Gravity¶
The gravity problem uses an integral equation approach for solving the forward and inverse problem. This module supports both gravity and gravity gradient modeling.
Gravity Integral eq. approach¶

class
SimPEG.potential_fields.gravity.
Simulation3DIntegral
(*args, **kwargs)[source]¶ Bases:
SimPEG.potential_fields.base.BasePFSimulation
Gravity simulation in integral form.
Required Properties:
actInd (
Array
): Array of active cells (ground), a list or numpy array of <class ‘bool’>, <class ‘int’> with shape (*)counter (
Counter
): A SimPEG.utils.Counter object, an instance of Countermesh (
BaseMesh
): a discretize mesh instance, an instance of BaseMeshsensitivity_path (
String
): path to store the sensitivty, a unicode string, Default: ./sensitivity/None
solver_opts (
Dictionary
): solver options as a kwarg dict, a dictionarystore_sensitivities (
StringChoice
): Compute and store G, any of “disk”, “ram”, “forward_only”, Default: ramsurvey (
BaseSurvey
): a survey object, an instance of BaseSurvey
Optional Properties:
linear_model (
PhysicalProperty
): The model for a linear problem, a physical propertymodel (
Model
): Inversion model., a numpy array of <class ‘float’>, <class ‘int’> with shape (*, *) or (*)model_map (
Mapping
): Mapping of The model for a linear problem to the inversion model., a SimPEG Maprho (
PhysicalProperty
): Physical property, a physical property, Default: 1.0rhoMap (
Mapping
): Mapping of Physical property to the inversion model., a SimPEG Map
Other Properties:
model_deriv (
Derivative
): Derivative of The model for a linear problem wrt the model.rhoDeriv (
Derivative
): Derivative of Physical property wrt the model.

property
rho
¶ Physical property

property
rhoMap
¶ Mapping of Physical property to the inversion model.

property
rhoDeriv
¶ Derivative of Physical property wrt the model.

fields
(m)[source]¶ u = fields(m) The field given the model. :param numpy.ndarray m: model :rtype: numpy.ndarray :return: u, the fields

property
G
¶ Gravity forward operator

property
gtg_diagonal
¶ Diagonal of GtG

evaluate_integral
(receiver_location, components)[source]¶ Compute the forward linear relationship between the model and the physics at a point and for every components of the survey.
 Parameters
receiver_location (numpy.ndarray) – array with shape (n_receivers, 3) Array of receiver locations as x, y, z columns.
components (list[str]) – List of gravity components chosen from: ‘gx’, ‘gy’, ‘gz’, ‘gxx’, ‘gxy’, ‘gxz’, ‘gyy’, ‘gyz’, ‘gzz’, ‘guv’
 Rtype numpy.ndarray
rows
 Returns
ndarray with shape (n_components, n_cells) Dense array mapping of the contribution of all active cells to data components:
rows = g_1 = [g_1x g_1y g_1z] g_2 = [g_2x g_2y g_2z] ... g_c = [g_cx g_cy g_cz]

Jtvec_approx
(m, v, f=None)[source]¶ Approximate effect of transpose of J(m) on a vector v. :param numpy.ndarray m: model :param numpy.ndarray v: vector to multiply :param Fields f: fields :rtype: numpy.ndarray :return: JTv

Jvec_approx
(m, v, f=None)[source]¶ Approximate effect of J(m) on a vector v :param numpy.ndarray m: model :param numpy.ndarray v: vector to multiply :param Fields f: fields :rtype: numpy.ndarray :return: approxJv

property
Solver
¶ Solver has been deprecated. See simulation.solver for documentation

property
actInd
¶ actInd (
Array
): Array of active cells (ground), a list or numpy array of <class ‘bool’>, <class ‘int’> with shape (*)

clean_on_model_update
= []¶

deleteTheseOnModelUpdate
= []¶

classmethod
deserialize
(value, trusted=False, strict=False, assert_valid=False, **kwargs)[source]¶ Creates HasProperties instance from serialized dictionary
This uses the Property deserializers to deserialize all JSONcompatible dictionary values into their corresponding Property values on a new instance of a HasProperties class. Extra keys in the dictionary that do not correspond to Properties will be ignored.
Parameters:
value  Dictionary to deserialize new instance from.
trusted  If True (and if the input dictionary has
'__class__'
keyword and this class is in the registry), the new HasProperties class will come from the dictionary. If False (the default), only the HasProperties class this method is called on will be constructed.strict  Requires
'__class__'
, if present on the input dictionary, to match the deserialized instance’s class. Also disallows unused properties in the input dictionary. Default is False.assert_valid  Require deserialized instance to be valid. Default is False.
Any other keyword arguments will be passed through to the Property deserializers.

