# The total number of cells
nC = mesh.nC
# An (nC, 2) array containing the cell-center locations
cc = mesh.gridCC
# A boolean array specifying which cells lie on the boundary
bInd = mesh.cellBoundaryInd
# Plot the cell areas (2D "volume")
s = mesh.vol
fig = plt.figure(figsize=(6, 6))
ax = fig.add_subplot(111)
mesh.plotImage(s, grid=True, ax=ax)
ax.set_xbound(mesh.x0[0], mesh.x0[0] + np.sum(mesh.hx))
ax.set_ybound(mesh.x0[1], mesh.x0[1] + np.sum(mesh.hy))
ax.set_title("Cell Areas")
###############################################
# 3D Example
# ----------
#
# Here we show how the same approach can be used to create and extract
# properties from a 3D tensor mesh.
#
nc = 10 # number of core mesh cells in x, y and z
dh = 10 # base cell width in x, y and z
class TDEMHorizontalLoopCylWidget(object):
"""TDEMCylWidgete"""
survey = None
srcList = None
mesh = None
f = None
activeCC = None
srcLoc = None
mesh2D = None
mu = None
counter = 0
def __init__(self):
self.genMesh()
self.getCoreDomain()
# url = "http://em.geosci.xyz/_images/disc_dipole.png"
# response = requests.get(url)
# self.im = Image.open(StringIO(response.content))
self.time = np.logspace(-5, -2, 41)
def mirrorArray(self, x, direction="x"):
X = x.reshape((self.nx_core, self.ny_core), order="F")
if direction == "x" or direction == "y":
X2 = np.vstack((-np.flipud(X), X))
else:
X2 = np.vstack((np.flipud(X), X))
return X2
def genMesh(self, h=0.0, cs=3.0, ncx=15, ncz=30, npad=20):
"""
Generate cylindrically symmetric mesh
"""
# TODO: Make it adaptive due to z location
hx = [(cs, ncx), (cs, npad, 1.3)]
hz = [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)]
self.mesh = CylMesh([hx, 1, hz], "00C")
def getCoreDomain(self, mirror=False, xmax=200, zmin=-200, zmax=200.0):
self.activeCC = (self.mesh.gridCC[:, 0] <= xmax) & (np.logical_and(
self.mesh.gridCC[:, 2] >= zmin, self.mesh.gridCC[:, 2] <= zmax))
self.gridCCactive = self.mesh.gridCC[self.activeCC, :][:, [0, 2]]
xind = self.mesh.vectorCCx <= xmax
yind = np.logical_and(self.mesh.vectorCCz >= zmin,
self.mesh.vectorCCz <= zmax)
self.nx_core = xind.sum()
self.ny_core = yind.sum()
# if self.mesh2D is None:
hx = np.r_[self.mesh.hx[xind][::-1], self.mesh.hx[xind]]
hz = self.mesh.hz[yind]
self.mesh2D = TensorMesh([hx, hz], x0="CC")
def getCoreModel(self, Type):
if Type == "Layer":
active = self.mesh2D.vectorCCy < self.z0
ind1 = (self.mesh2D.vectorCCy < self.z0) & (self.mesh2D.vectorCCy
>= self.z1)
ind2 = (self.mesh2D.vectorCCy < self.z1) & (self.mesh2D.vectorCCy
>= self.z2)
mapping2D = maps.SurjectVertical1D(
self.mesh2D) * maps.InjectActiveCells(
self.mesh2D, active, self.sig0, nC=self.mesh2D.nCy)
model2D = np.ones(self.mesh2D.nCy) * self.sig3
model2D[ind1] = self.sig1
model2D[ind2] = self.sig2
model2D = model2D[active]
elif Type == "Sphere":
active = self.mesh2D.gridCC[:, 1] < self.z0
ind1 = (self.mesh2D.gridCC[:, 1] <
self.z1) & (self.mesh2D.gridCC[:, 1] >= self.z1 - self.h)
ind2 = (np.sqrt((self.mesh2D.gridCC[:, 0])**2 +
(self.mesh2D.gridCC[:, 1] - self.z2)**2) <= self.R)
mapping2D = maps.InjectActiveCells(self.mesh2D,
active,
self.sig0,
nC=self.mesh2D.nC)
model2D = np.ones(self.mesh2D.nC) * self.sigb
model2D[ind1] = self.sig1
model2D[ind2] = self.sig2
model2D = model2D[active]
return model2D, mapping2D
def getBiotSavrt(self, rxLoc):
"""
Compute Biot-Savart operator: Gz and Gx
"""
self.Gz = BiotSavartFun(self.mesh, rxLoc, component="z")
self.Gx = BiotSavartFun(self.mesh, rxLoc, component="x")
def setThreeLayerParam(self,
h1=12,
h2=12,
sig0=1e-8,
sig1=1e-2,
sig2=1e-2,
sig3=1e-2,
chi=0.0):
self.h1 = h1 # 1st layer thickness
self.h2 = h2 # 2nd layer thickness
self.z0 = 0.0
self.z1 = self.z0 - h1
self.z2 = self.z0 - h1 - h2
self.sig0 = sig0 # 0th layer \sigma (assumed to be air)
self.sig1 = sig1 # 1st layer \sigma
self.sig2 = sig2 # 2nd layer \sigma
self.sig3 = sig3 # 3rd layer \sigma
active = self.mesh.vectorCCz < self.z0
ind1 = (self.mesh.vectorCCz < self.z0) & (self.mesh.vectorCCz >=
self.z1)
ind2 = (self.mesh.vectorCCz < self.z1) & (self.mesh.vectorCCz >=
self.z2)
self.mapping = maps.SurjectVertical1D(
self.mesh) * maps.InjectActiveCells(
self.mesh, active, sig0, nC=self.mesh.nCz)
model = np.ones(self.mesh.nCz) * sig3
model[ind1] = sig1
model[ind2] = sig2
self.m = model[active]
self.mu = np.ones(self.mesh.nC) * mu_0
self.mu[self.mesh.gridCC[:, 2] < 0.0] = (1.0 + chi) * mu_0
return self.m
def setLayerSphereParam(self,
d1=6,
h=6,
d2=16,
R=4,
sig0=1e-8,
sigb=1e-2,
sig1=1e-1,
sig2=1.0,
chi=0.0):
self.z0 = 0.0 # Surface elevation
self.z1 = self.z0 - d1 # Depth to layer
self.h = h # Thickness of layer
self.z2 = self.z0 - d2 # Depth to center of sphere
self.R = R # Radius of sphere
self.sig0 = sig0 # Air conductivity
self.sigb = sigb # Background conductivity
self.sig1 = sig1 # Layer conductivity
self.sig2 = sig2 # Sphere conductivity
active = self.mesh.gridCC[:, 2] < self.z0
ind1 = (self.mesh.gridCC[:, 2] < self.z1) & (self.mesh.gridCC[:, 2] >=
self.z1 - self.h)
ind2 = (np.sqrt((self.mesh.gridCC[:, 0])**2 +
(self.mesh.gridCC[:, 2] - self.z2)**2) <= self.R)
self.mapping = maps.InjectActiveCells(self.mesh,
active,
sig0,
nC=self.mesh.nC)
model = np.ones(self.mesh.nC) * sigb
model[ind1] = sig1
model[ind2] = sig2
self.m = model[active]
self.mu = np.ones(self.mesh.nC) * mu_0
self.mu[self.mesh.gridCC[:, 2] < 0.0] = (1.0 + chi) * mu_0
return self.m
def simulate(self, srcLoc, rxLoc, time, radius=1.0):
bz = tdem.receivers.PointMagneticFluxDensity(rxLoc,
time,
orientation="z")
# dbzdt = EM.TDEM.Rx.Point_dbdt(rxLoc, time, orientation="z")
src = tdem.sources.CircularLoop(
[bz],
waveform=tdem.sources.StepOffWaveform(),
location=srcLoc,
radius=radius)
self.srcList = [src]
survey = tdem.survey.Survey(self.srcList)
sim = tdem.Simulation3DMagneticFluxDensity(self.mesh,
survey=survey,
sigmaMap=self.mapping)
sim.time_steps = [
(1e-06, 10),
(5e-06, 10),
(1e-05, 10),
(5e-5, 10),
(1e-4, 10),
(5e-4, 10),
(1e-3, 10),
]
self.f = sim.fields(self.m)
self.sim = sim
dpred = sim.dpred(self.m, f=self.f)
return dpred
@property
def Pfx(self):
if getattr(self, "_Pfx", None) is None:
self._Pfx = self.mesh.getInterpolationMat(
self.mesh.gridCC[self.activeCC, :], locType="Fx")
return self._Pfx
@property
def Pfz(self):
if getattr(self, "_Pfz", None) is None:
self._Pfz = self.mesh.getInterpolationMat(
self.mesh.gridCC[self.activeCC, :], locType="Fz")
return self._Pfz
def getFields(self, itime):
src = self.srcList[0]
Ey = self.mesh.aveE2CC * self.f[src, "e", itime]
Jy = utils.sdiag(self.sim.sigma) * Ey
self.Ey = utils.mkvc(self.mirrorArray(Ey[self.activeCC],
direction="y"))
self.Jy = utils.mkvc(self.mirrorArray(Jy[self.activeCC],
direction="y"))
self.Bx = utils.mkvc(
self.mirrorArray(self.Pfx * self.f[src, "b", itime],
direction="x"))
self.Bz = utils.mkvc(
self.mirrorArray(self.Pfz * self.f[src, "b", itime],
direction="z"))
self.dBxdt = utils.mkvc(
self.mirrorArray(-self.Pfx * self.mesh.edgeCurl *
self.f[src, "e", itime],
direction="x"))
self.dBzdt = utils.mkvc(
self.mirrorArray(-self.Pfz * self.mesh.edgeCurl *
self.f[src, "e", itime],
direction="z"))
def getData(self):
src = self.srcList[0]
Pfx = self.mesh.getInterpolationMat(self.rxLoc, locType="Fx")
Pfz = self.mesh.getInterpolationMat(self.rxLoc, locType="Fz")
Pey = self.mesh.getInterpolationMat(self.rxLoc, locType="Ey")
self.Ey = (Pey * self.f[src, "e", :]).flatten()
self.Bx = (Pfx * self.f[src, "b", :]).flatten()
self.Bz = (Pfz * self.f[src, "b", :]).flatten()
self.dBxdt = (-Pfx * self.mesh.edgeCurl *
self.f[src, "e", :]).flatten()
self.dBzdt = (-Pfz * self.mesh.edgeCurl *
self.f[src, "e", :]).flatten()
def plotField(
self,
Field="B",
view="vec",
scale="linear",
itime=0,
Geometry=True,
Scenario=None,
Fixed=False,
vmin=None,
vmax=None,
):
# Printout for null cases
if (Field == "B") & (view == "y"):
print(
"Think about the problem geometry. There is NO By in this case."
)
elif (Field == "dBdt") & (view == "y"):
print(
"Think about the problem geometry. There is NO dBy/dt in this case."
)
elif (Field == "E") & (view == "x") | (Field == "E") & (view == "z"):
print(
"Think about the problem geometry. There is NO Ex or Ez in this case. Only Ey."
)
elif (Field == "J") & (view == "x") | (Field == "J") & (view == "z"):
print(
"Think about the problem geometry. There is NO Jx or Jz in this case. Only Jy."
