 'setLowerBound'):
if self.verbose:
print('Lower limit set to', limits[0])
self.tM.setLowerBound(limits[0])
if hasattr(self.tM, 'setUpperBound'):
if self.verbose:
print('Upper limit set to', limits[1])
self.tM.setUpperBound(limits[1])
nModel = self.fop.regionManager().parameterCount()
startModel = pg.RVector(nModel, 0.0)
for i in range(len(self.managers)):
startModel += pg.RVector(nModel,
pg.median(self.trans[i].inv(self.managers[i].createApparentData(self.data[i]))))
startModel /= len(self.managers)
self.fop.setStartModel(startModel)
self.inv.setData(self.dataVals)
self.inv.setRelativeError(self.dataErrs)
self.inv.setLambda(lam)
self.model = self.inv.start()
self.model = self.model(self.fop.regionManager().paraDomain().cellMarkers())
return self.model
def invert(self, data=None, mesh=None, lam=20, limits=None, **kwargs):
"""TODO."""
if 'verbose' in kwargs:
self.setVerbose(kwargs.pop('verbose'))
self.setData(data)
self.setMesh(mesh)
nModel = self.fop.regionManager().parameterCount()
startModel = None
if limits is not None:
if hasattr(self.tM, 'setLowerBound'):
if self.verbose:
print('Lower limit set to', limits[0])
self.tM.setLowerBound(limits[0])
if hasattr(self.tM, 'setUpperBound'):
if self.verbose:
print('Upper limit set to', limits[1])
self.tM.setUpperBound(limits[1])
startModel = pg.RVector(nModel, (limits[1] - limits[0]) / 2.0)
else:
for i in range(len(self.managers)):
startModel += pg.RVector(
nModel,
pg.median(self.trans[i].inv(
self.managers[i].createApparentData(self.data[i]))))
startModel /= len(self.managers)
self.inv.setModel(startModel)
self.fop.regionManager().setZWeight(1.0)
self.inv.setData(self.dataVals)
self.inv.setRelativeError(self.dataErrs)
self.inv.setLambda(lam)
self.mod = self.inv.run()
self.mod = self.mod(
self.fop.regionManager().paraDomain().cellMarkers())
return self.mod
def createJacobian(self, model):
print('=' * 100)
if self.complex():
modelRe = model[0:int(len(model)/2)]
modelIm = model[int(len(model)/2):len(model)]
modelC = pg.toComplex(modelRe, modelIm)
print("Real", min(modelRe), max(modelRe))
print("Imag", min(modelIm), max(modelIm))
u = self.prepareJacobian_(modelC)
if self._J.rows() == 0:
#re(data)/re(mod) = im(data)/im(mod)
# we need a local copy until we have a gimli internal reference counter FIXTHIS
M1 = pg.RMatrix()
M2 = pg.RMatrix()
self.matrixHeap.append(M1)
self.matrixHeap.append(M2)
JRe = self._J.addMatrix(M1)
JIm = self._J.addMatrix(M2)
self._J.addMatrixEntry(JRe, 0, 0)
self._J.addMatrixEntry(JIm, 0, len(modelRe), -1.0)
self._J.addMatrixEntry(JIm, self.data().size(), 0, 1.0)
self._J.addMatrixEntry(JRe, self.data().size(), len(modelRe))
else:
self._J.clean()
k = pg.RVector(self.data()('k'))
self.data().set('k', k*0.0 + 1.0)
dMapResponse = pb.DataMap()
dMapResponse.collect(self.electrodes(), self.solution())
respRe = dMapResponse.data(self.data(), False, False)
respIm = dMapResponse.data(self.data(), False, True)
#CVector resp(toComplex(respRe, respIm));
#RVector am(abs(resp) * dataContainer_->get("k"));
#RVector ph(-phase(resp));
print("respRe", pg.median(respRe), min(respRe), max(respRe))
print("respIm", pg.median(respIm), min(respIm), max(respIm))
JC = pg.CMatrix()
self.createJacobian_(modelC, u, JC)
for i in range(JC.rows()):
#JC[i] *= 1.0/(modelC*modelC) * k[i]
JC[i] /= (modelC * modelC) / k[i]
self._J.mat(0).copy(pg.real(JC))
self._J.mat(1).copy(pg.imag(JC))
#self.createJacobian_(modelRe*0.0+1.0, pg.real(u), self._J.mat(1))
#self.createJacobian_(modelRe*0.0+1.0, pg.imag(u), self._J.mat(2))
#self.createJacobian_(modelRe*0.0+1.0, pg.imag(u), self._J.mat(3))
sumsens0 = pg.RVector(self._J.mat(0).rows())
sumsens1 = pg.RVector(self._J.mat(0).rows())
sumsens2 = pg.RVector(self._J.mat(0).rows())
for i in range(self._J.mat(0).rows()):
#self._J.mat(0)[i] *= 1./modelRe / respRe[i]
#self._J.mat(1)[i] *= 1./modelIm / respRe[i]
#self._J.mat(2)[i] *= 1./modelRe / respIm[i]
#self._J.mat(3)[i] *= 1./modelIm / respIm[i]
#self._J.mat(0)[i] *= 1./(modelRe * modelRe) * k[i]
#self._J.mat(1)[i] *= 1./(modelRe * modelIm) * k[i]
#self._J.mat(2)[i] *= 1./(modelIm * modelRe) * k[i]
#self._J.mat(3)[i] *= 1./(modelIm * modelIm) * k[i]
sumsens0[i] = sum(self._J.mat(0)[i])
sumsens1[i] = sum(self._J.mat(1)[i])
sumsens2[i] = abs(sum(JC[i]))
print(pg.median(sumsens0), min(sumsens0), max(sumsens0))
print(pg.median(sumsens1), min(sumsens1), max(sumsens1))
print(pg.median(sumsens2), min(sumsens2), max(sumsens2))
self.data().set('k', k)
self._J.recalcMatrixSize()
else:
# self.setVerbose(True)
u = self.prepareJacobian_(model)
#J = pg.RMatrix()
if self._J.rows() == 0:
print('#' * 100)
M1 = pg.RMatrix()
Jid = self._J.addMatrix(M1)
self._J.addMatrixEntry(Jid, 0, 0)
else:
self._J.clean()
self.createJacobian_(model, u, self._J.mat(0))
self._J.recalcMatrixSize()
def invert(self, data=None, vals=None, err=None, mesh=None, **kwargs):
"""Run the full inversion.
