mirror of
https://github.com/wassname/simpeg.git
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Merge branch 'master' of https://github.com/simpeg/simpegem into em/dev
Conflicts: .coveragerc .gitignore .travis.yml docs/api_Utils.rst docs/conf.py docs/index.rst requirements.txt setup.py
This commit is contained in:
Rowan Cockett
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from __future__ import division
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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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from SimPEG import Utils
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def hzAnalyticDipoleF(r, freq, sigma, secondary=True, mu=mu_0):
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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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from SimPEG import EM
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freq = np.logspace(-1, 6, 61)
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test = EM.Analytics.FDEM.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*freq*mu*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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hz = hz-hp
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if hz.ndim == 1:
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hz = Utils.mkvc(hz,2)
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return hz
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def MagneticDipoleWholeSpace(XYZ, srcLoc, sig, f, moment=1., orientation='X', mu = mu_0):
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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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.. plot::
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from SimPEG import EM
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import matplotlib.pyplot as plt
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freqs = np.logspace(-2,5,100)
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Bx, By, Bz = EM.Analytics.FDEM.AnalyticMagDipoleWholeSpace([0,100,0], [0,0,0], 1e-2, freqs, m=1, orientation='Z')
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plt.loglog(freqs, np.abs(Bz.real)/mu_0, 'b')
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plt.loglog(freqs, np.abs(Bz.imag)/mu_0, 'r')
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plt.legend(('real','imag'))
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plt.show()
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"""
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XYZ = Utils.asArray_N_x_Dim(XYZ, 3)
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dx = XYZ[:,0]-srcLoc[0]
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dy = XYZ[:,1]-srcLoc[1]
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dz = XYZ[:,2]-srcLoc[2]
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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*sig )
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kr = k*r
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front = moment / (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*Hx
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By = mu*Hy
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Bz = mu*Hz
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if Bx.ndim is 1:
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Bx = Utils.mkvc(Bx,2)
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if By.ndim is 1:
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By = Utils.mkvc(By,2)
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if Bz.ndim is 1:
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Bz = Utils.mkvc(Bz,2)
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return Bx, By, Bz
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def ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', mu=mu_0):
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XYZ = Utils.asArray_N_x_Dim(XYZ, 3)
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dx = XYZ[:,0]-srcLoc[0]
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dy = XYZ[:,1]-srcLoc[1]
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dz = XYZ[:,2]-srcLoc[2]
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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*sig )
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kr = k*r
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front = current * length / (4. * np.pi * sig * r**3) * np.exp(-1j*k*r)
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mid = -k**2 * r**2 + 3*1j*k*r + 3
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# Ex = front*((dx**2 / r**2)*mid + (k**2 * r**2 -1j*k*r))
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# Ey = front*(dx*dy / r**2)*mid
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# Ez = front*(dx*dz / r**2)*mid
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if orientation.upper() == 'X':
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Ex = front*((dx**2 / r**2)*mid + (k**2 * r**2 -1j*k*r-1.))
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Ey = front*(dx*dy / r**2)*mid
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Ez = front*(dx*dz / r**2)*mid
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return Ex, Ey, Ez
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elif orientation.upper() == 'Y':
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# x--> y, y--> z, z-->x
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Ey = front*((dy**2 / r**2)*mid + (k**2 * r**2 -1j*k*r-1.))
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Ez = front*(dy*dz / r**2)*mid
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Ex = front*(dy*dx / r**2)*mid
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return Ex, Ey, Ez
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elif orientation.upper() == 'Z':
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# x --> z, y --> x, z --> y
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Ez = front*((dz**2 / r**2)*mid + (k**2 * r**2 -1j*k*r-1.))
