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)

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

Mcc	Cell center inner product matrix.
MccRho	Cell center property inner product matrix.
MccRhoI	Cell center property inner product inverse matrix.
MccSigma	Cell center property inner product matrix.
MccSigmaI	Cell center property inner product inverse matrix.
Me	Edge inner product matrix.
MeI	Edge inner product inverse matrix.
MeRho	Edge property inner product matrix.
MeRhoI	Edge property inner product inverse matrix.
MeSigma	Edge property inner product matrix.
MeSigmaI	Edge property inner product inverse matrix.
Mf	Face inner product matrix.
MfI	Face inner product inverse matrix.
MfRho	Face property inner product matrix.
MfRhoI	Face property inner product inverse matrix.
MfSigma	Face property inner product matrix.
MfSigmaI	Face property inner product inverse matrix.
Mn	Node inner product matrix.
MnI	Node inner product inverse matrix.
MnRho	Node property inner product matrix.
MnRhoI	Node property inner product inverse matrix.
MnSigma	Node property inner product matrix.
MnSigmaI	Node property inner product inverse matrix.
bc_type	Type of boundary condition to use for simulation.
clean_on_model_update	A list of solver objects to clean when the model is updated
counter	SimPEG Counter object to store iterations and run-times.
deleteTheseOnModelUpdate	matrices to be deleted if the model for conductivity/resistivity is updated
mesh	Mesh for the simulation.
model	The inversion model.
needs_model	True if a model is necessary
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)).
rho	Electrical resistivity (ohm m) physical property model.
rhoDeriv	Derivative of Electrical resistivity (Ohm m) wrt the model.
rhoMap	Mapping of the inversion model to Electrical resistivity (Ohm m).
sensitivity_path	Path to directory where sensitivity file is stored.
sigma	Electrical conductivity (s/m) physical property model.
sigmaDeriv	Derivative of Electrical conductivity (S/m) wrt the model.
sigmaMap	Mapping of the inversion model to Electrical conductivity (S/m).
solver	Numerical solver used in the forward simulation.
solver_opts	Solver-specific parameters.
storeJ	Whether to store the sensitivity matrix
surface_faces	Array defining which boundary faces to interpret as surfaces of Neumann boundary
survey	The DC survey object.
verbose	Verbose progress printout.

Ainv
MccI
Vol

Methods

Jtvec(m, v[, f])	Compute adjoint sensitivity matrix (J^T) and vector (v) product.
Jtvec_approx(m, v[, f])	Approximation of the Jacobian transpose times a vector for the model provided.
Jvec(m, v[, f])	Compute sensitivity matrix (J) and vector (v) product.
Jvec_approx(m, v[, f])	Approximation of the Jacobian times a vector for the model provided.
MccRhoDeriv(u[, v, adjoint])	Derivative of MccProperty with respect to the model.
MccRhoIDeriv(u[, v, adjoint])	Derivative of MccPropertyI with respect to the model.
MccSigmaDeriv(u[, v, adjoint])	Derivative of MccProperty with respect to the model.
MccSigmaIDeriv(u[, v, adjoint])	Derivative of MccPropertyI with respect to the model.
MeRhoDeriv(u[, v, adjoint])	Derivative of MeProperty with respect to the model.
MeRhoIDeriv(u[, v, adjoint])	Derivative of MePropertyI with respect to the model.
MeSigmaDeriv(u[, v, adjoint])	Derivative of MeProperty with respect to the model.
MeSigmaIDeriv(u[, v, adjoint])	Derivative of MePropertyI with respect to the model.
MfRhoDeriv(u[, v, adjoint])	Derivative of MfProperty with respect to the model.
MfRhoIDeriv(u[, v, adjoint])	I Derivative of MfPropertyI with respect to the model.
MfSigmaDeriv(u[, v, adjoint])	Derivative of MfProperty with respect to the model.
MfSigmaIDeriv(u[, v, adjoint])	I Derivative of MfPropertyI with respect to the model.
MnRhoDeriv(u[, v, adjoint])	Derivative of MnProperty with respect to the model.
MnRhoIDeriv(u[, v, adjoint])	Derivative of MnPropertyI with respect to the model.
MnSigmaDeriv(u[, v, adjoint])	Derivative of MnProperty with respect to the model.
MnSigmaIDeriv(u[, v, adjoint])	Derivative of MnPropertyI with respect to the model.
dpred([m, f])	Predicted data for the model provided.
fields([m, calcJ])	Return the computed geophysical fields for the model provided.
fieldsPair	alias of Fields3DCellCentered
getA([resistivity])	Make the A matrix for the cell centered DC resistivity problem A = D MfRhoI G
getJtJdiag(m[, W, f])	Return the diagonal of JtJ
getRHS()	RHS for the DC problem q
getRHSDeriv(source, v[, adjoint])	Derivative of the right hand side with respect to the model
getSourceTerm()	Evaluates the sources, and puts them in matrix form :rtype: tuple :return: q (nC or nN, nSrc)
make_synthetic_data(m[, relative_error, ...])	Make synthetic data for the model and Gaussian noise provided.
residual(m, dobs[, f])	The data residual.

getADeriv
getJ
setBC