1.Introduction

2.The Bam event data

3.The XML Project File

4.Image subsampling

5.Non-Linear Inversion

6.Linear Inversion

7.Moment tensor and "beach ball" calculation

8.CFF Stress Transfer

9.Forward Modeling

10. Projection into the Line-Of-Sight

11. References

1. Introduction

This tutorial is aimed at making the user familiar with the main modeling functionalities, by means of a complete modeling session of a seismic event, the Mw 6.6 earthquake occurred near the city of Bam (Iran) on December 26th, 2003. The tutorial starts with the Image Subsampling of a displacement map, then the coseismic displacement is modeled via Non-Linear Inversion and Linear Inversion, to retrieve the position of the fault and its slip distribution. The latter is then used to calculate the CFF Stress Transfer induced by the earthquake on the fault itself; finally, the retrieved model is used in a Forward Modeling to generate the raster maps of predicted displacement, projected into the Line-Of-Sight.

Though this tutorial gets through the main modeling features, it does not involve all the technical and scientific modeling aspects. In most cases, only one of the possible processing configurations is presented: we strongly suggest the user to refer to the linked help pages for a complete description of all the available options.

We remark that modeling is, in general, a non-unique problem: different solutions can lead to comparable results, equally able to reproduce the observed data. Only the experience and an incisive data analysis can lead to realistic solutions.  

Tips and Notes are provided to improve the modeling strategy and/or highlight further software functionalities.

2. The Bam event data

This tutorial is based on the displacement map generated with a pair of SAR images acquired by the Envisat satellite from the European Space Agency. This map has been obtained with an interferometric processing carried out with the SARscape interferometric module; the images have been acquired on December 3rd, 2003 and February 11th, 2004 and have a spatial baseline of about 4 m. In this tutorial the displacement is modeled with a single fault with distributed slip.

Refer to the cited literature (Wang et al., 2004; Funning et al, 2005) for a review of the event.

REFER TO YOUR LOCAL DISTRIBUTOR TO GET THE DATA FOR THIS TUTORIAL.

To run the tutorial, you need the following files:

•Bam_envisat_dsc_disp: displacement map (m) obtained from a descending Envisat image pair;

•Bam_envisat_dsc_ALOS: map of the Line-Of-Sight azimuth angle (deg);

•Bam_envisat_dsc_ILOS: map of the Line-Of-Sight incident angle (deg);

•Bam_SRTM_dem: SRTM digital elevation model with 90 m resolution;

•Bam_project_backup.xml: XML Project File (see next paragraph);

•Subsampling_areas.shp: shapefile containing the areas to sample the displacement map.

All the images are in a UTM-WGS84, Zone 40 North, projection.

3. The XML Project File

The main modeling panels requires the setting of an XML Project File. This file allows to save the input configuration of any processing for a quick restore in any moment. Most of the processing outputs are stored in the XML Project File as well, allowing an efficient project portability.

In this tutorial, an XML Project File created from scratch and named Bam_project.xml will be used. Though a project file with all the sections already set is provided with the tutorial data (Bam_project_backup.xml), we suggest the use of a new one to get confident with its use.

4. Image subsampling

Since modeling is predomintaly carried out with vector data, Image Subsampling is a mandatory task to create a vector dataset of values sampled from the InSAR displacement maps.This can be due in two ways: by sampling the image over regularly spaced points in manually defined areas (mesh from vector file) or with the Quadtree algorithm. In this tutorial we use the first approach, which needs the definition of the areas and their sampling resolution by means of a shapefile. This file is provided with the input data (Subsampling_areas.shp) where two areas with density 500 m and 2000 m, close and far from the  fault, respectively, are already set (Fig. 1).

