pygimli.physics.gravimetry

Solve gravimetric and magneto static problems in 2d and 3D analytical

Overview

Functions

BZPoly(pnts, poly, mag[, openPoly]) TODO WRITEME.
BaZCylinderHoriz(pnts, R, pos, M) Magnetic anomaly for a horizontal cylinder.
BaZSphere(pnts, R, pos, M) Magnetic anomaly for a sphere.
gradGZCylinderHoriz(r, a, rho[, pos]) TODO WRITEME.
gradGZHalfPlateHoriz(pnts, t, rho[, pos]) TODO WRITEME.
gradGZSphere(r, rad, rho[, pos]) TODO WRITEME.
gradUCylinderHoriz(r, a, rho[, pos]) 2D Gradient of gravimetric potential of horizontal cylinder.
gradUHalfPlateHoriz(pnts, t, rho[, pos]) TODO WRITEME.
gradUSphere(r, rad, rho[, pos]) Gravitational field of a sphere.
solveGravimetry(mesh[, dDensity, pnts, complete]) Solve gravimetric response.
uCylinderHoriz(pnts, rad, rho[, pos]) Gravitational potential of horizonzal cylinder.
uSphere(r, rad, rho[, pos]) Gravitational potential of a sphere.

Classes

GravimetryModelling([verbose]) Gravimetry modelling operator.

Functions

BZPoly

pygimli.physics.gravimetry.BZPoly(pnts, poly, mag, openPoly=False)[source]

TODO WRITEME.

Parameters:
pnts : list

Measurement points [[p1x, p1z], [p2x, p2z],…]

poly : list

Polygon [[p1x, p1z], [p2x, p2z],…]

mag : [M_x, M_y, M_z]

Magnetization = [M_x, M_y, M_z]

BaZCylinderHoriz

pygimli.physics.gravimetry.BaZCylinderHoriz(pnts, R, pos, M)[source]

Magnetic anomaly for a horizontal cylinder.

Calculate the vertical component of the anomalous magnetic field Bz for a buried horizontal cylinder at position pos with radius R for a given magnetization M at measurement points pnts.

TODO .. only 2D atm

Parameters:
pnts : [[x,z], ]

measurement points – array[x,y,z]

R : float

radius

pos : [float, float]

[x,z] – sphere center

M : [float, float]

[Mx, Mz] – magnetization

BaZSphere

pygimli.physics.gravimetry.BaZSphere(pnts, R, pos, M)[source]

Magnetic anomaly for a sphere.

Calculate the vertical component of the anomalous magnetic field Bz for a buried sphere at position pos with radius R for a given magnetization M at measurement points pnts.

Parameters:
pnts : [[x,y,z], ]

measurement points – array[x,y,z]

R : float

radius

pos : [float, float, float]

[x,y,z] – sphere center

M : [float, float, float]

[Mx, My, Mz] – magnetization

gradGZCylinderHoriz

pygimli.physics.gravimetry.gradGZCylinderHoriz(r, a, rho, pos=(0.0, 0.0))[source]

TODO WRITEME.

\[g = -grad u(r), with r = [x,z], |r| = \sqrt(x^2+z^2)\]
Parameters:
r : list[[x, z]]

Observation positions

a : float

Cylinder radius in [meter]

rho :

Density in [kg/m^3]

Returns:
grad gz, [gz_x, gz_z]

Examples using pygimli.physics.gravimetry.gradGZCylinderHoriz

gradGZHalfPlateHoriz

pygimli.physics.gravimetry.gradGZHalfPlateHoriz(pnts, t, rho, pos=(0.0, 0.0))[source]

TODO WRITEME.

\[g = -\nabla u\]
Parameters:
pnts : array (\(n\times 2\))

n 2 dimensional measurement points

t : float

Plate thickness in \([\text{m}]\)

rho : float

Density in \([\text{kg}/\text{m}^3]\)

Returns:
gz : array

Gradient of z-component of g \(\nabla(\frac{\partial u}{\partial\vec{r}}_z)\)

Examples using pygimli.physics.gravimetry.gradGZHalfPlateHoriz

gradGZSphere

pygimli.physics.gravimetry.gradGZSphere(r, rad, rho, pos=(0.0, 0.0, 0.0))[source]

TODO WRITEME.

\[g = -\nabla u\]
Parameters:
r : [float, float, float]

position vector

rad : float

radius of the sphere

rho : float

density in [kg/m^3]

Returns:
[d g_z /dx, d g_z /dy, d g_z /dz]

gradUCylinderHoriz

pygimli.physics.gravimetry.gradUCylinderHoriz(r, a, rho, pos=(0.0, 0.0))[source]

2D Gradient of gravimetric potential of horizontal cylinder.

