Model¶

class emg3d.models.Model(grid, property_x=1.0, property_y=None, property_z=None, mu_r=None, epsilon_r=None, mapping='Resistivity')[source]¶

Bases: object

A model containing the electromagnetic properties of the Earth.

A model provides the required model parameters to the solver. The x-, y-, and z-directed electrical properties are by default resistivities. However, they can be defined as resistivities, \(\rho\ (\Omega\,\mathrm{m})\), or conductivities, \(\sigma\ (\mathrm{S/m})\), either on a linear or on a logarithmic scale (log or ln), by choosing the appropriate mapping. 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 works for the diffusive approximation. When the displacement part in Maxwell’s equations becomes too dominant it will start to fail (high frequencies or very high electric permittivity).

Parameters

gridTensorMesh

The grid; a emg3d.meshes.TensorMesh instance.

property_{x;y;z}{None, array_like}, default: 1 (x), None (y, z)

Electrical material property in x-, y-, and z-directions. The properties are stored as Fortran-ordered arrays with the shape given by grid.shape. The provided value must be broadcastable to that shape.

By default, property refers to electrical resistivity. However, this can be changed with an appropriate mapping (the internals of emg3d work, irrelevant of the map, with electrical conductivities).

The properties have to be of finite value, bigger than zero (on linear scale). The four supported anisotropy cases are:

x;y=None;z=None: isotropic (y=z=x);
x;y=None;z: vertical transverse isotropy VTI (y=x);
x;y;z=None: horizontal transverse isotropy HTI (z=x);
x;y;z: triaxial anisotropy.

If a property is not initiated it cannot be set later on (e.g., if a VTI model is created, it is not possible to set property_y later on, instead, a new model has to be initiated).

mu_r, epsilon_r{None, array_like}, default: None

Relative magnetic permeability (-) and relative electric permittivity (-), respectively, both isotropic. The properties are stored as Fortran-ordered arrays with the shape given by grid.shape. The provided value must be broadcastable to that shape.

The properties have to be of finite value, bigger than zero.

The relative magnetic permeability is assumed to be 1 if not provided.

The relative electric permittivity is assumed to be 0 if not provided, which ignores the displacement part completely (diffusive approximation)

mappingstr, default: ‘Resistivity’

Defines what type the electrical input property_{x;y;z}-values correspond to. The implemented types are:

'Resistivity'; ρ (Ω m);
'Conductivity'; σ (S/m);
'LgResistivity'; log_10(ρ);
'LgConductivity'; log_10(σ);
'LnResistivity'; log_e(ρ);
'LnConductivity'; log_e(σ).

Attributes Summary

`epsilon_r`	Relative electric permittivity.
`mu_r`	Relative magnetic permeability.
`property_x`	Electrical property in x-direction.
`property_y`	Electrical property in y-direction.
`property_z`	Electrical property in z-direction.

Methods Summary

`copy`()	Return a copy of the Model.
`from_dict`(inp)	Convert dictionary into `emg3d.models.Model` instance.
`interpolate_to_grid`(grid, **interpolate_opts)	Interpolate the model to a new grid.
`to_dict`([copy])	Store the necessary information in a dict for serialization.

Attributes Documentation

epsilon_r¶: Relative electric permittivity.

mu_r¶: Relative magnetic permeability.

property_x¶: Electrical property in x-direction.

property_y¶: Electrical property in y-direction.

property_z¶: Electrical property in z-direction.

Methods Documentation

copy()[source]¶: Return a copy of the Model.

classmethod from_dict(inp)[source]¶

Convert dictionary into emg3d.models.Model instance.

Parameters

inpdict: Dictionary as obtained from emg3d.models.Model.to_dict. The dictionary needs the keys property_x, property_y, property_z, mu_r, epsilon_r, grid, and mapping; grid itself is also a dict which needs the keys hx, hy, hz, and origin.

Returns

modelModel: A emg3d.models.Model instance.

interpolate_to_grid(grid, **interpolate_opts)[source]¶

Interpolate the model to a new grid.

If the provided grid is identical to the grid of the model, it returns the actual model (not a copy).

Parameters

gridTensorMesh: Grid of the new model; a emg3d.meshes.TensorMesh instance.
interpolate_optsdict: Passed through to emg3d.maps.interpolate. Defaults are method='volume', log=True, and extrapolate=True.

Returns

objModel: A new emg3d.models.Model instance on grid.

to_dict(copy=False)[source]¶

Store the necessary information in a dict for serialization.

Parameters

copybool, default: False: If True, returns a deep copy of the dict.

Returns

outdict: Dictionary containing all information to re-create the Model.

expand_grid_model

VolumeModel