The data and error needed to be set before.
The meshes will be created if necessary.
DOCUMENTME!!!
Parameters
----------
lam : float [20]
regularization parameter
zWeight : float [0.7]
relative vertical weight
maxIter : int [20]
maximum iteration number
robustdata : bool [False]
robust data reweighting using an L1 scheme (IRLS reweighting)
blockymodel : bool [False]
blocky model constraint using L1 reweighting roughness vector
startModelIsReference : bool [False]
startmodel is the reference model for the inversion
forwarded to createMesh
depth
quality
paraDX
maxCellArea
"""
if 'verbose' in kwargs:
self.setVerbose(kwargs.pop('verbose'))
if data is not None:
# setDataContainer would be better
self.setData(data)
if vals is not None:
self.dataContainer.set(self.dataToken(), vals)
if err is not None:
self.dataContainer.set('err', vals)
# check for data container here
dataVals = self.dataContainer(self.dataToken())
errVals = self.dataContainer('err')
if mesh is not None:
self.setMesh(mesh)
if self.mesh is None:
self.createMesh(depth=kwargs.pop('depth', None),
quality=kwargs.pop('quality', 34.0),
maxCellArea=kwargs.pop('maxCellArea', 0.0),
paraDX=kwargs.pop('paraDX', 0.3))
self.inv.setData(dataVals)
self.inv.setError(errVals, not self.errIsAbsolute)
zWeight = kwargs.pop('zWeight', 0.7)
if 'zweight' in kwargs:
zWeight = kwargs.pop('zweight', 0.7)
print("zweight option will be removed soon. Please use zWeight.")
self.fop.regionManager().setZWeight(zWeight)
self.inv.setLambda(kwargs.pop('lam', 20))
self.inv.setMaxIter(kwargs.pop('maxIter', 20))
self.inv.setRobustData(kwargs.pop('robustData', False))
self.inv.setBlockyModel(kwargs.pop('blockyModel', False))
self.inv.setRecalcJacobian(kwargs.pop('recalcJacobian', True))
# TODO: ADD MORE KWARGS
pc = self.fop.regionManager().parameterCount()
startModel = kwargs.pop('startModel',
pg.RVector(pc, pg.median(dataVals)))
self.inv.setModel(startModel)
# self.fop.setStartModel(startModel)
if kwargs.pop('startModelIsReference', False):
self.inv.setReferenceModel(startModel)
# Run the inversion
if len(kwargs) > 0:
print("Keyword arguments unknown:")
print(kwargs)
print("Warning! There are unknown kwargs arguments.")
model = self.inv.run()
self.model = model(self.paraDomain.cellMarkers())
return self.model
def invert(self, data, values=None, verbose=0, **kwargs):
"""
Invert the given data.
A parametric mesh for the inversion will be created if non is given
before.