)
elif (Field == "E") & (view == "vec"):
print(
"Think about the problem geometry. E only has components along y. Vector plot not possible"
)
elif (Field == "J") & (view == "vec"):
print(
"Think about the problem geometry. J only has components along y. Vector plot not possible"
)
elif Field == "Model":
plt.figure(figsize=(7, 6))
ax = plt.subplot(111)
if Scenario == "Sphere":
model2D, mapping2D = self.getCoreModel("Sphere")
elif Scenario == "Layer":
model2D, mapping2D = self.getCoreModel("Layer")
if Fixed:
clim = (np.log10(vmin), np.log10(vmax))
else:
clim = None
out = self.mesh2D.plotImage(np.log10(mapping2D * model2D),
ax=ax,
clim=clim)
cb = plt.colorbar(out[0], ax=ax, format="$10^{%.1f}$")
cb.set_label("$\sigma$ (S/m)")
ax.set_xlabel("Distance (m)")
ax.set_ylabel("Depth (m)")
ax.set_title("Conductivity Model")
plt.show()
else:
plt.figure(figsize=(10, 6))
ax = plt.subplot(111)
vec = False
if view == "vec":
tname = "Vector "
title = tname + Field + "-field"
elif view == "amp":
tname = "|"
title = tname + Field + "|-field"
else:
title = Field + view + "-field"
if Field == "B":
label = "Magnetic field (T)"
if view == "vec":
vec = True
val = np.c_[self.Bx, self.Bz]
elif view == "x":
val = self.Bx
elif view == "z":
val = self.Bz
else:
return
elif Field == "dBdt":
label = "Time derivative of magnetic field (T/s)"
if view == "vec":
vec = True
val = np.c_[self.dBxdt, self.dBzdt]
elif view == "x":
val = self.dBxdt
elif view == "z":
val = self.dBzdt
else:
return
elif Field == "E":
label = "Electric field (V/m)"
if view == "y":
val = self.Ey
else:
return
elif Field == "J":
label = "Current density (A/m$^2$)"
if view == "y":
val = self.Jy
else:
return
if Fixed:
if scale == "log":
vmin, vmax = (np.log10(vmin), np.log10(vmax))
out = ax.scatter(np.zeros(3) - 1000,
np.zeros(3),
c=np.linspace(vmin, vmax, 3))
utils.plot2Ddata(
self.mesh2D.gridCC,
val,
vec=vec,
ax=ax,
contourOpts={
"cmap": "viridis",
"vmin": vmin,
"vmax": vmax
},
ncontour=200,
scale=scale,
)
else:
out = utils.plot2Ddata(
self.mesh2D.gridCC,
val,
vec=vec,
ax=ax,
contourOpts={"cmap": "viridis"},
ncontour=200,
scale=scale,
)[0]
if scale == "linear":
cb = plt.colorbar(out, ax=ax, format="%.2e")
elif scale == "log":
cb = plt.colorbar(out, ax=ax, format="$10^{%.1f}$")
else:
raise Exception("We consdier only linear and log scale!")
cb.set_label(label)
xmax = self.mesh2D.gridCC[:, 0].max()
if Geometry:
if Scenario == "Layer":
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.srcLoc[2],
"w-",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.z0,
"w--",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.z1,
"w--",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.z2,
"w--",
lw=1)
ax.plot(0, self.srcLoc[2], "ko", ms=4)
ax.plot(self.rxLoc[0, 0], self.srcLoc[2], "ro", ms=4)
elif Scenario == "Sphere":
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.srcLoc[2],
"k-",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.z0,
"w--",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.z1,
"w--",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * (self.z1 - self.h),
"w--",
lw=1)
Phi = np.linspace(0, 2 * np.pi, 41)
ax.plot(
self.R * np.cos(Phi),
self.z2 + self.R * np.sin(Phi),
"w--",
lw=1,
)
ax.plot(0, self.srcLoc[2], "ko", ms=4)
ax.plot(self.rxLoc[0, 0], self.srcLoc[2], "ro", ms=4)
ax.set_xlabel("Distance (m)")
ax.set_ylabel("Depth (m)")
title = (title + "\nt = " +
"{:.2e}".format(self.sim.times[itime] * 1e3) + " ms")
ax.set_title(title)
ax.set_xlim(-190, 190)
ax.set_ylim(-190, 190)
plt.show()
######################################################
# LAYER WIDGET
######################################################
def InteractivePlane_Layer(self,
scale="log",
fieldvalue="E",
compvalue="y"):
def foo(
Update,
Field,
AmpDir,
Component,
Sigma0,
Sigma1,
Sigma2,
Sigma3,
Sus,
h1,
h2,
Scale,
rxOffset,
z,
radius,
itime,
Geometry=True,
Fixed=False,
vmin=None,
vmax=None,
):
if AmpDir == "Direction (B or dBdt)":
Component = "vec"
self.setThreeLayerParam(
h1=h1,
h2=h2,
sig0=Sigma0,
sig1=Sigma1,
sig2=Sigma2,
sig3=Sigma3,
chi=Sus,
)
self.srcLoc = np.array([0.0, 0.0, z])
self.rxLoc = np.array([[rxOffset, 0.0, z]])
self.radius = radius
if Update:
self.simulate(self.srcLoc, self.rxLoc, self.time, self.radius)
self.getFields(itime)
return self.plotField(
Field=Field,
view=Component,
scale=Scale,
Geometry=Geometry,
itime=itime,
Scenario="Layer",
Fixed=Fixed,
vmin=vmin,
vmax=vmax,
)
out = widgetify(
foo,
Update=widgets.widget_bool.Checkbox(value=True,
description="Update"),
Field=widgets.ToggleButtons(
options=["E", "B", "dBdt", "J", "Model"], value=fieldvalue),
AmpDir=widgets.ToggleButtons(
options=["None", "Direction (B or dBdt)"], value="None"),
Component=widgets.ToggleButtons(options=["x", "y", "z"],
value=compvalue,
description="Comp."),
Sigma0=widgets.FloatText(value=1e-8,
continuous_update=False,
description="$\sigma_0$ (S/m)"),
Sigma1=widgets.FloatText(value=0.01,
continuous_update=False,
description="$\sigma_1$ (S/m)"),
Sigma2=widgets.FloatText(value=0.01,
continuous_update=False,
description="$\sigma_2$ (S/m)"),
Sigma3=widgets.FloatText(value=0.01,
continuous_update=False,
description="$\sigma_3$ (S/m)"),
Sus=widgets.FloatText(value=0.0,
continuous_update=False,
description="$\chi$"),
h1=widgets.FloatSlider(
min=2.0,
max=50.0,
step=2.0,
value=20.0,
continuous_update=False,
description="$h_1$ (m)",
),
h2=widgets.FloatSlider(
min=2.0,
max=50.0,
step=2.0,
value=20.0,
continuous_update=False,
description="$h_2$ (m)",
),
Scale=widgets.ToggleButtons(options=["log", "linear"],
value="linear"),
rxOffset=widgets.FloatSlider(
min=0.0,
max=50.0,
step=2.0,
value=10.0,
continuous_update=False,
description="$\Delta x$(m)",
),
z=widgets.FloatSlider(
min=0.0,
max=50.0,
step=2.0,
value=0.0,
continuous_update=False,
description="$\Delta z$ (m)",
),
itime=widgets.IntSlider(
min=1,
max=70,
step=1,
value=1,
continuous_update=False,
description="Time index",
),
radius=widgets.FloatSlider(
min=2.0,
max=50.0,
step=2.0,
value=2.0,
continuous_update=False,
description="Tx radius (m)",
),
Fixed=widgets.widget_bool.Checkbox(value=False,
description="Fixed"),
vmin=FloatText(value=None, description="vmin"),
vmax=FloatText(value=None, description="vmax"),
)
return out
def InteractiveData_Layer(self, fieldvalue="B", compvalue="z"):
def foo(Field, Component, Scale):
if (Field == "B") & (Component == "y") | (Field == "dBdt") & (
Component == "y"):
print(
"Think about the problem geometry. There is NO By in this case."
)
elif (Field == "E") & (Component == "x") | (Field == "E") & (
Component == "z"):
print(
"Think about the problem geometry. There is NO Ex or Ez in this case. Only Ey."
)
else:
plt.figure()
ax = plt.subplot(111)
# bType = "b"
self.getData()
if Field == "B":
label = "Magnetic field (T)"
if Component == "x":
title = "Bx"
val = self.Bx
elif Component == "z":
title = "Bz"
val = self.Bz
else:
# ax.imshow(self.im)
ax.set_xticks([])
ax.set_yticks([])
plt.show()
print(
"Think about the problem geometry. There is NO By in this case."
)
elif Field == "dBdt":
label = "Time dervative of magnetic field (T/s)"
if Component == "x":
title = "dBx/dt"
val = self.dBxdt
elif Component == "z":
title = "dBz/dt"
val = self.dBzdt
else:
# ax.imshow(self.im)
ax.set_xticks([])
ax.set_yticks([])
plt.show()
print(
"Think about the problem geometry. There is NO dBy/dt in this case."
)
elif Field == "E":
label = "Electric field (V/m)"
title = "Ey"
if Component == "y":
val = self.Ey
else:
# ax.imshow(self.im)
ax.set_xticks([])
ax.set_yticks([])
plt.show()
print(
"Think about the problem geometry. There is NO Ex or Ez in this case."
)
elif Field == "J":
print(
"The conductivity at the location is 0. Therefore there is no electrical current here."
