Radial Anisotropy: Flow in the mantle

An anisotropic shear velocity model of the Earth’s mantle using normal modes, body waves, surface waves and long-period waveforms

What is the nature of flow in the mantle?
How fast do waves travel anywhere on Earth?
Where can radial anisotropy be robustly detected?
Can we reconcile a broad spectrum of seismic data? What are the benefits?

We use normal-mode splitting functions in addition to surface-wave phase anomalies, body-wave travel times and long-period waveforms to construct a three-dimensional model of anisotropic shear-wave velocity in the Earth's mantle. This is the first tomographic study to exploit the sensitivity of mode-splitting data to constrain radial anisotropy in the Earth's mantle jointly with several other types of data. Our modeling approach inverts for mantle velocity and anisotropy as well as transition-zone discontinuity topographies, and incorporates new crustal corrections for the splitting functions that are consistent with the nonlinear corrections we employ for the waveforms. Our preferred anisotropic model, S362ANI+M, is an update to the earlier model S362ANI, which did not include normal-mode splitting functions in its derivation.

Zenodo Repository

All the data and software can be downloaded from our Open Access Zenodo repository.


Please mail your inquiries to Raj Moulik (rajmoulik.com) at [email protected] 


[I] We develop a new method to invert jointly four distinct types of seismic data for anisotropic shear velocities and discontinuity topographies in the Earth's mantle while accounting accurately for the crustal structure.
[II] We show that the mode-splitting data require strong isotropic vS heterogeneity in the transition zone and changes to the southern hemisphere in the mid to lower mantle.
[III] We report the improved consistency between recent studies on the long-wavelength isotropic structure, especially in the transition zone and the lower mantle.
[IV] We show that the datasets used in this study, especially the mode-splitting data, do not require radial anisotropy in the deep mantle.
[V] We demonstrate that the mode-splitting data suppress spurious anisotropic anomalies in the mid mantle and reduce even-degree tradeoffs between anisotropic and isotropic variations in the lowermost mantle.


Please cite the following work if you use this data or software.

  • Moulik, P. & Ekström, G., 2014. An anisotropic shear velocity model of the Earth's mantle using normal modes, body waves, surface waves and long-period waveforms, Geophys. J. Int.199(3), 1713-1738, doi: 10.1093/gji/ggu356pdf

You can also cite the dataset and software from this Zenodo page (Optional).

  • Moulik, P. & Ekström, G., 2014. Dataset and Software for An anisotropic shear velocity model of the Earth's mantle using normal modes, body waves, surface waves and long-period waveforms. In Geophys. J. Int. (v1.0, Vol. 199, pp. 1713–1738). Zenodo. doi: 10.5281/zenodo.8357379

Download data products:

All the following data and software can be downloaded from our Zenodo repository.

  • S362ANIplusM_Figures.tar.gz - contains all figures from the paper in .png format
  • S362ANI+M_MapViewsCrossSections.pdf - Some cross sections and map views at various depths in the mantle
  • S362ANI+MCoefficients of the spline basis functions for each parameter. Refer cij in equation 11.  This is our preferred global model of shear-wave velocity. In this model, radial anisotropy is confined to the uppermost mantle (that is, since the anisotropy is parameterized with only the four uppermost splines, it becomes very small below a depth of 250 km, and vanishes at 410 km). This is an updated version of S362ANI (Kustowski et al., 2008) which did not include normal modes in its derivation. Please note the stronger isotropic shear velocity anomalies in the transition zone.
  • STW105 - reference model used in S362ANI+M. Described in Kustowski et al. (2008)
  • setup.cfg -  Some configuration metadata relevant to this model for reproducibility.
  • epix.tar.gz - Perturbations in horizontally (vsh) and vertically polarized shear velocity (vsv), Voigt-average isotropic velocity (vs), ansotropy (as) and topography of the internal boundaries. This is calculated from the spline coefficients at every 1 by 1 degree cell-centered pixel and at every ~25 km depth region from Moho to the core-mantle boundary and stored in extended pixel format (.epix) ASCII files. 
  • S362ANI+M.BOX25km_PIX1X1.avni.nc4 -  The perturbations in a standard AVNI format that utilizes the NETCDF4 container format. This file can be read in Python using either xarray or AVNI libraries. For example, to plot vs perturbations at 24.4-50 km depth range
    • import xarray as xr
    • ds = xr.open_dataset('S362ANI+M.BOX25km_PIX1X1.avni.nc4')
    • ds.vs[0].plot()
  • Fortran Code
    • readme - contains a description of all files in the folder below
    • PROGRAMS.tar.gz - tools for obtaining model values at specific locations and some GMT plotting tools
  • GRD.tar.gz - longitude-latitide-velocity files with vsh, vsv, and Voigt average in km/s evaluated on a grid of points at many depths in the mantle