Model

class emg3d.models.Model(grid, property_x=1.0, property_y=None, property_z=None, mu_r=None, epsilon_r=None, mapping='Resistivity', **kwargs)

Bases: object

Create a model instance.

Class to provide model parameters (x-, y-, and z-directed properties [resistivity or conductivity; linear or on log_10/log_e-scale], electric permittivity and magnetic permeability) to the solver. Relative magnetic permeability \(\mu_\mathrm{r}\) is by default set to one and electric permittivity \(\varepsilon_\mathrm{r}\) is by default set to zero, but they can also be provided (isotropically). Keep in mind that the multigrid method as implemented in emg3d only works for the diffusive approximation. As soon as the displacement-part in the Maxwell’s equations becomes too dominant it will fail (high frequencies or very high electric permittivity).

Parameters:

grid : TensorMesh

Grid on which to apply model.

property_{x;y;z} : float or ndarray; default to 1.

Material property in x-, y-, and z-directions. If ndarray, they must have the shape of grid.vnC (F-ordered) or grid.nC.

By default, property refers to electrical resistivity. However, this can be changed with an appropriate map. For more info, see the description of the parameter mapping. The internals of emg3d work, irrelevant of the map, with electrical conductivities.

Resistivities and conductivities have to be bigger than zero and smaller than infinity (if provided on a linear scale; not on logarithmic scales).

mu_r : None, float, or ndarray

Relative magnetic permeability (isotropic). If ndarray it must have the shape of grid.vnC (F-ordered) or grid.nC. Default is None, which corresponds to 1., but avoids the computation of zeta. Magnetic permeability has to be bigger than zero and smaller than infinity.

epsilon_r : None, float, or ndarray

Relative electric permittivity (isotropic). If ndarray it must have the shape of grid.vnC (F-ordered) or grid.nC. The displacement part is completely neglected (diffusive approximation) if set to None, which is the default. Electric permittivity has to be bigger than zero and smaller than infinity.

mapping : str

Defines what type the input property_{x;y;z}-values correspond to. By default, they represent resistivities (Ohm.m). The implemented types are:

• ‘Conductivity’; σ (S/m),
• ‘LgConductivity’; log_10(σ),
• ‘LnConductivity’; log_e(σ),
• ‘Resistivity’; ρ (Ohm.m); Default,
• ‘LgResistivity’; log_10(ρ),
• ‘LnResistivity’; log_e(ρ).

Attributes Summary

epsilon_r	Electric permittivity.
mu_r	Magnetic permeability.
property_x	Property in x-direction.
property_y	Property in y-direction.
property_z	Property in z-direction.

Methods Summary

copy()	Return a copy of the Model.
from_dict(inp)	Convert the dictionary into a Model instance.
interpolate2grid(grid, new_grid, …)	Interpolate Model located on grid to new_grid.
to_dict([copy])	Store the necessary information of the Model in a dict.

Attributes Documentation

epsilon_r

Electric permittivity.

mu_r

Magnetic permeability.

property_x

Property in x-direction.

property_y

Property in y-direction.

property_z

Property in z-direction.

Methods Documentation

copy()

Return a copy of the Model.

classmethod from_dict(inp)

Convert the dictionary into a Model instance.

Parameters:

inp : dict

Dictionary as obtained from Model.to_dict(). The dictionary needs the keys property_x, property_y, property_z, mu_r, epsilon_r, vnC, and mapping.

Returns:

obj : Model instance

interpolate2grid(grid, new_grid, **grid2grid_opts)

Interpolate Model located on grid to new_grid.

Parameters:

grid, new_grid : TensorMesh

Input and output model grids; emg3d.meshes.TensorMesh instances.

grid2grid_opts : dict

Passed through to maps.grid2grid(). Defaults are method=’volume’, log=True, and extrapolate=True.

Returns:

NewModel : Model

New Model instance on new_grid.

to_dict(copy=False)

Store the necessary information of the Model in a dict.