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   Slabs on command
Is there convincing tomographic evidence for whole mantle convection?

Don L. Anderson

Seismological Laboratory, California Institute of Technology, Pasadena, CA 91125

dla@gps.caltech.edu


Click here to download a PowerPoint presentation illustrating this webpage


 

Abstract

The approach of visual inspection of selected tomographic cross-sections, coupled with the assumption that tomography is simply a mantle thermometer (red = hot, blue = cold), has great potential for misleading Earth scientists who are not seismologists, and even those who are, but are unfamiliar with the shortcomings of the particular experiment at issue. Geochemical and geodynamic interpretations that involve large-scale mass transfer through the entire thickness of the mantle are often based on simplistic and indefensible interpretations of a few brightly colored images that may have been specially selected to make the strongest case possible in support of plumes. Seismic experiments that give superior resolution in particular areas, i.e., high-frequency, high-resolution studies, reveal a much more complex mantle than tomography does–a mantle that is not well explained by simplistic, conventional models.

The controversy

Allegre (1997) states that it is increasingly accepted that the Earth’s mantle has a two-layer structure. This was based on the standard geochemical two-reservoir, two-layer assumption. Kamber & Collerson (1999) claim that growing geophysical and geochemical evidence continues to support the original “standard” two-layer model. This is based on the assumption that the upper mantle is homogenized by vigorous mantle convection and that if MORB is derived from the upper mantle, nothing else can be.

At the same time, van der Hilst et al. (1997 and elsewhere) state the view, which they describe as a consensus, that slabs of subducted lithosphere sink deep into the lower mantle. This contradicts the two-layer model. It is based on the visual impressions of a few dramatic color cross-sections and the assumption that “blue” (i.e., high seismic velocity) unambiguously represents cold, sinking, dense slabs. The implication is that present-day mantle convection is dominated by whole-mantle flow. Whole-mantle circulation schemes have subsequently become increasingly complex (e.g., Meyzen et al., 2007; Bercovici & Karato, 2003).

Tomography can give an imcomplete or misleading picture

Global tomography is a powerful but imperfect tool. The whole-mantle convection interpretation of tomography, although widely held, particularly in the isotope geochemistry and geodynamic communities, is nevertheless not a consensus view of seismologists. Travel-time tomography, used alone, is particularly limited:

  • Seismic ray coverage in the Earth is sparse and spotty. Many regions are devoid of rays. This lack of data cannot be remedied by using improved inversion theories. Any experiment, including seismic tomography, must deal with the limitations dictated by the distribution and quality of the available data, sampling theory, and trade-offs between diverse structures within the Earth (Spakman & Nolet, 1988).

    It is likely that the Earth possesses a substantial component in the null-space of any mix of data (e.g., Shapiro & Ritzwoller, 2004). This is also true for isotope data and box models. Methods are available to control the over-interpretation of sparse data, but these guarantee neither physical acceptability of the resulting model nor a model that resembles the real Earth. Simply put, if a region is not sampled by seismic waves, its structure cannot be retrieved by tomography or any other seismic experiment. This remains true despite published maps and cross sections that include these regions along with adjacent, well-sampled regions.

  • The visual appearance of displayed results can be radically changed by adjusting the color scheme (Figures 1-3) or reference model, smoothing, cropping, or carefully selecting cross-sections. The resulting images may be convincing but are in truth misleading (Spakman et al., 1989). Images that were not selected for publication may give a completely different impression.

  • The results depend crucially on the ray geometry, which is constrained by the geometry of the earthquakes and seismic stations (see Vasco et al., 1994 for maps of the coverage) and, to a lesser extent, by the details of the mathematical techniques employed (Spakman & Nolet, 1988; Spakman et al., 1989; Shapiro & Ritzwoller, 2004).

  • Presently existing algorithms and inversion methods cannot correct completely for various problems such as anisotropy, the finite frequency of the seismic waves used and earthquake source complexities.

  • Global tomographic models have poor resolution. Other studies involving, for example, high-frequency reflections, scattering, and coda waves, reveal a more complex picture of the mantle than is available from tomographic studies that use long-period waves and large-scale smoothing.

Figure 1. A slab on command! Line of section traverses Japan (from Ricard et al., 2005).

