SimPEG.maps.ParametricEllipsoid

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

Bases: SimPEG.maps.ParametricBlock

Mapping for a rectangular block within a wholespace.

This mapping is used when the cells lying below the Earth’s surface can be parameterized by an ellipsoid 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 (${\sigma }_b$), parameters for the center of the ellipsoid ($x_b[,y_b,z_b]$) and parameters for the dimensions along each Cartesian direction ($dx[,dy,dz]$)

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

$$\begin{array}{r}\mathbf{m}=\{\begin{array}{l}1D:[{\sigma }_0,{\sigma }_b,x_b,dx]\\ 2D:[{\sigma }_0,{\sigma }_b,x_b,dx,y_b,dy]\\ 3D:[{\sigma }_0,{\sigma }_b,x_b,dx,y_b,dy,z_b,dz]\end{array}\end{array}$$

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

$$\mathbf{u}(\mathbf{m})={\sigma }_0+({\sigma }_b-{\sigma }_0)[\frac{1}{2}+{\pi }^{-1}\arctan (a\mathit{\eta }(x_b,y_b,z_b,dx,dy,dz))]$$

where a is a parameter that impacts the sharpness of the arctan function, and

$$\mathit{\eta }(x_b,y_b,z_b,dx,dy,dz)=1-\sum _{\xi \in (x,y,z)}[(\frac{2({\mathit{\xi }}_{\mathit{c}}-{\xi }_b)}{d\xi }{)}^2+{\epsilon }^2]$$

${\mathit{\xi }}_{\mathit{c}}$ is a place holder for vectors containing the x, [y and z] cell center locations of the mesh, ${\xi }_b$ is a placeholder for the x[, y and z] location for the center of the block, and $d\xi$ is a placeholder for the x[, y and z] dimensions of the block.

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.

epsilonfloat

Epsilon value used in the ekblom representation of the block

Examples