)
if Scale == "log":
val_p, val_n = DisPosNegvalues(val)
ax.plot(self.sim.times[10:] * 1e3, val_p[10:], "k-")
ax.plot(self.sim.times[10:] * 1e3, val_n[10:], "k--")
ax.legend(("(+)", "(-)"), loc=1, fontsize=10)
else:
ax.plot(self.sim.times[10:] * 1e3, val[10:], "k.-")
ax.set_xscale("log")
ax.set_yscale(Scale)
ax.set_xlabel("Time (ms)")
ax.set_ylabel(label)
ax.set_title(title)
ax.grid(True)
plt.show()
out = widgetify(
foo,
Field=widgets.ToggleButtons(options=["E", "B", "dBdt"],
value=fieldvalue),
Component=widgets.ToggleButtons(options=["x", "y", "z"],
value=compvalue,
description="Comp."),
Scale=widgets.ToggleButtons(options=["log", "linear"],
value="log"),
)
return out
######################################################
# SPHERE WIDGET
######################################################
def InteractivePlane_Sphere(self,
scale="log",
fieldvalue="E",
compvalue="y"):
def foo(
Update,
Field,
AmpDir,
Component,
Sigma0,
Sigmab,
Sigma1,
Sigma2,
Sus,
d1,
h,
d2,
R,
Scale,
rxOffset,
z,
radius,
itime,
Geometry=True,
Fixed=False,
vmin=None,
vmax=None,
):
if AmpDir == "Direction (B or dBdt)":
Component = "vec"
self.setLayerSphereParam(
d1=d1,
h=h,
d2=d2,
R=R,
sig0=Sigma0,
sigb=Sigmab,
sig1=Sigma1,
sig2=Sigma2,
chi=Sus,
)
self.srcLoc = np.array([0.0, 0.0, z])
self.rxLoc = np.array([[rxOffset, 0.0, z]])
self.radius = radius
if Update:
self.simulate(self.srcLoc, self.rxLoc, self.time, self.radius)
self.getFields(itime)
return self.plotField(
Field=Field,
view=Component,
scale=Scale,
Geometry=Geometry,
itime=itime,
Scenario="Sphere",
Fixed=Fixed,
vmin=vmin,
vmax=vmax,
)
out = widgetify(
foo,
Update=widgets.widget_bool.Checkbox(value=True,
description="Update"),
Field=widgets.ToggleButtons(
options=["E", "B", "dBdt", "J", "Model"], value=fieldvalue),
AmpDir=widgets.ToggleButtons(
options=["None", "Direction (B or dBdt)"], value="None"),
Component=widgets.ToggleButtons(options=["x", "y", "z"],
value=compvalue,
description="Comp."),
Sigma0=widgets.FloatText(value=1e-8,
continuous_update=False,
description="$\sigma_0$ (S/m)"),
Sigmab=widgets.FloatText(value=0.01,
continuous_update=False,
description="$\sigma_b$ (S/m)"),
Sigma1=widgets.FloatText(value=0.01,
continuous_update=False,
description="$\sigma_1$ (S/m)"),
Sigma2=widgets.FloatText(value=1.0,
continuous_update=False,
description="$\sigma_2$ (S/m)"),
Sus=widgets.FloatText(value=0.0,
continuous_update=False,
description="$\chi$"),
d1=widgets.FloatSlider(
min=0.0,
max=50.0,
step=2.0,
value=0.0,
continuous_update=False,
description="$d_1$ (m)",
),
h=widgets.FloatSlider(
min=2.0,
max=40.0,
step=2.0,
value=20.0,
continuous_update=False,
description="$h$ (m)",
),
d2=widgets.FloatSlider(
min=20.0,
max=80.0,
step=2.0,
value=60.0,
continuous_update=False,
description="$d_2$ (m)",
),
R=widgets.FloatSlider(
min=2.0,
max=40.0,
step=2.0,
value=30.0,
continuous_update=False,
description="$R$ (m)",
),
Scale=widgets.ToggleButtons(options=["log", "linear"],
value="linear"),
rxOffset=widgets.FloatSlider(
min=0.0,
max=50.0,
step=2.0,
value=10.0,
continuous_update=False,
description="$\Delta x$(m)",
),
z=widgets.FloatSlider(
min=0.0,
max=50.0,
step=2.0,
value=0.0,
continuous_update=False,
description="$\Delta z$ (m)",
),
radius=widgets.FloatSlider(
min=2.0,
max=50.0,
step=2.0,
value=2.0,
continuous_update=False,
description="Tx radius (m)",
),
itime=widgets.IntSlider(
min=1,
max=70,
step=1,
value=1,
continuous_update=False,
description="Time index",
),
Fixed=widgets.widget_bool.Checkbox(value=False,
description="Fixed"),
vmin=FloatText(value=None, description="vmin"),
vmax=FloatText(value=None, description="vmax"),
)
return out
def InteractiveData_Sphere(self, fieldvalue="B", compvalue="z"):
def foo(Field, Component, Scale):
if (Field == "B") & (Component == "y") | (Field == "dBdt") & (
Component == "y"):
print(
"Think about the problem geometry. There is NO By in this case."
)
elif (Field == "E") & (Component == "x") | (Field == "E") & (
Component == "z"):
print(
"Think about the problem geometry. There is NO Ex or Ez in this case. Only Ey."
)
else:
plt.figure()
ax = plt.subplot(111)
# bType = "b"
self.getData()
if Field == "B":
label = "Magnetic field (T)"
if Component == "x":
title = "Bx"
val = self.Bx
elif Component == "z":
title = "Bz"
val = self.Bz
else:
# ax.imshow(self.im)
ax.set_xticks([])
ax.set_yticks([])
plt.show()
print(
"Think about the problem geometry. There is NO By in this case."
)
elif Field == "dBdt":
label = "Time dervative of magnetic field (T/s)"
if Component == "x":
title = "dBx/dt"
val = self.dBxdt
elif Component == "z":
title = "dBz/dt"
val = self.dBzdt
else:
# ax.imshow(self.im)
ax.set_xticks([])
ax.set_yticks([])
plt.show()
print(
"Think about the problem geometry. There is NO dBy/dt in this case."
)
elif Field == "E":
label = "Electric field (V/m)"
title = "Ey"
if Component == "y":
val = self.Ey
else:
# ax.imshow(self.im)
ax.set_xticks([])
ax.set_yticks([])
plt.show()
print(
"Think about the problem geometry. There is NO Ex or Ez in this case."
)
elif Field == "J":
print(
"The conductivity at the location is 0. Therefore there is no electrical current here."
)
if Scale == "log":
val_p, val_n = DisPosNegvalues(val)
ax.plot(self.sim.times[10:] * 1e3, val_p[10:], "k-")
ax.plot(self.sim.times[10:] * 1e3, val_n[10:], "k--")
ax.legend(("(+)", "(-)"), loc=1, fontsize=10)
else:
ax.plot(self.sim.times[10:] * 1e3, val[10:], "k.-")
ax.set_xscale("log")
ax.set_yscale(Scale)
ax.set_xlabel("Time (ms)")
ax.set_ylabel(label)
ax.set_title(title)
ax.grid(True)
plt.show()
out = widgetify(
foo,
Field=widgets.ToggleButtons(options=["E", "B", "dBdt"],
value=fieldvalue),
Component=widgets.ToggleButtons(options=["x", "y", "z"],
value=compvalue,
description="Comp."),
Scale=widgets.ToggleButtons(options=["log", "linear"],
value="log"),
)
return out
edges_y = mesh.gridEy
wx = (-edges_x[:, 1] / np.sqrt(np.sum(edges_x**2, axis=1))) * np.exp(
-(edges_x[:, 0]**2 + edges_x[:, 1]**2) / 6**2)
wy = (edges_y[:, 0] / np.sqrt(np.sum(edges_y**2, axis=1))) * np.exp(
-(edges_y[:, 0]**2 + edges_y[:, 1]**2) / 6**2)
w = np.r_[wx, wy]
curl_w = CURL * w
# Plot Gradient of u
fig = plt.figure(figsize=(10, 5))
ax1 = fig.add_subplot(121)
mesh.plotImage(u, ax=ax1, v_type="N")
ax1.set_title("u at cell centers")
ax2 = fig.add_subplot(122)
mesh.plotImage(grad_u,
ax=ax2,
v_type="E",
view="vec",
stream_opts={
"color": "w",
"density": 1.0
})
ax2.set_title("gradient of u on edges")
fig.show()
# Run inversion
recovered_model = inv.run(starting_model)
############################################################
# Plotting True Model and Recovered Model
# ---------------------------------------
#
# Load the true model
true_model = np.loadtxt(str(model_filename))
# Plot True Model
fig = plt.figure(figsize=(6, 5.5))
ax1 = fig.add_axes([0.15, 0.15, 0.65, 0.75])
mesh.plotImage(true_model, ax=ax1, grid=True, pcolorOpts={"cmap": "viridis"})
ax1.set_title("True Model")
ax2 = fig.add_axes([0.82, 0.15, 0.05, 0.75])
norm = mpl.colors.Normalize(vmin=np.min(true_model), vmax=np.max(true_model))
cbar = mpl.colorbar.ColorbarBase(ax2,
norm=norm,
orientation="vertical",
cmap=mpl.cm.viridis)
cbar.set_label("Velocity (m/s)", rotation=270, labelpad=15, size=12)
plt.show()
# Plot Recovered Model
fig = plt.figure(figsize=(6, 5.5))
M = TensorMesh(h, x0)
ccMesh = M.gridCC
# ------------------- Test conductivities! --------------------------
print('Testing 1 block conductivity')
p0 = np.array([0.5, 0.5, 0.5])[:testDim]
p1 = np.array([1.0, 1.0, 1.0])[:testDim]
vals = np.array([100, 1e-6])
sigma = defineBlockConductivity(ccMesh, p0, p1, vals)
# Plot sigma model
print(sigma.shape)
M.plotImage(sigma)
print('Done with block! :)')
plt.show()
# -----------------------------------------
print('Testing the two layered model')
vals = np.array([100, 1e-5])
depth = 1.0
sigma = defineTwoLayeredConductivity(ccMesh, depth, vals)
M.plotImage(sigma)
print(sigma)
print('layer model!')
plt.show()
v = np.r_[vx, vy]
Mf = mesh.getFaceInnerProduct() # Edge inner product matrix
ipf = np.dot(v, Mf * v)
# The analytic solution of (v, v)
ipt = np.pi * sig**2
# Plot the vector function
fig = plt.figure(figsize=(5, 5))
ax = fig.add_subplot(111)
mesh.plotImage(v,
ax=ax,
vType='F',
view='vec',
streamOpts={
'color': 'w',
'density': 1.0
})
ax.set_title('v at cell faces')
fig.show()
# Verify accuracy
print('ACCURACY')
print('Analytic solution: ', ipt)
print('Edge variable approx.:', ipe)
print('Face variable approx.:', ipf)
##############################################
# Inverse of Inner Product Matricies
I = sdiag(np.ones(mesh.nC)) # Identity matrix
B = I + dt * M
s = Mc_inv * q
Binv = SolverLU(B)
# Plot the vector field
fig = plt.figure(figsize=(15, 15))
ax = 9 * [None]
ax[0] = fig.add_subplot(332)
mesh.plotImage(u,
ax=ax[0],
vType='F',
view='vec',
streamOpts={
'color': 'w',
'density': 1.0
},
clim=[0., 10.])
ax[0].set_title('Divergence free vector field')
ax[1] = fig.add_subplot(333)
ax[1].set_aspect(10, anchor='W')
cbar = mpl.colorbar.ColorbarBase(ax[1], orientation='vertical')
cbar.set_label('Velocity (m/s)', rotation=270, labelpad=5)
# Perform backward Euler and plot
n = 3
from SimPEG import Mesh
import matplotlib.pyplot as plt
cs = 20
ncx, ncy, ncz = 41, 41, 40
hx = np.ones(ncx)*cs
hy = np.ones(ncy)*cs
hz = np.ones(ncz)*cs
mesh = TensorMesh([hx, hy, hz], 'CCC')
srcLoc = np.r_[0., 0., 0.]
Ax = MagneticLoopVectorPotential(srcLoc, mesh.gridEx, 'x', 200)
Ay = MagneticLoopVectorPotential(srcLoc, mesh.gridEy, 'y', 200)
Az = MagneticLoopVectorPotential(srcLoc, mesh.gridEz, 'z', 200)
A = np.r_[Ax, Ay, Az]
B0 = mesh.edgeCurl*A
J0 = mesh.edgeCurl.T*B0
# mesh.plotImage(A, vType = 'Ex')
# mesh.plotImage(A, vType = 'Ey')
mesh.plotImage(B0, vType = 'Fx')
mesh.plotImage(B0, vType = 'Fy')
mesh.plotImage(B0, vType = 'Fz')
# # mesh.plotImage(J0, vType = 'Ex')
# mesh.plotImage(J0, vType = 'Ey')
# mesh.plotImage(J0, vType = 'Ez')
plt.show()
if __name__ == '__main__':
from SimPEG import Mesh
import matplotlib.pyplot as plt
cs = 20
ncx, ncy, ncz = 41, 41, 40
hx = np.ones(ncx) * cs
hy = np.ones(ncy) * cs
hz = np.ones(ncz) * cs
mesh = TensorMesh([hx, hy, hz], 'CCC')
srcLoc = np.r_[0., 0., 0.]
