geoana.em.tdem.peak_time

geoana.em.tdem.peak_time(z, sigma, mu=1.25663706212e-06)

Compute peak time for a plane wave in a homogeneous electromagnetic media.

For a particular distance along the propagation path of a planewave in a homogeneous media, the peak time is the time at which the maximum signal amplitude is observed. In other words, it is simple computation for when the peak of the planewave will arrive.

For the quasistatic case (no electric displacement), the peak time is given by:

\[t_{max} = \frac{\mu \sigma z^2}{6}\]

where \(\mu\) is the magnetic permeability, \(\sigma\) is the electrical conductivity and z is the propagation distance.

Parameters:

zfloat or numpy.ndarray

propagation distance from the planewave source (m)

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

Peak time/times in seconds. 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.