Figure 2. A plume on command. (A) from Bijwaard & Spakman (1999). Colour scale saturates at ±0.5% of the anomaly, which is only a tenth of the strengh of the upper mantle low-velocity anomaly. (B) same model is replotted with a colour scale that saturates only at the strongest upper-mantle anomalies, and a longer line of section, which reveals a similar, even more plume-like body, beneath Hudson Bay.

 

Figure 3. Cross sections through Japan showing shallow-bottoming slabs. Other authors have used a different color scheme but similar seismic models to “prove” deep slab penetration (from Fukao et al., 2001).

Color 2D cross-sections are particularly unreliable for giving a correct impression of the results of a tomographic study. Although vivid and impressive to nonspecialists, they are not the overwhelming, compelling and convincing evidence that they are commonly presented as being. A few cross sections cannot adequately express the information content of a typical 3D tomographic study. A filtered, smoothed, essentially three-color cross-section has two orders of magnitude less information than the original model, which in turn utilizes only about 1% of the information content of the seismic waves used (i.e., their arrival times at stations). In view of this it is astonishing that sweeping conclusions have been drawn based on visual inspection of single selected slices through models.

Seismic velocity is not a thermometer

Seismic velocity depends on:

  • Phase (i.e., the presence or absence of partial melt),
  • Composition (lithology, mineralogy and chemistry), and
  • Temperature.

There is a fundamental ambiguity problem in the interpretation of seismic velocities, including tomographic images, because the effects of these three factors are not easily separated out. Of the three, the presence of partial melt has the strongest effect on seismic velocities and temperature the weakest.

Nevertheless, tomographic images are often interpreted assuming that a simple velocity–density–temperature correlation exists. High velocity (blue) is generally attributed to cold, dense, sinking material, and low velocity (red) as hot, low-density, rising material (Figures 4 & 5). This is unsafe.

Figure 4. The large, red, 2000-km-wide feature extends from the southern hemisphere under the Shona and Bouvet volcanic regions up to the Afar region at the surface, some 7000 km distant. It has been assumed to be a continuous hot feature that penetrates the whole mantle, and dubbed a "superplume" (from Ritsema, 2005).

Figure 5. The red tomographic feature under Africa has been interpreted as a hot rising plume but it could be a cold iron-rich sinker, or be neutrally buoyant. A different color saturation scheme could make the region under South America appear to be an enormous blue slab. (from Ivanov, 2005).

High-velocity regions are not necessarily cold, dense sinkers. Residuum left after melt extraction, and cratonic roots are examples of high-velocity material that has low density and is buoyant. Conversely, eclogite at ambient mantle temperatures can have low velocities and a range of densities. The global low-velocity zone beneath the “mantle lid” has velocities up to ~20% low compared with the IASP91 standard global seismic velocity model. This cannot be explained solely by temperature; partial melt is required (Tan & Helmberger, 2007). The African and south Pacific “superplumes” are vast, low-velocity bodies in the lower mantle whose low velocities have been shown to result from anomalously high density and not to high temperature (Trampert et al., 2004)

In a peridotite mantle, topography on the transition zone boundaries may be used as a proxy for temperature. High-temperature regions are predicted have thin transition zones. However, the thickness of the transition zone shows no correlation with low-seismic-velocity regions in the lower mantle, with the “superplumes”, or with upper mantle tectonics. The only correlations observed are that oceans have relatively thin transition zones and slab-rich subduction-zone regions have relatively thick transition zones (e.g., Deuss, 2007; see also transition zone pages).

Interpretations

Recent papers defend or present modifications to the standard one- and two-layer models of geodynamics and geochemistry (e.g., van der Hilst et al., 1997; Kellogg & Wasserburg, 1990; Kellogg et al., 1999), without changing the basic assumptions of a well-stirred homogeneous upper mantle, an accessible lower mantle and a correlation between isotopes and seismic models (e.g., Helffrich & Wood, 2001; DePaolo & Manga, 2003; van der Hilst, 2004; Meyzen et al., 2007; Bercovici & Karato, 2003). These represent one particular train of thought about the accessibilty of the lower mantle to slabs and surface volcanoes. The non-uniqueness of tomographic and geochemical models, and compositional and dynamic interpretations of them, are intrinsic limitations but are seldom addressed. However, the non-uniqueness is obvious when one looks at the large number of published models that are based on essentially the same data.