Parameters
----------
"""
self.fop.setVerbose(verbose)
self.inv.setVerbose(verbose)
self.inv.setMaxIter(kwargs.pop('maxiter', 10))
self.inv.setLambda(kwargs.pop('lambd', 10))
if self.paraMesh is None:
self.paraMesh = createParaMesh2dGrid(data.sensorPositions(),
**kwargs)
self.setParaMesh(self.paraMesh)
if verbose:
print(self.paraMesh)
# pg.show(self.paraMesh)
err = data('err')
rhoa = data('rhoa')
startModel = pg.RVector(self.fop.regionManager().parameterCount(),
pg.median(rhoa))
self.fop.setData(data)
self.inv.setForwardOperator(self.fop)
# check err here
self.inv.setData(rhoa)
self.inv.setError(err)
self.inv.setModel(startModel)
model = self.inv.run()
if values is not None:
if isinstance(values, pg.RVector):
values = [values]
elif isinstance(values, np.ndarray):
if values.ndim == 1:
values = [values]
allModel = pg.RMatrix(len(values), len(model))
self.inv.setVerbose(False)
for i in range(len(values)):
print(i)
tic = time.time()
self.inv.setModel(model)
self.inv.setReferenceModel(model)
dData = pg.abs(values[i] / rhoa)
relModel = self.inv.invSubStep(pg.log(dData))
allModel[i] = model * pg.exp(relModel)
print(i, "/", len(values), " : ", time.time()-tic,
"s min/max: ", min(allModel[i]), max(allModel[i]))
return allModel
return model
def calcSeismics(meshIn, vP):
"""Do seismic computations."""
meshSeis = meshIn.createH2()
meshSeis = mt.appendTriangleBoundary(
meshSeis, xbound=25, ybound=22.0, marker=1, quality=32.0, area=0.3,
smooth=True, markerBoundary=1, isSubSurface=False, verbose=False)
print(meshSeis)
meshSeis = meshSeis.createH2()
meshSeis = meshSeis.createH2()
# meshSeis = meshSeis.createP2()
meshSeis.smooth(1, 1, 1, 4)
vP = pg.interpolate(meshIn, vP, meshSeis.cellCenters())
mesh = meshSeis
vP = pg.solver.fillEmptyToCellArray(mesh, vP)
print(mesh)
# ax, cbar = pg.show(mesh, data=vP)
# pg.show(mesh, axes=ax)
geophPointsX = np.arange(-19, 19.1, 1)
geophPoints = np.vstack((geophPointsX, np.zeros(len(geophPointsX)))).T
sourcePos = geophPoints[4]
c = mesh.findCell(sourcePos)
h1 = pg.findBoundary(c.boundaryNodes(0)).size()
h2 = pg.findBoundary(c.boundaryNodes(1)).size()
h3 = pg.findBoundary(c.boundaryNodes(2)).size()
print([h1, h2, h3])
h = pg.median([h1, h2, h3])
# h = pg.median(mesh.boundarySizes())
f0scale = 0.25
cfl = 0.5
dt = cfl * h / max(vP)
print("Courant-Friedrich-Lewy number:", cfl)
tmax = 40./min(vP)
times = np.arange(0.0, tmax, dt)
solutionName = createCacheName('seis', mesh, times) + "cfl-" + str(cfl)
try:
# u = pg.load(solutionName + '.bmat')
uI = pg.load(solutionName + 'I.bmat')
except Exception as e:
print(e)
f0 = f0scale * 1./dt
print("h:", round(h, 2),
"dt:", round(dt, 5),
"1/dt:", round(1/dt, 1),
"f0", round(f0, 2),
"Wavelength: ", round(max(vP)/f0, 2), " m")
uSource = ricker(times, f0, t0=1./f0)
plt.figure()
plt.plot(times, uSource, '-*')
plt.show(block=0)
plt.pause(0.01)
u = solvePressureWave(mesh, vP, times, sourcePos=sourcePos,
uSource=uSource, verbose=10)
u.save(solutionName)
uI = pg.RMatrix()
print("interpolate node to cell data ... ")
pg.interpolate(mesh, u, mesh.cellCenters(), uI)
print("... done")
uI.save(solutionName+'I')
# nodes = [mesh.findNearestNode(p) for p in geophPoints]
# fig = plt.figure()
# axs = fig.add_subplot(1,1,1)
# drawSeismogramm(axs, mesh, u, nodes, dt, i=None)
# plt.show()
dpi = 92
scale = 1
fig = plt.figure(facecolor='white',
figsize=(scale*800/dpi, scale*490/dpi), dpi=dpi)
ax = fig.add_subplot(1, 1, 1)
gci = pg.mplviewer.drawModel(ax, mesh, data=uI[0],
cMin=-1, cMax=1, cmap='bwr')
pg.mplviewer.drawMeshBoundaries(ax, meshIn, hideMesh=1)
ax.set_xlim((-20, 20))
ax.set_ylim((-15, 0))
ax.set_ylabel('Depth [m]')
ax.set_xlabel('$x$ [m]')
ticks = ax.yaxis.get_majorticklocs()
tickLabels = []
for t in ticks:
tickLabels.append(str(int(abs(t))))
ax.set_yticklabels(tickLabels)
plt.tight_layout()
# ax, cbar = pg.show(mesh, data=vP)
# pg.showNow()
# ax = fig.add_subplot(1,1,1)
def animate(i):
i = i*5