Ax = MagneticLoopVectorPotential(srcLoc, mesh.gridEx, 'x', 200)
Ay = MagneticLoopVectorPotential(srcLoc, mesh.gridEy, 'y', 200)
Az = MagneticLoopVectorPotential(srcLoc, mesh.gridEz, 'z', 200)
A = np.r_[Ax, Ay, Az]
B0 = mesh.edgeCurl * A
J0 = mesh.edgeCurl.T * B0
# mesh.plotImage(A, vType = 'Ex')
# mesh.plotImage(A, vType = 'Ey')
mesh.plotImage(B0, vType='Fx')
mesh.plotImage(B0, vType='Fy')
mesh.plotImage(B0, vType='Fz')
# # mesh.plotImage(J0, vType = 'Ex')
# mesh.plotImage(J0, vType = 'Ey')
# mesh.plotImage(J0, vType = 'Ez')
plt.show()
h = 2 * np.ones(50)
mesh = TensorMesh([h, h], x0="CC")
A2 = mesh.aveCC2F # cell centers to faces
A3 = mesh.aveN2CC # nodes to cell centers
A4 = mesh.aveF2CC # faces to cell centers
# Create a variable on cell centers
v = 100.0 * np.ones(mesh.nC)
xy = mesh.gridCC
v[(xy[:, 1] > 0)] = 0.0
v[(xy[:, 1] < -10.0) & (xy[:, 0] > -10.0) & (xy[:, 0] < 10.0)] = 50.0
fig = plt.figure(figsize=(10, 10))
ax1 = fig.add_subplot(221)
mesh.plotImage(v, ax=ax1)
ax1.set_title("Variable at cell centers")
# Apply cell centers to faces averaging
ax2 = fig.add_subplot(222)
mesh.plotImage(A2 * v, ax=ax2, v_type="F")
ax2.set_title("Cell centers to faces")
# Use the transpose to go from cell centers to nodes
ax3 = fig.add_subplot(223)
mesh.plotImage(A3.T * v, ax=ax3, v_type="N")
ax3.set_title("Cell centers to nodes using transpose")
# Use the transpose to go from cell centers to faces
ax4 = fig.add_subplot(224)
mesh.plotImage(A4.T * v, ax=ax4, v_type="F")
v = np.r_[vx, vy]
Mf = mesh.getFaceInnerProduct() # Edge inner product matrix
ipf = np.dot(v, Mf * v)
# The analytic solution of (v, v)
ipt = np.pi * sig**2
# Plot the vector function
fig = plt.figure(figsize=(5, 5))
ax = fig.add_subplot(111)
mesh.plotImage(v,
ax=ax,
v_type="F",
view="vec",
stream_opts={
"color": "w",
"density": 1.0
})
ax.set_title("v at cell faces")
fig.show()
# Verify accuracy
print("ACCURACY")
print("Analytic solution: ", ipt)
print("Edge variable approx.:", ipe)
print("Face variable approx.:", ipf)
##############################################
# Inverse of Inner Product Matricies
h = 2 * np.ones(50)
mesh = TensorMesh([h, h], x0='CC')
A2 = mesh.aveCC2F # cell centers to faces
A3 = mesh.aveN2CC # nodes to cell centers
A4 = mesh.aveF2CC # faces to cell centers
# Create a variable on cell centers
v = 100. * np.ones(mesh.nC)
xy = mesh.gridCC
v[(xy[:, 1] > 0)] = 0.
v[(xy[:, 1] < -10.) & (xy[:, 0] > -10.) & (xy[:, 0] < 10.)] = 50.
fig = plt.figure(figsize=(10, 10))
ax1 = fig.add_subplot(221)
mesh.plotImage(v, ax=ax1)
ax1.set_title('Variable at cell centers')
# Apply cell centers to faces averaging
ax2 = fig.add_subplot(222)
mesh.plotImage(A2 * v, ax=ax2, v_type='F')
ax2.set_title('Cell centers to faces')
# Use the transpose to go from cell centers to nodes
ax3 = fig.add_subplot(223)
mesh.plotImage(A3.T * v, ax=ax3, v_type='N')
ax3.set_title('Cell centers to nodes using transpose')
# Use the transpose to go from cell centers to faces
ax4 = fig.add_subplot(224)
mesh.plotImage(A4.T * v, ax=ax4, v_type='F')
# Define the model. Models in SimPEG are vector arrays.
model = background_velocity * np.ones(mesh.nC)
ind_block = model_builder.getIndicesBlock(np.r_[-50, 20], np.r_[50, -20],
mesh.gridCC)
model[ind_block] = block_velocity
# Define a mapping from the model (velocity) to the slowness. If your model
# consists of slowness values, you can use *maps.IdentityMap*.
model_mapping = maps.ReciprocalMap()
# Plot Velocity Model
fig = plt.figure(figsize=(6, 5.5))
ax1 = fig.add_axes([0.15, 0.15, 0.65, 0.75])
mesh.plotImage(model, ax=ax1, grid=True, pcolorOpts={"cmap": "viridis"})
ax1.set_xlabel("x (m)")
ax1.set_ylabel("y (m)")
ax1.plot(x, y_sources, "ro") # source locations
ax1.plot(x, y_receivers, "ko") # receiver locations
ax2 = fig.add_axes([0.82, 0.15, 0.05, 0.75])
norm = mpl.colors.Normalize(vmin=np.min(model), vmax=np.max(model))
cbar = mpl.colorbar.ColorbarBase(ax2,
norm=norm,
orientation="vertical",
cmap=mpl.cm.viridis)
cbar.set_label("$Velocity (m/s)$", rotation=270, labelpad=15, size=12)
#######################################################
# Simulation: Arrival Time
rho = np.zeros(mesh.nC)
rho[kneg] = -1
rho[kpos] = 1
# LU factorization and solve
AinvM = SolverLU(A)
phi = AinvM * rho
# Compute electric fields
E = Mf_inv * DIV.T * Mc * phi
# Plotting
fig = plt.figure(figsize=(14, 4))
ax1 = fig.add_subplot(131)
mesh.plotImage(rho, vType='CC', ax=ax1)
ax1.set_title('Charge Density')
ax2 = fig.add_subplot(132)
mesh.plotImage(phi, vType='CC', ax=ax2)
ax2.set_title('Electric Potential')
ax3 = fig.add_subplot(133)
mesh.plotImage(E,
ax=ax3,
vType='F',
view='vec',
streamOpts={
'color': 'w',
'density': 1.0
})
I = sdiag(np.ones(mesh.nC)) # Identity matrix
B = I + dt * M
s = Mc_inv * q
Binv = SolverLU(B)
# Plot the vector field
fig = plt.figure(figsize=(15, 15))
ax = 9 * [None]
ax[0] = fig.add_subplot(332)
mesh.plotImage(
u,
ax=ax[0],
v_type="F",
view="vec",
stream_opts={"color": "w", "density": 1.0},
clim=[0.0, 10.0],
)
ax[0].set_title("Divergence free vector field")
ax[1] = fig.add_subplot(333)
ax[1].set_aspect(10, anchor="W")
cbar = mpl.colorbar.ColorbarBase(ax[1], orientation="vertical")
cbar.set_label("Velocity (m/s)", rotation=270, labelpad=5)
# Perform backward Euler and plot
n = 3
for ii in range(300):
class HarmonicVMDCylWidget(object):
"""FDEMCylWidgete"""
survey = None
srcList = None
mesh = None
f = None
activeCC = None
srcLoc = None
mesh2D = None
mu = None
def __init__(self):
self.genMesh()
self.getCoreDomain()
# url = "http://em.geosci.xyz/_images/disc_dipole.png"
# response = requests.get(url)
# self.im = Image.open(StringIO(response.content))
def mirrorArray(self, x, direction="x"):
X = x.reshape((self.nx_core, self.ny_core), order="F")
if direction == "x" or direction == "y":
X2 = np.vstack((-np.flipud(X), X))
else:
X2 = np.vstack((np.flipud(X), X))
return X2
def genMesh(self, h=0.0, cs=3.0, ncx=15, ncz=30, npad=20):
"""
Generate cylindrically symmetric mesh
"""
# TODO: Make it adaptive due to z location
hx = [(cs, ncx), (cs, npad, 1.3)]
hz = [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)]
self.mesh = CylMesh([hx, 1, hz], "00C")
def getCoreDomain(self, mirror=False, xmax=100, zmin=-100, zmax=100.0):
self.activeCC = (self.mesh.gridCC[:, 0] <= xmax) & (np.logical_and(
self.mesh.gridCC[:, 2] >= zmin, self.mesh.gridCC[:, 2] <= zmax))
self.gridCCactive = self.mesh.gridCC[self.activeCC, :][:, [0, 2]]
xind = self.mesh.vectorCCx <= xmax
yind = np.logical_and(self.mesh.vectorCCz >= zmin,
self.mesh.vectorCCz <= zmax)
self.nx_core = xind.sum()
self.ny_core = yind.sum()
# if self.mesh2D is None:
hx = np.r_[self.mesh.hx[xind][::-1], self.mesh.hx[xind]]
hz = self.mesh.hz[yind]
self.mesh2D = TensorMesh([hx, hz], x0="CC")
def getCoreModel(self, Type):
if Type == "Layer":
active = self.mesh2D.vectorCCy < self.z0
ind1 = (self.mesh2D.vectorCCy < self.z0) & (self.mesh2D.vectorCCy
>= self.z1)
ind2 = (self.mesh2D.vectorCCy < self.z1) & (self.mesh2D.vectorCCy
>= self.z2)
mapping2D = maps.SurjectVertical1D(
self.mesh2D) * maps.InjectActiveCells(
self.mesh2D, active, self.sig0, nC=self.mesh2D.nCy)
model2D = np.ones(self.mesh2D.nCy) * self.sig3
model2D[ind1] = self.sig1
model2D[ind2] = self.sig2
model2D = model2D[active]
elif Type == "Sphere":
active = self.mesh2D.gridCC[:, 1] < self.z0
ind1 = (self.mesh2D.gridCC[:, 1] <
self.z1) & (self.mesh2D.gridCC[:, 1] >= self.z1 - self.h)
ind2 = (np.sqrt((self.mesh2D.gridCC[:, 0])**2 +
(self.mesh2D.gridCC[:, 1] - self.z2)**2) <= self.R)
mapping2D = maps.InjectActiveCells(self.mesh2D,
active,
self.sig0,
nC=self.mesh2D.nC)
model2D = np.ones(self.mesh2D.nC) * self.sigb
model2D[ind1] = self.sig1
model2D[ind2] = self.sig2
model2D = model2D[active]
return model2D, mapping2D
def getBiotSavrt(self, rxLoc):
"""
Compute Biot-Savart operator: Gz and Gx
"""
self.Gz = BiotSavartFun(self.mesh, rxLoc, component="z")
self.Gx = BiotSavartFun(self.mesh, rxLoc, component="x")
def setThreeLayerParam(self,
h1=12,
h2=12,
sig0=1e-8,
sig1=1e-1,
sig2=1e-2,
sig3=1e-2,
chi=0.0):
self.h1 = h1 # 1st layer thickness
self.h2 = h2 # 2nd layer thickness
self.z0 = 0.0
self.z1 = self.z0 - h1
self.z2 = self.z0 - h1 - h2
self.sig0 = sig0 # 0th layer \sigma (assumed to be air)
self.sig1 = sig1 # 1st layer \sigma
self.sig2 = sig2 # 2nd layer \sigma
self.sig3 = sig3 # 3rd layer \sigma
active = self.mesh.vectorCCz < self.z0
ind1 = (self.mesh.vectorCCz < self.z0) & (self.mesh.vectorCCz >=
self.z1)
ind2 = (self.mesh.vectorCCz < self.z1) & (self.mesh.vectorCCz >=
self.z2)
self.mapping = maps.SurjectVertical1D(
self.mesh) * maps.InjectActiveCells(
self.mesh, active, sig0, nC=self.mesh.nCz)
model = np.ones(self.mesh.nCz) * sig3
model[ind1] = sig1
model[ind2] = sig2
self.m = model[active]
self.mu = np.ones(self.mesh.nC) * mu_0
self.mu[self.mesh.gridCC[:, 2] < 0.0] = (1.0 + chi) * mu_0
return self.m
def setLayerSphereParam(self,
d1=6,
h=6,
d2=16,
R=4,
sig0=1e-8,
sigb=1e-2,
sig1=1e-1,
sig2=1.0,
chi=0.0):
self.z0 = 0.0 # Surface elevation
self.z1 = self.z0 - d1 # Depth to layer
self.h = h # Thickness of layer
self.z2 = self.z0 - d2 # Depth to center of sphere
self.R = R # Radius of sphere
self.sig0 = sig0 # Air conductivity
self.sigb = sigb # Background conductivity
self.sig1 = sig1 # Layer conductivity
self.sig2 = sig2 # Sphere conductivity
active = self.mesh.gridCC[:, 2] < self.z0
ind1 = (self.mesh.gridCC[:, 2] < self.z1) & (self.mesh.gridCC[:, 2] >=
self.z1 - self.h)
ind2 = (np.sqrt((self.mesh.gridCC[:, 0])**2 +
(self.mesh.gridCC[:, 2] - self.z2)**2) <= self.R)
