def test_ana_forward(self):
survey = PF.BaseMag.BaseMagSurvey()
Inc = 45.
Dec = 45.
Btot = 51000
b0 = PF.MagAnalytics.IDTtoxyz(Inc, Dec, Btot)
survey.setBackgroundField(Inc, Dec, Btot)
xr = np.linspace(-300, 300, 41)
yr = np.linspace(-300, 300, 41)
X, Y = np.meshgrid(xr, yr)
Z = np.ones((xr.size, yr.size))*150
rxLoc = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
survey.rxLoc = rxLoc
self.prob.pair(survey)
u = self.prob.fields(self.chi)
B = u['B']
bxa, bya, bza = PF.MagAnalytics.MagSphereAnaFunA(rxLoc[:, 0], rxLoc[:, 1], rxLoc[:, 2], 100., 0., 0., 0., 0.01, b0, 'secondary')
dpred = survey.projectFieldsAsVector(B)
err = np.linalg.norm(dpred-np.r_[bxa, bya, bza])/np.linalg.norm(np.r_[bxa, bya, bza])
self.assertTrue(err < 0.08)
def test_ana_forward(self):
survey = PF.BaseMag.BaseMagSurvey()
Inc = 45.0
Dec = 45.0
Btot = 51000
b0 = PF.MagAnalytics.IDTtoxyz(Inc, Dec, Btot)
survey.setBackgroundField(Inc, Dec, Btot)
xr = np.linspace(-300, 300, 41)
yr = np.linspace(-300, 300, 41)
X, Y = np.meshgrid(xr, yr)
Z = np.ones((xr.size, yr.size)) * 150
rxLoc = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
survey.rxLoc = rxLoc
self.prob.pair(survey)
u = self.prob.fields(self.chi)
B = u["B"]
bxa, bya, bza = PF.MagAnalytics.MagSphereAnaFunA(
rxLoc[:, 0], rxLoc[:, 1], rxLoc[:, 2], 100.0, 0.0, 0.0, 0.0, 0.01, b0, "secondary"
)
dpred = survey.projectFieldsAsVector(B)
err = np.linalg.norm(dpred - np.r_[bxa, bya, bza]) / np.linalg.norm(np.r_[bxa, bya, bza])
self.assertTrue(err < 0.08)
def run(plotIt=True):
"""
PF: Magnetics: Analytics
========================
Comparing the magnetics field in Vancouver to Seoul
"""
xr = np.linspace(-300, 300, 41)
yr = np.linspace(-300, 300, 41)
X, Y = np.meshgrid(xr, yr)
Z = np.ones((np.size(xr), np.size(yr)))*150
# Bz component in Korea
inckr = -8. + 3./60
deckr = 54. + 9./60
btotkr = 50898.6
Bokr = PF.MagAnalytics.IDTtoxyz(inckr, deckr, btotkr)
bx, by, bz = PF.MagAnalytics.MagSphereAnaFunA(
X, Y, Z, 100., 0., 0., 0., 0.01, Bokr, 'secondary'
)
Bzkr = np.reshape(bz, (np.size(xr), np.size(yr)), order='F')
# Bz component in Canada
incca = 16. + 49./60
decca = 70. + 19./60
btotca = 54692.1
Boca = PF.MagAnalytics.IDTtoxyz(incca, decca, btotca)
bx, by, bz = PF.MagAnalytics.MagSphereAnaFunA(
X, Y, Z, 100., 0., 0., 0., 0.01, Boca, 'secondary'
)
Bzca = np.reshape(bz, (np.size(xr), np.size(yr)), order='F')
if plotIt:
import matplotlib.pyplot as plt
from mpl_toolkits.axes_grid1 import make_axes_locatable
fig = plt.figure(figsize=(14, 5))
ax1 = plt.subplot(121)
dat1 = plt.imshow(Bzkr, extent=[min(xr), max(xr), min(yr), max(yr)])
divider = make_axes_locatable(ax1)
cax1 = divider.append_axes("right", size="5%", pad=0.05)
ax1.set_xlabel('East-West (m)')
ax1.set_ylabel('South-North (m)')
plt.colorbar(dat1, cax=cax1)
ax1.set_title('$B_z$ field at Seoul, South Korea')
ax2 = plt.subplot(122)
dat2 = plt.imshow(Bzca, extent=[min(xr), max(xr), min(yr), max(yr)])
divider = make_axes_locatable(ax2)
cax2 = divider.append_axes("right", size="5%", pad=0.05)
ax2.set_xlabel('East-West (m)')
ax2.set_ylabel('South-North (m)')
plt.colorbar(dat2, cax=cax2)
ax2.set_title('$B_z$ field at Vancouver, Canada')
plt.show()
def run(plotIt=True, nFreq=1):
"""
MT: 3D: Forward
===============
Forward model 3D MT data.
