simpeg.data_misfit.L2DataMisfit#

class simpeg.data_misfit.L2DataMisfit(data, simulation, debug=False, counter=None, **kwargs)[source]#

Bases: BaseDataMisfit

Least-squares data misfit.

Define the data misfit as the L2-norm of the weighted residual between observed data and predicted data for a given model. I.e.:

$${\varphi }_d(\mathbf{m})=\Vert {\mathbf{W}}_{\mathbf{d}}({\mathbf{d}}_{\text{pred}}-{\mathbf{d}}_{\text{obs}}){\Vert }_2^2$$

where ${\mathbf{d}}_{\text{obs}}$ is the observed data vector, ${\mathbf{d}}_{\text{pred}}$ is the predicted data vector for a model vector $\mathbf{m}$, and ${\mathbf{W}}_{\mathbf{d}}$ is the data weighting matrix. The diagonal elements of ${\mathbf{W}}_{\mathbf{d}}$ are the reciprocals of the data uncertainties $\mathit{\epsilon }$. Thus:

$${\mathbf{W}}_{\mathbf{d}}=\text{diag}\left({\mathit{\epsilon }}^{-1}\right)$$

Parameters:

datasimpeg.data.Data

A SimPEG data object that has observed data and uncertainties.

simulationsimpeg.simulation.BaseSimulation

A SimPEG simulation object.

debugbool

Print debugging information.

counterNone or simpeg.utils.Counter

Assign a SimPEG Counter object to store iterations and run-times.

Attributes

W	The data weighting matrix.
counter	SimPEG Counter object to store iterations and run-times.
data	A SimPEG data object.
debug	Print debugging information.
mapping	Mapping from the model to the quantity evaluated in the object function.
nD	Number of data.
nP	Number of model parameters.
shape	Shape of the Jacobian.
simulation	A SimPEG simulation object.

Methods

__call__(m[, f])	Evaluate the residual for a given model.
deriv(m[, f])	Gradient of the data misfit function evaluated for the model provided.
deriv2(m, v[, f])	Hessian of the data misfit function evaluated for the model provided.
map_class	alias of IdentityMap
residual(m[, f])	Computes the data residual vector for a given model.
test([x, num, random_seed])	Run a convergence test on both the first and second derivatives.

Galleries and Tutorials using simpeg.data_misfit.L2DataMisfit#

Maps: ComboMaps

Maps: ComboMaps

PF: Gravity: Tiled Inversion Linear

PF: Gravity: Tiled Inversion Linear

Magnetic inversion on a TreeMesh

Magnetic inversion on a TreeMesh

Magnetic inversion on a TreeMesh

Magnetic inversion on a TreeMesh

Magnetic Amplitude inversion on a TreeMesh

Magnetic Amplitude inversion on a TreeMesh

3D DC inversion of Dipole Dipole array

3D DC inversion of Dipole Dipole array

Parametric DC inversion with Dipole Dipole array

Parametric DC inversion with Dipole Dipole array

2D inversion of Loop-Loop EM Data

2D inversion of Loop-Loop EM Data

EM: TDEM: 1D: Inversion

EM: TDEM: 1D: Inversion

EM: TDEM: 1D: Inversion with VTEM waveform

EM: TDEM: 1D: Inversion with VTEM waveform

Method of Equivalent Sources for Removing VRM Responses

Method of Equivalent Sources for Removing VRM Responses

FLOW: Richards: 1D: Inversion

FLOW: Richards: 1D: Inversion

Petrophysically guided inversion (PGI): Linear example

Petrophysically guided inversion (PGI): Linear example

Petrophysically guided inversion: Joint linear example with nonlinear relationships

Petrophysically guided inversion: Joint linear example with nonlinear relationships

Heagy et al., 2017 1D RESOLVE and SkyTEM Bookpurnong Inversions

Heagy et al., 2017 1D RESOLVE and SkyTEM Bookpurnong Inversions

Heagy et al., 2017 1D RESOLVE Bookpurnong Inversion

Heagy et al., 2017 1D RESOLVE Bookpurnong Inversion

Heagy et al., 2017 1D FDEM and TDEM inversions

Heagy et al., 2017 1D FDEM and TDEM inversions

PF: Gravity: Laguna del Maule Bouguer Gravity

PF: Gravity: Laguna del Maule Bouguer Gravity

Straight Ray with Volume Data Misfit Term

Straight Ray with Volume Data Misfit Term

Sparse Norm Inversion for Total Magnetic Intensity Data on a Tensor Mesh

Sparse Norm Inversion for Total Magnetic Intensity Data on a Tensor Mesh

Cross-gradient Joint Inversion of Gravity and Magnetic Anomaly Data

Cross-gradient Joint Inversion of Gravity and Magnetic Anomaly Data

Joint PGI of Gravity + Magnetic on an Octree mesh using full petrophysical information

Joint PGI of Gravity + Magnetic on an Octree mesh using full petrophysical information

Joint PGI of Gravity + Magnetic on an Octree mesh without petrophysical information

Joint PGI of Gravity + Magnetic on an Octree mesh without petrophysical information

Sparse Norm Inversion of 2D Seismic Tomography Data

Sparse Norm Inversion of 2D Seismic Tomography Data

Linear Least-Squares Inversion

Linear Least-Squares Inversion

Sparse Inversion with Iteratively Re-Weighted Least-Squares

Sparse Inversion with Iteratively Re-Weighted Least-Squares

1D Inversion of Time-Domain Data for a Single Sounding

1D Inversion of Time-Domain Data for a Single Sounding

Least-Squares 1D Inversion of Sounding Data

Least-Squares 1D Inversion of Sounding Data

Sparse 1D Inversion of Sounding Data

Sparse 1D Inversion of Sounding Data

Parametric 1D Inversion of Sounding Data

Parametric 1D Inversion of Sounding Data

2.5D DC Resistivity Least-Squares Inversion

2.5D DC Resistivity Least-Squares Inversion

2.5D DC Resistivity Inversion with Sparse Norms

2.5D DC Resistivity Inversion with Sparse Norms

3D Least-Squares Inversion of DC Resistivity Data

3D Least-Squares Inversion of DC Resistivity Data

2.5D DC Resistivity and IP Least-Squares Inversion

2.5D DC Resistivity and IP Least-Squares Inversion

3D Least-Squares Inversion of DC and IP Data

3D Least-Squares Inversion of DC and IP Data

Least-Squares Inversion of Gravity Anomaly Data

Least-Squares Inversion of Gravity Anomaly Data

Sparse Norm Inversion of Gravity Anomaly Data

Sparse Norm Inversion of Gravity Anomaly Data

1D Inversion of for a Single Sounding

1D Inversion of for a Single Sounding