self.mapping = maps.InjectActiveCells(self.mesh,
active,
sig0,
nC=self.mesh.nC)
model = np.ones(self.mesh.nC) * sigb
model[ind1] = sig1
model[ind2] = sig2
self.m = model[active]
self.mu = np.ones(self.mesh.nC) * mu_0
self.mu[self.mesh.gridCC[:, 2] < 0.0] = (1.0 + chi) * mu_0
return self.m
def simulate(self, srcLoc, rxLoc, freqs):
bzr = fdem.receivers.PointMagneticFluxDensitySecondary(
rxLoc, orientation="z", component="real")
bzi = fdem.receivers.PointMagneticFluxDensitySecondary(
rxLoc, orientation="z", component="imag")
self.srcList = [
fdem.sources.MagDipole([bzr, bzi],
frequency=freq,
location=srcLoc,
orientation="Z") for freq in freqs
]
survey = fdem.survey.Survey(self.srcList)
sim = fdem.Simulation3DMagneticFluxDensity(self.mesh,
survey=survey,
sigmaMap=self.mapping,
mu=self.mu,
solver=Pardiso)
self.f = sim.fields(self.m)
self.sim = sim
dpred = sim.dpred(self.m, f=self.f)
self.srcLoc = srcLoc
self.rxLoc = rxLoc
return dpred
def getFields(self, bType="b", ifreq=0):
src = self.srcList[ifreq]
Pfx = self.mesh.getInterpolationMat(self.mesh.gridCC[self.activeCC, :],
locType="Fx")
Pfz = self.mesh.getInterpolationMat(self.mesh.gridCC[self.activeCC, :],
locType="Fz")
Ey = self.mesh.aveE2CC * self.f[src, "e"]
Jy = utils.sdiag(self.sim.sigma) * Ey
self.Ey = utils.mkvc(self.mirrorArray(Ey[self.activeCC],
direction="y"))
self.Jy = utils.mkvc(self.mirrorArray(Jy[self.activeCC],
direction="y"))
self.Bx = utils.mkvc(
self.mirrorArray(Pfx * self.f[src, bType], direction="x"))
self.Bz = utils.mkvc(
self.mirrorArray(Pfz * self.f[src, bType], direction="z"))
def getData(self, bType="b"):
Pfx = self.mesh.getInterpolationMat(self.rxLoc, locType="Fx")
Pfz = self.mesh.getInterpolationMat(self.rxLoc, locType="Fz")
Pey = self.mesh.getInterpolationMat(self.rxLoc, locType="Ey")
self.Ey = (Pey * self.f[:, "e"]).flatten()
self.Bx = (Pfx * self.f[:, bType]).flatten()
self.Bz = (Pfz * self.f[:, bType]).flatten()
def plotField(
self,
Field="B",
ComplexNumber="real",
view="vec",
scale="linear",
Frequency=100,
Geometry=True,
Scenario=None,
):
# Printout for null cases
if (Field == "B") & (view == "y"):
print(
"Think about the problem geometry. There is NO By in this case."
)
elif (Field == "E") & (view == "x") | (Field == "E") & (view == "z"):
print(
"Think about the problem geometry. There is NO Ex or Ez in this case. Only Ey."
)
elif (Field == "J") & (view == "x") | (Field == "J") & (view == "z"):
print(
"Think about the problem geometry. There is NO Jx or Jz in this case. Only Jy."
)
elif (Field == "E") & (view == "vec"):
print(
"Think about the problem geometry. E only has components along y. Vector plot not possible"
)
elif (Field == "J") & (view == "vec"):
print(
"Think about the problem geometry. J only has components along y. Vector plot not possible"
)
elif (view == "vec") & (ComplexNumber == "Amp") | (view == "vec") & (
ComplexNumber == "Phase"):
print(
"Cannot show amplitude or phase when vector plot selected. Set 'AmpDir=None' to see amplitude or phase."
)
elif Field == "Model":
plt.figure(figsize=(7, 6))
ax = plt.subplot(111)
if Scenario == "Sphere":
model2D, mapping2D = self.getCoreModel("Sphere")
elif Scenario == "Layer":
model2D, mapping2D = self.getCoreModel("Layer")
out = self.mesh2D.plotImage(np.log10(mapping2D * model2D), ax=ax)
cb = plt.colorbar(out[0], ax=ax, format="$10^{%.1f}$")
cb.set_label("$\sigma$ (S/m)")
ax.set_xlabel("Distance (m)")
ax.set_ylabel("Depth (m)")
ax.set_title("Conductivity Model")
plt.show()
else:
plt.figure(figsize=(10, 6))
ax = plt.subplot(111)
vec = False
if view == "vec":
tname = "Vector "
title = tname + Field + "-field"
elif view == "amp":
tname = "|"
title = tname + Field + "|-field"
else:
if ComplexNumber == "real":
tname = "Re("
elif ComplexNumber == "imag":
tname = "Im("
elif ComplexNumber == "amplitude":
tname = "Amp("
elif ComplexNumber == "phase":
tname = "Phase("
title = tname + Field + view + ")-field"
if Field == "B":
label = "Magnetic field (T)"
if view == "vec":
vec = True
if ComplexNumber == "real":
val = np.c_[self.Bx.real, self.Bz.real]
elif ComplexNumber == "imag":
val = np.c_[self.Bx.imag, self.Bz.imag]
else:
return
elif view == "x":
if ComplexNumber == "real":
val = self.Bx.real
elif ComplexNumber == "imag":
val = self.Bx.imag
elif ComplexNumber == "amplitude":
val = abs(self.Bx)
elif ComplexNumber == "phase":
val = np.angle(self.Bx)
elif view == "z":
if ComplexNumber == "real":
val = self.Bz.real
elif ComplexNumber == "imag":
val = self.Bz.imag
elif ComplexNumber == "amplitude":
val = abs(self.Bz)
elif ComplexNumber == "phase":
val = np.angle(self.Bz)
else:
return
elif Field == "E":
label = "Electric field (V/m)"
if view == "y":
if ComplexNumber == "real":
val = self.Ey.real
elif ComplexNumber == "imag":
val = self.Ey.imag
elif ComplexNumber == "amplitude":
val = abs(self.Ey)
elif ComplexNumber == "phase":
val = np.angle(self.Ey)
else:
return
elif Field == "J":
label = "Current density (A/m$^2$)"
if view == "y":
if ComplexNumber == "real":
val = self.Jy.real
elif ComplexNumber == "imag":
val = self.Jy.imag
elif ComplexNumber == "amplitude":
val = abs(self.Jy)
elif ComplexNumber == "phase":
val = np.angle(self.Jy)
else:
return
out = utils.plot2Ddata(
self.mesh2D.gridCC,
val,
vec=vec,
ax=ax,
contourOpts={"cmap": "viridis"},
ncontour=200,
scale=scale,
)
cb = plt.colorbar(out[0], ax=ax, format="%.2e")
cb.set_label(label)
xmax = self.mesh2D.gridCC[:, 0].max()
if Geometry:
if Scenario == "Layer":
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.srcLoc[2],
"w-",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.z0,
"w--",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.z1,
"w--",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.z2,
"w--",
lw=1)
ax.plot(0, self.srcLoc[2], "ko", ms=4)
ax.plot(self.rxLoc[0, 0], self.srcLoc[2], "ro", ms=4)
elif Scenario == "Sphere":
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.srcLoc[2],
"k-",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.z0,
"w--",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.z1,
"w--",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * (self.z1 - self.h),
"w--",
lw=1)
Phi = np.linspace(0, 2 * np.pi, 41)
ax.plot(
self.R * np.cos(Phi),
self.z2 + self.R * np.sin(Phi),
"w--",
lw=1,
)
ax.plot(0, self.srcLoc[2], "ko", ms=4)
ax.plot(self.rxLoc[0, 0], self.srcLoc[2], "ro", ms=4)
ax.set_xlabel("Distance (m)")
ax.set_ylabel("Depth (m)")
title = title + "\nf = " + "{:.2e}".format(Frequency) + " Hz"
ax.set_title(title)
plt.show()
######################################################
# LAYER WIDGET
######################################################
def InteractivePlane_Layer(self,
scale="log",
fieldvalue="B",
compvalue="z"):
def foo(
Field,
AmpDir,
Component,
ComplexNumber,
Sigma0,
Sigma1,
Sigma2,
Sigma3,
Sus,
h1,
h2,
Scale,
rxOffset,
z,
ifreq,
Geometry=True,
):
Frequency = 10**((ifreq - 1.0) / 3.0 - 2.0)
if ComplexNumber == "Re":
ComplexNumber = "real"
elif ComplexNumber == "Im":
ComplexNumber = "imag"
elif ComplexNumber == "Amp":
ComplexNumber = "amplitude"
elif ComplexNumber == "Phase":
ComplexNumber = "phase"
if AmpDir == "Direction (B or Bsec)":
# ComplexNumber = "real"
Component = "vec"
if Field == "Bsec":
bType = "bSecondary"
Field = "B"
else:
bType = "b"
self.setThreeLayerParam(
h1=h1,
h2=h2,
sig0=Sigma0,
sig1=Sigma1,
sig2=Sigma2,
sig3=Sigma3,
chi=Sus,
)
srcLoc = np.array([0.0, 0.0, z])
rxLoc = np.array([[rxOffset, 0.0, z]])
self.simulate(srcLoc, rxLoc, np.r_[Frequency])
if Field != "Model":
self.getFields(bType=bType)
return self.plotField(
Field=Field,
ComplexNumber=ComplexNumber,
view=Component,
scale=Scale,
Frequency=Frequency,
Geometry=Geometry,
Scenario="Layer",
)
out = widgetify(
foo,
Field=widgets.ToggleButtons(
options=["E", "B", "Bsec", "J", "Model"], value="E"),
AmpDir=widgets.ToggleButtons(
options=["None", "Direction (B or Bsec)"], value="None"),
Component=widgets.ToggleButtons(options=["x", "y", "z"],
value="y",
description="Comp."),
ComplexNumber=widgets.ToggleButtons(
options=["Re", "Im", "Amp", "Phase"],
value="Re",
description="Re/Im"),
Sigma0=widgets.FloatText(value=1e-8,
continuous_update=False,
description="$\sigma_0$ (S/m)"),
Sigma1=widgets.FloatText(value=0.01,
continuous_update=False,
description="$\sigma_1$ (S/m)"),
Sigma2=widgets.FloatText(value=0.01,
continuous_update=False,
description="$\sigma_2$ (S/m)"),
Sigma3=widgets.FloatText(value=0.01,
continuous_update=False,
description="$\sigma_3$ (S/m)"),
Sus=widgets.FloatText(value=0.0,
continuous_update=False,
description="$\chi$"),
h1=widgets.FloatSlider(
min=2.0,
max=40.0,
step=2.0,
value=10.0,
continuous_update=False,
description="$h_1$ (m)",
),
h2=widgets.FloatSlider(
min=2.0,
max=40.0,
step=2.0,
value=10.0,
continuous_update=False,
description="$h_2$ (m)",
),
Scale=widgets.ToggleButtons(options=["log", "linear"],
value="linear"),
rxOffset=widgets.FloatSlider(
min=0.0,
max=50.0,
step=2.0,
value=10.0,
continuous_update=False,
description="$\Delta x$(m)",
),
z=widgets.FloatSlider(
min=0.0,
max=50.0,
step=2.0,
value=0.0,
continuous_update=False,
description="$\Delta z$ (m)",
),
ifreq=widgets.IntSlider(
min=1,
max=31,
step=1,
value=16,
continuous_update=False,
description="f index",
),
)
return out
def InteractiveData_Layer(self, fieldvalue="B", compvalue="z", z=0.0):
frequency = np.logspace(2, 5, 31)
self.simulate(self.srcLoc, self.rxLoc, frequency)
def foo(Field, Component, Scale):
# Printout for null cases
if (Field == "B") & (Component == "y") | (Field == "Bsec") & (
Component == "y"):
print(
"Think about the problem geometry. There is NO By in this case."