"""
# Make a mesh
M = simpeg.Mesh.TensorMesh([[(100,5,-1.5),(100.,10),(100,5,1.5)],[(100,5,-1.5),(100.,10),(100,5,1.5)],[(100,5,1.6),(100.,10),(100,3,2)]], x0=['C','C',-3529.5360])
# Setup the model
conds = [1e-2,1]
sig = simpeg.Utils.ModelBuilder.defineBlock(M.gridCC,[-1000,-1000,-400],[1000,1000,-200],conds)
sig[M.gridCC[:,2]>0] = 1e-8
sig[M.gridCC[:,2]<-600] = 1e-1
sigBG = np.zeros(M.nC) + conds[0]
sigBG[M.gridCC[:,2]>0] = 1e-8
## Setup the the survey object
# Receiver locations
rx_x, rx_y = np.meshgrid(np.arange(-500,501,50),np.arange(-500,501,50))
rx_loc = np.hstack((simpeg.Utils.mkvc(rx_x,2),simpeg.Utils.mkvc(rx_y,2),np.zeros((np.prod(rx_x.shape),1))))
# Make a receiver list
rxList = []
for loc in rx_loc:
# NOTE: loc has to be a (1,3) np.ndarray otherwise errors accure
for rx_orientation in ['xx','xy','yx','yy']:
rxList.append(NSEM.Rx.Point_impedance3D(simpeg.mkvc(loc,2).T,rx_orientation, 'real'))
rxList.append(NSEM.Rx.Point_impedance3D(simpeg.mkvc(loc,2).T,rx_orientation, 'imag'))
for rx_orientation in ['zx','zy']:
rxList.append(NSEM.Rx.Point_tipper3D(simpeg.mkvc(loc,2).T,rx_orientation, 'real'))
rxList.append(NSEM.Rx.Point_tipper3D(simpeg.mkvc(loc,2).T,rx_orientation, 'imag'))
# Source list
srcList =[]
for freq in np.logspace(3,-3,nFreq):
srcList.append(NSEM.Src.Planewave_xy_1Dprimary(rxList,freq))
# Survey MT
survey = NSEM.Survey(srcList)
## Setup the problem object
problem = NSEM.Problem3D_ePrimSec(M, sigmaPrimary=sigBG)
problem.pair(survey)
problem.Solver = Solver
# Calculate the data
fields = problem.fields(sig)
dataVec = survey.eval(fields)
# Make the data
mtData = NSEM.Data(survey,dataVec)
# Add plots
if plotIt:
pass
def setUp(self):
# Define inducing field and sphere parameters
H0 = (50000., 60., 270.)
self.b0 = PF.MagAnalytics.IDTtoxyz(-H0[1], H0[2], H0[0])
self.rad = 2.
self.chi = 0.01
# Define a mesh
cs = 0.2
hxind = [(cs, 21)]
hyind = [(cs, 21)]
hzind = [(cs, 21)]
mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCC')
# Get cells inside the sphere
sph_ind = PF.MagAnalytics.spheremodel(mesh, 0., 0., 0., self.rad)
# Adjust susceptibility for volume difference
Vratio = (4. / 3. * np.pi * self.rad**3.) / (np.sum(sph_ind) * cs**3.)