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Ex = front*(dz*dx / r**2)*mid
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Ey = front*(dz*dy / r**2)*mid
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return Ex, Ey, Ez
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# return Ey, Ez, Ex
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from SimPEG import Utils, np
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from scipy.constants import mu_0, epsilon_0
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from simpegEM.Utils.EMUtils import k
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def getKc(freq,sigma,a,b,mu=mu_0,eps=epsilon_0):
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a = float(a)
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b = float(b)
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# return 1./(2*np.pi) * np.sqrt(b / a) * np.exp(-1j*k(freq,sigma,mu,eps)*(b-a))
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return np.sqrt(b / a) * np.exp(-1j*k(freq,sigma,mu,eps)*(b-a))
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def _r2(xyz):
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return np.sum(xyz**2,1)
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def _getCasingHertzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
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Kc1 = getKc(freq,sigma[1],a,b,mu[1],eps)
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nobs = obsloc.shape[0]
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dxyz = obsloc - np.c_[np.ones(nobs)]*np.r_[srcloc]
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r2 = _r2(dxyz[:,:2])
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sqrtr2z2 = np.sqrt(r2 + dxyz[:,2]**2)
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k2 = k(freq,sigma[2],mu[2],eps)
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return Kc1 * moment / (4.*np.pi) *np.exp(-1j*k2*sqrtr2z2) / sqrtr2z2
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def _getCasingHertzMagDipoleDeriv_r(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
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HertzZ = _getCasingHertzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
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nobs = obsloc.shape[0]
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dxyz = obsloc - np.c_[np.ones(nobs)]*np.r_[srcloc]
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r2 = _r2(dxyz[:,:2])
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sqrtr2z2 = np.sqrt(r2 + dxyz[:,2]**2)
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k2 = k(freq,sigma[2],mu[2],eps)
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return -HertzZ * np.sqrt(r2) / sqrtr2z2 * (1j*k2 + 1./ sqrtr2z2)
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def _getCasingHertzMagDipoleDeriv_z(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
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HertzZ = _getCasingHertzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
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nobs = obsloc.shape[0]
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dxyz = obsloc - np.c_[np.ones(nobs)]*np.r_[srcloc]
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r2z2 = _r2(dxyz)
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sqrtr2z2 = np.sqrt(r2z2)
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k2 = k(freq,sigma[2],mu[2],eps)
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return -HertzZ*dxyz[:,2] /sqrtr2z2 * (1j*k2 + 1./sqrtr2z2)
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def _getCasingHertzMagDipole2Deriv_z_r(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
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HertzZ = _getCasingHertzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
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dHertzZdr = _getCasingHertzMagDipoleDeriv_r(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
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nobs = obsloc.shape[0]
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dxyz = obsloc - np.c_[np.ones(nobs)]*np.r_[srcloc]
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r2 = _r2(dxyz[:,:2])
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r = np.sqrt(r2)
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z = dxyz[:,2]
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sqrtr2z2 = np.sqrt(r2 + z**2)
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k2 = k(freq,sigma[2],mu[2],eps)
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return dHertzZdr*(-z/sqrtr2z2)*(1j*k2+1./sqrtr2z2) + HertzZ*(z*r/sqrtr2z2**3)*(1j*k2 + 2./sqrtr2z2)
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def _getCasingHertzMagDipole2Deriv_z_z(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
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HertzZ = _getCasingHertzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
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dHertzZdz = _getCasingHertzMagDipoleDeriv_z(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
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nobs = obsloc.shape[0]
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dxyz = obsloc - np.c_[np.ones(nobs)]*np.r_[srcloc]
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r2 = _r2(dxyz[:,:2])
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r = np.sqrt(r2)
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z = dxyz[:,2]
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sqrtr2z2 = np.sqrt(r2 + z**2)
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k2 = k(freq,sigma[2],mu[2],eps)
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return (dHertzZdz*z + HertzZ)/sqrtr2z2*(-1j*k2 - 1./sqrtr2z2) + HertzZ*z/sqrtr2z2**3*(1j*k2*z + 2.*z/sqrtr2z2)
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def getCasingEphiMagDipole(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
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return 1j * omega(freq) * mu * _getCasingHertzMagDipoleDeriv_r(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
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def getCasingHrMagDipole(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
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return _getCasingHertzMagDipole2Deriv_z_r(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
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def getCasingHzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
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d2HertzZdz2 = _getCasingHertzMagDipole2Deriv_z_z(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
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k2 = k(freq,sigma[2],mu[2],eps)
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HertzZ = _getCasingHertzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
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return d2HertzZdz2 + k2**2 * HertzZ
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def getCasingBrMagDipole(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
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return mu_0 * getCasingHrMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
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def getCasingBzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
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return mu_0 * getCasingHzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
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@@ -0,0 +1,12 @@
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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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def hzAnalyticDipoleT(r, t, sigma):
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theta = np.sqrt((sigma*mu_0)/(4*t))
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tr = theta*r
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etr = erf(tr)
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t1 = (9/(2*tr**2) - 1)*etr
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t2 = (1/np.sqrt(pi))*(9/tr + 4*tr)*np.exp(-tr**2)
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hz = (t1 - t2)/(4*pi*r**3)
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return hz
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@@ -0,0 +1,3 @@
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from TDEM import hzAnalyticDipoleT
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from FDEM import hzAnalyticDipoleF
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from FDEMcasing import *
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