# SimPEG.electromagnetics.natural_source.Simulation3DPrimarySecondary#

class SimPEG.electromagnetics.natural_source.Simulation3DPrimarySecondary(mesh, survey=None, sigmaPrimary=None, **kwargs)[source]#

A NSEM problem solving a e formulation and a primary/secondary fields decomposition.

By eliminating the magnetic flux density using

$\mathbf{b} = \frac{1}{i \omega} \left(-\mathbf{C} \mathbf{e} \right)$

we can write Maxwell’s equations as a second order system in $$\mathbf{e}$$ only:

$\left[ \mathbf{C}^{\top} \mathbf{M_{\mu^{-1}}^f} \mathbf{C} + i \omega \mathbf{M_{\sigma}^e} \right] \mathbf{e}_{s} = i \omega \mathbf{M_{\sigma_{p}}^e} \mathbf{e}_{p}$

which we solve for $$\mathbf{e_s}$$. The total field $$\mathbf{e} = \mathbf{e_p} + \mathbf{e_s}$$.

The primary field is estimated from a background model (commonly as a 1D model).

Attributes

 Mcc Cell center inner product matrix. MccMu Cell center property inner product matrix. MccMuI Cell center property inner product inverse matrix. MccMui Cell center property inner product matrix. MccMuiI Cell center property inner product inverse 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. MeMu Edge property inner product matrix. MeMuI Edge property inner product inverse matrix. MeMui Edge property inner product matrix. MeMuiI Edge property 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. MfMu Face property inner product matrix. MfMuI Face property inner product inverse matrix. MfMui Face property inner product matrix. MfMuiI Face property 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. MnMu Node property inner product matrix. MnMuI Node property inner product inverse matrix. MnMui Node property inner product matrix. MnMuiI Node property 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. 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 forward_only If True, A-inverse not stored at each frequency in forward simulation. mesh Mesh for the simulation. model The inversion model. mu Magnetic permeability (h/m) physical property model. muDeriv Derivative of Magnetic Permeability (H/m) wrt the model. muMap Mapping of the inversion model to Magnetic Permeability (H/m). mui Inverse magnetic permeability (m/h) physical property model. muiDeriv Derivative of Inverse Magnetic Permeability (m/H) wrt the model. muiMap Mapping of the inversion model to Inverse Magnetic Permeability (m/H). needs_model True if a model is necessary permittivity Dielectric permittivity (F/m) 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). sigmaPrimary A background model, use for the calculation of the primary fields. solver Numerical solver used in the forward simulation. solver_opts Solver-specific parameters. storeInnerProduct Whether to store inner product matrices storeJ Whether to store the sensitivity matrix survey The simulations survey. verbose Verbose progress printout.
 MccI Vol

Methods

 Jtvec(m, v[, f]) Sensitivity transpose times a vector Jtvec_approx(m, v[, f]) Approximation of the Jacobian transpose times a vector for the model provided. Jvec(m, v[, f]) Sensitivity times a vector. Jvec_approx(m, v[, f]) Approximation of the Jacobian times a vector for the model provided. MccMuDeriv(u[, v, adjoint]) Derivative of MccProperty with respect to the model. MccMuIDeriv(u[, v, adjoint]) Derivative of MccPropertyI with respect to the model. MccMuiDeriv(u[, v, adjoint]) Derivative of MccProperty with respect to the model. MccMuiIDeriv(u[, v, adjoint]) Derivative of MccPropertyI with respect to the model. 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. MeMuDeriv(u[, v, adjoint]) Derivative of MeProperty with respect to the model. MeMuIDeriv(u[, v, adjoint]) Derivative of MePropertyI with respect to the model. MeMuiDeriv(u[, v, adjoint]) Derivative of MeProperty with respect to the model. MeMuiIDeriv(u[, v, adjoint]) Derivative of MePropertyI 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. MfMuDeriv(u[, v, adjoint]) Derivative of MfProperty with respect to the model. MfMuIDeriv(u[, v, adjoint]) I Derivative of MfPropertyI with respect to the model. MfMuiDeriv(u[, v, adjoint]) Derivative of MfProperty with respect to the model. MfMuiIDeriv(u[, v, adjoint]) I Derivative of MfPropertyI 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. MnMuDeriv(u[, v, adjoint]) Derivative of MnProperty with respect to the model. MnMuIDeriv(u[, v, adjoint]) Derivative of MnPropertyI with respect to the model. MnMuiDeriv(u[, v, adjoint]) Derivative of MnProperty with respect to the model. MnMuiIDeriv(u[, v, adjoint]) Derivative of MnPropertyI 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]) Solve the forward problem for the fields. fieldsPair alias of Fields3DElectricField getA(freq) System matrix getADeriv_mui(freq, u, v[, adjoint]) Product of the derivative of the system matrix with respect to the permeability model and a vector. getADeriv_sigma(freq, u, v[, adjoint]) Product of the derivative of our system matrix with respect to the conductivity model and a vector getJ(m[, f]) Method to form full J given a model m getJtJdiag(m[, W, f]) Return the diagonal of JtJ getRHS(freq) Right hand side for the system getRHSDeriv(freq, src, v[, adjoint]) Derivative of the Right-hand side with respect to the model. getSourceTerm(freq) Evaluates the sources for a given frequency and puts them in matrix form make_synthetic_data(m[, relative_error, ...]) Make synthetic data for the model and Gaussian noise provided. residual(m, dobs[, f]) The data residual.