model = np.ones(mesh.nC) * self.chi * Vratio
self.model = model[sph_ind]
# Creat reduced identity map for Linear Pproblem
idenMap = Maps.IdentityMap(nP=int(sum(sph_ind)))
# Create plane of observations
xr = np.linspace(-20, 20, 21)
yr = np.linspace(-20, 20, 21)
X, Y = np.meshgrid(xr, yr)
# Move obs plane 2 radius away from sphere
Z = np.ones((xr.size, yr.size)) * 2. * self.rad
self.locXyz = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
rxLoc = PF.BaseMag.RxObs(self.locXyz)
srcField = PF.BaseMag.SrcField([rxLoc], param=H0)
self.survey = PF.BaseMag.LinearSurvey(srcField)
self.prob_xyz = PF.Magnetics.MagneticIntegral(mesh,
mapping=idenMap,
actInd=sph_ind,
forwardOnly=True,
rtype='xyz')
self.prob_tmi = PF.Magnetics.MagneticIntegral(mesh,
mapping=idenMap,
actInd=sph_ind,
forwardOnly=True,
rtype='tmi')
def setUp(self):
# Define sphere parameters
self.rad = 2.
self.rho = 0.1
# Define a mesh
cs = 0.2
hxind = [(cs, 21)]
hyind = [(cs, 21)]
hzind = [(cs, 21)]
mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCC')
# Get cells inside the sphere
sph_ind = PF.MagAnalytics.spheremodel(mesh, 0., 0., 0., self.rad)
# Adjust density for volume difference
Vratio = (4. / 3. * np.pi * self.rad**3.) / (np.sum(sph_ind) * cs**3.)
model = np.ones(mesh.nC) * self.rho * Vratio
self.model = model[sph_ind]
# Create reduced identity map for Linear Pproblem
idenMap = Maps.IdentityMap(nP=int(sum(sph_ind)))
# Create plane of observations
xr = np.linspace(-20, 20, 21)
yr = np.linspace(-20, 20, 21)
X, Y = np.meshgrid(xr, yr)
# Move obs plane 2 radius away from sphere
Z = np.ones((xr.size, yr.size)) * 2. * self.rad
self.locXyz = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
rxLoc = PF.BaseGrav.RxObs(self.locXyz)
srcField = PF.BaseGrav.SrcField([rxLoc])
self.survey = PF.BaseGrav.LinearSurvey(srcField)
self.prob_xyz = PF.Gravity.GravityIntegral(mesh,
mapping=idenMap,
actInd=sph_ind,
forwardOnly=True,
rtype='xyz')
self.prob_z = PF.Gravity.GravityIntegral(mesh,
mapping=idenMap,
actInd=sph_ind,
forwardOnly=True,
rtype='z')
def setUp(self):
# Define inducing field and sphere parameters
H0 = (50000., 60., 270.)
self.b0 = PF.MagAnalytics.IDTtoxyz(-H0[1], H0[2], H0[0])
self.rad = 2.
self.chi = 0.01
# Define a mesh
cs = 0.2
hxind = [(cs, 21)]
hyind = [(cs, 21)]
hzind = [(cs, 21)]
mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCC')
# Get cells inside the sphere
sph_ind = PF.MagAnalytics.spheremodel(mesh, 0., 0., 0., self.rad)
# Adjust susceptibility for volume difference
Vratio = (4./3.*np.pi*self.rad**3.) / (np.sum(sph_ind)*cs**3.)
model = np.ones(mesh.nC)*self.chi*Vratio
self.model = model[sph_ind]
# Creat reduced identity map for Linear Pproblem
idenMap = Maps.IdentityMap(nP=int(sum(sph_ind)))
# Create plane of observations
xr = np.linspace(-20, 20, 21)
yr = np.linspace(-20, 20, 21)
X, Y = np.meshgrid(xr, yr)
# Move obs plane 2 radius away from sphere
Z = np.ones((xr.size, yr.size))*2.*self.rad
self.locXyz = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
rxLoc = PF.BaseMag.RxObs(self.locXyz)
srcField = PF.BaseMag.SrcField([rxLoc], param=H0)
self.survey = PF.BaseMag.LinearSurvey(srcField)
self.prob_xyz = PF.Magnetics.MagneticIntegral(mesh, mapping=idenMap,
actInd=sph_ind,
forwardOnly=True,
rtype='xyz')
self.prob_tmi = PF.Magnetics.MagneticIntegral(mesh, mapping=idenMap,
actInd=sph_ind,
forwardOnly=True,
rtype='tmi')
def setUp(self):
# Define sphere parameters
self.rad = 2.
