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https://github.com/wassname/simpeg.git
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Dave Marchant
39 lines
1.3 KiB
Python
39 lines
1.3 KiB
Python
import numpy as np
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from scipy.constants import mu_0, pi
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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 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
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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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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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return A |