SimPEG.electromagnetics.static.spontaneous_potential.Simulation3DCellCentered#

class SimPEG.electromagnetics.static.spontaneous_potential.Simulation3DCellCentered(mesh, survey=None, sigma=None, rho=None, q=None, qMap=None, **kwargs)[source]#

Bases: Simulation3DCellCentered

A Spontaneous potential simulation.

Parameters:

meshdiscretize.base.BaseMesh
surveyspontaneous_potential.Survey
sigma, rhofloat or array_like: The conductivity/resistivity model of the subsurface.
qfloat, array_like, optional: The charge density accumulation rate model (C/(s m^3)), also physically represents the volumetric current density (A/m^3).
qMapSimPEG.maps.IdentityMap, optional: The mapping used to go from the simulation model to q. Set this to invert for q.
**kwargs: arguments passed on to resistivity.Simulation3DCellCentered

Notes

The charge density accumulation rate, \(q\), is related to the spontaneous electric potential, \(\phi\), with the same PDE, that relates current sources to potential in the resistivity case.

\[- \nabla \cdot \sigma \nabla \phi = q\]

This equation is solve for potential with a finite volume approach, discretized with \(\phi\) and \(q\) on cell centers, electrical conductivity :math`sigma` as a cell property, and therefore current density lives on the faces between cells.

By default the boundary conditions assume a Robin condition on the subsurface boundaries, and a zero Nuemann boundary at the top. For more details on the boundary conditions, check out the resistivity simulations.

Attributes

`deleteTheseOnModelUpdate`	matrices to be deleted if the model for conductivity/resistivity is updated
`q`	Charge density accumulation rate (c/(s m^3)) physical property model.
`qDeriv`	Derivative of Charge density accumulation rate (C/(s m^3)) wrt the model.
`qMap`	Mapping of the inversion model to Charge density accumulation rate (C/(s m^3)).

Methods

`getRHS`()	RHS for the DC problem q
`getRHSDeriv`(source, v[, adjoint])	Derivative of the right hand side with respect to the model