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On Walter Brown & Plate Tectonics (1997)

Tim Thompson


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I am writing this in response to posts I have seen to, from Jim Lippard, with regards to the discussion between Glenn Morton and Walter Brown, on the topic of subduction in plate tectonics. I have reviewed the material on Dr. Brown's web pages, and I have concluded that, like his discussion of the tidal interaction between the earth and the moon, his discussion of subduction is trivially false, and far less interesting than his own self confidence would imply. My primary intention is to show the main arguments in outline form, with copious references to the literature, where the detailed technical arguments can be followed in as much detail as the reader desires.

Walter Brown presents his explanation for why subduction of plates into the lithosphere cannot occur, in one of his technical notes, in his web page collection: Does Subduction Really Occur?

The model presented on this page consists of a single inequality that relates the downward force on the plate to the friction resisting the plate's downward motion. The forces, he reasons, must be greater than the frictional resistance, or subduction cannot occur. He presents his equation, and a numerical evaluation of it, shows that the net force is less than the frictional resistance, and so 'proves' that subduction cannot occur. But the inequality he presents is wrong, and therefore his results must be re-examined in light of a correct solution to the problem.

Brown makes two major errors at once. First, he uses a model of solid-to-solid friction. But the mantle and plate must be treated as viscous fluids, not as a solid-to-solid system, so his chosen friction model is unphysical. To compound the error, Brown uses a (fluid) lithostatic pressure for the mantle, which is inconsistent with the (solid) friction model. Second, he evaluates his unphysical inequality with the wrong numbers anyway. Brown uses mechanical properties for rock from an engineering handbook (not surprising for an engineer) to provide numerical values, but those values are inappropriate for materials under mantle conditions. Brown says, for instance, that the properties are independent of both composition and temperature, up to 350 degrees Celsius. However, temperatures far higher than that are encountered in the mantle, and Brown makes no mention of pressure at all. It is well known, and has been for many years, that mantle properties are very much temperature and pressure dependent, and that rock creep under mantle conditions is very much dependent on composition and grain size. Both Brown's model, and its numerical evaluation, are wrong.

Although the falsification of Brown's model is a trivial exercise, we should go further, and decide whether or not plate tectonics and subduction really are physically reasonable, and whether or not it is fair to say that subduction is actually an observed, rather than an inferred process. My answer in both cases is "yes".

First, consider whether or not subduction is physically reasonable. That it is, should be fairly obvious. A correct view, that a fluid plate is falling through a surrounding fluid medium, does not violate any of our basic physical sensibilities. The plate is more dense, and more viscous, because of its lower temperature, and will continue to sink through the less viscous mantle until buoyancy forces reverse the trend. Research shows that this does indeed happen; plates subducted at a shallow angle do not penetrate into the deeper mantle, but rather reverse course as their temperature equilibrates with the surrounding mantle, while plates subducted at a sharp angle, do penetrate the deeper mantle (Christensen, 1996).

Next, consider whether or not it is fair to say that subduction is an "observed" phenomenon. It is, and the key lies in the observations that density variations in the mantle, implied by seismic velocities, show us the subducting plates in a manner vary similar to that in which an X-ray shows up the bones of a skeleton, and that double planed earthquake zones not only outline the subducting plates, but also indicate differing earthquake mechanisms above and below the plate, as one would expect (McGuire & Wiens, 1995; Compte & Suarez, 1994; Prevot et al., 1994; Wiens, McGuire & Shore, 1993). Note also that deep focus earthquakes occur only in subduction zones, and that earthquakes of all varieties are strongly concentrated at plate boundaries.

Brown's specific criticism of van der Hilst, Widiyantoro & Engdahl, 1997, that the subducted slabs are not where they are supposed to be, or not where one might expect them, is also easily falsified. As the plates plunge downward (i.e., subduct), the continents continue their lateral motion and override the subducting slab. This is very well illustrated by Wen & Anderson, 1995. Although pre-dating the van der Hilst et al. paper by two years, Wen & Anderson figures 1 & 3 nicely predict the arrangement of deep subducted plates observed by van der Hilst at al., and in their figures 1c & 1d. Agreement here is quite pronounced for the Americas, Indonesia, and the area east of Australia. Furthermore, Brown seems to ignore altogether the dramatic demonstration in van der Hilst et al., figure 5a, which certainly appears to show a subducting slab beneath central America. Christensen, 1996, also discusses the general topic of the effect of plate motion on subduction.