)
elif (Field == "E") & (Component == "x") | (Field == "E") & (
Component == "z"):
print(
"Think about the problem geometry. There is NO Ex or Ez in this case. Only Ey."
)
else:
plt.figure()
ax = plt.subplot(111)
bType = "b"
if (Field == "Bsec") or (Field == "B"):
if Field == "Bsec":
bType = "bSecondary"
Field = "B"
self.getData(bType=bType)
label = "Magnetic field (T)"
if Component == "x":
title = "Bx"
valr = self.Bx.real
vali = self.Bx.imag
elif Component == "z":
title = "Bz"
valr = self.Bz.real
vali = self.Bz.imag
else:
# ax.imshow(self.im)
ax.set_xticks([])
ax.set_yticks([])
print(
"Think about the problem geometry. There is NO By in this case."
)
elif Field == "E":
self.getData(bType=bType)
label = "Electric field (V/m)"
title = "Ey"
if Component == "y":
valr = self.Ey.real
vali = self.Ey.imag
else:
# ax.imshow(self.im)
ax.set_xticks([])
ax.set_yticks([])
print(
"Think about the problem geometry. There is NO Ex or Ez in this case."
)
elif Field == "J":
print(
"The conductivity at the location is 0. Therefore there is no electrical current here."
)
if Scale == "log":
valr_p, valr_n = DisPosNegvalues(valr)
vali_p, vali_n = DisPosNegvalues(vali)
ax.plot(frequency, valr_p, "k-")
ax.plot(frequency, valr_n, "k--")
ax.plot(frequency, vali_p, "r-")
ax.plot(frequency, vali_n, "r--")
ax.legend(("Re (+)", "Re (-)", "Im (+)", "Im (-)"),
loc=4,
fontsize=10)
else:
ax.plot(frequency, valr, "k.-")
ax.plot(frequency, vali, "r.-")
ax.legend(("Re", "Im"), loc=4, fontsize=10)
ax.set_xscale("log")
ax.set_yscale(Scale)
ax.set_xlabel("Frequency (Hz)")
ax.set_ylabel(label)
ax.set_title(title)
ax.grid(True)
plt.show()
out = widgetify(
foo,
Field=widgets.ToggleButtons(options=["E", "B", "Bsec"],
value=fieldvalue),
Component=widgets.ToggleButtons(options=["x", "y", "z"],
value=compvalue,
description="Comp."),
Scale=widgets.ToggleButtons(options=["log", "linear"],
value="log"),
)
return out
######################################################
# SPHERE WIDGET
######################################################
def InteractivePlane_Sphere(self,
scale="log",
fieldvalue="B",
compvalue="z"):
def foo(
Field,
AmpDir,
Component,
ComplexNumber,
Sigma0,
Sigmab,
Sigma1,
Sigma2,
Sus,
d1,
h,
d2,
R,
Scale,
rxOffset,
z,
ifreq,
Geometry=True,
):
Frequency = 10**((ifreq - 1.0) / 3.0 - 2.0)
if ComplexNumber == "Re":
ComplexNumber = "real"
elif ComplexNumber == "Im":
ComplexNumber = "imag"
elif ComplexNumber == "Amp":
ComplexNumber = "amplitude"
elif ComplexNumber == "Phase":
ComplexNumber = "phase"
if AmpDir == "Direction (B or Bsec)":
# ComplexNumber = "real"
Component = "vec"
if Field == "Bsec":
bType = "bSecondary"
Field = "B"
else:
bType = "b"
self.setLayerSphereParam(
d1=d1,
h=h,
d2=d2,
R=R,
sig0=Sigma0,
sigb=Sigmab,
sig1=Sigma1,
sig2=Sigma2,
chi=Sus,
)
srcLoc = np.array([0.0, 0.0, z])
rxLoc = np.array([[rxOffset, 0.0, z]])
self.simulate(srcLoc, rxLoc, np.r_[Frequency])
if Field != "Model":
self.getFields(bType=bType)
return self.plotField(
Field=Field,
ComplexNumber=ComplexNumber,
Frequency=Frequency,
view=Component,
scale=Scale,
Geometry=Geometry,
Scenario="Sphere",
)
out = widgetify(
foo,
Field=widgets.ToggleButtons(
options=["E", "B", "Bsec", "J", "Model"], value="E"),
AmpDir=widgets.ToggleButtons(
options=["None", "Direction (B or Bsec)"], value="None"),
Component=widgets.ToggleButtons(options=["x", "y", "z"],
value="y",
description="Comp."),
ComplexNumber=widgets.ToggleButtons(
options=["Re", "Im", "Amp", "Phase"],
value="Re",
description="Re/Im"),
Sigma0=widgets.FloatText(value=1e-8,
continuous_update=False,
description="$\sigma_0$ (S/m)"),
Sigmab=widgets.FloatText(value=0.01,
continuous_update=False,
description="$\sigma_b$ (S/m)"),
Sigma1=widgets.FloatText(value=0.01,
continuous_update=False,
description="$\sigma_1$ (S/m)"),
Sigma2=widgets.FloatText(value=0.01,
continuous_update=False,
description="$\sigma_2$ (S/m)"),
Sus=widgets.FloatText(value=0.0,
continuous_update=False,
description="$\chi$"),
d1=widgets.FloatSlider(
min=0.0,
max=50.0,
step=2.0,
value=0.0,
continuous_update=False,
description="$d_1$ (m)",
),
h=widgets.FloatSlider(
min=2.0,
max=20.0,
step=2.0,
value=10.0,
continuous_update=False,
description="$h$ (m)",
),
d2=widgets.FloatSlider(
min=10.0,
max=50.0,
step=2.0,
value=30.0,
continuous_update=False,
description="$d_2$ (m)",
),
R=widgets.FloatSlider(
min=2.0,
max=20.0,
step=2.0,
value=10.0,
continuous_update=False,
description="$R$ (m)",
),
Scale=widgets.ToggleButtons(options=["log", "linear"],
value="linear"),
rxOffset=widgets.FloatSlider(
min=0.0,
max=50.0,
step=2.0,
value=10.0,
continuous_update=False,
description="$\Delta x$(m)",
),
z=widgets.FloatSlider(
min=0.0,
max=50.0,
step=2.0,
value=0.0,
continuous_update=False,
description="$\Delta z$ (m)",
),
ifreq=widgets.IntSlider(
min=1,
max=31,
step=1,
value=16,
continuous_update=False,
description="f index",
),
)
return out
def InteractiveData_Sphere(self, fieldvalue="B", compvalue="z", z=0.0):
frequency = np.logspace(2, 5, 31)
self.simulate(self.srcLoc, self.rxLoc, frequency)
def foo(Field, Component, Scale):
# Printout for null cases
if (Field == "B") & (Component == "y") | (Field == "Bsec") & (
Component == "y"):
print(
"Think about the problem geometry. There is NO By in this case."
)
elif (Field == "E") & (Component == "x") | (Field == "E") & (
Component == "z"):
print(
"Think about the problem geometry. There is NO Ex or Ez in this case. Only Ey."
)
else:
plt.figure()
ax = plt.subplot(111)
bType = "b"
if (Field == "Bsec") or (Field == "B"):
if Field == "Bsec":
bType = "bSecondary"
Field = "B"
self.getData(bType=bType)
label = "Magnetic field (T)"
if Component == "x":
title = "Bx"
valr = self.Bx.real
vali = self.Bx.imag
elif Component == "z":
title = "Bz"
valr = self.Bz.real
vali = self.Bz.imag
else:
# ax.imshow(self.im)
ax.set_xticks([])
ax.set_yticks([])
print(
"Think about the problem geometry. There is NO By in this case."
)
elif Field == "E":
self.getData(bType=bType)
label = "Electric field (V/m)"
title = "Ey"
if Component == "y":
valr = self.Ey.real
vali = self.Ey.imag
else:
# ax.imshow(self.im)
ax.set_xticks([])
ax.set_yticks([])
print(
"Think about the problem geometry. There is NO Ex or Ez in this case."
)
elif Field == "J":
print(
"The conductivity at the location is 0. Therefore there is no electrical current here."
