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
2026-08-12 12:30:37 +08:00 · 2015-11-04 09:59:11 -08:00
parent 1aade8155d e85da0d15b
commit e622dfb5cc
37 changed files with 5141 additions and 0 deletions
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+from SimPEG import Utils, np
+from scipy.constants import mu_0, epsilon_0
+from simpegEM.Utils.EMUtils import k
+
+def getKc(freq,sigma,a,b,mu=mu_0,eps=epsilon_0):
+    a = float(a)
+    b = float(b)
+    # return 1./(2*np.pi) * np.sqrt(b / a) * np.exp(-1j*k(freq,sigma,mu,eps)*(b-a))
+    return np.sqrt(b / a) * np.exp(-1j*k(freq,sigma,mu,eps)*(b-a))
+
+def _r2(xyz):
+    return np.sum(xyz**2,1)
+
+def _getCasingHertzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
+    Kc1 = getKc(freq,sigma[1],a,b,mu[1],eps)
+
+    nobs = obsloc.shape[0]
+    dxyz = obsloc - np.c_[np.ones(nobs)]*np.r_[srcloc]
+    
+    r2 = _r2(dxyz[:,:2])
+    sqrtr2z2 = np.sqrt(r2 + dxyz[:,2]**2)
+    k2 = k(freq,sigma[2],mu[2],eps) 
+    
+    return Kc1 * moment / (4.*np.pi) *np.exp(-1j*k2*sqrtr2z2) / sqrtr2z2
+
+
+def _getCasingHertzMagDipoleDeriv_r(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
+    HertzZ = _getCasingHertzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
+    
+    nobs = obsloc.shape[0]
+    dxyz = obsloc - np.c_[np.ones(nobs)]*np.r_[srcloc]
+    
+    r2 = _r2(dxyz[:,:2])
+    sqrtr2z2 = np.sqrt(r2 + dxyz[:,2]**2)
+    k2 = k(freq,sigma[2],mu[2],eps) 
+    
+    return -HertzZ * np.sqrt(r2) / sqrtr2z2 * (1j*k2 + 1./ sqrtr2z2)
+
+
+def _getCasingHertzMagDipoleDeriv_z(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
+    HertzZ = _getCasingHertzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
+    
+    nobs = obsloc.shape[0]
+    dxyz = obsloc - np.c_[np.ones(nobs)]*np.r_[srcloc]
+    
+    r2z2 = _r2(dxyz)
+    sqrtr2z2 = np.sqrt(r2z2)
+    k2 = k(freq,sigma[2],mu[2],eps) 
+    
+    return -HertzZ*dxyz[:,2] /sqrtr2z2 * (1j*k2 + 1./sqrtr2z2)
+
+def _getCasingHertzMagDipole2Deriv_z_r(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
+    HertzZ = _getCasingHertzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
+    dHertzZdr = _getCasingHertzMagDipoleDeriv_r(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
+    
+    nobs = obsloc.shape[0]
+    dxyz = obsloc - np.c_[np.ones(nobs)]*np.r_[srcloc]
+
+    r2 = _r2(dxyz[:,:2])
+    r = np.sqrt(r2)
+    z = dxyz[:,2]
+    sqrtr2z2 = np.sqrt(r2 + z**2)
+    k2 = k(freq,sigma[2],mu[2],eps) 
+    
+    return dHertzZdr*(-z/sqrtr2z2)*(1j*k2+1./sqrtr2z2) + HertzZ*(z*r/sqrtr2z2**3)*(1j*k2 + 2./sqrtr2z2)
+
+def _getCasingHertzMagDipole2Deriv_z_z(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
+    HertzZ = _getCasingHertzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
+    dHertzZdz = _getCasingHertzMagDipoleDeriv_z(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
+    
+    nobs = obsloc.shape[0]
+    dxyz = obsloc - np.c_[np.ones(nobs)]*np.r_[srcloc]
+
+    r2 = _r2(dxyz[:,:2])
+    r = np.sqrt(r2)
+    z = dxyz[:,2]
+    sqrtr2z2 = np.sqrt(r2 + z**2)
+    k2 = k(freq,sigma[2],mu[2],eps) 
+    
+    return (dHertzZdz*z + HertzZ)/sqrtr2z2*(-1j*k2 - 1./sqrtr2z2) + HertzZ*z/sqrtr2z2**3*(1j*k2*z + 2.*z/sqrtr2z2)
+    
+def getCasingEphiMagDipole(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
+    return 1j * omega(freq) * mu * _getCasingHertzMagDipoleDeriv_r(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
+
+def getCasingHrMagDipole(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
+    return _getCasingHertzMagDipole2Deriv_z_r(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
+
+def getCasingHzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
+    d2HertzZdz2 = _getCasingHertzMagDipole2Deriv_z_z(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
+    k2 = k(freq,sigma[2],mu[2],eps)
+    HertzZ = _getCasingHertzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
+    return d2HertzZdz2 + k2**2 * HertzZ
+
+def getCasingBrMagDipole(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
+    return mu_0 * getCasingHrMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
+
+def getCasingBzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
+    return mu_0 * getCasingHzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)