Figure 1. Sampling areas with resolution values (left) and resulting points (right)

Once the file with the sampling areas is available:

1.Open the Image Subsampling panel;

2.Set the following files:

•“Subsampling Image”: Bam_envisat_dsc_disp

•“Azimuth LOS image”: Bam_envisat_dsc_ALOS

•“Incidence LOS image”: Bam_envisat_dsc_ILOS

•“DEM”: Bam_SRTM_dem

3.Set Mesh from vector file as “Subsampling method”

4.Set in “Vector File” the Subsampling_areas.shp file (or a newly created one)

5.Set in “Output Shapefile” the Bam_sampled_points.shp name

6.Click “Start” and wait for the “END” message.

By using the Subsampling_areas.shp as it is provided with the tutorial data, the Bam_sampled_points.shp will contain 7448 points (Fig. 2) with the related attributes. This shapefile of points represents, in the modeling tools, an InSAR dataset.

Figure 2. Subsampled points and relative attributes

5. Non-Linear Inversion

With the Non-Linear Inversion we want to reproduce the observed displacement by means of a geophysical source, assuming that nothing is known about the source and all its parameters must be inferred from the InSAR dataset just created. In this tutorial we model the data with a single fault (see Elastic Dislocation), but we invert also a further parameter, accounting for a possible offset that could affect the data; this is advisable when the reference point in the interferogram could have been set in a deforming area.

In the Non-Linear Inversion the use of the XML Project File is mandatory and must be set:

1.Open the "Non-Linear and Linear Inversion” panel;

2.Select the “Non-Linear” tab;

3.Set the “XML Project File” to Bam_project.xml.

Dataset setting

The InSAR dataset created with the displacement map subsampling is added as follows:

1.Click on the “Add…” button in the “Dataset(s)” list and select the Bam_sampled_points.shp;

2.Open the Parameter setting panel through the “Edit…” button;

3.Flag the “Invert for orbital surface” (default option);

4.Set 0 as “Polynomial degree”;

5.Click on “Commit”.

By setting 0 as polynomial degree, you let the inversion to assess also a possible offset that may affect the data.

Source setting

In this tutorial we assume that all the source parameters are unknown; however, we must set, for each parameters, a range of allowed values between a minimum and a maximum. Since the Elastic Dislocation source is characterized by an high number of parameters, we developed a specific tool to initialize the source based on the Global Centroid Moment Tensor on-line catalogue. This tool only needs the CMT event identifier, which can be preliminarily retrieved as follows:

1.Open the http://www.globalcmt.org/CMTsearch.html site;

2.Set the following parameterse:

·Starting Date - Year: 2003

·Starting Date - Month: 12

·Starting Date - Day: 26

·Ending Date - Number of days: 1

·Moment magnitude range with 6 <= Mw <= 7

3.Click on “Done”;

4.Two events should fit this constraints: we will use the identifier of the “SOUTHERN IRAN” event (122603B).

Once the CMT event identifier is known, you can initialize the source to invert:

1.In the Non-Linear Inversion panel, click on the “New…” button from the “Source(s)” list;

2.Select Elastic dislocation (Okada) from the pull down menu;

3.Click on the "Initialize from CMT solution…" button to open the Initialize Values from CMT Catalogue panel;

4.Set the event identifier (122603B) in the “Insert the CMT identifier” field and click the “Search” button (it could take a while to get the result);

5.From the pull down menu select “Plane 1” then click “Commit”;

6.Set “Bam_fault” as “Source name”, then click “Commit” to return to the main  panel;

7.Click on the “Start” button to run the inversion;

8.Click “Yes” to the “XML Project File updated” dialog box;

9.Wait until the “END” message (it could take few minutes);

10.Click “No” to the “Focal Mechanism” dialog box

Figure 3. Source parameters automatically initialized with the CMT solution

When the Non-Linear Inversion ends, the Bam_project.xml file is updated with the results: inverted model parameters, InSAR data offset, RMS of the residuals between observed and modeled data, geodetic moment, moment magnitude, etc… All the information are written in the “ModelingRoot”-”NonLinearInversion”-”NLOutput” section.