Calculate .. in mGal at position pos

\[g = -G[m^3/(kg s^2)] * dM[kg/m] * 1/r[1/m] * grad(r)[1/1] = [m^3/(kg s^2)] * [kg/m] * 1/m * [1/1] == m/s^2\]
Parameters:
r : list[[x, z]]

Observation positions

a : float

Cylinder radius in [meter]

pos : [x,z]

Center position of cylinder.

rho : float

Delta density in [kg/m^3]

Returns:
g : [dudx, dudz]

Gradient of gravimetry potential.

Examples using pygimli.physics.gravimetry.gradUCylinderHoriz

gradUHalfPlateHoriz

pygimli.physics.gravimetry.gradUHalfPlateHoriz(pnts, t, rho, pos=(0.0, 0.0))[source]

TODO WRITEME.

Analytical solution

g = -grad u,

Parameters:
pnts :
t :
rho :

Density in [kg/m^3]

Returns:
gz:

z-component of g .. math:: nabla(partial u/partialvec{r})_z

Examples using pygimli.physics.gravimetry.gradUHalfPlateHoriz

gradUSphere

pygimli.physics.gravimetry.gradUSphere(r, rad, rho, pos=(0.0, 0.0, 0.0))[source]

Gravitational field of a sphere.

\[g = -G[m^3/(kg s^2)] * dM[kg] * 1/r^2 1/m^2] * \grad(r)[1/1] = [m^3/(kg s^2)] * [kg] * 1/m^2 * [1/1] == m/s^2\]
Parameters:
r : [float, float, float]

position vector

rad : float

radius of the sphere

rho : float

density in [kg/m^3]

Returns:
[gx, gy, gz] : [float*3]

gravitational acceleration (note that gz points negative)

solveGravimetry

pygimli.physics.gravimetry.solveGravimetry(mesh, dDensity=None, pnts=None, complete=False)[source]

Solve gravimetric response.

2D with pygimli.physics.gravimetry.lineIntegralZ_WonBevis

3D with pygimli.physics.gravimetry.gravMagBoundarySinghGup

TOWRITE

Parameters:
mesh : GIMLI::Mesh

2d or 3d mesh with or without cells.

dDensity : float | array

Density difference.

  • float – solve for positive boundary marker only.
    Assuming one inhomogeneity.
  • [[int, float]] – solve for multiple positive boundaries TOIMPL
  • array – solve for one delta density value per cell
  • None – return per cell kernel matrix G TOIMPL
pnts : [[x_i, y_i]]

List of measurement positions.

complete : bool [False]

If True return whole solution or matrix for [dgx, dgy, dgz] and … TODO

Examples using pygimli.physics.gravimetry.solveGravimetry

uCylinderHoriz

pygimli.physics.gravimetry.uCylinderHoriz(pnts, rad, rho, pos=(0.0, 0.0))[source]

Gravitational potential of horizonzal cylinder.

TODO

uSphere

pygimli.physics.gravimetry.uSphere(r, rad, rho, pos=None)[source]

Gravitational potential of a sphere.

Gravitational potential of a sphere with radius and density at a given position.

\[u = -G * dM * \frac{1}{r}\]
Parameters:
r : [float, float, float]

position vector

rad : float

radius of the sphere

rho : float

density

pos : [float, float, float]

position of sphere (0.0, 0.0, 0.0)

Classes

GravimetryModelling

class pygimli.physics.gravimetry.GravimetryModelling(verbose=True)[source]

Gravimetry modelling operator.

