geoana.em.static.DipoleHalfSpace.potential

DipoleHalfSpace.potential(xyz_m, xyz_n=None)

Electric potential for a dipole in a halfspace.

This method computes the potential for a dipole in a halfspace at the set of gridded xyz locations provided. Where \(\rho\) is the electric resistivity, I is the current and R is the distance between the locations we want to evaluate at and the dipole source.

Parameters:

xyz_m(…, 3) numpy.ndarray

Location of the M voltage electrode.

xyz_n(…, 3) numpy.ndarray, optional

Location of the N voltage electrode.

Returns:

V(…, ) np.ndarray

Electric potential of dipole source in units V.

Examples

Here, we define a dipole source in a halfspace to compute potential.

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from mpl_toolkits.axes_grid1 import make_axes_locatable
>>> from geoana.em.static import DipoleHalfSpace

Define the dipole source.

>>> rho = 1.0
>>> current = 1.0
>>> location_a = np.r_[-1, 0, 0]
>>> location_b = np.r_[1, 0, 0]
>>> simulation = DipoleHalfSpace(
>>>     current=current, rho=rho, location_a=location_a, location_b=location_b
>>> )

Now we create a set of gridded locations and compute the electric potential.

>>> X, Y = np.meshgrid(np.linspace(-2, 2, 20), np.linspace(-2, 2, 20))
>>> Z = np.zeros_like(X)
>>> xyz = np.stack((X, Y, Z), axis=-1)
>>> v1 = simulation.potential(xyz)
>>> v2 = simulation.potential(xyz - np.r_[2, 0, 0], xyz + np.r_[2, 0, 0])

Finally, we plot the electric potential.

>>> fig, axs = plt.subplots(1, 2, figsize=(18,12))
>>> titles = ['3 Electrodes', '4 Electrodes']
>>> for ax, V, title in zip(axs.flatten(), [v1, v2], titles):
>>>     im = ax.pcolor(X, Y, V, shading='auto')
>>>     divider = make_axes_locatable(ax)
>>>     cax = divider.append_axes("right", size="5%", pad=0.05)
>>>     cb = plt.colorbar(im, cax=cax)
>>>     cb.set_label(label= 'Potential (V)')
>>>     ax.set_ylabel('Y coordinate ($m$)')
>>>     ax.set_xlabel('X coordinate ($m$)')
>>>     ax.set_aspect('equal')
>>>     ax.set_title(title)
>>> plt.tight_layout()
>>> plt.show()

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