Here we show the result obtained with the source initialized as in Fig. 3. If the flags “Generate output shapefile” in the Inversion Settings (accessible through the “Inversion settings…” button in the inversion panel) are set, the following files have also been created:

•Bam_fault_nonlinear.shp, with the best fit source and its parameters as attributes;

•Bam_sampled_points_nonlinear.shp, containing the observed and modeled data (see the output attributes after the inversion for the InSAR dataset).

Figure 4. Modeled points, fault parameters and other general parameters after the Non-Linear Inversion automatically initialized with the CMT values.

The results of Fig. 4 show that the source automatic initialization with CMT values has already led to reasonable results. However further improvements of the Non-Linear Inversion are still possible.

In Fig. 4 the "Dip" reached the upper limit (79°), and this indicates that higher values could be preferred. In fact, the "Strike" and "Dip" ranges only allow to explore westward dipping faults, while the deformation pattern suggests an eastward dipping plane (see Fig. 1). Therefore we run again the Non-Linear Inversion with modified “Strike” and “Dip” ranges, as shown in Fig. 5 (see the Elastic Dislocation source for "Strike" and "Dip" angle conventions). To set the new ranges click on the “Edit…” button under on the “Source(s)” list.

Figure 5. Modified ranges (in red) for the second inversion with a eastward dipping source

After editing the ranges, run again the Non-Linear Inversion and check that all the parameters now fall within the ranges. You can also navigate through the “NLOutput” section of the Bam_project.xml file to verify that the RMS of the residuals is slightly lower than before, showing that this second solution better reproduces the observed data.

Figure 6. Modeled points, fault parameters and other general parameters after the Non-Linear Inversion with revised ranges for "Strike" and "Dip".

6. Linear inversion

With the Non-Linear Inversion a mean source with a mean and unique slip value of 1.44 m has been inferred (Fig. 6). With the Linear Inversion we retrieve a more realistic slip distribution over the fault plane by means of a Elastic dislocation model. Before the inversion parameter setting, the XML Project File must be specified:

1.Open the “Non-Linear and Linear Inversion” panel;

2.Select the “Linear” tab;

3.Set the “XML Project File” to Bam_project.xml.

Dataset setting

The InSAR dataset to invert is loaded as in the Non-Linear Inversion (just make sure you switched to the “Linear Inversion” tab in the panel):

1.Click on the “Add…” button in the “Dataset(s)” list and select the Bam_sampled_points.shp;

2.Open the Parameter setting panel through the “Edit…” button;

3.Flag the “Invert for orbital surface” (default option);

4.Set 0 as “Polynomial degree”;

5.Click on “Commit”.

Source setting

The starting point of the Linear Inversion, in this tutorial, is the source calculated through the Non-Linear Inversion: instead of creating a new source from scratch with the “New…” button, we load the Non-Linear Inversion results. This can be done in two ways: loading the Bam_fault_nonlinear.shp (created after the inversion) through the “Add from file…” button or retrieving the plane parameters with the “Load from XML…” button, which allow to explore the content of any XML Project File.

To extract the source from the XML Project File:

1.Click on the “Load from XML…” button under the “Source(s)” list;

2.Select the Bam_project.xml file;

3.In the XML section, select “Non-Linear Inversion - Output”;

4.Select, from the “Bam_fault [Elastic dislocastion (Okada)]” item;

5.Click “Commit”.

Figure 7. Fault from Non-Linear Inversion (gray rectangle) extended and subdivided into 30x15 patches; blue points represent the observed displacement in the Line-Of-Sight.  

