MATLAB functions for visualization and modeling of shear wave splitting observations:

• Optimized for the output of SplitLab (Wüstefeld et al. 2008) and StackSplit (Grund 2017).
• The modeling routine is applicable for the energy minimization method (Silver & Chan 1991).
• Extended and strongly modified from sws_tools by Michael Grund.

If you make use of this material, please acknowledge the relating publications in which framework these functions were implemented:

• Ritter, Joachim R. R., Fröhlich, Yvonne, Sanz Alonso, Yasmin & Grund, Michael (2022). Short-scale laterally varying SK(K)S shear wave splitting at BFO, Germany – implications for the determination of anisotropic structures. Journal of Seismology, 26, 1137-1156. https://doi.org/10.1007/s10950-022-10112-w.
• Grund, Michael & Ritter, Joachim R. R. (2020). Shear-wave splitting beneath Fennoscandia – evidence for dipping structures and laterally varying multilayer anisotropy. Geophysical Journal International, 223, 1525-1547. https://doi.org/10.1093/gji/ggaa388.
• Grund, Michael (2019). Exploring geodynamics at different depths with shear wave splitting. Dissertation, Karlsruhe Institute of Technology (KIT). https://doi.org/10.5445/IR/1000091425.

Furthermore you can cite the Zenodo DOI given above.

How to use: Header of function SWS_Analysis_BASICS_stereoplot.m

• Plot single-event analysis results (output of SplitLab)
  • Rotation-correlation method (Bowman & Ando 1987)
  • Energy minimization method (Silver & Chan 1991)
  • Eigenvalue method (Silver & Chan 1991)
• Plot multi-event analysis results (output of StackSplit)
  • Stacking of error surfaces (STACK; Wolfe & Silver 1998, Restivo & Helffrich 1999)
  • Splits of simultaneous inversion of multiple waveforms (SIMW; Roy et al. 2017)
• Color-code bars with respect to the fast polarization direction (see Requirements/Colormaps)
• Shade background or backazimuth sector

Example figures: Generated with the provided TEST_data_stereoplot

• Under development

How to use: README; header of function SWS_modeling_calc_misfit.m
Details: Supporting Information of Grund & Ritter (2020)

• Model types
  • Transverse isotropy
  • Structural anisotropy: one horizontal layer (H1), one dipping layer (T1), two horizontal layers (H2)
• Forward calculation
  • Synthetic splitting parameters based on the energy minimization method (Silver & Chan 1991)
  • Ray theory reference frame
• Observation (output of SplitLab and StackSplit)
  • Single-event analysis: energy minimization method (Silver & Chan 1991)
  • Multi-event analysis: stacking of error surfaces (STACK; Wolfe & Silver 1998, Restivo & Helffrich 1999), simultaneous inversion of multiple waveforms (SIMW; Roy et al. 2017)
• Comparison of forward calculation and observation
  • Calculation and minimizing the root mean square error regarding the splitting parameters
  • Joint fitting of fast polarization direction and delay time, separate fitting of the fast polarization direction
• Result visualization
  • Backazimuthal variation of the splitting parameters (forward calculation and observation)
  • Model type distribution (bar plot)
  • Model parameter distribution (scatter plot)
  • Stereoplot of synthetic splitting parameters (polar plot)
• Result data
  • Model parameters for each model type as separate *.txt files

Example figures: Generated with the provided TEST_data_modeling

Tested with: R2022a, R2021a,b under Linux and Windows

• MATLAB: Forward calculation
  • Deep Learning Toolbox
  • Mapping Toolbox
  • MATLAB Seismic Anisotropy Toolkit (MSAT) (Walker & Wookey 2012)
• Data: Shear wave splitting observations
  • Output *.txt files (nulls, splits) of SplitLab version 1.5.0 (Wüstefeld et al. 2008) or 1.2.1 (Porritt 2014)
  • Output *.mat structure and *.txt files (STACK, SIMW) of StackSplit (Grund 2017)
• Colormaps (optional): Color-coding of the fast polarization direction and the root mean square error
  • MatPlotLib Perceptually Uniform Colormaps
    version v2.1.3, MATLAB File Exchange, last access 2022 June 26
  • crameri perceptually uniform scientific colormaps
    version v1.09, MATLAB File Exchange, last access 2023 April 10; based on Crameri (2021)
  • cmocean perceptually-uniform colormaps
    version v2.02, MATLAB File Exchange, last access 2022 June 18; based on Thyng et al. (2016)

release	publication	Zenodo DOI
dev	reflects main branch
v1.0	related to Ritter, Fröhlich, Sanz Alonso & Grund (2022)

For details of the individual releases as well as for changes and differences compared to sws_tools by Michael Grund see the changelog.

