SimPEG.maps.ParametricLayer#

class SimPEG.maps.ParametricLayer(mesh, **kwargs)[source]#

Bases: SimPEG.maps.BaseParametric

Mapping for a horizontal layer within a wholespace.

This mapping is used when the cells lying below the Earth’s surface can be parameterized by horizontal layer within a homogeneous medium. The model is defined by the physical property value for the background (\(\sigma_0\)), the physical property value for the layer (\(\sigma_1\)), the elevation for the middle of the layer (\(z_L\)) and the thickness of the layer \(h\).

For this mapping, the set of input model parameters are organized:

\[\mathbf{m} = [\sigma_0, \;\sigma_1,\; z_L , \; h]\]

The mapping \(\mathbf{u}(\mathbf{m})\) from the model to the mesh is given by:

\[\mathbf{u}(\mathbf{m}) = \sigma_0 + \frac{(\sigma_1 - \sigma_0)}{\pi} \Bigg [ \arctan \Bigg ( a \bigg ( \mathbf{z_c} - z_L + \frac{h}{2} \bigg ) \Bigg ) - \arctan \Bigg ( a \bigg ( \mathbf{z_c} - z_L - \frac{h}{2} \bigg ) \Bigg ) \Bigg ]\]

where \(\mathbf{z_c}\) is a vectors containing the vertical cell center locations for all active cells in the mesh, and \(a\) is a parameter which defines the sharpness of the boundaries between the layer and the background.

Parameters

meshdiscretize.BaseMesh: A discretize mesh
indActivenumpy.ndarray: Active cells array. Can be a boolean numpy.ndarray of length mesh.nC or a numpy.ndarray of int containing the indices of the active cells.
slopefloat: Directly define the constant a in the mapping function which defines the sharpness of the boundaries.
slopeFactfloat: Scaling factor for the sharpness of the boundaries based on cell size. Using this option, we set a = slopeFact / dh.