dpred
(m, f=None)[source]¶ Create the projected data from a model. The fields, f, (if provided) will be used for the predicted data instead of recalculating the fields (which may be expensive!).
\[d_\text{pred} = P(f(m))\]Where P is a projection of the fields onto the data space.

equal
(other)[source]¶ Determine if two HasProperties instances are equivalent
Equivalence is determined by checking if all Property values on two instances are equal, using
Property.equal
.

property
forwardOnly
¶ The forwardOnly property has been deprecated. Please set the store_sensitivites property instead. This will be removed in version 0.15.0 of SimPEG

property
linear_model
¶ The model for a linear problem

make_synthetic_data
(m, relative_error=0.05, noise_floor=0.0, f=None, add_noise=False, **kwargs)[source]¶ Make synthetic data given a model, and a standard deviation. :param numpy.ndarray m: geophysical model :param numpy.ndarray relative_error: standard deviation :param numpy.ndarray noise_floor: noise floor :param numpy.ndarray f: fields for the given model (if precalculated)

property
mesh
¶ mesh (
BaseMesh
): a discretize mesh instance, an instance of BaseMesh

property
model
¶ model (
Model
): Inversion model., a numpy array of <class ‘float’>, <class ‘int’> with shape (*, *) or (*)

property
model_deriv
¶ Derivative of The model for a linear problem wrt the model.

property
model_map
¶ Mapping of The model for a linear problem to the inversion model.

property
n_cpu
¶ The parallelized property has been removed. If interested, try out loading dask for parallelism by doing
import SimPEG.dask
. This will be removed in version 0.15.0 of SimPEG

property
needs_model
¶ True if a model is necessary

property
parallelized
¶ The parallelized property has been removed. If interested, try out loading dask for parallelism by doing
import SimPEG.dask
. This will be removed in version 0.15.0 of SimPEG

residual
(m, dobs, f=None)[source]¶ The data residual:
\[\mu_\text{data} = \mathbf{d}_\text{pred}  \mathbf{d}_\text{obs}\] Parameters
m (numpy.ndarray) – geophysical model
f (numpy.ndarray) – fields
 Return type
 Returns
data residual

property
sensitivity_path
¶ sensitivity_path (
String
): path to store the sensitivty, a unicode string, Default: ./sensitivity/

serialize
(include_class=True, save_dynamic=False, **kwargs)[source]¶ Serializes a HasProperties instance to dictionary
This uses the Property serializers to serialize all Property values to a JSONcompatible dictionary. Properties that are undefined are not included. If the HasProperties instance contains a reference to itself, a
properties.SelfReferenceError
will be raised.Parameters:
include_class  If True (the default), the name of the class will also be saved to the serialized dictionary under key
'__class__'
save_dynamic  If True, dynamic properties are written to the serialized dict (default: False).
Any other keyword arguments will be passed through to the Property serializers.

property
solver
¶ None

property
solverOpts
¶ solverOpts has been deprecated. See solver_opts for documentation

property
solver_opts
¶ solver_opts (
Dictionary
): solver options as a kwarg dict, a dictionary

property
store_sensitivities
¶ store_sensitivities (
StringChoice
): Compute and store G, any of “disk”, “ram”, “forward_only”, Default: ram

property
survey
¶ survey (
BaseSurvey
): a survey object, an instance of BaseSurvey
Gravity Survey¶

class
SimPEG.potential_fields.gravity.
Survey
(*args, **kwargs)[source]¶ Bases:
SimPEG.survey.BaseSurvey
Base Gravity Survey
Required Properties:
counter (
Counter
): A SimPEG counter object, an instance of Countersource_list (a list of
BaseSrc
): A list of sources for the survey, a list (each item is an instance of BaseSrc)

