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Added functions to split electric field into "galvanic" and "inductive" portions.

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micmitch
2016-06-13 17:35:52 -07:00
parent 5e3c1da8e2
commit 093f441331
1 changed files with 96 additions and 6 deletions
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SimPEG/EM/Analytics/FDEM_fields.py
+96 -6
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@@ -4,10 +4,6 @@ from scipy.constants import mu_0, pi
from scipy.special import erf
from SimPEG import Utils
# def E_galvanic_from_ElectricDipoleWholeSpaced
# def E_inductive_from_ElectricDipoleWholeSpaced
def E_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', mu=mu_0):
epsilon = 8.854187817*(10.**-12)
omega = 2.*np.pi*f
@@ -49,8 +45,86 @@ def E_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1.,
return Ex, Ey, Ez
# def J_galvanic_from_ElectricDipoleWholeSpaced
# def J_inductive_from_ElectricDipoleWholeSpaced
def E_galvanic_from_ElectricDipoleWholeSpaced(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', mu=mu_0):
epsilon = 8.854187817*(10.**-12)
omega = 2.*np.pi*f
XYZ = Utils.asArray_N_x_Dim(XYZ, 3)
# Check
if XYZ.shape[0] > 1 & f.shape[0] > 1:
raise Exception("I/O type error: For multiple field locations only a single frequency can be specified.")
dx = XYZ[:,0]-srcLoc[0]
dy = XYZ[:,1]-srcLoc[1]
dz = XYZ[:,2]-srcLoc[2]
r = np.sqrt( dx**2. + dy**2. + dz**2.)
# k = np.sqrt( -1j*2.*np.pi*f*mu*sig )
k = np.sqrt( omega**2. *mu*epsilon -1j*omega*mu*sig )
front = current * length / (4.*np.pi*sig* r**3) * np.exp(-1j*k*r)
mid = -k**2 * r**2 + 3*1j*k*r + 3
if orientation.upper() == 'X':
Ex_galvanic = front*((dx**2 / r**2)*mid + (-1j*k*r-1.))
Ey_galvanic = front*(dx*dy / r**2)*mid
Ez_galvanic = front*(dx*dz / r**2)*mid
return Ex_galvanic, Ey_galvanic, Ez_galvanic
elif orientation.upper() == 'Y':
# x--> y, y--> z, z-->x
Ey_galvanic = front*((dy**2 / r**2)*mid + (-1j*k*r-1.))
Ez_galvanic = front*(dy*dz / r**2)*mid
Ex_galvanic = front*(dy*dx / r**2)*mid
return Ex_galvanic, Ey_galvanic, Ez_galvanic
elif orientation.upper() == 'Z':
# x --> z, y --> x, z --> y
Ez_galvanic = front*((dz**2 / r**2)*mid + (-1j*k*r-1.))
Ex_galvanic = front*(dz*dx / r**2)*mid
Ey_galvanic = front*(dz*dy / r**2)*mid
return Ex_galvanic, Ey_galvanic, Ez_galvanic
def E_inductive_from_ElectricDipoleWholeSpaced(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', mu=mu_0):
epsilon = 8.854187817*(10.**-12)
omega = 2.*np.pi*f
XYZ = Utils.asArray_N_x_Dim(XYZ, 3)
# Check
if XYZ.shape[0] > 1 & f.shape[0] > 1:
raise Exception("I/O type error: For multiple field locations only a single frequency can be specified.")
dx = XYZ[:,0]-srcLoc[0]
dy = XYZ[:,1]-srcLoc[1]
dz = XYZ[:,2]-srcLoc[2]
r = np.sqrt( dx**2. + dy**2. + dz**2.)
# k = np.sqrt( -1j*2.*np.pi*f*mu*sig )
k = np.sqrt( omega**2. *mu*epsilon -1j*omega*mu*sig )
front = current * length / (4.*np.pi*sig* r**3) * np.exp(-1j*k*r)
if orientation.upper() == 'X':
Ex_inductive = front*(k**2 * r**2)
Ey_inductive = 0
Ez_inductive = 0
return Ex_inductive, Ey_inductive, Ez_inductive
elif orientation.upper() == 'Y':
# x--> y, y--> z, z-->x
Ey_inductive = front*(k**2 * r**2)
Ez_inductive = 0
Ex_inductive = 0
return Ex_inductive, Ey_inductive, Ez_inductive
elif orientation.upper() == 'Z':
# x --> z, y --> x, z --> y
Ez_inductive = front*(k**2 * r**2)
Ex_inductive = 0
Ey_inductive = 0
return Ex_inductive, Ey_inductive, Ez_inductive
def J_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', mu=mu_0):
Ex, Ey, Ez = E_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', mu=mu_0)
@@ -60,6 +134,22 @@ def J_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1.,
return Jx, Jy, Jz
def J_galvanic_from_ElectricDipoleWholeSpaced(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', mu=mu_0):
Ex_galvanic, Ey_galvanic, Ez_galvanic = E_galvanic_from_ElectricDipoleWholeSpaced(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', mu=mu_0)
Jx_galvanic = sig*Ex_galvanic
Jy_galvanic = sig*Ey_galvanic
Jz_galvanic = sig*Ez_galvanic
return Jx_galvanic, Jy_galvanic, Jz_galvanic
def J_inductive_from_ElectricDipoleWholeSpaced(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', mu=mu_0):
Ex_inductive, Ey_inductive, Ez_inductive = E_inductive_from_ElectricDipoleWholeSpaced(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', mu=mu_0)
Jx_inductive = sig*Ex_inductive
Jy_inductive = sig*Ey_inductive
Jz_inductive = sig*Ez_inductive
return Jx_inductive, Jy_inductive, Jz_inductive
def H_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', mu=mu_0):
epsilon = 8.854187817*(10.**-12)
omega = 2.*np.pi*f