Quantitative seismology vs visual tomography

In qualitative tomography the reader depends on the visual impression created by the designer of the published image. Tomographic cross-sections that have been interpreted as evidence for deep slab penetration can also be plotted with different color scales (e.g., Ricard et al., 2005) to suggest stagnant slabs in the upper mantle (Fukao et al., 2001). The visual impressions given by cross-sections depend heavily on the orientation and the vertical and horizontal cropping. Artifacts such as streaking, bleeding and smearing, the results of sparse ray coverage, smoothing and unmodeled anisotropy, are inevitable and may not be obvious if not pointed out by the authors. A Google Image search on mantle tomography slabs or slabs tomography will bring up many images that could be used to argue in a number of different ways.

Cartoons should be viewed with particular skepticism. They are often presented in order to illustrate a model that is not shown in any one data set, even using carefully chosen, cropped and colored cross sections. For example, when color schemes are chosen to emphasise continuous red features, blue featues often disappear (Figure 6). Thus, to illustrate conceptual models involving both upwelling plumes and downgoing slabs, cartoons may be the only resort (e.g., Figure 5).

Figure 6. When the color scheme, reference model and cross-sections are chosen to emphasize continuous red features, one usually does not see the "whole-mantle slabs", and vice versa. For this reason, cartoon interpretations are drawn (the "having your cake and eating it" approach, e.g., Figure 5). This image could have been plotted differently to make it appear as though there is a whole mantle slab is under South America (from Ritsema, 2005).

Quantitative analysis of tomographic results involves the calculation of correlations and spectra and quantitative hypothesis testing. Analyses based on the correlations between density, shear velocity, and compressional velocity, for example, are much more powerful than merely glancing uncritically at a single cross-section. Correlation coefficients between seismic velocities and densities for very long wavelength features are given by Ishii & Tromp (2004) (Figure 7). Various regions are evident:

  1. The upper 200 km. Seismic parameters show positive correlations and surface tectonics correlates well with velocity. This region scatters short-period seismic waves strongly.
  2. 200-1000 km depth. Density and seismic velocity are anti-correlated. This means that long-wavelength, low-velocity features are dense. Eclogite and carbonated or iron-rich peridotite layers would have this property. An example of a high-velocity, buoyant material is depleted harzburgite. Quantitative and statistical methods for determining the depth of subduction show that the best correlation of tomography with ancient subduction zones is at 800-900 km depth. High-velocity slabs can be high-density but global techniques for determining density do not apply to such small features.
  3. 1000-2000 km depth. Density and velocity correlate but compressional and shear seismic velocities have relatively low correlations. This region has very low amplitude anomalies and is characterized by a few very large features with weak seismic anomalies.
  4. 2000-2600 km depth. This region exhibits negligible density-velocity correlations but significant compressional and shear-velocity correlations.
  5. Below ~2600 km is a thermochemical layer with low correlations and regions of ultra-low shear velocity [Ed: see also The D” region page].

 

Figure 7. Correlation coefficients between models of shear and compressional velocities (solid: S&P), shear velocity and density (dotted: S&ρ), and compressional velocity and density (dashed: P&ρ) as a function of depth. For the number of free parameters in these models, the correlation is statistically significant at the 90% confidence level if the correlation coefficient is greater than 0.25 (from Ishi & Tromp, 2004).

Detail is smoothed out in the global tomography images that have been used to argue for simple one-layer convection (but see Figure 8). However, other seismological approaches provide evidence for heterogeneity on both large scales (Ishii & Tromp, 2004; Trampert et al., 2004) and small scales, for the upper mantle (Shearer & Earle, 2004; Baig & Dahlen, 2004; Fuchs et al., 2002; Thybo et al., 2003). Scattering of high-frequency waves indicates a heterogeneous upper mantle (Shearer & Earle, 2004; Baig & Dahlen, 2004) with robust (reproducible) reflectors as deep as 1300 km (Deuss & Woodhouse, 2002). The upper mantle is much more heterogeneous than the bulk of the lower mantle (Gudmundsson et al., 1990; Vasco & Johnson, 1998).