if i > len(uI)-1:
return
print("Frame:", i, "/", len(uI))
ui = uI[i]
ui = ui / max(pg.abs(ui))
ui = pg.logDropTol(ui, 1e-2)
cMax = max(pg.abs(ui))
pg.mplviewer.setMappableData(gci, ui,
cMin=-cMax, cMax=cMax,
logScale=False)
# plt.pause(0.001)
anim = animation.FuncAnimation(fig, animate,
frames=int(len(uI)/5),
interval=0.001, repeat=0) # , blit=True)
out = 'seis' + str(f0scale) + "cfl-" + str(cfl)
anim.save(out + ".mp4", writer=None, fps=20, dpi=dpi, codec=None,
bitrate=24*1024, extra_args=None, metadata=None,
extra_anim=None, savefig_kwargs=None)
try:
print("create frames ... ")
os.system('mkdir -p anim-' + out)
os.system('ffmpeg -i ' + out + '.mp4 anim-' + out + '/movie%d.jpg')
except:
pass
def createJacobian(self, model):
print('=' * 100)
if self.complex():
modelRe = model[0:int(len(model) / 2)]
modelIm = model[int(len(model) / 2):len(model)]
modelC = pg.toComplex(modelRe, modelIm)
print("Real", min(modelRe), max(modelRe))
print("Imag", min(modelIm), max(modelIm))
u = self.prepareJacobian_(modelC)
if self._J.rows() == 0:
#re(data)/re(mod) = im(data)/im(mod)
# we need a local copy until we have a gimli internal reference counter FIXTHIS
M1 = pg.RMatrix()
M2 = pg.RMatrix()
self.matrixHeap.append(M1)
self.matrixHeap.append(M2)
JRe = self._J.addMatrix(M1)
JIm = self._J.addMatrix(M2)
self._J.addMatrixEntry(JRe, 0, 0)
self._J.addMatrixEntry(JIm, 0, len(modelRe), -1.0)
self._J.addMatrixEntry(JIm, self.data().size(), 0, 1.0)
self._J.addMatrixEntry(JRe, self.data().size(), len(modelRe))
else:
self._J.clean()
k = pg.RVector(self.data()('k'))
self.data().set('k', k * 0.0 + 1.0)
dMapResponse = pb.DataMap()
dMapResponse.collect(self.electrodes(), self.solution())
respRe = dMapResponse.data(self.data(), False, False)
respIm = dMapResponse.data(self.data(), False, True)
#CVector resp(toComplex(respRe, respIm));
#RVector am(abs(resp) * dataContainer_->get("k"));
#RVector ph(-phase(resp));
print("respRe", pg.median(respRe), min(respRe), max(respRe))
print("respIm", pg.median(respIm), min(respIm), max(respIm))
JC = pg.CMatrix()
self.createJacobian_(modelC, u, JC)
for i in range(JC.rows()):
#JC[i] *= 1.0/(modelC*modelC) * k[i]
JC[i] /= (modelC * modelC) / k[i]
self._J.mat(0).copy(pg.real(JC))
self._J.mat(1).copy(pg.imag(JC))
#self.createJacobian_(modelRe*0.0+1.0, pg.real(u), self._J.mat(1))
#self.createJacobian_(modelRe*0.0+1.0, pg.imag(u), self._J.mat(2))
#self.createJacobian_(modelRe*0.0+1.0, pg.imag(u), self._J.mat(3))
sumsens0 = pg.RVector(self._J.mat(0).rows())
sumsens1 = pg.RVector(self._J.mat(0).rows())
sumsens2 = pg.RVector(self._J.mat(0).rows())
for i in range(self._J.mat(0).rows()):
#self._J.mat(0)[i] *= 1./modelRe / respRe[i]
#self._J.mat(1)[i] *= 1./modelIm / respRe[i]
#self._J.mat(2)[i] *= 1./modelRe / respIm[i]
#self._J.mat(3)[i] *= 1./modelIm / respIm[i]
#self._J.mat(0)[i] *= 1./(modelRe * modelRe) * k[i]
#self._J.mat(1)[i] *= 1./(modelRe * modelIm) * k[i]
#self._J.mat(2)[i] *= 1./(modelIm * modelRe) * k[i]
#self._J.mat(3)[i] *= 1./(modelIm * modelIm) * k[i]
sumsens0[i] = sum(self._J.mat(0)[i])
sumsens1[i] = sum(self._J.mat(1)[i])
sumsens2[i] = abs(sum(JC[i]))
print(pg.median(sumsens0), min(sumsens0), max(sumsens0))
print(pg.median(sumsens1), min(sumsens1), max(sumsens1))
print(pg.median(sumsens2), min(sumsens2), max(sumsens2))
self.data().set('k', k)
self._J.recalcMatrixSize()
else:
# self.setVerbose(True)
u = self.prepareJacobian_(model)
#J = pg.RMatrix()
if self._J.rows() == 0:
print('#' * 100)
M1 = pg.RMatrix()
Jid = self._J.addMatrix(M1)
self._J.addMatrixEntry(Jid, 0, 0)
else:
self._J.clean()
self.createJacobian_(model, u, self._J.mat(0))
self._J.recalcMatrixSize()
#fop = pb.DCSRMultiElectrodeModelling(mesh, data)
fop = pg.physics.ert.ERTModelling(mesh, data)
fop.regionManager().region(1).setBackground(True)
fop.createRefinedForwardMesh(refine=True, pRefine=False)
inv = pg.RInversion(data("rhoa"), fop, verbose=True, dosave=True)
