Test with an analytic and some documentation.

simpegEM/Utils/Ana/FEM.py

@@ -2,9 +2,24 @@ import numpy as np
 from scipy.constants import mu_0, pi
 from scipy.special import erf
 
-def hzAnalyticDipoleF(r, freq, sigma):
+def hzAnalyticDipoleF(r, freq, sigma, secondary=True):
     """
     4.56 in Ward and Hohmann
+
+    .. plot::
+
+        import matplotlib.pyplot as plt
+        import simpegEM as EM
+        freq = np.logspace(-1, 6, 61)
+        test = EM.Utils.Ana.FEM.hzAnalyticDipoleF(100, freq, 0.001, secondary=False)
+        plt.loglog(freq, abs(test.real))
+        plt.loglog(freq, abs(test.imag))
+        plt.title('Response at $r$=100m')
+        plt.xlabel('Frequency')
+        plt.ylabel('Response')
+        plt.legend(('real','imag'))
+        plt.show()
+
     """
     r = np.abs(r)
     k = np.sqrt(-1j*2.*np.pi*freq*mu_0*sigma)
@@ -13,5 +28,11 @@ def hzAnalyticDipoleF(r, freq, sigma):
     front = m / (2. * np.pi * (k**2) * (r**5) )
     back = 9 - ( 9 + 9j * k * r - 4 * (k**2) * (r**2) - 1j * (k**3) * (r**3)) * np.exp(-1j*k*r)
     hz = front*back
-    hp =-1/(4*np.pi*r**3)
-    return hz-hp
+
+    if secondary:
+        hp =-1/(4*np.pi*r**3)
+        return hz-hp
+
+    return hz
+
+