mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-29 04:10:59 +08:00
rowanc1
102 lines
3.5 KiB
Python
102 lines
3.5 KiB
Python
from SimPEG import *
|
|
from scipy.special import ellipk, ellipe
|
|
|
|
def MagneticLoopVectorPotential(txLoc, obsLoc, component, radius):
|
|
"""
|
|
Calculate the vector potential of horizontal circular loop
|
|
at given locations
|
|
|
|
:param numpy.ndarray txLoc: Location of the transmitter(s) (x, y, z)
|
|
:param numpy.ndarray,SimPEG.Mesh obsLoc: Where the potentials will be calculated (x, y, z) or a SimPEG Mesh
|
|
:param str,list component: The component to calculate - 'x', 'y', or 'z' if an array, or grid type if mesh, can be a list
|
|
:param numpy.ndarray I: Input current of the loop
|
|
:param numpy.ndarray radius: radius of the loop
|
|
:rtype: numpy.ndarray
|
|
:return: The vector potential each dipole at each observation location
|
|
"""
|
|
|
|
if type(component) in [list, tuple]:
|
|
out = range(len(component))
|
|
for i, comp in enumerate(component):
|
|
out[i] = MagneticLoopVectorPotential(txLoc, obsLoc, comp, radius)
|
|
return np.concatenate(out)
|
|
|
|
if isinstance(obsLoc, Mesh.BaseMesh):
|
|
mesh = obsLoc
|
|
assert component in ['Ex','Ey','Ez','Fx','Fy','Fz'], "Components must be in: ['Ex','Ey','Ez','Fx','Fy','Fz']"
|
|
return MagneticLoopVectorPotential(txLoc, getattr(mesh,'grid'+component), component[1], radius)
|
|
|
|
txLoc = np.atleast_2d(txLoc)
|
|
obsLoc = np.atleast_2d(obsLoc)
|
|
|
|
n = obsLoc.shape[0]
|
|
nTx = txLoc.shape[0]
|
|
|
|
if component=='z':
|
|
A = np.zeros((n, nTx))
|
|
if nTx ==1:
|
|
return A.flatten()
|
|
return A
|
|
|
|
else:
|
|
|
|
A = np.zeros((n, nTx))
|
|
for i in range (nTx):
|
|
x = obsLoc[:, 0] - txLoc[i, 0]
|
|
y = obsLoc[:, 1] - txLoc[i, 1]
|
|
z = obsLoc[:, 2] - txLoc[i, 2]
|
|
r = np.sqrt(x**2 + y**2)
|
|
m = (4 * radius * r) / ((radius + r)**2 + z**2)
|
|
m[m > 1.] = 1.
|
|
# m might be slightly larger than 1 due to rounding errors
|
|
# but ellipke requires 0 <= m <= 1
|
|
K = ellipk(m)
|
|
E = ellipe(m)
|
|
ind = (r > 0) & (m < 1)
|
|
# % 1/r singular at r = 0 and K(m) singular at m = 1
|
|
Aphi = np.zeros(n)
|
|
# % Common factor is (mu * I) / pi with I = 1 and mu = 4e-7 * pi.
|
|
Aphi[ind] = 4e-7 / np.sqrt(m[ind]) * np.sqrt(radius / r[ind]) *((1. - m[ind] / 2.) * K[ind] - E[ind])
|
|
if component == 'x':
|
|
A[ind, i] = Aphi[ind] * (-y[ind] / r[ind] )
|
|
elif component == 'y':
|
|
A[ind, i] = Aphi[ind] * ( x[ind] / r[ind] )
|
|
else:
|
|
raise ValueError('Invalid component')
|
|
|
|
if nTx == 1:
|
|
return A.flatten()
|
|
return A
|
|
|
|
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 = Mesh.TensorMesh([hx, hy, hz], 'CCC')
|
|
txLoc = np.r_[0., 0., 0.]
|
|
Ax = MagneticLoopVectorPotential(txLoc, mesh.gridEx, 'x', 200)
|
|
Ay = MagneticLoopVectorPotential(txLoc, mesh.gridEy, 'y', 200)
|
|
Az = MagneticLoopVectorPotential(txLoc, 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()
|
|
|
|
|