)
if Scale == "log":
valr_p, valr_n = DisPosNegvalues(valr)
vali_p, vali_n = DisPosNegvalues(vali)
ax.plot(frequency, valr_p, "k-")
ax.plot(frequency, valr_n, "k--")
ax.plot(frequency, vali_p, "r-")
ax.plot(frequency, vali_n, "r--")
ax.legend(("Re (+)", "Re (-)", "Im (+)", "Im (-)"),
loc=4,
fontsize=10)
else:
ax.plot(frequency, valr, "k.-")
ax.plot(frequency, vali, "r.-")
ax.legend(("Re", "Im"), loc=4, fontsize=10)
ax.set_xscale("log")
ax.set_yscale(Scale)
ax.set_xlabel("Frequency (Hz)")
ax.set_ylabel(label)
ax.set_title(title)
ax.grid(True)
plt.show()
out = widgetify(
foo,
Field=widgets.ToggleButtons(options=["E", "B", "Bsec"],
value=fieldvalue),
Component=widgets.ToggleButtons(options=["x", "y", "z"],
value=compvalue,
description="Comp."),
Scale=widgets.ToggleButtons(options=["log", "linear"],
value="log"),
)
return out
kneg = (xycc[:, 0] == -10) & (xycc[:, 1] == 0) # -ve charge distr. at (-10, 0)
kpos = (xycc[:, 0] == 10) & (xycc[:, 1] == 0) # +ve charge distr. at (10, 0)
rho = np.zeros(mesh.nC)
rho[kneg] = -1
rho[kpos] = 1
# LU factorization and solve
AinvM = SolverLU(A)
phi = AinvM * rho
# Compute electric fields
E = Mf_inv * DIV.T * Mc * phi
# Plotting
fig = plt.figure(figsize=(14, 4))
ax1 = fig.add_subplot(131)
mesh.plotImage(rho, v_type="CC", ax=ax1)
ax1.set_title("Charge Density")
ax2 = fig.add_subplot(132)
mesh.plotImage(phi, v_type="CC", ax=ax2)
ax2.set_title("Electric Potential")
ax3 = fig.add_subplot(133)
mesh.plotImage(
E, ax=ax3, v_type="F", view="vec", stream_opts={"color": "w", "density": 1.0}
)
ax3.set_title("Electric Fields")
class MagneticDipoleApp(object):
"""docstring for MagneticDipoleApp"""
mesh = None
component = None
z = None
inclination = None
declination = None
length = None
dx = None
moment = None
depth = None
data = None
profile = None
xy_profile = None
clim = None
def __init__(self):
super(MagneticDipoleApp, self).__init__()
def id_to_cartesian(self, inclination, declination):
ux = np.cos(inclination / 180.0 * np.pi) * np.sin(
declination / 180.0 * np.pi)
uy = np.cos(inclination / 180.0 * np.pi) * np.cos(
declination / 180.0 * np.pi)
uz = -np.sin(inclination / 180.0 * np.pi)
return np.r_[ux, uy, uz]
def dot_product(self, b_vec, orientation):
b_tmi = np.dot(b_vec, orientation)
return b_tmi
def simulate_dipole(
self,
component,
target,
inclination,
declination,
length,
dx,
moment,
depth,
profile,
fixed_scale,
show_halfwidth,
):
self.component = component
self.target = target
self.inclination = inclination
self.declination = declination
self.length = length
self.dx = dx
self.moment = moment
self.depth = depth
self.profile = profile
self.fixed_scale = fixed_scale
self.show_halfwidth = show_halfwidth
nT = 1e9
nx = ny = int(length / dx)
hx = np.ones(nx) * dx
hy = np.ones(ny) * dx
self.mesh = TensorMesh((hx, hy), "CC")
z = np.r_[1.0]
orientation = self.id_to_cartesian(inclination, declination)
if self.target == "Dipole":
md = em.static.MagneticDipoleWholeSpace(location=np.r_[0, 0,
-depth],
orientation=orientation,
moment=moment)
xyz = utils.ndgrid(self.mesh.vectorCCx, self.mesh.vectorCCy, z)
b_vec = md.magnetic_flux_density(xyz)
elif self.target == "Monopole (+)":
md = em.static.MagneticPoleWholeSpace(location=np.r_[0, 0, -depth],
orientation=orientation,
moment=moment)
xyz = utils.ndgrid(self.mesh.vectorCCx, self.mesh.vectorCCy, z)
b_vec = md.magnetic_flux_density(xyz)
elif self.target == "Monopole (-)":
md = em.static.MagneticPoleWholeSpace(location=np.r_[0, 0, -depth],
orientation=orientation,
moment=moment)
xyz = utils.ndgrid(self.mesh.vectorCCx, self.mesh.vectorCCy, z)
b_vec = -md.magnetic_flux_density(xyz)
# Project to the direction of earth field
if component == "Bt":
rx_orientation = orientation.copy()
elif component == "Bg":
rx_orientation = orientation.copy()
xyz_up = utils.ndgrid(self.mesh.vectorCCx, self.mesh.vectorCCy,
z + 1.0)
b_vec -= md.magnetic_flux_density(xyz_up)
elif component == "Bx":
rx_orientation = self.id_to_cartesian(0, 0)
elif component == "By":
rx_orientation = self.id_to_cartesian(0, 90)
elif component == "Bz":
rx_orientation = self.id_to_cartesian(90, 0)
self.data = self.dot_product(b_vec, rx_orientation) * nT
# Compute profile
if (profile == "North") or (profile == "None"):
self.xy_profile = np.c_[np.zeros(self.mesh.nCx),
self.mesh.vectorCCx]
elif profile == "East":
self.xy_profile = np.c_[self.mesh.vectorCCx,
np.zeros(self.mesh.nCx)]
self.inds_profile = utils.closestPoints(self.mesh, self.xy_profile)
self.data_profile = self.data[self.inds_profile]
def simulate_two_monopole(
self,
component,
inclination,
declination,
length,
dx,
moment,
depth_n,
depth_p,
profile,
fixed_scale,
show_halfwidth,
):
self.component = component
self.inclination = inclination
self.declination = declination
self.length = length
self.dx = dx
self.moment = moment
self.depth = depth_n
self.depth = depth_p
self.profile = profile
self.fixed_scale = fixed_scale
self.show_halfwidth = show_halfwidth
nT = 1e9
nx = ny = int(length / dx)
hx = np.ones(nx) * dx
hy = np.ones(ny) * dx
self.mesh = TensorMesh((hx, hy), "CC")
z = np.r_[1.0]
orientation = self.id_to_cartesian(inclination, declination)
md_n = em.static.MagneticPoleWholeSpace(location=np.r_[0, 0, -depth_n],
orientation=orientation,
moment=moment)
md_p = em.static.MagneticPoleWholeSpace(location=np.r_[0, 0, -depth_p],
orientation=orientation,
moment=moment)
xyz = utils.ndgrid(self.mesh.vectorCCx, self.mesh.vectorCCy, z)
b_vec = -md_n.magnetic_flux_density(xyz) + md_p.magnetic_flux_density(
xyz)
# Project to the direction of earth field
if component == "Bt":
rx_orientation = orientation.copy()
elif component == "Bx":
rx_orientation = self.id_to_cartesian(0, 0)
elif component == "By":
rx_orientation = self.id_to_cartesian(0, 90)
elif component == "Bz":
rx_orientation = self.id_to_cartesian(90, 0)
elif component == "Bg":
rx_orientation = orientation.copy()
xyz_up = utils.ndgrid(self.mesh.vectorCCx, self.mesh.vectorCCy,
z + 1.0)
b_vec -= -md_n.magnetic_flux_density(xyz_up)
b_vec -= md_p.magnetic_flux_density(xyz_up)
self.data = self.dot_product(b_vec, rx_orientation) * nT
# Compute profile
if (profile == "North") or (profile == "None"):
self.xy_profile = np.c_[np.zeros(self.mesh.nCx),
self.mesh.vectorCCx]
elif profile == "East":
self.xy_profile = np.c_[self.mesh.vectorCCx,
np.zeros(self.mesh.nCx)]
self.inds_profile = utils.closestPoints(self.mesh, self.xy_profile)
self.data_profile = self.data[self.inds_profile]
def get_prism(self, dx, dy, dz, x0, y0, elev, prism_inc, prism_dec):
prism = definePrism()
prism.dx, prism.dy, prism.dz, prism.z0 = dy, dx, dz, elev
prism.x0, prism.y0 = x0, y0
prism.pinc, prism.pdec = prism_inc, prism_dec
return prism
def plot_prism(self, prism, dip=30, azim=310):
return plotObj3D(prism, self.survey, dip, azim,
self.mesh.vectorCCx.max())
def simulate_prism(
self,
component,
inclination,
declination,
length,
dx,
B0,
kappa,
depth,
profile,
fixed_scale,
show_halfwidth,
prism_dx,
prism_dy,
prism_dz,
prism_inclination,
prism_declination,
):
self.component = component
self.inclination = -inclination # -ve accounts for LH modeling in SimPEG
self.declination = declination
self.length = length
self.dx = dx
self.B0 = B0
self.kappa = kappa
self.depth = depth
self.profile = profile
self.fixed_scale = fixed_scale
self.show_halfwidth = show_halfwidth
# prism parameter
self.prism = self.get_prism(
prism_dx,
prism_dy,
prism_dz,
0,
0,
-depth,
prism_inclination,
prism_declination,
)
nx = ny = int(length / dx)
hx = np.ones(nx) * dx
hy = np.ones(ny) * dx
self.mesh = TensorMesh((hx, hy), "CC")
z = np.r_[1.0]
B = np.r_[B0, -inclination,
declination] # -ve accounts for LH modeling in SimPEG
# Project to the direction of earth field
if component == "Bt":
uType = "tf"
elif component == "Bx":
uType = "bx"
elif component == "By":
uType = "by"
elif component == "Bz":
uType = "bz"
xyz = utils.ndgrid(self.mesh.vectorCCx, self.mesh.vectorCCy, z)
out = createMagSurvey(np.c_[xyz, np.ones(self.mesh.nC)], B)
self.survey = out[0]
self.dobs = out[1]
self.sim = Simulation()
self.sim.prism = self.prism
self.sim.survey = self.survey
self.sim.susc = kappa
self.sim.uType, self.sim.mType = uType, "induced"
self.data = self.sim.fields()[0]
# Compute profile
if (profile == "North") or (profile == "None"):
self.xy_profile = np.c_[np.zeros(self.mesh.nCx),
self.mesh.vectorCCx]
elif profile == "East":
self.xy_profile = np.c_[self.mesh.vectorCCx,
np.zeros(self.mesh.nCx)]
self.inds_profile = utils.closestPoints(self.mesh, self.xy_profile)
self.data_profile = self.data[self.inds_profile]
def plot_map(self):
length = self.length
data = self.data
profile = self.profile
fig = plt.figure(figsize=(5, 6))
ax1 = plt.subplot2grid((8, 4), (0, 0), rowspan=5, colspan=3)
ax2 = plt.subplot2grid((8, 4), (6, 0), rowspan=2, colspan=3)
if (self.clim is None) or (not self.fixed_scale):
self.clim = data.min(), data.max()
out = self.mesh.plotImage(self.data,
pcolorOpts={"cmap": "jet"},
ax=ax1,
clim=self.clim)
cax = fig.add_axes([0.75, 0.45, 0.02, 0.5])
ratio = abs(self.clim[0] / self.clim[1])
if ratio < 0.05:
ticks = [self.clim[0], self.clim[1]]
else:
ticks = [self.clim[0], 0, self.clim[1]]
cb = plt.colorbar(out[0], ticks=ticks, format="%.3f", cax=cax)
cb.set_label("nT", labelpad=-40, y=-0.05, rotation=0)
ax1.set_aspect(1)
ax1.set_ylabel("Northing")
ax1.set_xlabel("Easting")
if profile == "North":
# xy_profile = np.c_[np.zeros(self.mesh.nCx), self.mesh.vectorCCx]
ax1.text(1, length / 2 - length / 2 * 0.1, "B", color="w")
ax1.text(1, -length / 2, "A", color="w")
elif profile == "East":
# xy_profile = np.c_[self.mesh.vectorCCx, np.zeros(self.mesh.nCx)]
ax1.text(length / 2 - length / 2 * 0.1, 1, "B", color="w")
ax1.text(-length / 2, 1, "A", color="w")
ax1.set_xticks([])
ax1.set_yticks([])
ax2.yaxis.tick_right()