Figure 8. “It is now well established that oceanic plates sink into the lower mantle at subduction zones…” (image from Zhao et al., 2004).

Summary

Global tomography has been used to address the controversy of whether the upper and lower mantles convect separately or as one. However, the seismic tomographic method for imaging the mantle suffers from several major problems which preclude the results from simply showing coherent structures, temperature distributions or flow patterns. Transition zone boundary topography often contradicts simple dynamic models based on uncritical visual inspection of color cross-sections. Tomography is useful for hypothesis testing and for designing higher resolution experiments, but it cannot directly and alone reveal mantle dynamics. Waveform modeling, correlation statistics and reflectivity studies are better suited for gaining insight into that. High-resolution and scattering studies give more information about the homogeneity and heterogeneity of the mantle.

 


 

Resources: words and pictures

The theoretical and observational limitations of global tomography are well known to experienced seismologists. Sometimes, however, it is claimed that a new technique can resolve features that were invisible to previous investigators, even when fewer data are used. These claims are discussed in the first reference below. The other references discuss the limitations and artifacts of tomography and give a number of models.

The mapping of seismic velocity into composition, lithology, temperature and flow field is not straightforward, and may even be impossible. The following references are useful in this regard.

  • Anderson, Don L., New Theory of the Earth 2nd Edition; (ISBN-13: 9780521849593) DOI: 10.2277/0521849594. 408 pp, 2007.
  • Ishii, M., & J. Tromp, J. Constraining large-scale mantle heterogeneity using mantle and inner-core sensitive modes, Physics Earth Planet. Interiors, 146, 113–124, 2004.
  • Lee, K.K.M. et al., Equations of state of the high-pressure phases of a natural peridotite and implications for the Earth’s lower mantle, Earth Planet. Sci. Lett., 223, 381–393, 2004.
  • Trampert, J., Vacher, P. & Vlaar, N., Sensitivities of seismic velocities to temperature, pressure and composition in the lower mantle, Phys. Earth Planet. Interiors, 124, 255–267, 2001.
  • Trampert, J., Deschamps, F. Resovsky, J. & Yuen, D., Probabalistic tomography maps chemical heterogeneities throughout the lower mantle, Science, 306, 853–856, 2004.

The simplified interpretations of color tomographic cross-sections that form the basis of geochemical and geodynamic “standard models” are based on just a few color-saturated cross-sections. These have been superceded. If one examines a large number of unsaturated maps and cross-sections (see links below) one does not get the impression of a one-layer pattern, or wholesale sinking of slabs into the lower mantle. This is confirmed by quantitative analysis and high-frequency seismology. For example, convection modeling results for layered mantle flow (Cizkova & Matyska, 2004) look more like tomographic cross-sections than do whole-mantle convection simulations.

High-resolution seismology results can be found on the web at the following sites;

http://www.sciencemag.org/cgi/data/1138074/DC1/1
http://epsc.wustl.edu/seismology/michael/CIG/workshop06/lectures/Levander_talk.pdf
http://www.ruf.rice.edu/~ctlee/2006LevanderLee.pdf
www.mantleplumes.org/ Baikal.html
http://www.mantleplumes.org/Iceland1.html

Search Goggle Images with the following search strings;

Levander receiver-function imaging
receiver functions
receiver functions Iceland Yellowstone
Yellowstone receiver functions Dueker

