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Purpose

This panel is used to run the Linear inversion of geodetic data, simultaneously combining an arbitrary number of observed datasets and sources.

An example involving this panel can be found in the tutorial.

Technical Note

 

The linear inversion is generally carried out after the Non-Linear Inversion out to retrieve a slip distribution over a fault or the opening distribution in the modeling of dikes and sills in volcanic context. However, in the case of complex signals where tectonic and volcanic sources are simultaneously contributing, point pressure sources can also be considered in the inversion. For these sources, the only parameter retrievable by linear inversion is the volume variation.

A number of options are available: positivity/negativity constraints on the slip/opening distribution, fixed/variable/bounded rake for slip distributions, regular of full resolution (automatic) fault subdivision, compensation for topography effects, a priori regularization through a damping factor (this is common to all the sources and set in the Option folder).

After the inversion ends, the Calculate and Draw Focal Mechanism panel is automatically invoked to see the results, only when tectonic sources are used.

For complex problem with multiple events or overlapping signals, there is also the possibility of introducing “fixed sources”, that are sources not retrieved by inversion (for instance, coming from the inversion of other data) whose contribution is in any case accounted for in the inversion.

The panel is organized with folders: 

 

The INPUT Dataset folder allows to add the geodetic dataset(s) to invert; see the InSAR dataset and GPS dataset to invert. The “**CHECK PARAMETERS**” string indicates that some parameters must be set (‘EDIT DATASET’ – ‘Edit parameters…’ button).

The INPUT Sources folder allows to create, recover and setup the sources used to model the geodetic data. Three sources are available: Elastic dislocation source, used to model the surface displacement induced by a uniform dislocation for a rectangular source in an elastic and homogeneous half-space [Okada, 1985]; Point pressure source, used to model the surface displacement induced by an expanding or compressing point-source [Mogi, 1958]. The "Edit..." button must be used to properly set the source(s).

The Options folder allows to set the damping factor and the coordinate system of output sources.

After the processing, OUTPUT Datasets and OUTPUT Sources folders are added to the panel, with information on the modeled data and sources, with a Report folder containing text summary of the processing.

NOTE: The first time an XML Project File is open, if a completed Non-Linear inversion is found, the input folders can be automatically initialized according to the output of the non-linear inversion.

 

In this panel the use of the XML Project File is mandatory

 

INPUT Datasets

 

ADD DATASETS

 Add from file…: Add a geodetic (InSAR or GPS) dataset from shapefile

 From XML Project File…: Retrieve a dataset from an already existing XML Project File.

EDIT DATASETS

 Edit parameters…: set the dataset properties with the Dataset Parameter Setting panel

 Remove: remove the selected dataset(s) from the list

VIEW DATASETS

 Plot 2D:  open a graphic viewer to see the dataset

 

INPUT Sources

 

ADD SOURCES

 New

         Elastic Dislocation (Okada): open the panel to set the parameters of an elastic dislocation/opening

         Point Pressure (Mogi): open the panel to set the parameters of a point volume source

 Import

         From Shapefile: add a source from an InSAR or GPS shapefile

         From XML Project File…: retrieve a source from an existing XML Project File

EDIT SOURCES

 Edit parameters…: set the source properties through a source dependent panel

 Remove: remove the selected source(s) from the list

 

VIEW SOURCES

 Plot 2D: open a graphic viewer to see the source in a geocoded map

 Plot 3D: open a graphic viewer to see the source in a 3D geocoded map;

EXPORT SOURCES

 Save to shapefile…: allow the user to save the sources in a shapefile

 

Options

 

Dumping Factor

Strength of the regularization factor, for slip and opening distributions.

Source coordinate system

Coordinate system used for the output sources. This is automatically set equal to the first dataset added, but it can be changed either among the available systems in the menu list of through the Change… button. When the coordinate system is changed, all the sources already set in the INPUT Sources folder are automatically modified accordingly.

 

OUTPUT Datasets

This folder is available after the inversion

VIEW DATASETS

 Plot 2D:  open a graphic viewer to see the dataset (observed, modelled and residuals) in a geocoded map

 View parameters…: open a panel with a detailed text report about the modelled dataset

 

OUTPUT Sources

This folder is available after the inversion.

VIEW SOURCES

 Plot 2D:  open a graphic viewer to see the best fit sources

 Plot 2D – Frontal View (fault only): open a graphic viewer to see the best fit sources in the fault coordinates (strike/dip)

Plot 3D:  open a graphic viewer to see the best fit sources in 3D

View parameters…: read the parameters of the output sources

EXPORT SOURCES

 Save to shapefile…: allow the user to save the sources in a shapefile (it is automatically done after the inversion)

 

Report

This tab is available after the inversion and it shows a summary of the linear inversion performance. Information are provided about the modelled sources (source parameters, geodetic moment, event magnitude, etc.) and datasets (RMS of the residuals, RMS of the original dataset).

 

XML Project File section

 

New...

Create a new XML Project File content into the panel.

 

Open...

Open the XML Project File content into the panel.

 

Save

Save the XML Project File content from the panel.

 

Save as...

Save the XML Project File content from the panel defining the project name.

 

Close

Close the XML Project File content from the panel.

 

Output Files

 

_linear.shp

Modeled datasets and sources after the linear inversion.

 

General Functions

 

Start        

Start of the processing.

 

Cancel        

The window will be closed.

 

Help        

Specific help document section.

 

 

References

 

Atzori et al. (2019), InSAR full-resolution analysis of the 2017–2018 M>6 earthquakes in Mexico, Rem. Sens. Env., 234, 111461

Mogi, K. (1958), Relations between eruptions of various volcanoes and the deformation of the ground surface around them, Bull. Earth Res. Inst., 36, 99–134.

Okada, Y. (1985), Surface deformation due to shear and tensile faults in a half-space, Bull. Seismol. Soc. Am., 75, 1135–1154.