simpeg.electromagnetics.static.spontaneous_potential.HydraulicHeadMap

class simpeg.electromagnetics.static.spontaneous_potential.HydraulicHeadMap(mesh, L)

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:

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