Joint Velocity-Density Model: Thermo-chemical Structure

The relationship between large scale variations in anisotropic shear velocity, density and compressional velocity in the Earth’s mantle

Is there a chemically distinct reservoir in the Earth?
Do superplumes overly denser-than-average material?
Can we detect these anomalies with seismic data?
Can we evaluate statistical significance of the features in tomography?

This study presents the strongest evidence till date (ca. 2015) of large-scale thermo-chemical heterogeneities in the lowermost mantle using the full spectrum of seismic data. A large data set of surface-wave phase anomalies, body-wave travel times, normal-mode splitting functions and long-period waveforms is used to investigate the scaling between shear velocity, density and compressional velocity in the Earth's mantle (ϱ=dln ρ/dln vS, ν=dln vS/dln vP). Our preferred joint model consists of denser-than-average anomalies (∼1% peak-to-peak) at the base of the mantle roughly coincident with the low-velocity superplumes. The relative variation of shear velocity, density and compressional velocity in our study disfavors a purely thermal contribution to heterogeneity in the lowermost mantle, with implications for the long-term stability and evolution of superplumes.

Zenodo Repository

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


Please mail your inquiries to Raj Moulik ( at [email protected] 


[I] New methodology to construct joint models with various levels of scaling complexity in order to detect seismological signatures of chemical heterogeneity
[II] The datasets considered cannot be fit concurrently with a uniform ν or a positive and uniform ϱ throughout the mantle (S362ANI+M was constructed assuming a uniform ν).
[III] Several features persist after the inclusion of new and larger data sets: anti-correlation between bulk-sound and shear velocities in the lowermost mantle as well as an increase in ν in the lower mantle.
[IV] Recent measurements 0S2 splitting, in particular, are largely incompatible with perfectly correlated vS-ρ structure.
[IV] A way to significantly improve the fits to various data sets is by allowing independent density perturbations in the lowermost mantle.

Note on Odd Degree Structure:

Since the self-coupled normal-mode splitting observations constrain only even-degree density variations, all inversions strongly disfavored even-degree vS-ρ correlation (R2 ~ –0.46 to –0.25) in the lowermost mantle, which also disfavors a purely thermal contribution to heterogeneity in this region. However, the starting assumptions on positive vS-ρ correlation persisted in the remaining regions and for odd degree variations. In viscosity inversions with the geoid, opposing sign of the correlation of the longest wavelength even-versus odd-degree structure maps into a region of reduced viscosity in the lower mantle (Rudolph et al., 2020, doi:10.1029/2020gc009335). While important for such dynamical implications, odd-degree density variations in the lowermost mantle are poorly constrained in this study and should not be interpreted. We therefore used even-degree variations up to degree 6 for our inferences on thermo-chemical variations in the lowermost mantle (Figure 14), and provide those values in the files below.


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

  • Moulik, P. & Ekström, G., 2016. The relationships between large-scale variations in shear velocity, density and compressional velocity in the Earth's mantle, J. Geophys. Res.121, doi: 10.1002/2015JB012679pdf

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

  • Moulik, P. & Ekström, G. (2016). Dataset and Software for The Relationships Between Large-scale Variations in Shear Velocity, Density, and Compressional Velocity in the Earth's Mantle. In J. Geophys. Res. Solid Earth (v1.0, Vol. 121, pp. 2737–2771). Zenodo. doi: 10.5281/zenodo.8356540

Download data products:

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

  • ME16_Figures(.tar.gz or .pdf) - contains all figures from the paper in .png format
  • ME16Coefficients of the spline basis functions for each parameter. Refer cij in equation 3.  This is our preferred global model of anisotropic elastic parameters and density. Density variations are allowed to deviate from a constant scaling with shear-velocity variations in the lowermost mantle, which is required to fit the longest-period normal modes (e.g. 0S2). 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+M (Moulik and Ekström, 2014) which did not solve independently for density and compressional-wave velocity variations and imposed a constant scaling throughout the mantle instead (ϱ=0, ν=1/0.55). 
  • STW105 - reference model used in ME16. 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 shear-wave (vs) and compressional-wave velocity (vp), density (rho). anisotropy (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. Even-degree variations up to degree 6 are provided for density (rho_even6) and isotropic shear-wave velocity (vs_even6), which should be used for density inferences on thermochemical structure (See note above).
  • ME16.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 even-degree variations up to degree 6 in Voigt-averaged shear velocity perturbations at the bottom of the mantle (2875-2891 km depth)
    • import xarray as xr
    • ds = xr.open_dataset('ME16.BOX25km_PIX1X1.avni.nc4')
    • ds['vs_even6'][-1].plot()
  • PROGRAMS.tar.gz - Fortran tools for obtaining model values at specific locations. After creating the executables from source code in the src folder, the readme script generates most of the epix files provided in epix.tar.gz above.
  • profilescaling.txt - contains the median scaling ratios as used in Figure 15(a).
  • scaling3D_MoulikJGR16.tar.gz - contains the scaling ratios and poisson ratio calculated from the joint model, as used in Figure 15(b).