The source retrieved from the Non-Linear Inversion is added to the “Source(s)” list with the flag “*** CHECK PARAMETERS ***”, notifying that more information must be provided before running the inversion. To complete the source setup and change the source dimension:

1.Select the source in the “Source(s)” list and click the “Edit…” button;

2.Change the “Point reference” to 4;

3.Set the “Length (m)” field to “30000.”;

4.Set the “Width (m)” field to “15000.”;

5.Set the “Depth (m)” field to “0.”;

6.Set “Fixed rake” as Inversion Type;

7.Set the “PATCHES ALONG STRIKE” field to “30” and “PATCHES ALONG DIP” field to “15”;

8.Set the “Damping value” to 0.05

9.Only for ENVI 5.0 or higher, click the “Draw Source in ENVI 5.x” button to see the source in the ENVI view (a reference layer must be already present);

10.Click the “Commit” button;

11.Click on "Start" to run the inversion;

12.Answer “No” to the “Focal Mechanism” dialog box after the inversion ends.

In the Linear Inversion we extended the initial fault to a 30x15 km source, subdivided into patches of 1 km. After clicking on the “Start” button, the Bam_project.xml file is updated: the ”LinInput” and ”LinOptions” sections in “ModelingRoot”-”LinearInversion” are immediately created (or updated), while the "LinOutput" section is added at the processing end. The results of the Linear Inversion are shown in Fig. 8.

Figure 8. Modeled points, slip distribution and other parameters after Linear Inversion

If the flags “Generate output shapfile” in the Inversion Settings (accessible through the “Inversion settings…” button in the inversion panel) are set, the following files have been created:

•Bam_fault_linear.shp: containing the best fit source and its parameters;

•Bam_sampled_points_linear.shp: containing the observed and modeled data (see the output attributes after the inversion for the InSAR dataset)

7. Moment Tensor and “beach ball” calculation

The Calculate and Draw Focal Mechanism panel can be used to calculate the seismic moment, to moment tensor and to draw the beach ball of the focal mechanism. This can be accomplished with a new source created from scratch or loading an existing source from a shapefile or an XML Project File. In this tutorial, we load the results of the Linear Inversion from the Bam_project.xml file:

1.Open the Calculate and Draw Focal Mechanism panel;

2.Click on the “Add from XML…” button;

3.Select the Bam_project.xml file;

4.Form the “XML section” pull down menu, select “Linear Inversion – Output”;

5.Select in the source list the “Bam_fault [Fault patches(Okada)]” item and click “Commit”;

6.In the main panel, select the source just loaded and click “Start” (Fig. 9).

Figure 9. Moment tensor and focal mechanism for the modeled source of the Bam earthquake

8. CFF Stress Transfer

This tool can be used to calculate the stress change induced by one or more sources onto other sources acting as receivers. In the case of Bam, where only one source is involved, we calculate the stress change induced by the fault on the slipped plane itself.

This task requires the setting of the XML Project File:

1.Open the CFF Stress Transfer panel;

2.Set the “XML Project File” to Bam_project.xml.

The input and receiver sources are retrieved, as in previous tasks, from the Bam_project.xml file itself:

1.Click on the “Add from XML…” button under the “INPUT SOURCE(S)” list;

2.Select the Bam_project.xml file;

3.From the “XML section” pull down menu, select “Linear Inversion – Output”;

4.Select in the source list the Bam fault item and click “Commit”;

5.Click on the “Add from XML…” button under the “RECEIVER SOURCE(S)” list;

6.Repeat the steps from 2 to 4;

7.Set the flag "Automatically create output Shapefiles";

8.Click on the “Start” button in the main panel and wait for the “END” message.

After the processing, the output source, i.e. the receiver with the CFF values, can be loaded into a GIS, as in Fig. 10.

Figure 10. Stress change induced by the slip of Fig. 8, over the Bam fault itself.

9. Forward Modeling

In this step, we use the source obtained via Linear Inversion to calculate the surface displacement in the East, North and Up directions. Forward Modeling can be carried out over a set of points, stored in a shapefile, or creating three raster files containing the East, North and Up components. In this tutorial we create a raster output, using the Bam_envisat_dsc_disp (the original displacement map from the interferometric processing) as reference to set the output extent and resolution. The latter is reduced from 25 m to 250 m to speed up the processing.