datTrans = pg.RTransLog()
modTrans = pg.RTransLog()
inv.setMaxIter(10)
inv.setTransData(datTrans)
inv.setTransModel(modTrans)
inv.setError(data('err'))
inv.setModel(
pg.RVector(fop.regionManager().parameterCount(), pg.median(data('rhoa'))))
inv.setLambda(5)
model = inv.run()
modelMesh = fop.regionManager().paraDomain()
a, cbar = pg.show(modelMesh, model)
##C = fop.contraintsMatrix()
#S = fop.jacobian()
#print(S)
#modelMesh = fop.regionManager().paraDomain()
#fig = pg.plt.figure()
#ax = [fig.add_subplot(2,2,i) for i in range(1,5)]
poly.createEdge(nodes[1], nodes[2], 3) # hom neumann (outflow)
poly.createEdge(nodes[2], nodes[3], 2) # hom dirichlet (isolation)
poly.createEdge(nodes[3], nodes[0], 4) # hom dirichlet (isolation)
mesh = createMesh(poly, quality=34, area=0.05, smooth=[0,10])
return mesh
dx = 0.2
x = np.arange(-20, 20., dx)
y = np.arange(-20, 0.0, dx)[::-1]
mesh = pg.createGrid(x=x, y=y)
mesh = createMesh2()
print(mesh)
h = pg.median(mesh.boundarySizes())
v1 = 1000
v2 = 3000
tmax = 10.1/v1
z = 2.
f0 = 1000.0 # A low wavelength of 50 Hz
velocities = pg.RVector(mesh.cellCount(), v1)
for c in mesh.cells():
velocities[c.id()] = v1
if c.center()[1] < -z:
velocities[c.id()] = v2
def calcSeismics(meshIn, vP):
"""Do seismic computations."""
meshSeis = meshIn.createH2()
meshSeis = mt.appendTriangleBoundary(meshSeis,
xbound=25,
ybound=22.0,
marker=1,
quality=32.0,
area=0.3,
smooth=True,
markerBoundary=1,
isSubSurface=False,
verbose=False)
print(meshSeis)
meshSeis = meshSeis.createH2()
meshSeis = meshSeis.createH2()
# meshSeis = meshSeis.createP2()
meshSeis.smooth(1, 1, 1, 4)
vP = pg.interpolate(meshIn, vP, meshSeis.cellCenters())
mesh = meshSeis
vP = pg.solver.fillEmptyToCellArray(mesh, vP)
print(mesh)
# ax, cbar = pg.show(mesh, data=vP)
# pg.show(mesh, axes=ax)
geophPointsX = np.arange(-19, 19.1, 1)
geophPoints = np.vstack((geophPointsX, np.zeros(len(geophPointsX)))).T
sourcePos = geophPoints[4]
c = mesh.findCell(sourcePos)
h1 = pg.findBoundary(c.boundaryNodes(0)).size()
h2 = pg.findBoundary(c.boundaryNodes(1)).size()
h3 = pg.findBoundary(c.boundaryNodes(2)).size()
print([h1, h2, h3])
h = pg.median([h1, h2, h3])
# h = pg.median(mesh.boundarySizes())
f0scale = 0.25
cfl = 0.5
dt = cfl * h / max(vP)
print("Courant-Friedrich-Lewy number:", cfl)
tmax = 40. / min(vP)
times = np.arange(0.0, tmax, dt)
solutionName = createCacheName('seis', mesh, times) + "cfl-" + str(cfl)
try:
# u = pg.load(solutionName + '.bmat')
uI = pg.load(solutionName + 'I.bmat')
except Exception as e:
print(e)
f0 = f0scale * 1. / dt
print("h:", round(h, 2), "dt:", round(dt, 5), "1/dt:",
round(1 / dt, 1), "f0", round(f0, 2), "Wavelength: ",
round(max(vP) / f0, 2), " m")
uSource = ricker(times, f0, t0=1. / f0)
plt.figure()
plt.plot(times, uSource, '-*')
plt.show(block=0)
plt.pause(0.01)
u = solvePressureWave(mesh,
vP,
times,
sourcePos=sourcePos,
uSource=uSource,
verbose=10)
u.save(solutionName)
uI = pg.RMatrix()
print("interpolate node to cell data ... ")
pg.interpolate(mesh, u, mesh.cellCenters(), uI)
print("... done")
uI.save(solutionName + 'I')
# nodes = [mesh.findNearestNode(p) for p in geophPoints]
# fig = plt.figure()
# axs = fig.add_subplot(1,1,1)
# drawSeismogramm(axs, mesh, u, nodes, dt, i=None)
# plt.show()
dpi = 92
scale = 1
fig = plt.figure(facecolor='white',
figsize=(scale * 800 / dpi, scale * 490 / dpi),
dpi=dpi)
ax = fig.add_subplot(1, 1, 1)
gci = pg.mplviewer.drawModel(ax,
mesh,
data=uI[0],
cMin=-1,
cMax=1,
cmap='bwr')
pg.mplviewer.drawMeshBoundaries(ax, meshIn, hideMesh=1)
ax.set_xlim((-20, 20))
ax.set_ylim((-15, 0))
ax.set_ylabel('Depth [m]')
ax.set_xlabel('$x$ [m]')
ticks = ax.yaxis.get_majorticklocs()
tickLabels = []
for t in ticks:
tickLabels.append(str(int(abs(t))))
ax.set_yticklabels(tickLabels)
plt.tight_layout()
# ax, cbar = pg.show(mesh, data=vP)
# pg.showNow()
# ax = fig.add_subplot(1,1,1)
def animate(i):
i = i * 5
if i > len(uI) - 1:
return
