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First stab at analytic functions for the fields from a harmonic electric dipole source. Not sure about the exception that I try to throw if multiple frequencies and multiple evaluation locations are both specified.

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micmitch
2016-05-27 14:56:48 -07:00
parent 28d67e3112
commit 1960b52dfd
1 changed files with 106 additions and 13 deletions
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SimPEG/EM/Analytics/FDEM_fields.py
+106 -13
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@@ -5,24 +5,27 @@ from scipy.special import erf
from SimPEG import Utils
def ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', mu=mu_0):
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
XYZ = Utils.asArray_N_x_Dim(XYZ, 3)
# Check
if XYZ.shape[0] > 1 & f.length > 1
except:
print "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 )
kr = k*r
# 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)
front = current * length / (4.*np.pi*sig* r**3) * np.exp(-1j*k*r)
mid = -k**2 * r**2 + 3*1j*k*r + 3
# Ex = front*((dx**2 / r**2)*mid + (k**2 * r**2 -1j*k*r))
# Ey = front*(dx*dy / r**2)*mid
# Ez = front*(dx*dz / r**2)*mid
if orientation.upper() == 'X':
Ex = front*((dx**2 / r**2)*mid + (k**2 * r**2 -1j*k*r-1.))
Ey = front*(dx*dy / r**2)*mid
@@ -42,10 +45,100 @@ def ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orienta
Ex = front*(dz*dx / r**2)*mid
Ey = front*(dz*dy / r**2)*mid
return Ex, Ey, Ez
# return Ey, Ez, Ex
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)
Jx = sig*Ex
Jy = sig*Ey
Jz = sig*Ez
return Jx, Jy, Jz
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
XYZ = Utils.asArray_N_x_Dim(XYZ, 3)
# Check
if XYZ.shape[0] > 1 & f.length > 1
except:
print "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* r**2) * (-1j*k*r + 1) * np.exp(-1j*k*r)
if orientation.upper() == 'X':
Hy = front*(-dz / r)
Hz = front*(dy / r)
Hx = np.zeros_like(Hy)
return Hx, Hy, Hz
elif orientation.upper() == 'Y':
Hx = front*(dz / r)
Hz = front*(-dx / r)
Hy = np.zeros_like(Hx)
return Hx, Hy, Hz
elif orientation.upper() == 'Z':
Hx = front*(-dy / r)
Hy = front*(dx / r)
Hz = np.zeros_like(Hx)
return Hx, Hy, Hz
def B_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', mu=mu_0):
Hx, Hy, Hz = H_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', mu=mu_0)
Bx = mu*Hx
By = mu*Hy
Bz = mu*Hz
return Bx, By, Bz
def A_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', mu=mu_0):
def J_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', mu=mu_0):
def H_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', mu=mu_0):
def B_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', mu=mu_0):
mu*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
XYZ = Utils.asArray_N_x_Dim(XYZ, 3)
# Check
if XYZ.shape[0] > 1 & f.length > 1
except:
print "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( omega**2. *mu*epsilon -1j*omega*mu*sig )
front = current * length / (4.*np.pi*r)
if orientation.upper() == 'X':
Ax = front*np.exp(-1j*k*r)
Ay = np.zeros_like(Ax)
Az = np.zeros_like(Ax)
return Ax, Ay, Az
elif orientation.upper() == 'Y':
Ay = front*np.exp(-1j*k*r)
Ax = np.zeros_like(Ay)
Az = np.zeros_like(Ay)
return Ax, Ay, Az
elif orientation.upper() == 'Z':
Az = front*np.exp(-1j*k*r)
Ax = np.zeros_like(Ay)
Ay = np.zeros_like(Ay)
return Ax, Ay, Az