• 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:

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:

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.

 

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