def _getCasingHertzMagDipole2Deriv_z_r(srcloc,
obsloc,
freq,
sigma,
a,
b,
mu=mu_0 * np.ones(3),
eps=epsilon_0,
moment=1.0):
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 + 1.0 / sqrtr2z2) + HertzZ * (
z * r / sqrtr2z2**3) * (1j * k2 + 2.0 / sqrtr2z2)
def getCasingHzMagDipole(srcloc,
obsloc,
freq,
sigma,
a,
b,
mu=mu_0 * np.ones(3),
eps=epsilon_0,
moment=1.0):
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 _Propagate(f, thickness, sig, chg, taux, c, mu_r, eps_r, n):
if isinstance(eps_r, float):
epsmodel = np.ones_like(sig) * eps_r
else:
epsmodel = eps_r
if isinstance(mu_r, float):
mumodel = np.ones_like(sig) * mu_r
else:
epsmodel = mu_r
sigcm = np.zeros_like(sig, dtype="complex_")
if chg == 0.0 or taux == 0.0 or c == 0.0:
sigcm = sig
else:
for j in range(1, len(sigcm)):
sigcm[j] = _PCC(sig[j], chg[j], taux[j], c[j], f)
sigcm = np.append(np.r_[0.0], sigcm)
mu = np.append(np.r_[1.0], mumodel) * mu_0
eps = np.append(np.r_[1.0], epsmodel) * epsilon_0
H = np.append(np.r_[1.2 * (1e5)], thickness)
K = k(f, sigcm, mu, eps)
Z = _ImpZ(f, mu, K)
EH = np.matrix(np.zeros((2, n + 1), dtype="complex_"), dtype="complex_")
UD = np.matrix(np.zeros((2, n + 1), dtype="complex_"), dtype="complex_")
UD[1, -1] = 1.0
for i in range(-2, -(n + 2), -1):
UD[:, i] = _Tinv(H[i + 1], K[i]) * _Pinv(Z[i]) * _P(
Z[i + 1]) * UD[:, i + 1]
UD = UD / ((np.abs(UD[0, :] + UD[1, :])).max())
for j in range(0, n + 1):
EH[:, j] = np.matrix([[
1.0,
1,
], [-1.0 / Z[j], 1.0 / Z[j]]]) * UD[:, j]
return UD, EH, Z, K
def _getCasingHertzMagDipoleDeriv_z(srcloc,
obsloc,
freq,
sigma,
a,
b,
mu=mu_0 * np.ones(3),
eps=epsilon_0,
moment=1.0):
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 + 1.0 / sqrtr2z2)
def _getCasingHertzMagDipole(srcloc,
obsloc,
freq,
sigma,
a,
b,
mu=mu_0 * np.ones(3),
eps=epsilon_0,
moment=1.0):
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 / (4.0 * np.pi) * np.exp(
-1j * k2 * sqrtr2z2) / sqrtr2z2
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))