simpeg.directives.UpdateSensitivityWeights#

class simpeg.directives.UpdateSensitivityWeights(every_iteration=False, threshold_value=1e-12, threshold_method='amplitude', normalization_method='maximum', **kwargs)[source]#

Bases: InversionDirective

Sensitivity weighting for linear and non-linear least-squares inverse problems.

This directive computes the root-mean squared sensitivities for the forward simulation(s) attached to the inverse problem, then truncates and scales the result to create cell weights which are applied in the regularization. The underlying theory is provided below in the Notes section.

This directive requires that the map for the regularization function is either class:simpeg.maps.Wires or class:simpeg.maps.Identity. In other words, the sensitivity weighting cannot be applied for parametric inversion. In addition, the simulation(s) connected to the inverse problem must have a getJ or getJtJdiag method.

This directive’s place in the DirectivesList must be before any directives which update the preconditioner for the inverse problem (i.e. UpdatePreconditioner), and must be before any directives that estimate the starting trade-off parameter (i.e. EstimateBeta_ByEig and EstimateBetaMaxDerivative).

Parameters:
every_iterationbool

When True, update sensitivity weighting at every model update; non-linear problems. When False, create sensitivity weights for starting model only; linear problems.

thresholdfloat

Threshold value for smallest weighting value.

threshold_method{‘amplitude’, ‘global’, ‘percentile’}

Threshold method for how threshold_value is applied:

  • amplitude:

    the smallest root-mean squared sensitivity is a fractional percent of the largest value; must be between 0 and 1.

  • global:

    threshold_value is added to the cell weights prior to normalization; must be greater than 0.

  • percentile:

    the smallest root-mean squared sensitivity is set using percentile threshold; must be between 0 and 100.

normalization_method{‘maximum’, ‘min_value’, None}

Normalization method applied to sensitivity weights.

Options are:

  • maximum:

    sensitivity weights are normalized by the largest value such that the largest weight is equal to 1.

  • minimum:

    sensitivity weights are normalized by the smallest value, after thresholding, such that the smallest weights are equal to 1.

  • None:

    normalization is not applied.

Attributes

debug

verbose.debug has been deprecated.

dmisfit

Data misfit associated with the directive.

everyIter

every_iteration.everyIter has been deprecated.

every_iteration

Update sensitivity weights when model is updated.

invProb

Inverse problem associated with the directive.

inversion

Inversion object associated with the directive.

normalization

normalization_method.normalization has been deprecated.

normalization_method

Normalization method applied to sensitivity weights.

opt

Optimization algorithm associated with the directive.

reg

Regularization associated with the directive.

simulation

Return simulation for all data misfits.

survey

Return survey for all data misfits

threshold

threshold_value.threshold has been deprecated.

threshold_method

Threshold method for how threshold_value is applied:

threshold_value

Threshold value used to set minimum weighting value.

verbose

Whether or not to print debugging information.

Methods

endIter()

Execute end of iteration.

finish()

Update inversion parameter(s) according to directive at end of inversion.

initialize()

Compute sensitivity weights upon starting the inversion.

update()

Update sensitivity weights

validate(directiveList)

Validate directive against directives list.

Notes

Let J represent the Jacobian. To create sensitivity weights, root-mean squared (RMS) sensitivities s are computed by summing the squares of the rows of the Jacobian:

s=[iJi,2]1/2

The dynamic range of RMS sensitivities can span many orders of magnitude. When computing sensitivity weights, thresholding is generally applied to set a minimum value.

Thresholding:

If global thresholding is applied, we add a constant τ to the RMS sensitivities:

s~=s+τ

In the case of percentile thresholding, we let s% represent a given percentile. Thresholding to set a minimum value is applied as follows:

s~j={sjforsjs%s%forsj<s%

If absolute thresholding is applied, we define η as a fractional percent. In this case, thresholding is applied as follows:

s~j={sjforsjηsmaxηsmaxforsj<ηsmax

Galleries and Tutorials using simpeg.directives.UpdateSensitivityWeights#

PF: Gravity: Tiled Inversion Linear

PF: Gravity: Tiled Inversion Linear

Magnetic inversion on a TreeMesh with remanence

Magnetic inversion on a TreeMesh with remanence

Magnetic inversion on a TreeMesh

Magnetic inversion on a TreeMesh

Magnetic Amplitude inversion on a TreeMesh

Magnetic Amplitude inversion on a TreeMesh

PF: Gravity: Laguna del Maule Bouguer Gravity

PF: Gravity: Laguna del Maule Bouguer Gravity

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

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

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

1D Inversion of for a Single Sounding

1D Inversion of for a Single Sounding

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

Compare weighting strategy with Inversion of surface Gravity Anomaly Data

Compare weighting strategy with Inversion of surface Gravity Anomaly Data

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

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

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

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

Sparse Inversion with Iteratively Re-Weighted Least-Squares

Sparse Inversion with Iteratively Re-Weighted Least-Squares

Cross-gradient Joint Inversion of Gravity and Magnetic Anomaly Data

Cross-gradient Joint Inversion of Gravity and Magnetic Anomaly Data