self.rho = 0.1
# Define a mesh
cs = 0.2
hxind = [(cs, 21)]
hyind = [(cs, 21)]
hzind = [(cs, 21)]
mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCC')
# Get cells inside the sphere
sph_ind = PF.MagAnalytics.spheremodel(mesh, 0., 0., 0., self.rad)
# Adjust density for volume difference
Vratio = (4./3.*np.pi*self.rad**3.) / (np.sum(sph_ind)*cs**3.)
model = np.ones(mesh.nC)*self.rho*Vratio
self.model = model[sph_ind]
# Create reduced identity map for Linear Pproblem
idenMap = Maps.IdentityMap(nP=int(sum(sph_ind)))
# Create plane of observations
xr = np.linspace(-20, 20, 21)
yr = np.linspace(-20, 20, 21)
X, Y = np.meshgrid(xr, yr)
# Move obs plane 2 radius away from sphere
Z = np.ones((xr.size, yr.size))*2.*self.rad
self.locXyz = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
rxLoc = PF.BaseGrav.RxObs(self.locXyz)
srcField = PF.BaseGrav.SrcField([rxLoc])
self.survey = PF.BaseGrav.LinearSurvey(srcField)
self.prob_xyz = PF.Gravity.GravityIntegral(mesh, mapping=idenMap,
actInd=sph_ind,
forwardOnly=True,
rtype='xyz')
self.prob_z = PF.Gravity.GravityIntegral(mesh, mapping=idenMap,
actInd=sph_ind,
forwardOnly=True,
rtype='z')
# Get cells inside the sphere
sph_ind = PF.MagAnalytics.spheremodel(mesh, 0., 0., 0., rad)
# Adjust susceptibility for volume difference
Vratio = (4./3.*np.pi*rad**3.) / (np.sum(sph_ind)*cs**3.)
model = np.zeros(mesh.nC)
model[sph_ind] = chi*Vratio
m = model[sph_ind]
# Creat reduced identity map for Linear Pproblem
idenMap = Maps.IdentityMap(nP=int(sum(sph_ind)))
# Create plane of observations
xr = np.linspace(-10, 10, 21)
yr = np.linspace(-10, 10, 21)
X, Y = np.meshgrid(xr, yr)
# Move obs plane 2 radius away from sphere
Z = np.ones((xr.size, yr.size))*2.*rad
locXyz = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
rxLoc = PF.BaseMag.RxObs(locXyz)
srcField = PF.BaseMag.SrcField([rxLoc], param=H0)
survey = PF.BaseMag.LinearSurvey(srcField)
prob_xyz = PF.Magnetics.MagneticIntegral(mesh, chiMap=idenMap,
actInd=sph_ind,
forwardOnly=True,
rtype='xyz')
prob_tmi = PF.Magnetics.MagneticIntegral(mesh, chiMap=idenMap,
actInd=sph_ind,
nc = np.ceil(dl_len/dx)+3 padx = dx*np.power(1.4,range(1,15)) # Creating padding cells h1 = np.r_[padx[::-1], np.ones(nc)*dx , padx] # Create mesh with 0 coordinate centerer on the ginput points in cell center mesh2d = Mesh.TensorMesh([h1, mesh.hz], x0=(-np.sum(padx)-dx/2,mesh.x0[2])) # Create array of points for interpolating from 3D to 2D mesh xx = Tx[0][0,0] + mesh2d.vectorCCx * np.cos(azm) yy = Tx[0][1,0] + mesh2d.vectorCCx * np.sin(azm) zz = mesh2d.vectorCCy [XX,ZZ] = np.meshgrid(xx,zz) [YY,ZZ] = np.meshgrid(yy,zz) xyz2d = np.c_[mkvc(XX),mkvc(YY),mkvc(ZZ)] #plt.scatter(xx,yy,s=20,c='y') F = interpolation.NearestNDInterpolator(mesh.gridCC,model) m2D = np.reshape(F(xyz2d),[mesh2d.nCx,mesh2d.nCy]).T #============================================================================== # mesh2d = Mesh.TensorMesh([mesh.hx, mesh.hz], x0=(mesh.x0[0]-endl[0,0],mesh.x0[2])) # m3D = np.reshape(model, (mesh.nCz, mesh.nCy, mesh.nCx)) # m2D = m3D[:,1,:]