The combination of tomography, double seismic zones, the distribution of tensional & compressional earthquake mechanisms, and the fact that deep focus earthquakes occur only in subduction zones, makes it very difficult to avoid the conclusion that subduction is an observed process.

References cited

  • Compte, D. & G. Suarez. "An Inverted Double Seismic Zone in Chile - Evidence of Phase Transformation in the Subducted Slab." Science, 263:(212-215), 14 January 1994
  • Christensen, Ulrich R. "The influence of plate migration on slab penetration into the lower mantle." Earth and Planetary Science Letters, 140:(27-39), 1996
  • McGuire, J.J.& D.A. Wiens. "A Double Seismic Zone in New Britain and the Morphology of the Solomon Plate at Intermediate Depths." Geophysical Research Letters, 22:(1965-1968), 1 August 1995
  • Prevot, R.; J.L. Chatelain, S.W. Roecker & J.R. Grasso. "A Shallow Double Seismic Zone Beneath the Central New Hebrides (Vanuatu) - Evidence for Fragmentation and Accretion of the Descending Plate." Geophysical Research Letters, 21:(2159-2162), 15 September 1994
  • van der Hilst, R.D.; S. Widiyantoro & E.R. Engdahl. "Evidence for deep mantle circulation from global tomography." Nature, 386:(578-584), 10 April 1997
  • Wen, Lianxing & Don L. Anderson "The fate of slabs inferred from seismic tomography and 130 million years of subduction." Earth and Planetary Science Letters, 133:(185-198), 1995
  • Wiens, D.A.; J.J. McGuire & P.J. Shore "Evidence for transformational faulting from a deep double seismic zone in Tonga." Nature, 364:(790-793), 26 August 1993

Also see these uncited references for further reading

  • Green II, Harry W. "Solving the Paradox of Deep Earthquakes." Scientific American, 271:(64-71), September, 1994
  • Hynes, Andrew; Jafar Arkani-Hamed & Reinhard Greiling. "Subduction of continental margins and the uplift of high-pressure metamorphic rocks." Earth and Planetary Science Letters 140:(13-25), 1996
  • Iidaka, T. & Y. Furukawa. "Double Seismic Zone for Deep Earthquakes in the Izu-Bonin Subduction Zone." Science, 263:(1116-1118), 25 February 1994
  • Jacobs, J.A. "Deep Interior of the Earth." Chapman and Hall, 1992 Vol. 6 in the series "Topics in the Earth Sciences." ISBN 0-412-36570-7 QE509.J27 [University College of Wales, Aberystwyth, and University of Cambridge]
  • Keary, Philip & Frederick J. Vine. "Global Tectonics." Blackwell Science, 2nd ed., 1996 ISBN 0-86542-924-3 QE 511.4.K34
  • Poirer, Jean-Paul. "Introduction to the Physics of the Earth's Interior." Cambridge University Press, 1991 Vol. 3 in the series "Cambridge Topics in Mineral Physics and Chemistry." ISBN 0-521-38097-9 (H) ISBN 0-521-38801-5 (P) QE 509.P64 [Institut de Physique de Globe, Paris]
  • Shimenda, Alexander I. "Subduction: Insights from Physical Modeling." Kluwer Academic Publishers, 1994 Vol. 11 in the series "Modern Approaches in Geophysics." ISBN 0-7923-3042-0 QE 511.46.S54 [Laboratoire de Geophysique et Tectonique, Universite de Montpellier II, Montpellier, France]
  • Wang, K.L. & G.C. Rogers. "An Explanation for the Double Seismic Layers North of the Mendocino Triple Junction." Geophysical Research Letters, 21:(121-124), 15 January 1994