References

  • Allegre, C.J. 1997, Limitation on the mass exchange between the upper and lower mantle: The evolving convection regime of the Earth, Earth Planet. Sci. Lett., 150, 1–6.
  • Baig, P. & Dahlen, A.M. 2004, Traveltime biases in random media 1164 and the S-wave discrepancy, Geophys. J. Int,. 158, 922–938, 1165 doi:10.1111/j.1365-246X.2004.02341.x.
  • Bercovici, D. & Karato, S., 2003, Whole mantle convection and transition-zone water filter, Nature, 425, 39-44.
  • Deuss, A., & J.H. Woodhouse, 2002, A systematic search for mantle discontinuities using SS-precursors, Geophys. Res. Lett., 29,10.1029/2002GL014768.
  • Fuchs, K., Tittgemeyer, M., Ryberg, T., & Wenzel, F., 2002, Global Significance of a Sub-Moho Boundary Layer (SMBL) deduced from high-resolution seismic observations, Int. Geol. Rev., 44, 671–685.
  • Fukao, Y., Widiyantoro, S., & Obayashi, M., 2001, Stagnant slabs in the upper and lower mantle transition region, Rev. Geophys., 28, 291–323.
  • Gudmundsson, Ó., J.H. Davies, & R.W. Clayton, 1990, Stochastic analysis of global travel-time data: Mantle heterogeneity and errors in the ISC data, Geophys. J. Int., 102, 25-43.
  • Helffrich, G.R. & Wood, B.J., 2001, The Earth's mantle, Nature, 412, 501-507.
  • Ishii, M., & J. Tromp, 2004, Constraining large-scale mantle heterogeneity using mantle and inner-core sensitive modes, Physics Earth Planet. Interiors, 146, 113–124.
  • Kamber, B.S. & Collerson, K.D. 1999, Origin of ocean island basalts: a new model based on lead and helium isotope systematics, J. Geophys. Res., 104, 479–91.
  • Kellogg, L.H. & Wasserburg, G.J. 1990, The role of plumes in mantle helium fluxes, Earth Planet. Sci. Lett., 99, 276–289.
  • Kellogg, L. H. et al. 1999, Compositional stratification in the deep mantle, Science, 410, 1049– 1056.
  • Meyzen, C.M. et al. 2007, Isotopic portrayal of the Earth's upper mantle flow field, Nature, 447, 1069-1074.
  • Ricard, Y., Mattern, E. & Matas, J. 2005, Synthetic tomographic images of slabs from mineral physics, in, Earth's Deep Interior: Structure, Composition, and Evolution, van der Hilst, R.D., Bass, J.D., Matas, J., and Trampert, J. (Eds.), Geophysical Monograph, American Geophysical Union, Washington, D.C., 160, 283-300.
  • Shapiro, N.M. & Ritzwoller, M.H., 2004, Thermodynamic constraints on seismic inversions, Geophys. J. Int., 157, 1175–1188, doi:10.1111/j.1365- 246X.2004.02254.x.
  • Shearer, P.M., & Earle, P.S., 2004, The global short-period wavefield modelled with a Monte Carlo seismic phonon method, Geophys. J. Int., 158, 1103–1117.
  • Spakman, W. & Nolet, G., 1988, Imaging algorithms, accuracy and resolution in delay time tomography, in Mathematical Geophysics, Vlaar et al. (eds.), Reidel, pp. 155–188.
  • Spakman, W., S. Stein, R.D. van der Hilst, & R. Wortel, 1989, Resolution experiments for NW Pacific subduction zone tomography, Geophys. Res. Lett., 16, 1097–1100.
  • Thybo, H., Nielsen, L., & Perchuc, E., Sesimic scattering at the top of the mantle transition zone, Earth Planet. Sci. Lett., 216, 259-269, 2003.
  • Trampert, J., Deschamps, F. Resovsky, J. & Yuen, D. 2004, Probabalistic tomography maps chemical heterogeneities throughout the lower mantle, Science, 306, 853–856.
  • van der Hilst, R. D., Widiyantoro, S. & Engdahl, E. R., 1997, Evidence of deep mantle circulation from global tomography, Nature, 386, 578–584.
  • van der Hilst, R.D., 2004, Changing views on Earth’s deep mantle, Science, 306, 817–818, 2004.
  • Vasco, D.W. & Johnson, L.R., 1998, Whole Earth structure estimated from seismic arrival times, J. Geophys. Res., 103, 2633-2671.
  • Vasco, D.W., Johnson, L.R., Pulliam, R.J. & Earle, P.S., 1994, Robust inversion of IASP91 travel time residuals for mantle P and S velocity structure, earthquake mislocations, and station corrections, J. Geophys. Res., 99, 13,727–13,755.
  • Zhao, D., L. Jianshe & T. Rongyu, 2004, Origin of the Changbai intra-plate volcanism in northeast China: Evidence from seismic tomography, Chinese Science Bulletin, 49, 1401-1408.
last updated 23rd September, 2007
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