mirror of
https://github.com/wassname/simpeg.git
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Lindsey Heagy
83 lines
2.2 KiB
Python
83 lines
2.2 KiB
Python
import numpy as np
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from scipy.constants import mu_0, pi
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from scipy.special import erf
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import matplotlib.pyplot as plt
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def hzAnalyticDipoleF(r, freq, sigma, secondary=True):
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"""
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4.56 in Ward and Hohmann
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.. plot::
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import matplotlib.pyplot as plt
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import simpegEM as EM
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freq = np.logspace(-1, 6, 61)
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test = EM.Utils.Ana.FEM.hzAnalyticDipoleF(100, freq, 0.001, secondary=False)
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plt.loglog(freq, abs(test.real))
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plt.loglog(freq, abs(test.imag))
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plt.title('Response at $r$=100m')
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plt.xlabel('Frequency')
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plt.ylabel('Response')
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plt.legend(('real','imag'))
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plt.show()
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"""
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r = np.abs(r)
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k = np.sqrt(-1j*2.*np.pi*f*mu_0*sigma)
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m = 1
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front = m / (2. * np.pi * (k**2) * (r**5) )
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back = 9 - ( 9 + 9j * k * r - 4 * (k**2) * (r**2) - 1j * (k**3) * (r**3)) * np.exp(-1j*k*r)
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hz = front*back
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if secondary:
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hp =-1/(4*np.pi*r**3)
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return hz-hp
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return hz
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def AnalyticMagDipoleWholeSpace(x,y,z,sig,f,xs=0.,ys=0.,zs=0.,m=1.,orientation='X'):
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"""
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Analytical solution for a dipole in a whole-space.
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Equation 2.57 of Ward and Hohmann
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TODOs:
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- set it up to instead take a mesh & survey
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- add E-fields
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- handle multiple frequencies
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- add divide by zero safety
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"""
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dx = x-xs
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dy = y-ys
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dz = z-zs
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r = np.sqrt( dx**2. + dy**2. + dz**2.)
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k = np.sqrt(-1j*2.*np.pi*f*mu_0*sig)
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kr = k*r
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front = m / (4.*pi * r**3.) * np.exp(-1j*kr)
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mid = -kr**2. + 3.*1j*kr + 3.
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if orientation.upper() == 'X':
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Hx = front*( (dx/r)**2. * mid + (kr**2. - 1j*kr - 1.) )
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Hy = front*( (dx*dy/r**2.) * mid )
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Hz = front*( (dx*dz/r**2.) * mid )
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elif orientation.upper() == 'Y':
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Hx = front*( (dy*dx/r**2.) * mid )
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Hy = front*( (dy/r)**2. * mid + (kr**2. - 1j*kr - 1.) )
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Hz = front*( (dy*dz/r**2.) * mid )
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elif orientation.upper() == 'Z':
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Hx = front*( (dx*dz/r**2.) * mid )
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Hy = front*( (dy*dz/r**2.) * mid )
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Hz = front*( (dz/r)**2. * mid + (kr**2. - 1j*kr - 1.) )
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Bx = mu_0*Hx
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By = mu_0*Hy
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Bz = mu_0*Hz
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return Bx, By, Bz
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