geoana.em.tdem.diffusion_distance

geoana.em.tdem.diffusion_distance(time, sigma, mu=1.25663706212e-06)

Compute diffusion distance for a plane wave in a homogeneous electromagnetic media.

For a planewave source in a homogeneous media, the diffusion distance is the propagation distance the peak has travelled at a given time. It is sometimes referred to as the peak distance. The diffusion distance is a simple computation for how far a planewave has travelled after a certain time.

For the quasistatic case (no electric displacement), the diffusion distance is given by:

\[D = \sqrt{\frac{2 t}{\mu \sigma}}\]

where \(\mu\) is the magnetic permeability, \(\sigma\) is the electrical conductivity and t is the time.

Parameters:

timefloat or numpy.ndarray

propagation time (s)

sigmafloat or numpy.ndarray

electrical conductivity (S/m)

mufloat or numpy.ndarray, optional

magnetic permeability (A/m). Default is the permeability of free-space (\(\mu_0\))

Returns:

float, np.ndarray

Diffusion distance in meters. The dimensions for return will depend on whether floats or arrays were used to define the propagation distance and physical properties of the medium.

Notes

The inputs values will be broadcasted together following normal numpy rules, and will support general shapes. Therefore every input, except for the secondary flag, can be arrays of the same shape.