FMTOMO Summary

FMTOMO is a Fortran90 software package that has been designed for 3-D traveltime tomography. The forward problem of traveltime prediction is solved using a multi-stage fast marching method (FMM), which is a sophisticated grid-based eikonal solver. The inverse problem of adjusting model parameters to satisfy data observations and any imposed regularization is solved using a subspace scheme, which minimizes an objective function simultaneously along multiple search directions that together span a subspace of model space. The method is iterative non-linear in that the inversion step assumes local linearity, but repeated application of FMM and subspace inversion allows the non-linear relationship between velocity and traveltime perturbations to be reconciled.

Figure 1. Cross-section through a 3-D model which illustrates the types of structures and phases that can be dealt with by FMTOMO.

A very detailed 70 page instruction manual has been assembled to describe FMTOMO. You can download it as a PDF here:

instructions.pdf (2.8 MB)


  • Model structure is represented by subhorizontal layers in spherical coordinates. Within a layer, velocity is permitted to vary smoothly in all three dimensions. It is also possible to specify media that are described only by continuous velocity variations (i.e. no interfaces).
  • The geometry of layer boundaries may also vary, thus allowing a wide variety of structures to be represented (e.g. subducting slabs).
  • Phases comprising any number of reflection and refraction branches may be tracked, including P-S conversions.
  • Teleseismic phases may also be computed through a spherically symmetric reference model (ak135) to the edge of the 3-D model region, after which the FMM scheme is used to track the remaining propagation path.
  • Velocity and interface structure, as well as source location, may be separately or simultaneously constrained in the inversion.
  • A wide variety of datasets, including reflection, wide-angle, local earthquake and teleseismic may be used to constrain 3-D structure. Joint inversion of multiple datasets is also possible,
  • The use of spherical coordinates means that local regional and semi-global applications are possible (periodicity and degeneracy of the coordinate system at the poles are not accounted for).
  • GMT scripts are provided for plotting cross-sections through the output solution models.
  • Three worked examples are provided with the distribution to help understand how the package operates.


FMTOMO is written in Fortran90, and should run on most computers that have access to a fortran compiler such as gfortran. The complete source code, a detailed manual and example input files, can be downloaded here. Enquires should be directed to the author Nick Rawlinson. You will need to register with iEarth prior to download.

To unpack the contents of this file, type something like:

gunzip -c fmtomov1.0.tar.gz | tar xvof -

in an empty directory. A number of new sub-directories will be created. Instructions on how to use the code can be found in the sub-directory docs.


    Rawlinson, N., de Kool, M. and Sambridge, M., 2006. "Seismic wavefront tracking in 3-D heterogeneous media: applications with multiple data classes", Explor. Geophys., 37, 322-330.

    Rawlinson, N. and Urvoy, M., 2006. "Simultaneous inversion of active and passive source datasets for 3-D seismic structure with application to Tasmania", Geophys. Res. Lett., 33 L24313, doi:10.1029/2006GL028105.

    de Kool, M., Rawlinson, N. and Sambridge, M. 2006. "A practical grid based method for tracking multiple refraction and reflection phases in 3D heterogeneous media", Geophys. J. Int., 167, 253-270.