simpeg.electromagnetics.static.self_potential.HydraulicHeadMap#

class simpeg.electromagnetics.static.self_potential.HydraulicHeadMap(mesh, L)[source]#

Bases: LinearMap

Maps hydraulic head to charge density accumulation rate.

Parameters:
meshdiscretize.base.BaseMesh
Lfloat or (mesh.n_cells,) array_like

Cross coupling property model (A/m^2).

Attributes

A

The linear operator matrix.

b

Added part of the linear operation.

is_linear

Determine whether or not this mapping is a linear operation.

mesh

The mesh used for the mapping

nP

Number of parameters the mapping acts on.

shape

Dimensions of the mapping operator

Methods

deriv(m[, v])

Derivative of the mapping with respect to the input parameters.

dot(map1)

Multiply two mappings to create a simpeg.maps.ComboMap.

inverse(D)

The transform inverse is not implemented.

test([m, num, random_seed])

Derivative test for the mapping.

Notes

This map relates hydraulic head, \(h\), in m to the volumetric current density, \(q\), (A/m^3) using a cross coupling term to convert the negative gradient of hydrualic head into secondary current densities. This cross coupling parameter \(L\) is a multiplication of the hydraulic conductivity (m/s) of the material and the ionic density (C/m^3) of the fluid.

The mapping is:

\[q = \nabla \cdot L \nabla h\]