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seogi
101 lines
3.7 KiB
Python
101 lines
3.7 KiB
Python
import numpy as np
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from scipy.constants import mu_0, pi
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from SimPEG import Mesh
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def MagneticDipoleVectorPotential(txLoc, obsLoc, component, dipoleMoment=(0., 0., 1.)):
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"""
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Calculate the vector potential of a set of magnetic dipoles
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at given locations 'ref. <http://en.wikipedia.org/wiki/Dipole#Magnetic_vector_potential>'
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:param numpy.ndarray txLoc: Location of the transmitter(s) (x, y, z)
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:param numpy.ndarray,SimPEG.Mesh obsLoc: Where the potentials will be calculated (x, y, z) or a SimPEG Mesh
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:param str,list component: The component to calculate - 'x', 'y', or 'z' if an array, or grid type if mesh, can be a list
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:param numpy.ndarray dipoleMoment: The vector dipole moment
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:rtype: numpy.ndarray
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:return: The vector potential each dipole at each observation location
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"""
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if type(component) in [list, tuple]:
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out = range(len(component))
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for i, comp in enumerate(component):
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out[i] = MagneticDipoleVectorPotential(txLoc, obsLoc, comp, dipoleMoment=dipoleMoment)
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return np.concatenate(out)
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if isinstance(obsLoc, Mesh.BaseMesh):
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mesh = obsLoc
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assert component in ['Ex','Ey','Ez','Fx','Fy','Fz'], "Components must be in: ['Ex','Ey','Ez','Fx','Fy','Fz']"
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return MagneticDipoleVectorPotential(txLoc, getattr(mesh,'grid'+component), component[1], dipoleMoment=dipoleMoment)
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if component == 'x':
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dimInd = 0
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elif component == 'y':
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dimInd = 1
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elif component == 'z':
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dimInd = 2
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else:
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raise ValueError('Invalid component')
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txLoc = np.atleast_2d(txLoc)
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obsLoc = np.atleast_2d(obsLoc)
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dipoleMoment = np.atleast_2d(dipoleMoment)
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nEdges = obsLoc.shape[0]
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nTx = txLoc.shape[0]
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m = np.array(dipoleMoment).repeat(nEdges, axis=0)
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A = np.empty((nEdges, nTx))
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for i in range(nTx):
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dR = obsLoc - txLoc[i, np.newaxis].repeat(nEdges, axis=0)
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mCr = np.cross(m, dR)
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r = np.sqrt((dR**2).sum(axis=1))
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A[:, i] = +(mu_0/(4*pi)) * mCr[:,dimInd]/(r**3)
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if nTx == 1:
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return A.flatten()
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return A
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def MagneticDipoleFields(txLoc, obsLoc, component, dipoleMoment=1.):
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"""
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Calculate the vector potential of a set of magnetic dipoles
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at given locations 'ref. <http://en.wikipedia.org/wiki/Dipole#Magnetic_vector_potential>'
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:param numpy.ndarray txLoc: Location of the transmitter(s) (x, y, z)
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:param numpy.ndarray obsLoc: Where the potentials will be calculated (x, y, z)
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:param str component: The component to calculate - 'x', 'y', or 'z'
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:param numpy.ndarray dipoleMoment: The vector dipole moment (vertical)
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:rtype: numpy.ndarray
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:return: The vector potential each dipole at each observation location
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"""
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if component=='x':
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dimInd = 0
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elif component=='y':
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dimInd = 1
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elif component=='z':
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dimInd = 2
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else:
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raise ValueError('Invalid component')
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txLoc = np.atleast_2d(txLoc)
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obsLoc = np.atleast_2d(obsLoc)
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dipoleMoment = np.atleast_2d(dipoleMoment)
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nFaces = obsLoc.shape[0]
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nTx = txLoc.shape[0]
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m = np.array(dipoleMoment).repeat(nFaces, axis=0)
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B = np.empty((nFaces, nTx))
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for i in range(nTx):
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dR = obsLoc - txLoc[i, np.newaxis].repeat(nFaces, axis=0)
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r = np.sqrt((dR**2).sum(axis=1))
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if dimInd == 0:
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B[:, i] = +(mu_0/(4*pi)) /(r**3) * (3*dR[:,2]*dR[:,0]/r**2)
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elif dimInd == 1:
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B[:, i] = +(mu_0/(4*pi)) /(r**3) * (3*dR[:,2]*dR[:,1]/r**2)
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elif dimInd == 2:
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B[:, i] = +(mu_0/(4*pi)) /(r**3) * (3*dR[:,2]**2/r**2-1)
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else:
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raise Exception("Not Implemented")
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if nTx == 1:
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return B.flatten()
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return B
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