print("Frame:", i, "/", len(uI))
ui = uI[i]
ui = ui / max(pg.abs(ui))
ui = pg.logDropTol(ui, 1e-2)
cMax = max(pg.abs(ui))
pg.mplviewer.setMappableData(gci,
ui,
cMin=-cMax,
cMax=cMax,
logScale=False)
# plt.pause(0.001)
anim = animation.FuncAnimation(fig,
animate,
frames=int(len(uI) / 5),
interval=0.001,
repeat=0) # , blit=True)
out = 'seis' + str(f0scale) + "cfl-" + str(cfl)
anim.save(out + ".mp4",
writer=None,
fps=20,
dpi=dpi,
codec=None,
bitrate=24 * 1024,
extra_args=None,
metadata=None,
extra_anim=None,
savefig_kwargs=None)
try:
print("create frames ... ")
os.system('mkdir -p anim-' + out)
os.system('ffmpeg -i ' + out + '.mp4 anim-' + out + '/movie%d.jpg')
except:
pass
fop = pb.DCSRMultiElectrodeModelling(mesh, data)
fop.regionManager().region(1).setBackground(True)
fop.createRefinedForwardMesh(refine=True, pRefine=False)
inv = pg.RInversion(data("rhoa"), fop, verbose=True, dosave=True)
datTrans = pg.RTransLog()
modTrans = pg.RTransLog()
inv.setMaxIter(1)
inv.setTransData(datTrans)
inv.setTransModel(modTrans)
inv.setError(data('err'))
inv.setModel(pg.RVector(fop.regionManager().parameterCount(),
pg.median(data('rhoa'))))
inv.setLambda(5)
model = inv.run()
# C = fop.contraintsMatrix()
# S = fop.jacobian()
modelMesh = fop.regionManager().paraDomain()
pg.showLater(1)
ax, cbar = pg.show(modelMesh, model)
pg.show(modelMesh, data.sensorPositions(), axes=ax, showLater=1)
pg.show(modelMesh, axes=ax)
def createJacobian(self, model):
"""Create Jacobian matrix."""
if self.subPotentials is None:
self.response(model)
J = self.jacobian()
J.resize(self.data.size(), self.regionManager().parameterCount())
cells = self.mesh().findCellByMarker(0, -1)
Si = pg.ElementMatrix()
St = pg.ElementMatrix()
u = self.subPotentials
pg.tic()
if self.verbose():
print("Calculate sensitivity matrix for model: ",
min(model), max(model))
Jt = pg.RMatrix(self.data.size(),
self.regionManager().parameterCount())
for kIdx, w in enumerate(self.w):
k = self.k[kIdx]
w = self.w[kIdx]
Jt *= 0.
A = pg.ElementMatrixMap()
for i, c in enumerate(cells):
modelIdx = c.marker()
# 2.5D
Si.u2(c)
Si *= k * k
Si += St.ux2uy2uz2(c)
# 3D
# Si.ux2uy2uz2(c); w = w* 2
A.add(modelIdx, Si)
for dataIdx in range(self.data.size()):
a = int(self.data('a')[dataIdx])
b = int(self.data('b')[dataIdx])
m = int(self.data('m')[dataIdx])
n = int(self.data('n')[dataIdx])
Jt[dataIdx] = A.mult(u[kIdx][a] - u[kIdx][b],
u[kIdx][m] - u[kIdx][n])
J += w * Jt
m2 = model*model
k = self.data('k')
for i in range(J.rows()):
J[i] /= (m2 / k[i])
if self.verbose():
sumsens = np.zeros(J.rows())
for i in range(J.rows()):
sumsens[i] = pg.sum(J[i])
print("sens sum: median = ", pg.median(sumsens),
" min = ", pg.min(sumsens),
" max = ", pg.max(sumsens))
pg.loadMatrixCol(abmnr, "sond1-100.ves") ab2 = abmnr[0] mn2 = abmnr[1] rhoa = abmnr[2] transRho = pg.RTransLogLU(1., 1000.) transThk = pg.RTransLog() transRhoa = pg.RTransLog() f = pg.DC1dModelling(nlay, ab2, mn2) f.region(0).setTransModel(transThk) f.region(1).setTransModel(transRho) paraDepth = max(ab2) / 3 f.region(0).setStartValue(max(ab2) / 3. / nlay / 2.) f.region(1).setStartValue(pg.median(rhoa)) model = f.createStartVector() model[nlay] *= 1.5 inv = pg.RInversion(rhoa, f, True) inv.setModel(model) inv.setTransData(transRhoa) inv.setRelativeError(errPerc / 100.0) inv.setLambda(lam) inv.setMarquardtScheme(0.9) model = inv.run() fig, ax = plt.subplots(nrows=2) ax[0].loglog(rhoa, ab2, 'rx-', inv.response(), ab2, 'b-') ax[0].set_ylim(max(ab2), min(ab2))
def main():
# read config file
conf_file = "inv.conf"
with open(conf_file, "r") as fd:
conf = json.load(fd)
# res = pb.Resistivity("input.dat")
# res.invert()
# np.savetxt('resistivity.vector', res.resistivity)
# return
# load data file
data = pg.DataContainerERT("input.dat")
# remove invalid data
oldsize = data.size()
data.removeInvalid()
newsize = data.size()
if newsize < oldsize:
print('Removed ' + str(oldsize - newsize) + ' values.')
