simpeg.potential_fields.gravity.Simulation3DDifferential

class simpeg.potential_fields.gravity.Simulation3DDifferential(mesh, rho=1.0, rhoMap=None, **kwargs)

Bases: BasePDESimulation

Finite volume simulation class for gravity.

Attributes

Mcc	Cell center inner product matrix.
Me	Edge inner product matrix.
MeI	Edge inner product inverse matrix.
Mf	Face inner product matrix.
MfI	Face inner product inverse matrix.
Mn	Node inner product matrix.
MnI	Node 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	A list of properties stored on this object to delete when the model is updated
mesh	Mesh for the simulation.
model	The inversion model.
needs_model	True if a model is necessary
rho	Specific density (g/cc) physical property model.
rhoDeriv	Derivative of Specific density (g/cc) wrt the model.
rhoMap	Mapping of the inversion model to Specific density (g/cc).
sensitivity_path	Path to directory where sensitivity file is stored.
solver	Numerical solver used in the forward simulation.
solver_opts	Solver-specific parameters.
survey	The survey for the simulation.
verbose	Verbose progress printout.

MccI
Vol

Methods

Jtvec(m, v[, f])	Compute the Jacobian transpose times a vector for the model provided.
Jtvec_approx(m, v[, f])	Approximation of the Jacobian transpose times a vector for the model provided.
Jvec(m, v[, f])	Compute the Jacobian times a vector for the model provided.
Jvec_approx(m, v[, f])	Approximation of the Jacobian times a vector for the model provided.
dpred([m, f])	Predicted data for the model provided.
fields([m])	Compute fields
getA()	GetA creates and returns the A matrix for the Gravity nodal problem
getRHS()	Return right-hand side for the linear system
make_synthetic_data(m[, relative_error, ...])	Make synthetic data for the model and Gaussian noise provided.
residual(m, dobs[, f])	The data residual.

Notes

From Blakely (1996), the scalar potential \(\phi\) outside the source region is obtained by solving a Poisson’s equation:

\[\nabla^2 \phi = 4 \pi \gamma \rho\]

where \(\gamma\) is the gravitational constant and \(\rho\) defines the distribution of density within the source region.

Applying the finite volumn method, we can solve the Poisson’s equation on a 3D voxel grid according to:

\[\big [ \mathbf{D M_f D^T} \big ] \mathbf{u} = - \mathbf{M_c \, \rho}\]