SimPEG.maps.ParametricCircleMap

class SimPEG.maps.ParametricCircleMap(mesh, logSigma=True, slope=0.1)

Bases: SimPEG.maps.IdentityMap

Mapping for a parameterized circle.

Define the mapping from a parameterized model for a circle in a wholespace to all cells within a 2D mesh. For a circle within a wholespace, the model is defined by 5 parameters: the background physical property value (\(\sigma_0\)), the physical property value for the circle (\(\sigma_c\)), the x location \(x_0\) and y location \(y_0\) for center of the circle, and the circle’s radius (\(R\)).

Let \(\mathbf{m} = [\sigma_0, \sigma_1, x_0, y_0, R]\) be the set of model parameters the defines a circle within a wholespace. The mapping \(\mathbf{u}(\mathbf{m})\) from the parameterized model to all cells within a 2D mesh is given by:

\[\mathbf{u}(\mathbf{m}) = \sigma_0 + (\sigma_1 - \sigma_0) \bigg [ \frac{1}{2} + \pi^{-1} \arctan \bigg ( a \big [ \sqrt{(\mathbf{x_c}-x_0)^2 + (\mathbf{y_c}-y_0)^2} - R \big ] \bigg ) \bigg ]\]

where \(\mathbf{x_c}\) and \(\mathbf{y_c}\) are vectors storing the x and y positions of all cell centers for the 2D mesh and \(a\) is a user-defined constant which defines the sharpness of boundary of the circular structure.

Parameters

meshdiscretize.BaseMesh

A 2D discretize mesh

logSigmabool

If True, parameters \(\sigma_0\) and \(\sigma_1\) represent the natural log of the physical property values for the background and circle, respectively.

slopefloat

A constant for defining the sharpness of the boundary between the circle and the wholespace. The sharpness increases as slope is increased.

Examples

Attributes

logSigma	Whether the input needs to be transformed by an exponential
nP	Number of parameters the mapping acts on; i.e. 5.
slope	Sharpness of the boundary.

Methods

deriv(m[, v])

Derivative of the mapping with respect to the input parameters.