if not data.allNonZero('rhoa'):
print("No or partial rhoa values.")
return
# check, compute error
if data.allNonZero('err'):
error = data('err')
else:
print("estimate data error")
error = conf["relativeError"] + conf["absoluteError"] / data('rhoa')
# create FOP
fop = pg.DCSRMultiElectrodeModelling(verbose=conf["verbose"])
fop.setThreadCount(psutil.cpu_count(logical=False))
fop.setData(data)
# create Inv
inv = pg.RInversion(verbose=conf["verbose"], dosave=False)
# variables tD, tM are needed to prevent destruct objects
tD = pg.RTransLog()
tM = pg.RTransLogLU()
inv.setTransData(tD)
inv.setTransModel(tM)
inv.setForwardOperator(fop)
# mesh
if conf["meshFile"] == "":
depth = conf["depth"]
if depth is None:
depth = pg.DCParaDepth(data)
poly = pg.meshtools.createParaMeshPLC(
data.sensorPositions(),
paraDepth=depth,
paraDX=conf["paraDX"],
paraMaxCellSize=conf["maxCellArea"],
paraBoundary=2,
boundary=2)
if conf["verbose"]:
print("creating mesh...")
mesh = pg.meshtools.createMesh(poly,
quality=conf["quality"],
smooth=(1, 10))
else:
mesh = pg.Mesh(pg.load(conf["meshFile"]))
mesh.createNeighbourInfos()
if conf["verbose"]:
print(mesh)
sys.stdout.flush() # flush before multithreading
fop.setMesh(mesh)
fop.regionManager().setConstraintType(1)
if not conf["omitBackground"]:
if fop.regionManager().regionCount() > 1:
fop.regionManager().region(1).setBackground(True)
if conf["meshFile"] == "":
fop.createRefinedForwardMesh(True, False)
else:
fop.createRefinedForwardMesh(conf["refineMesh"], conf["refineP2"])
paraDomain = fop.regionManager().paraDomain()
inv.setForwardOperator(fop) # necessary?
# inversion parameters
inv.setData(data('rhoa'))
inv.setRelativeError(error)
fop.regionManager().setZWeight(conf['zWeight'])
inv.setLambda(conf['lam'])
inv.setMaxIter(conf['maxIter'])
inv.setRobustData(conf['robustData'])
inv.setBlockyModel(conf['blockyModel'])
inv.setRecalcJacobian(conf['recalcJacobian'])
pc = fop.regionManager().parameterCount()
startModel = pg.RVector(pc, pg.median(data('rhoa')))
inv.setModel(startModel)
# Run the inversion
sys.stdout.flush() # flush before multithreading
model = inv.run()
resistivity = model(paraDomain.cellMarkers())
np.savetxt('resistivity.vector', resistivity)
print("Done.")
if __name__ == '__main__':
nlay = 4 # number of layers
lam = 200. # (initial) regularization parameter
errPerc = 3. # relative error of 3 percent
ab2 = np.logspace(-1, 2, 50) # AB/2 distance (current electrodes)
mn2 = ab2 / 3. # MN/2 distance (potential electrodes)
f = pg.DC1dModelling(nlay, ab2, mn2)
synres = [100., 500., 20., 800.] # synthetic resistivity
synthk = [0.5, 3.5, 6.] # synthetic thickness (nlay-th layer is infinite)
rhoa = f(synthk + synres)
rhoa = rhoa * (pg.randn(len(rhoa)) * errPerc / 100. + 1.)
transLog = pg.RTransLog()
inv = LSQRInversion(rhoa, f, transLog, transLog, True)
inv.setRelativeError(errPerc / 100)
startModel = pg.cat(pg.Vector(nlay - 1, 5),
pg.Vector(nlay, pg.median(rhoa)))
print(inv.response())
inv.setModel(startModel)
inv.setMarquardtScheme()
inv.setLambda(1000)
G = pg.RMatrix(rows=1, cols=len(startModel))
for i in range(3):
G[0][i] = 1
c = pg.Vector(1, pg.sum(synthk))
inv.setParameterConstraints(G, c, 100)
# print("Start", inv.chi2(), inv.relrms(), pg.sum(inv.model()(0, nlay-1)))
if 0:
for i in range(10):
inv.oneStep()
print(i, inv.chi2(), inv.relrms(), pg.sum(inv.model()(0,
nlay - 1)))
def invert(self, data, values=None, verbose=0, **kwargs):
"""
Invert the given data.