This task requires the setting of the XML Project File:

1.Open the Forward Modeling panel;

2.Set the “XML Project File” to Bam_project.xml.

To create the raster maps of the surface displacement:

1.Click on the “Add from XML…” button under the “INPUT SOURCE(S)” list;

2.Select the Bam_project.xml file;

3.From the “XML section” pull down menu, select “Linear Inversion – Output”;

4.Select in the source list the “Bam_fault [Fault patches(Okada)]” item and click “Commit”;

5.In the “Forward Model Output” pull down menu, select “Raster”;

6.Click on “Get from image…” and select the Bam_envisat_dsc_disp file;

7.Change, if necessary, the “Output File” name and the path automatically created;

8.Check on the “Set raster info…” button;

9.Change to 250 the “Cell size”;

10.Click on the “Cartographic System” button and set the following parameters:

•“State”: UTM-GLOBAL

•“Hemisphere”: NORTH

•“Projection”: UTM

•“Zone”: 40

•“Ellipsoid”: WGS84

11.Click on “Commit” to close the “Set cartographic system” panel;

12.Click on “Commit” to close the “Raster Parameters”;

13.Click on “Start” and wait for the “END” message.

Unless you changed the output name, automatically generated, the processing will create the following files (Fig. 11):

•Bam_envisat_dsc_disp_forward_east: with the displacement East component;

•Bam_envisat_dsc_disp_forward_north: with the displacement North component;

•Bam_envisat_dsc_disp_forward_up: with the displacement Up component.

After Forward Modeling, the Bam_project.xml file is automatically updated with the section “ModelingRoot”-“ForwardModeling”. You can navigate through the XML tags to inspect its content.

Figure 11. East, North and Up components of the displacement generated by the slip distribution retrieved via Linear Inversion.

10. Projection into the Line-Of-Sight

In the last step, the three maps resulting from Forward Modeling are combined together and projected into the direction of a specific Line-Of-Sight. This panel just needs the three raster maps and the ALOS (Azimuth Line-Of-Sight) and the ILOS (Incidence Line-Of-Sight) images.

To run the LOS projection:

1.Open the Project raster to LOS panel;

2.Set the following files:

•“East component”: Bam_envisat_dsc_disp_forward_east

•“North component”: Bam_envisat_dsc_disp_forward_north

•“Up component”: Bam_envisat_dsc_disp_forward_up

•“Azimuth LOS image”: Bam_envisat_dsc_ALOS

•“Incidence LOS image”: Bam_envisat_dsc_ILOS

3.Set the “Output image” to Bam_envisat_dsc_disp_forward_los;

4.Set the “Raster extent” to “Same as the ALOS/ILOS components”;

5.Set the “Raster resolution” to “Same as the ALOS/ILOS components”;

6.Click on the “Start” button and wait for the “END” message.

After that, you can compare the Forward Modeling results projected into the LOS with the original displacement map, as in Fig. 12.

Figure 12. Comparison between the observed (left) and the modelled (right) displacement maps in the Line-Of-Sight

In this case, we calculated in the Linear Inversion an offset of 0.017 m (see Fig. 8); this value must be added to the modeled displacement of Fig. 12 (right) to obtain the complete modeled displacement.

11. References

Funning, G.J., B. Parsons, T.J. Wright, J.A. Jackson and Fielding, E. J. (2005), Surface displacements and source parameters of the 2003 Bam (Iran) earthquake from Envisat advanced synthetic aperture radar imagery, J. Geophys. Res., 110, B09406, doi:10.1029/2004JB003338.

Wang, R., Xia, Y., Grosser, H., Wetzel, H.-U., Kaufmann, H. and Zschau, J. (2004), The 2003 Bam (SE Iran) earthquake: precise source parameters from satellite radar interferometr, Geophy. J. Int., 159: 917–922. doi: 10.1111/j.1365-246X.2004.02476.x

 

© sarmap, January 2013