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__(arg1, model)

C++ signature :

clearConstraints(arg1)

C++ signature :

clearJacobian(arg1)

C++ signature :

constraints(arg1)

C++ signature :

constraintsRef(arg1)

C++ signature :

createConstraints(arg1)

C++ signature :

createDefaultStartModel(arg1)

C++ signature :

createJacobian(model)

Create Jacobian matrix for a density model.

createJacobian_mt(model, resp)

createMappedModel(arg1, model [[, background])

Read only extrapolation of model values given per cell marker to values given per cell.

createRefinedForwardMesh(arg1 [[, refine, …])

C++ signature :

createStartModel(arg1)

C++ signature :

createStartVector(arg1)

DEPRECATED use createStartModel

createStartmodel()

Create the default starting model.

data(arg1)

Return the associated data container.

deleteMesh(arg1)

Delete the actual mesh.

initConstraints(arg1)

C++ signature :

initJacobian(arg1)

C++ signature :

initRegionManager(arg1)

C++ signature :

jacobian(arg1)

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

jacobianRef(arg1)

C++ signature :

mapModel(arg1, model [[, background])

C++ signature :

mesh(arg1)

C++ signature :

multiThreadJacobian(arg1)

Return number of threads used for Jacobian generation.

region(arg1, marker)

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

regionManager(arg1)

C++ signature :

regionManagerRef(arg1)

C++ signature :

response(dDensity)

Calculate response for a given density distribution.

response_mt(arg1, model [[, i])

C++ signature :

responses(models, respos)

setConstraints(arg1, C)

C++ signature :

setData(arg1, data)

Change the associated data container

setJacobian(arg1, J)

C++ signature :

setMesh(arg1, mesh [[, ignoreRegionManager])

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

setMultiThreadJacobian(arg1, nThreads)

Set number of threads used for brute force Jacobian generation.

setRegionManager(arg1, reg)

C++ signature :

setSensorPositions(pnts)

Set measurement locations.

setStartModel(arg1, startModel)

C++ signature :

setThreadCount(arg1, nThreads)

Set the maximum number of allowed threads for MT calculation.

setVerbose(arg1, verbose)

Set verbose state.

solution(arg1)

C++ signature :

startModel(arg1)

C++ signature :

threadCount(arg1)

Return the maximum number of allowed threads for MT calculation

verbose(arg1)

Get verbose state.

__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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