A parametric mesh for the inversion will be created if non is given
before.
Parameters
----------
"""
self.fop.setVerbose(verbose)
self.inv.setVerbose(verbose)
self.inv.setMaxIter(kwargs.pop('maxiter', 10))
self.inv.setLambda(kwargs.pop('lambd', 10))
if self.paraMesh is None:
self.paraMesh = createParaMesh2dGrid(data.sensorPositions(),
**kwargs)
self.setParaMesh(self.paraMesh)
if verbose:
print(self.paraMesh)
# pg.show(self.paraMesh)
err = data('err')
rhoa = data('rhoa')
startModel = pg.RVector(self.fop.regionManager().parameterCount(),
pg.median(rhoa))
self.fop.setData(data)
self.inv.setForwardOperator(self.fop)
# check err here
self.inv.setData(rhoa)
self.inv.setError(err)
self.inv.setModel(startModel)
model = self.inv.run()
if values is not None:
if isinstance(values, pg.RVector):
values = [values]
elif isinstance(values, np.ndarray):
if values.ndim == 1:
values = [values]
allModel = pg.RMatrix(len(values), len(model))
self.inv.setVerbose(False)
for i in range(len(values)):
print(i)
tic = time.time()
self.inv.setModel(model)
self.inv.setReferenceModel(model)
dData = pg.abs(values[i] / rhoa)
relModel = self.inv.invSubStep(pg.log(dData))
allModel[i] = model * pg.exp(relModel)
print(i, "/", len(values), " : ",
time.time() - tic, "s min/max: ", min(allModel[i]),
max(allModel[i]))
return allModel
return model
def createJacobian(self, model):
"""Create Jacobian matrix."""
if self.subPotentials is None:
self.response(model)
J = self.jacobian()
J.resize(self.data.size(), self.regionManager().parameterCount())
cells = self.mesh().findCellByMarker(0, -1)
Si = pg.ElementMatrix()
St = pg.ElementMatrix()
u = self.subPotentials
pg.tic()
if self.verbose():
print("Calculate sensitivity matrix for model: ", min(model),
max(model))
Jt = pg.RMatrix(self.data.size(),
self.regionManager().parameterCount())
for kIdx, w in enumerate(self.w):
k = self.k[kIdx]
w = self.w[kIdx]
Jt *= 0.
A = pg.ElementMatrixMap()
for i, c in enumerate(cells):
modelIdx = c.marker()
# 2.5D
Si.u2(c)
Si *= k * k
Si += St.ux2uy2uz2(c)
# 3D
# Si.ux2uy2uz2(c); w = w* 2
A.add(modelIdx, Si)
for dataIdx in range(self.data.size()):
a = int(self.data('a')[dataIdx])
b = int(self.data('b')[dataIdx])
m = int(self.data('m')[dataIdx])
n = int(self.data('n')[dataIdx])
Jt[dataIdx] = A.mult(u[kIdx][a] - u[kIdx][b],
u[kIdx][m] - u[kIdx][n])
J += w * Jt
m2 = model * model
k = self.data('k')
for i in range(J.rows()):
J[i] /= (m2 / k[i])
if self.verbose():
sumsens = np.zeros(J.rows())
for i in range(J.rows()):
sumsens[i] = pg.sum(J[i])
print("sens sum: median = ", pg.median(sumsens), " min = ",
pg.min(sumsens), " max = ", pg.max(sumsens))
poly.createEdge(nodes[2], nodes[3], 2) # hom dirichlet (isolation)
poly.createEdge(nodes[3], nodes[0], 4) # hom dirichlet (isolation)
mesh = createMesh(poly, quality=34, area=0.05, smooth=[0, 10])
return mesh
dx = 0.2
x = np.arange(-20, 20., dx)
y = np.arange(-20, 0.0, dx)[::-1]
mesh = pg.createGrid(x=x, y=y)
mesh = createMesh2()
print(mesh)
h = pg.median(mesh.boundarySizes())
v1 = 1000
v2 = 3000
tmax = 10.1 / v1
z = 2.
f0 = 1000.0 # A low wavelength of 50 Hz
velocities = pg.RVector(mesh.cellCount(), v1)
for c in mesh.cells():
velocities[c.id()] = v1
if c.center()[1] < -z:
velocities[c.id()] = v2