• Modeling of multi-event analysis: Only using either STACK or SIMW results is supported
• Model parameter distribution for T1: Under development, not fully tested
• Synthetic stereoplot for T1 and H2: Backazimuths of predicted nulls are partly wrong
• Synthetic stereoplot for T1: Gray arrow is partly not exactly placed in the center

For bug reports, suggestions or recommendations feel free to open an issue or submit a pull request directly here on GitHub.

Bowman, J. R. & Ando, M. (1987). Shear-wave splitting in the upper-mantle wedge above the Tonga subduction zone. Geophysical Journal International, volume 88, issue 1, pages 25-41. https://doi.org/10.1111/j.1365-246X.1987.tb01367.x.

Crameri, F. (2021). Scientific colour maps, version 7.0.1. Zenodo. http://www.fabiocrameri.ch/colourmaps.php. https://zenodo.org/record/5501399.

Grund, M. (2017). StackSplit - a plugin for multi-event shear wave splitting analyses in SplitLab. Computers & Geosciences, volume 105, pages 43-50. https://doi.org/10.1016/j.cageo.2017.04.015. versions 1.0, 2.0, and 3.0 available at https://github.com/michaelgrund/stacksplit.

Grund, M. (2019). Exploring geodynamics at different depths with shear wave splitting. Dissertation, Karlsruhe Institute of Technology (KIT). https://doi.org/10.5445/IR/1000091425.

Grund, M. & Ritter, J. R. R. (2020). Shear-wave splitting beneath Fennoscandia – evidence for dipping structures and laterally varying multilayer anisotropy. Geophysical Journal International, volume 223, pages 1525-1547. https://doi.org/10.1093/gji/ggaa388.

Porritt, R. W. (2014). SplitLab version 1.2.1. available at https://robporritt.wordpress.com/software/.

Restivo, A. & Helffrich, G. (1999). Teleseismic shear wave splitting measurements in noisy environments. Geophysical Journal International, volume 137, pages 821-830. https://doi.org/10.1046/j.1365-246x.1999.00845.x.

Roy, C., Winter, A., Ritter, J. R. R. & Schweitzer, J. (2017). On the improvement of SKS splitting measurements by the Simultaneous Inversion of Multiple Waveforms (SIMW). Geophysical Journal International, volume 208, pages 1508-1523. https://doi.org/10.1093/gji/ggw470.

Silver, P. G. & Chan, W. W. (1991). Shear wave splitting and subcontinental mantle deformation. Journal of Geophysical Research, volume 96, issue B10, pages 16429-16454. https://doi.org/10.1029/91JB00899.

Thyng, K. M., Greene, C. A., Hetland, R. D., Zimmerle, H. M. & DiMarco, S. F. (2016). True colors of oceanography: Guidelines for effective and accurate colormap selection. Oceanography, volume 29, issue 3, pages 9-13. http://dx.doi.org/10.5670/oceanog.2016.66.

Walker, A. M. & Wookey, J. (2012). MSAT — A new toolkit for the analysis of elastic and seismic anisotropy. Computer & Geosciences, volume 49, pages 81-90. https://doi.org/10.1016/j.cageo.2012.05.031. available at https://www1.gly.bris.ac.uk/MSAT/, https://github.com/andreww/MSAT.

Wolfe, C. J. & Silver, P. G. (1998). Seismic anisotropy of oceanic upper mantle: Shear wave splitting methodologies and observations. Journal of Geophysical Research: Solid Earth, volume 103, issue B1, pages 749-771. https://doi.org/10.1029/97JB02023.

Wüstefeld, A., Bokelmann, G., Zaroli, C. & Barruol, G. (2008). SplitLab: A shear-wave splitting environment in Matlab. Computers & Geosciences, volume 34, issue 5, pages 515-528. https://doi.org/10.1016/j.cageo.2007.08.002. version 1.0.5 available at http://splitting.gm.univ-montp2.fr and version 1.9.0 available at https://github.com/IPGP/splitlab.