MCTomo

3D Monte Carlo tomography package using reversible jump McMC method and 3D Voronoi tessellation.

Authors:

• Xin Zhang x.zhang2@ed.ac.uk
• Andrew Curtis

Requirements

• A C compiler that supports C++11 and a Fortran compiler which supports Fortran 2003.

• CGAL 4.8 or later ( for 3d delaunay and Voronoi support) CGAL can be downloaded from (http://www.cgal.org/) and can be built and installed following [CGAL installation manual] (http://doc.cgal.org/latest/Manual/installation.html).

If you are using MAC OS X, CGAL can be installed by following way:

 sudo port install cgal

On debian/Ubuntu,

 sudo apt-get install libcgal-dev

• NetCDF4 or later ( support for storaging the samples in a protable way ). If you do not have a netcdf4 library, you can install it through a package management program, such as rpm, yum, homebrew, macports, adept, and others. Alternatively, you can download it from (http://www.unidata.ucar.edu/software/netcdf/docs/getting_and_building_netcdf.html). This is not necessary. If you do not want to use netcdf4 library, just leave the NETCDF variable undefined in the makefile.

Algorithms and Dependencies

Normal Modes

• The surface wave modal approximation code is from COMPUTER PROGRAM IN SEISMOLOGY wrote by Herrmann, R.B. (http://www.eas.slu.edu/eqc/eqccps.html).

Fast Marching

• The code used the fast marching method to calculate the first arrival times. The 2D fast marching code is from Nick Rawlinson (http://rses.anu.edu.au/seismology/soft/fmmcode/). For the 3D body wave tomography, we used a general N-dimensional fast marching code by Gomez, J.V. and Pardeiro, J. (https://github.com/jvgomez/fast_methods). Both of them are revised for our usage.

3D Voronoi

• The 3D Voronoi tessellation is calculated based on CGAL (see above). However, we still used the KD-tree method to convert the Voronoi diagram to a regular grid based representation (https://github.com/jmhodges/kdtree2).

Compilation

• Add your cgal include path (e.g. MYCGAL/include) and link path in the src/makefile

• If available and necessary, add your netcdf include path and link path in the src/makefile

• Then in the src directory

  make
  

Examples

Examples are in the examples directory

References

Zhang, X., Curtis, A., Galetti, E., & de Ridder, S., 2018. 3-D Monte Carlo surface wave tomography, Geophysical Journal International, 215(3), 1644–1658.

Zhang, X., Hansteen, F., Curtis, A., & de Ridder, S., 2020. 1D, 2D and 3D Monte Carlo ambient noise tomography using a dense passive seismic array installed on the North Sea seabed, Journal of Geophysical Research: Solid Earth, 125, e2019JB018552.

Zhang, X., Roy, C., Curtis, A., Nowacki, A., & Baptie, B., 2020. Imaging the subsurface using induced seismicity and ambient noise: 3D Tomographic Monte Carlo joint inversion of earthquake body wave travel times and ambient noise surface wave dispersion, Geophysical Journal International.