Methods

__call__((object)arg1, (object)model) C++ signature :
clearConstraints((object)arg1) C++ signature :
clearJacobian((object)arg1) C++ signature :
constraints((object)arg1) C++ signature :
constraintsRef((object)arg1) C++ signature :
createConstraints((object)arg1) C++ signature :
createDefaultStartModel((object)arg1) C++ signature :
createJacobian(model) Create Jacobian matrix for a density model.
createMappedModel((object)arg1, …) Read only extrapolation of model values given per cell marker to values given per cell.
createRefinedForwardMesh((object)arg1 [, …) C++ signature :
createStartModel((object)arg1) C++ signature :
createStartVector((object)arg1) DEPRECATED use createStartModel
createStartmodel() Create the default starting model.
data((object)arg1) Return the associated data container.
deleteMesh((object)arg1) Delete the actual mesh.
initConstraints((object)arg1) C++ signature :
initJacobian((object)arg1) C++ signature :
initRegionManager((object)arg1) C++ signature :
jacobian((object)arg1) Return the pointer to the Jacobian matrix associated with this forward operator.
jacobianRef((object)arg1) C++ signature :
mapModel((object)arg1, (object)model [, …) C++ signature :
mesh((object)arg1) C++ signature :
multiThreadJacobian((object)arg1) Return number of threads used for Jacobian generation.
region((object)arg1, (object)marker) Syntactic sugar for this->regionManager().region(marker).
regionManager((object)arg1) C++ signature :
regionManagerRef((object)arg1) C++ signature :
response(dDensity) Calculate response for a given density distribution.
response_mt((object)arg1, (object)model [, …) C++ signature :
setConstraints((object)arg1, (object)C) C++ signature :
setData((object)arg1, (object)data) Change the associated data container
setJacobian((object)arg1, (object)J) C++ signature :
setMesh((object)arg1, (object)mesh [, …) Set new mesh to the forward operator, optionally hold region parameter for the new mesh (i.e.
setMultiThreadJacobian((object)arg1, …) Set number of threads used for brute force Jacobian generation.
setRegionManager((object)arg1, (object)reg) C++ signature :
setSensorPositions(pnts) Set measurement locations.
setStartModel((object)arg1, (object)startModel) C++ signature :
setThreadCount((object)arg1, (object)nThreads) Set the maximum number of allowed threads for MT calculation.
setVerbose((object)arg1, (object)verbose) Set verbose state.
solution((object)arg1) C++ signature :
startModel((object)arg1) C++ signature :
threadCount((object)arg1) Return the maximum number of allowed threads for MT calculation
verbose((object)arg1) Get verbose state.
createJacobian_mt  
responses  
__init__(verbose=True)[source]

Constructor.

clearConstraints((object)arg1) → object :
C++ signature :
void* clearConstraints(GIMLI::ModellingBase {lvalue})

clearConstraints( (object)arg1) -> object :

C++ signature :
void* clearConstraints(ModellingBase_wrapper {lvalue})
clearJacobian((object)arg1) → object :
C++ signature :
void* clearJacobian(GIMLI::ModellingBase {lvalue})

clearJacobian( (object)arg1) -> object :

C++ signature :
void* clearJacobian(ModellingBase_wrapper {lvalue})
constraints((object)arg1) → object :
C++ signature :
GIMLI::MatrixBase* constraints(GIMLI::ModellingBase {lvalue})

constraints( (object)arg1) -> object :

C++ signature :
GIMLI::MatrixBase* constraints(ModellingBase_wrapper {lvalue})

constraints( (object)arg1) -> object :

C++ signature :
GIMLI::MatrixBase* constraints(GIMLI::ModellingBase {lvalue})

constraints( (object)arg1) -> object :

C++ signature :
GIMLI::MatrixBase* constraints(ModellingBase_wrapper {lvalue})
constraintsRef((object)arg1) → object :
C++ signature :
GIMLI::SparseMapMatrix<double, unsigned long> {lvalue} constraintsRef(GIMLI::ModellingBase {lvalue})

constraintsRef( (object)arg1) -> object :

C++ signature :
GIMLI::SparseMapMatrix<double, unsigned long> {lvalue} constraintsRef(GIMLI::ModellingBase {lvalue})
createConstraints((object)arg1) → object :
C++ signature :
void* createConstraints(GIMLI::ModellingBase {lvalue})

createConstraints( (object)arg1) -> object :

C++ signature :
void* createConstraints(ModellingBase_wrapper {lvalue})
createDefaultStartModel((object)arg1) → object :
C++ signature :
GIMLI::Vector<double> createDefaultStartModel(GIMLI::ModellingBase {lvalue})

createDefaultStartModel( (object)arg1) -> object :

C++ signature :
GIMLI::Vector<double> createDefaultStartModel(ModellingBase_wrapper {lvalue})
createJacobian(model)[source]

Create Jacobian matrix for a density model.