ax2.plot(self.mesh.vectorCCx, self.data_profile, "k", lw=2)
ax2.plot(self.mesh.vectorCCx,
np.zeros(self.mesh.nCx),
"k--",
color="grey",
lw=1)
ax2.set_xlim(-self.length / 2.0, self.length / 2.0)
ymin, ymax = ax2.get_ylim()
ax2.text(-self.length / 2.0, ymax, "A")
ax2.text(self.length / 2.0 - self.length / 2 * 0.05, ymax, "B")
ax2.set_yticks([self.clim[0], self.clim[1]])
if self.show_halfwidth:
x_half, data_half = self.get_half_width()
ax2.plot(x_half, data_half, "bo--")
ax2.set_xlabel(("Halfwidth: %.1fm") % (abs(np.diff(x_half))))
else:
ax2.set_xlabel(" ")
# plt.tight_layout()
if profile == "None":
ax2.remove()
else:
ax1.plot(self.xy_profile[:, 0], self.xy_profile[:, 1], "w")
def get_half_width(self, n_points=200):
ind_max = np.argmax(abs(self.data_profile))
A_half = self.data_profile[ind_max] / 2.0
if self.profile == "North":
x = self.xy_profile[:, 1]
else:
x = self.xy_profile[:, 0]
f = interp1d(x, self.data_profile)
x_int = np.linspace(x.min(), x.max(), n_points)
data_profile_int = f(x_int)
inds = np.argsort(abs(data_profile_int - A_half))
ind_first = inds[0]
for ind in inds:
dx = abs(x_int[ind_first] - x_int[ind])
if dx > self.dx:
ind_second = ind
break
inds = [ind_first, ind_second]
return x_int[inds], data_profile_int[inds]
def magnetic_dipole_applet(
self,
component,
target,
inclination,
declination,
length,
dx,
moment,
depth,
profile,
fixed_scale,
show_halfwidth,
):
self.simulate_dipole(
component,
target,
inclination,
declination,
length,
dx,
moment,
depth,
profile,
fixed_scale,
show_halfwidth,
)
self.plot_map()
def magnetic_two_monopole_applet(
self,
component,
inclination,
declination,
length,
dx,
moment,
depth_n,
depth_p,
profile,
fixed_scale,
show_halfwidth,
):
self.simulate_two_monopole(
component,
inclination,
declination,
length,
dx,
moment,
depth_n,
depth_p,
profile,
fixed_scale,
show_halfwidth,
)
self.plot_map()
def magnetic_prism_applet(
self,
plot,
component,
inclination,
declination,
length,
dx,
B0,
kappa,
depth,
profile,
fixed_scale,
show_halfwidth,
prism_dx,
prism_dy,
prism_dz,
prism_inclination,
prism_declination,
):
if plot == "field":
self.simulate_prism(
component,
inclination,
declination,
length,
dx,
B0,
kappa,
depth,
profile,
fixed_scale,
show_halfwidth,
prism_dx,
prism_dy,
prism_dz,
prism_inclination,
prism_declination,
)
self.plot_map()
elif plot == "model":
self.prism = self.get_prism(
prism_dx,
prism_dy,
prism_dz,
0,
0,
-depth,
prism_inclination,
prism_declination,
)
self.plot_prism(self.prism)
def interact_plot_model_dipole(self):
component = widgets.RadioButtons(
options=["Bt", "Bx", "By", "Bz", "Bg"],
value="Bt",
description="field",
disabled=False,
)
target = widgets.RadioButtons(
options=["Dipole", "Monopole (+)", "Monopole (-)"],
value="Dipole",
description="target",
disabled=False,
)
inclination = widgets.FloatSlider(description="I",
continuous_update=False,
min=-90,
max=90,
step=1,
value=90)
declination = widgets.FloatSlider(description="D",
continuous_update=False,
min=-180,
max=180,
step=1,
value=0)
length = widgets.FloatSlider(
description="length",
continuous_update=False,
min=2,
max=200,
step=1,
value=72,
)
dx = widgets.FloatSlider(
description="data spacing",
continuous_update=False,
min=0.1,
max=15,
step=0.1,
value=2,
)
moment = widgets.FloatText(description="M", value=30)
depth = widgets.FloatSlider(
description="depth",
continuous_update=False,
min=0,
max=50,
step=1,
value=10,
)
profile = widgets.RadioButtons(
options=["East", "North", "None"],
value="East",
description="profile",
disabled=False,
)
fixed_scale = widgets.Checkbox(value=False,
description="fixed scale",
disabled=False)
show_halfwidth = widgets.Checkbox(value=False,
description="half width",
disabled=False)
out = widgets.interactive_output(
self.magnetic_dipole_applet,
{
"component": component,
"target": target,
"inclination": inclination,
"declination": declination,
"length": length,
"dx": dx,
"moment": moment,
"depth": depth,
"profile": profile,
"fixed_scale": fixed_scale,
"show_halfwidth": show_halfwidth,
},
)
left = widgets.VBox(
[component, profile],
layout=Layout(width="20%",
height="400px",
margin="60px 0px 0px 0px"),
)
right = widgets.VBox(
[
target,
inclination,
declination,
length,
dx,
moment,
depth,
fixed_scale,
show_halfwidth,
],
layout=Layout(width="50%",
height="400px",
margin="20px 0px 0px 0px"),
)
widgets.VBox([out],
layout=Layout(width="70%",
height="400px",
margin="0px 0px 0px 0px"))
return widgets.HBox([left, out, right])
def interact_plot_model_two_monopole(self):
component = widgets.RadioButtons(
options=["Bt", "Bx", "By", "Bz", "Bg"],
value="Bt",
description="field",
disabled=False,
)
inclination = widgets.FloatSlider(description="I",
continuous_update=False,
min=-90,
max=90,
step=1,
value=90)
declination = widgets.FloatSlider(description="D",
continuous_update=False,
min=-180,
max=180,
step=1,
value=0)
length = widgets.FloatSlider(
description="length",
continuous_update=False,
min=2,
max=200,
step=1,
value=10,
)
dx = widgets.FloatSlider(
description="data spacing",
continuous_update=False,
min=0.1,
max=15,
step=0.1,
value=0.1,
)
moment = widgets.FloatText(description="M", value=30)
depth_n = widgets.FloatSlider(
description="depth$_{-Q}$",
continuous_update=False,
min=0,
max=200,
step=1,
value=0,
)
depth_p = widgets.FloatSlider(
description="depth$_{+Q}$",
continuous_update=False,
min=0,
max=200,
step=1,
value=1,
)
profile = widgets.RadioButtons(
options=["East", "North", "None"],
value="East",
description="profile",
disabled=False,
)
fixed_scale = widgets.Checkbox(value=False,
description="fixed scale",
disabled=False)
show_halfwidth = widgets.Checkbox(value=False,
description="half width",
disabled=False)
out = widgets.interactive_output(
self.magnetic_two_monopole_applet,
{
"component": component,
"inclination": inclination,
"declination": declination,
"length": length,
"dx": dx,
"moment": moment,
"depth_n": depth_n,
"depth_p": depth_p,
"profile": profile,
"fixed_scale": fixed_scale,
"show_halfwidth": show_halfwidth,
},
)
left = widgets.VBox(
[component, profile],
layout=Layout(width="20%",
height="400px",
margin="60px 0px 0px 0px"),
)
right = widgets.VBox(
[
inclination,
declination,
length,
dx,
moment,
depth_n,
depth_p,
fixed_scale,
show_halfwidth,
],
layout=Layout(width="50%",
height="400px",
margin="20px 0px 0px 0px"),
)
widgets.VBox([out],
layout=Layout(width="70%",
height="400px",
margin="0px 0px 0px 0px"))
return widgets.HBox([left, out, right])
def interact_plot_model_prism(self):
plot = widgets.RadioButtons(
options=["field", "model"],
value="field",
description="plot",
disabled=False,
)
component = widgets.RadioButtons(
options=["Bt", "Bx", "By", "Bz"],
value="Bt",
description="field",
disabled=False,
)
inclination = widgets.FloatSlider(description="I",
continuous_update=False,
min=-90,
max=90,
step=1,
value=90)
declination = widgets.FloatSlider(description="D",
continuous_update=False,
min=-180,
max=180,
step=1,
value=0)
length = widgets.FloatSlider(
description="length",
continuous_update=False,
min=2,
max=200,
step=1,
value=72,
)
dx = widgets.FloatSlider(
description="data spacing",
continuous_update=False,
min=0.1,
max=15,
step=0.1,
value=2,
)
kappa = widgets.FloatText(description="$\kappa$", value=0.1)
B0 = widgets.FloatText(description="B$_0$", value=56000)
depth = widgets.FloatSlider(
description="depth",
continuous_update=False,
min=0,
max=50,
step=1,
value=10,
)
profile = widgets.RadioButtons(
options=["East", "North", "None"],
value="East",
description="profile",
disabled=False,
)
fixed_scale = widgets.Checkbox(value=False,
description="fixed scale",
disabled=False)
show_halfwidth = widgets.Checkbox(value=False,
description="half width",
disabled=False)
prism_dx = widgets.FloatText(description="$\\triangle x$", value=1)
prism_dy = widgets.FloatText(description="$\\triangle y$", value=1)
prism_dz = widgets.FloatText(description="$\\triangle z$", value=1)
prism_inclination = widgets.FloatSlider(
description="I$_{prism}$",
continuous_update=False,
min=-90,
max=90,
step=1,
value=0,
)
prism_declination = widgets.FloatSlider(
description="D$_{prism}$",
continuous_update=False,
min=0,
max=180,
step=1,
value=0,
)
out = widgets.interactive_output(
self.magnetic_prism_applet,
{
"plot": plot,
"component": component,
"inclination": inclination,
"declination": declination,
"length": length,
"dx": dx,
"kappa": kappa,
"B0": B0,
"depth": depth,
"profile": profile,
"fixed_scale": fixed_scale,
"show_halfwidth": show_halfwidth,
"prism_dx": prism_dx,
"prism_dy": prism_dy,
"prism_dz": prism_dz,
"prism_inclination": prism_inclination,
"prism_declination": prism_declination,
},
)
left = widgets.VBox(
[plot, component, profile],
layout=Layout(width="20%",
height="400px",
margin="60px 0px 0px 0px"),
)
right = widgets.VBox(
[
inclination,
declination,
length,
dx,
B0,
kappa,
depth,
prism_dx,
prism_dy,
prism_dz,
prism_inclination,
prism_declination,
fixed_scale,
show_halfwidth,
],
layout=Layout(width="50%",
height="400px",
margin="20px 0px 0px 0px"),
)
widgets.VBox([out],
layout=Layout(width="70%",
height="400px",
margin="0px 0px 0px 0px"))
return widgets.HBox([left, out, right])
edges_y = mesh.gridEy
wx = ((-edges_x[:, 1] / np.sqrt(np.sum(edges_x**2, axis=1))) *
np.exp(-(edges_x[:, 0]**2 + edges_x[:, 1]**2) / 6**2))
wy = ((edges_y[:, 0] / np.sqrt(np.sum(edges_y**2, axis=1))) *
np.exp(-(edges_y[:, 0]**2 + edges_y[:, 1]**2) / 6**2))
w = np.r_[wx, wy]
curl_w = CURL * w
# Plot Gradient of u
fig = plt.figure(figsize=(10, 5))
ax1 = fig.add_subplot(121)
mesh.plotImage(u, ax=ax1, v_type='N')
ax1.set_title('u at cell centers')
ax2 = fig.add_subplot(122)
mesh.plotImage(grad_u,
ax=ax2,
v_type='E',
view='vec',
stream_opts={
'color': 'w',
'density': 1.0
})
ax2.set_title('gradient of u on edges')
fig.show()