Dataset and Software for The Relationships Between Large-scale Variations in Shear Velocity, Density, and Compressional Velocity in the Earth's Mantle

<p><strong>Is there a chemically distinct reservoir in the Earth?</strong><br><strong>Do superplumes overly denser-than-average material?</strong><br><strong>Can we detect these anomalies with seismic data?</strong><br><strong>Can we evaluate statistical significance of the features in tomography?</strong></p><p>This study presents the <strong>strongest evidence</strong> to date (ca. 2015) of <strong>large-scale thermo-chemical heterogeneities in the lowermost mantle</strong> 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.</p><p><strong>Note on Odd Degree Structure:</strong></p><p>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&nbsp;in the remaining&nbsp;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, <strong>odd-degree density variations in the lowermost mantle&nbsp;are poorly constrained in this study and should not be interpreted</strong>. We therefore used even-degree variations up to degree 6 for our inferences on&nbsp;thermo-chemical variations in the lowermost mantle (Figure 14), and provide those values in the files below.</p><p><strong>Feedback/Questions?</strong> Please contact Raj Moulik (<a href="https://rajmoulik.com">rajmoulik.com</a>) at <a href="mailto:moulik@caa.columbia.edu?subject=Query%20from%20Zenodo">moulik@caa.columbia.edu</a>&nbsp;</p><p><strong>Reference:</strong></p><p><i>Please cite the following work if you use this data or software.</i></p><ul><li>Moulik, P. &amp; Ekström, G., 2016. The relationships between large-scale variations in shear velocity, density and compressional velocity in the Earth's mantle,&nbsp;<i>J. Geophys. Res.</i>,&nbsp;<strong>121</strong>, doi:&nbsp;<a href="http://dx.doi.org/10.1002/2015JB012679">10.1002/2015JB012679</a>.&nbsp;<a href="https://rajmoulik.com/Publications/MoulikEkstrom_JGR2016.pdf"><i>pdf</i></a></li></ul><p><i>You can also cite the dataset and software&nbsp;from this Zenodo page (Optional).</i></p><p>Moulik, P. &amp; 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:&nbsp;<a href="https://doi.org/10.5281/zenodo.8356540">10.5281/zenodo.8356540</a></p><p><strong>Data Products:</strong></p><ul><li><strong>ME16_Figures(</strong><a href="https://zenodo.org/api/files/9aa99409-20ae-495e-b5a3-288fd57ecaeb/ME16_Figures.tar.gz"><strong>.tar.gz</strong></a><strong>&nbsp;or&nbsp;</strong><a href="https://zenodo.org/api/files/9aa99409-20ae-495e-b5a3-288fd57ecaeb/ME16_Figures.pdf"><strong>.pdf</strong></a><strong>)</strong>&nbsp;- contains all figures from the paper in .png format</li><li><a href="https://zenodo.org/api/files/9aa99409-20ae-495e-b5a3-288fd57ecaeb/ME16"><strong>ME16</strong></a><strong>&nbsp;-&nbsp;</strong>Coefficients of the spline basis functions for each parameter. Refer cij&nbsp;in equation 3.&nbsp; 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.&nbsp;0S2). Radial anisotropy is confined to the uppermost mantle (that is, since the anisotropy is parameterized with only the four uppermost&nbsp;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).</li><li><a href="https://zenodo.org/api/files/9aa99409-20ae-495e-b5a3-288fd57ecaeb/STW105"><strong>STW105</strong></a>&nbsp;- reference model used in ME16. Described in Kustowski et al. (2008)</li><li><a href="https://zenodo.org/api/files/9aa99409-20ae-495e-b5a3-288fd57ecaeb/setup.cfg"><strong>setup.cfg</strong></a><strong>&nbsp;-&nbsp; </strong>Some configuration metadata relevant to this model for reproducibility.</li><li><a href="https://zenodo.org/api/files/9aa99409-20ae-495e-b5a3-288fd57ecaeb/epix.tar.gz"><strong>epix.tar.gz</strong></a>&nbsp;- Perturbations in horizontally (<i>vsh</i>) and vertically polarized shear velocity (<i>vsv</i>), Voigt-average isotropic shear-wave (<i>vs</i>) and compressional-wave velocity (<i>vp</i>), density (<i>rho</i>). anisotropy (<i>as</i>) and topography of the internal boundaries. This is calculated from the spline coefficients at&nbsp;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 (<i>rho_even6)</i>&nbsp;and isotropic shear-wave&nbsp;velocity (<i>vs_even6</i>), which should be used for density inferences on thermochemical structure (See note above).</li><li><a href="https://zenodo.org/api/files/9aa99409-20ae-495e-b5a3-288fd57ecaeb/ME16.BOX25km_PIX1X1.avni.nc4"><strong>ME16.BOX25km_PIX1X1.avni.nc4</strong></a>&nbsp;-&nbsp; 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&nbsp;Voigt-averaged shear velocity&nbsp;perturbations at the bottom of the mantle (2875-2891 km depth)<ul><li><i>import xarray as xr</i></li><li><i>ds = xr.open_dataset('ME16.BOX25km_PIX1X1.avni.nc4')</i></li><li><i>ds['vs_even6'][-1].plot()</i></li></ul></li><li><a href="https://zenodo.org/api/files/9aa99409-20ae-495e-b5a3-288fd57ecaeb/PROGRAMS.tar.gz"><strong>PROGRAMS.tar.gz</strong></a>&nbsp;- Fortran tools for obtaining model values at specific locations. After creating the executables from source code in the&nbsp;<i>src</i>&nbsp;folder, the&nbsp;<i>readme</i>&nbsp;script generates most of&nbsp;the epix files provided in&nbsp;epix.tar.gz above<strong>.</strong></li><li><a href="https://zenodo.org/api/files/9aa99409-20ae-495e-b5a3-288fd57ecaeb/profilescaling.txt"><strong>profilescaling.txt</strong></a>&nbsp;- contains the median scaling ratios as used in Figure 15(a).</li><li><a href="https://zenodo.org/api/files/9aa99409-20ae-495e-b5a3-288fd57ecaeb/scaling3D_MoulikJGR16.tar.gz"><strong>scaling3D_MoulikJGR16.tar.gz</strong></a>&nbsp;- contains the scaling ratios and poisson ratio calculated from the joint model, as used in Figure 15(b).</li></ul>