Create Jacobian matrix for a density distribution (model) and store it internal.

createJacobian_mt(model, resp)
createMappedModel((object)arg1, (object)model[, (object)background=-1]) → object :

Read only extrapolation of model values given per cell marker to values given per cell. Exterior values will be set to background or prolongated for background = -1.

C++ signature :
GIMLI::Vector<double> createMappedModel(GIMLI::ModellingBase {lvalue},GIMLI::Vector<double> [,double=-1])
createRefinedForwardMesh((object)arg1[, (object)refine=True[, (object)pRefine=False]]) → object :
C++ signature :
void* createRefinedForwardMesh(GIMLI::ModellingBase {lvalue} [,bool=True [,bool=False]])
createStartModel((object)arg1) → object :
C++ signature :
GIMLI::Vector<double> createStartModel(GIMLI::ModellingBase {lvalue})
createStartVector((object)arg1) → object :

DEPRECATED use createStartModel

C++ signature :
GIMLI::Vector<double> createStartVector(GIMLI::ModellingBase {lvalue})
createStartmodel()[source]

Create the default starting model.

data((object)arg1) → object :

Return the associated data container.

C++ signature :
GIMLI::DataContainer {lvalue} data(GIMLI::ModellingBase {lvalue})
deleteMesh((object)arg1) → object :

Delete the actual mesh.

C++ signature :
void* deleteMesh(GIMLI::ModellingBase {lvalue})
initConstraints((object)arg1) → object :
C++ signature :
void* initConstraints(GIMLI::ModellingBase {lvalue})

initConstraints( (object)arg1) -> object :

C++ signature :
void* initConstraints(ModellingBase_wrapper {lvalue})
initJacobian((object)arg1) → object :
C++ signature :
void* initJacobian(GIMLI::ModellingBase {lvalue})

initJacobian( (object)arg1) -> object :

C++ signature :
void* initJacobian(ModellingBase_wrapper {lvalue})
initRegionManager((object)arg1) → object :
C++ signature :
void* initRegionManager(GIMLI::ModellingBase {lvalue})
jacobian((object)arg1) → object :

Return the pointer to the Jacobian matrix associated with this forward operator.

C++ signature :
GIMLI::MatrixBase* jacobian(GIMLI::ModellingBase {lvalue})
jacobian( (object)arg1) -> object :

Return the pointer to the Jacobian matrix associated with this forward operator.

C++ signature :
GIMLI::MatrixBase* jacobian(GIMLI::ModellingBase {lvalue})
jacobianRef((object)arg1) → object :
C++ signature :
GIMLI::Matrix<double> {lvalue} jacobianRef(GIMLI::ModellingBase {lvalue})

jacobianRef( (object)arg1) -> object :

C++ signature :
GIMLI::Matrix<double> {lvalue} jacobianRef(GIMLI::ModellingBase {lvalue})
mapModel((object)arg1, (object)model[, (object)background=0]) → object :
C++ signature :
void* mapModel(GIMLI::ModellingBase {lvalue},GIMLI::Vector<double> [,double=0])
mesh((object)arg1) → object :
C++ signature :
GIMLI::Mesh* mesh(GIMLI::ModellingBase {lvalue})
multiThreadJacobian((object)arg1) → object :

Return number of threads used for Jacobian generation.

C++ signature :
unsigned long multiThreadJacobian(GIMLI::ModellingBase {lvalue})
region((object)arg1, (object)marker) → object :

Syntactic sugar for this->regionManager().region(marker).

