SimPEG.maps.ParametricLayer

class SimPEG.maps.ParametricLayer(mesh, **kwargs)

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:

$$\mathbf{u}(\mathbf{m})={\sigma }_0+\frac{({\sigma }_1-{\sigma }_0)}{\pi }[\arctan (a({\mathbf{z}}_{\mathbf{c}}-z_L+\frac{h}{2}))-\arctan (a({\mathbf{z}}_{\mathbf{c}}-z_L-\frac{h}{2}))]$$

where ${\mathbf{z}}_{\mathbf{c}}$ 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.

Examples

Attributes

nP	Number of model parameters the mapping acts on; i.e 4
shape	Dimensions of the mapping

Methods

deriv(m)	Derivative of the mapping with respect to the input parameters.
mDict(m)	Return model parameters as a dictionary.

layer_cont

Galleries and Tutorials using SimPEG.maps.ParametricLayer

Maps: Parametric Block in a Layer

Maps: Parametric Block in a Layer

Maps: Parametrized Layer

Maps: Parametrized Layer

Heagy et al., 2017 Casing Example

Heagy et al., 2017 Casing Example