rxType
= None¶ receiver type

property
nRx
¶

property
receiver_locations
¶ receiver locations

property
nD
¶ Number of data

property
components
¶

property
Qfx
¶

property
Qfy
¶

property
Qfz
¶

classmethod
deserialize
(value, trusted=False, strict=False, assert_valid=False, **kwargs)[source]¶ Creates HasProperties instance from serialized dictionary
This uses the Property deserializers to deserialize all JSONcompatible dictionary values into their corresponding Property values on a new instance of a HasProperties class. Extra keys in the dictionary that do not correspond to Properties will be ignored.
Parameters:
value  Dictionary to deserialize new instance from.
trusted  If True (and if the input dictionary has
'__class__'
keyword and this class is in the registry), the new HasProperties class will come from the dictionary. If False (the default), only the HasProperties class this method is called on will be constructed.strict  Requires
'__class__'
, if present on the input dictionary, to match the deserialized instance’s class. Also disallows unused properties in the input dictionary. Default is False.assert_valid  Require deserialized instance to be valid. Default is False.
Any other keyword arguments will be passed through to the Property deserializers.

equal
(other)[source]¶ Determine if two HasProperties instances are equivalent
Equivalence is determined by checking if all Property values on two instances are equal, using
Property.equal
.

property
nSrc
¶ Number of Sources

projectFields
(u)[source]¶ This function projects the fields onto the data space.
First we project our B on to data location
\[\mathbf{B}_{rec} = \mathbf{P} \mathbf{B}\]then we take the dot product between B and b_0
\[\text{TMI} = \vec{B}_s \cdot \hat{B}_0\]

serialize
(include_class=True, save_dynamic=False, **kwargs)[source]¶ Serializes a HasProperties instance to dictionary
This uses the Property serializers to serialize all Property values to a JSONcompatible dictionary. Properties that are undefined are not included. If the HasProperties instance contains a reference to itself, a
properties.SelfReferenceError
will be raised.Parameters:
include_class  If True (the default), the name of the class will also be saved to the serialized dictionary under key
'__class__'
save_dynamic  If True, dynamic properties are written to the serialized dict (default: False).
Any other keyword arguments will be passed through to the Property serializers.

property
source_list
¶ source_list (a list of
BaseSrc
): A list of sources for the survey, a list (each item is an instance of BaseSrc)

property
srcList
¶ srcList has been deprecated. See source_list for documentation

validate
()[source]¶ Call all registered class validator methods
These are all methods decorated with
@properties.validator
. Validator methods are expected to raise a ValidationError if they fail.

property
vnD
¶ Vector number of data
Gravity Source¶

class
SimPEG.potential_fields.gravity.
SourceField
(*args, **kwargs)[source]¶ Bases:
SimPEG.survey.BaseSrc
Define the inducing field
Required Properties:
receiver_list (a list of
BaseRx
): receiver list, a list (each item is an instance of BaseRx)
Optional Properties:
location (
SourceLocationArray
): Location of the source [x, y, z] in 3D, a 1D array denoting the source location of <class ‘float’>, <class ‘int’> with shape (*)

parameters
= None¶

classmethod
deserialize
(value, trusted=False, strict=False, assert_valid=False, **kwargs)[source]¶ Creates HasProperties instance from serialized dictionary
This uses the Property deserializers to deserialize all JSONcompatible dictionary values into their corresponding Property values on a new instance of a HasProperties class. Extra keys in the dictionary that do not correspond to Properties will be ignored.
Parameters:
value  Dictionary to deserialize new instance from.
trusted  If True (and if the input dictionary has
'__class__'
keyword and this class is in the registry), the new HasProperties class will come from the dictionary. If False (the default), only the HasProperties class this method is called on will be constructed.strict  Requires
'__class__'
, if present on the input dictionary, to match the deserialized instance’s class. Also disallows unused properties in the input dictionary. Default is False.assert_valid  Require deserialized instance to be valid. Default is False.
Any other keyword arguments will be passed through to the Property deserializers.

equal
(other)[source]¶ Determine if two HasProperties instances are equivalent
Equivalence is determined by checking if all Property values on two instances are equal, using
Property.equal
.