C++ signature :
GIMLI::Region* region(GIMLI::ModellingBase {lvalue},int)
regionManager((object)arg1) → object :
C++ signature :
GIMLI::RegionManager regionManager(GIMLI::ModellingBase {lvalue})

regionManager( (object)arg1) -> object :

C++ signature :
GIMLI::RegionManager {lvalue} regionManager(GIMLI::ModellingBase {lvalue})
regionManagerRef((object)arg1) → object :
C++ signature :
GIMLI::RegionManager {lvalue} regionManagerRef(GIMLI::ModellingBase {lvalue})
response(dDensity)[source]

Calculate response for a given density distribution.

response_mt((object)arg1, (object)model[, (object)i=0]) → object :
C++ signature :
GIMLI::Vector<double> response_mt(GIMLI::ModellingBase {lvalue},GIMLI::Vector<double> [,unsigned long=0])

response_mt( (object)arg1, (object)model [, (object)i=0]) -> object :

C++ signature :
GIMLI::Vector<double> response_mt(ModellingBase_wrapper {lvalue},GIMLI::Vector<double> [,unsigned long=0])
responses(models, respos)
setConstraints((object)arg1, (object)C) → object :
C++ signature :
void* setConstraints(GIMLI::ModellingBase {lvalue},GIMLI::MatrixBase*)

setConstraints( (object)arg1, (object)C) -> object :

C++ signature :
void* setConstraints(ModellingBase_wrapper {lvalue},GIMLI::MatrixBase*)
setData((object)arg1, (object)data) → object :

Change the associated data container

C++ signature :
void* setData(GIMLI::ModellingBase {lvalue},GIMLI::DataContainer {lvalue})
setJacobian((object)arg1, (object)J) → object :
C++ signature :
void* setJacobian(GIMLI::ModellingBase {lvalue},GIMLI::MatrixBase*)

setJacobian( (object)arg1, (object)J) -> object :

C++ signature :
void* setJacobian(ModellingBase_wrapper {lvalue},GIMLI::MatrixBase*)
setMesh((object)arg1, (object)mesh [, (object)ignoreRegionManager=False]) -> object : Set new mesh to the forward operator, optionally hold region parameter for the new mesh (i.e. for roll a long)

Set new mesh to the forward operator, optionally hold region parameter for the new mesh (i.e. for roll a long)

C++ signature :
void* setMesh(GIMLI::ModellingBase {lvalue},GIMLI::Mesh [,bool=False])
setMultiThreadJacobian((object)arg1, (object)nThreads) → object :

Set number of threads used for brute force Jacobian generation. 1 is default. If nThreads is greater than 1 you need to implement response_mt with a read only response function. Maybe its worth set the single setThreadCount to 1 than, that you dont find yourself in a threading overkill.

C++ signature :
void* setMultiThreadJacobian(GIMLI::ModellingBase {lvalue},unsigned long)
setRegionManager((object)arg1, (object)reg) → object :
C++ signature :
void* setRegionManager(GIMLI::ModellingBase {lvalue},GIMLI::RegionManager*)
setSensorPositions(pnts)[source]

Set measurement locations. [[x,y,z],…].

setStartModel((object)arg1, (object)startModel) → object :
C++ signature :
void* setStartModel(GIMLI::ModellingBase {lvalue},GIMLI::Vector<double>)

setStartModel( (object)arg1, (object)startModel) -> object :

C++ signature :
void* setStartModel(ModellingBase_wrapper {lvalue},GIMLI::Vector<double>)
setThreadCount((object)arg1, (object)nThreads) → object :

Set the maximum number of allowed threads for MT calculation. Have to be greater than 0. Will also set ENV(OPENBLAS_NUM_THREADS) .. if used.

C++ signature :
void* setThreadCount(GIMLI::ModellingBase {lvalue},unsigned long)
setVerbose((object)arg1, (object)verbose) → object :

Set verbose state.

C++ signature :
void* setVerbose(GIMLI::ModellingBase {lvalue},bool)
solution((object)arg1) → object :
C++ signature :
GIMLI::Matrix<double> solution(GIMLI::ModellingBase {lvalue})
startModel((object)arg1) → object :
C++ signature :
GIMLI::Vector<double> startModel(GIMLI::ModellingBase {lvalue})

startModel( (object)arg1) -> object :

C++ signature :
GIMLI::Vector<double> startModel(ModellingBase_wrapper {lvalue})
threadCount((object)arg1) → object :

Return the maximum number of allowed threads for MT calculation

C++ signature :
unsigned long threadCount(GIMLI::ModellingBase {lvalue})
verbose((object)arg1) → object :

Get verbose state.

C++ signature :
bool verbose(GIMLI::ModellingBase {lvalue})

verbose( (object)arg1) -> object :

C++ signature :
bool verbose(GIMLI::ModellingBase {lvalue})


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