property
loc
¶ loc has been deprecated. See location for documentation

property
location
¶ location (
SourceLocationArray
): Location of the source [x, y, z] in 3D, a 1D array denoting the source location of <class ‘float’>, <class ‘int’> with shape (*)

property
nD
¶ Number of data

property
receiver_list
¶ receiver_list (a list of
BaseRx
): receiver list, a list (each item is an instance of BaseRx)

property
rxList
¶ rxList has been deprecated. See receiver_list for documentation

serialize
(include_class=True, save_dynamic=False, **kwargs)[source]¶ Serializes a HasProperties instance to dictionary
This uses the Property serializers to serialize all Property values to a JSONcompatible dictionary. Properties that are undefined are not included. If the HasProperties instance contains a reference to itself, a
properties.SelfReferenceError
will be raised.Parameters:
include_class  If True (the default), the name of the class will also be saved to the serialized dictionary under key
'__class__'
save_dynamic  If True, dynamic properties are written to the serialized dict (default: False).
Any other keyword arguments will be passed through to the Property serializers.

validate
()[source]¶ Call all registered class validator methods
These are all methods decorated with
@properties.validator
. Validator methods are expected to raise a ValidationError if they fail.

property
vnD
¶ Vector number of data
Gravity Receiver¶

class
SimPEG.potential_fields.gravity.
Point
(*args, **kwargs)[source]¶ Bases:
SimPEG.survey.BaseRx
Gravity point receiver class for integral formulation
 param numpy.ndarray locations
receiver locations index (ie.
np.c_[ind_1, ind_2, ...]
) param string component
receiver component “gx”, “gy”, “gz”, “gxx”, “gxy”, “gxz”, “gyy”, “gyz”, “gzz”, “guv”, “amp” [default]
Required Properties:
locations (
RxLocationArray
): Locations of the receivers (nRx x nDim), an array of receiver locations of <class ‘float’>, <class ‘int’> with shape (*, *)projGLoc (
StringChoice
): Projection grid location, default is CC, any of “CC”, “Fx”, “Fy”, “Fz”, “Ex”, “Ey”, “Ez”, “N”, Default: CCstoreProjections (
Boolean
): Store calls to getP (organized by mesh), a boolean, Default: True

classmethod
deserialize
(value, trusted=False, strict=False, assert_valid=False, **kwargs)[source]¶ Creates HasProperties instance from serialized dictionary
This uses the Property deserializers to deserialize all JSONcompatible dictionary values into their corresponding Property values on a new instance of a HasProperties class. Extra keys in the dictionary that do not correspond to Properties will be ignored.
Parameters:
value  Dictionary to deserialize new instance from.
trusted  If True (and if the input dictionary has
'__class__'
keyword and this class is in the registry), the new HasProperties class will come from the dictionary. If False (the default), only the HasProperties class this method is called on will be constructed.strict  Requires
'__class__'
, if present on the input dictionary, to match the deserialized instance’s class. Also disallows unused properties in the input dictionary. Default is False.assert_valid  Require deserialized instance to be valid. Default is False.
Any other keyword arguments will be passed through to the Property deserializers.

equal
(other)[source]¶ Determine if two HasProperties instances are equivalent
Equivalence is determined by checking if all Property values on two instances are equal, using
Property.equal
.

getP
(mesh, projGLoc=None)[source]¶ Returns the projection matrices as a list for all components collected by the receivers.
Note
Projection matrices are stored as a dictionary listed by meshes.

property
locations
¶ locations (
RxLocationArray
): Locations of the receivers (nRx x nDim), an array of receiver locations of <class ‘float’>, <class ‘int’> with shape (*, *)

property
locs
¶ locs has been deprecated. See locations for documentation

property
projGLoc
¶ projGLoc (
StringChoice
): Projection grid location, default is CC, any of “CC”, “Fx”, “Fy”, “Fz”, “Ex”, “Ey”, “Ez”, “N”, Default: CC

serialize
(include_class=True, save_dynamic=False, **kwargs)[source]¶ Serializes a HasProperties instance to dictionary
This uses the Property serializers to serialize all Property values to a JSONcompatible dictionary. Properties that are undefined are not included. If the HasProperties instance contains a reference to itself, a
properties.SelfReferenceError
will be raised.Parameters:
include_class  If True (the default), the name of the class will also be saved to the serialized dictionary under key
'__class__'
save_dynamic  If True, dynamic properties are written to the serialized dict (default: False).
Any other keyword arguments will be passed through to the Property serializers.