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U. R. Christensen and D. A. Yuen, J. Geophys. Res. 90, 10291 (1985); P. Machetel and P. Weber, Nature 350, 55 (1991); P. J. Tackley, D. J. Stevensen, G. A. Glatzmaier, G. Schubert, ibid. 361, 699 (1993); S. Honda, D. A. Yuen, S. Balachandar, D. Reuteler, Science 259, 1308 (1993); L. P. Solheim and W. R. Peltier, J. Geophys. Res. 99, 15861 (1994); P. J. Tackley, D. J. Stevensen, G. A. Glatzmaier, G. Schubert, ibid., p. 15877; J. Ita and S. D. King, ibid., p. 15919; C. Thoraval, P. Machetel, A. Cazenave, Nature 375, 777 (1995).
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U. R. Christensen and D. A. Yuen, J. Geophys. Res. 90, 10291 (1985); P. Machetel and P. Weber, Nature 350, 55 (1991); P. J. Tackley, D. J. Stevensen, G. A. Glatzmaier, G. Schubert, ibid. 361, 699 (1993); S. Honda, D. A. Yuen, S. Balachandar, D. Reuteler, Science 259, 1308 (1993); L. P. Solheim and W. R. Peltier, J. Geophys. Res. 99, 15861 (1994); P. J. Tackley, D. J. Stevensen, G. A. Glatzmaier, G. Schubert, ibid., p. 15877; J. Ita and S. D. King, ibid., p. 15919; C. Thoraval, P. Machetel, A. Cazenave, Nature 375, 777 (1995).
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U. R. Christensen and D. A. Yuen, J. Geophys. Res. 90, 10291 (1985); P. Machetel and P. Weber, Nature 350, 55 (1991); P. J. Tackley, D. J. Stevensen, G. A. Glatzmaier, G. Schubert, ibid. 361, 699 (1993); S. Honda, D. A. Yuen, S. Balachandar, D. Reuteler, Science 259, 1308 (1993); L. P. Solheim and W. R. Peltier, J. Geophys. Res. 99, 15861 (1994); P. J. Tackley, D. J. Stevensen, G. A. Glatzmaier, G. Schubert, ibid., p. 15877; J. Ita and S. D. King, ibid., p. 15919; C. Thoraval, P. Machetel, A. Cazenave, Nature 375, 777 (1995).
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Ita, J.1
King, S.D.2
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G. Nolet and M. J. R. Wortel, in The Encyclopedia of Solid Earth Geophysics, D. E. James, Ed. (Van Nostrand Reinhold, New York, 1989), pp. 775-788; G. Nolet, S. P. Grand, B. L. N. Kennett, J. Geophys. Res. 99, 23753 (1994).
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Nolet, G.1
Grand, S.P.2
Kennett, B.L.N.3
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0344533810
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note
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The reflection coefficient is the ratio of the reflected wave amplitude to the incident wave amplitude.
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20
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0344102444
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note
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SS and PP are the multiples of the direct S and P phases that contain a single reflection off Earth's surface midway between source and receiver. The precursors to SS and PP resulting from underside reflections off a discontinuity at depth d are termed SdS and PdP, respectively. For example. S410S indicates the S reflection off the bottom of the 410-km discontinuity.
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0344533809
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We obtained this factor by computing the effect of time shifts on the amplitude of the SS and PP reference pulses in the stacks, assuming that the time shifts have a Gaussian distribution characterized by a standard deviation, σ. The time shifts result from differences in the two-way surface-to-discontinuity travel times caused by both discontinuity topography and upper mantle velocity heterogeneity. In general, σ will vary depending on the wave type (for example, P or S) and the geographic diversity of ray geometries in the stack. For ScS waves, σ = 4 s was obtained for mixed continental and oceanic paths (3), whereas σ = 2.5 s has been estimated for SdS waves in purely oceanic regions (11). The limited distribution of reflection points contained within each of our source-receiver range bins is likely to decrease σ, whereas the mixture of continental and oceanic points is likely to increase σ. For σ values of 2, 3, and 4 s, SdS amplitudes in our stacks are reduced by 8, 16, and 28%, respectively. The time shifts for PdP phases are likely to be smaller than those for SdS. For σ values of 1.0, 1.7, and 2.5 s, PdP amplitudes are reduced by 4, 12, and 23%, respectively. Our amplitude corrections are based on σ = 2.5 s for SdS and σ = 1.7 s for PdP.
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27
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0031434882
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G. Helffrich and B. J. Wood, Geophys. J. Int. 126, F7 (1996); L. Stixrude, J. Geophys. Res. 102, 14835 (1997).
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J. Geophys. Res.
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Stixrude, L.1
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0344102443
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note
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For linear velocity and density gradients, our observed SdS and PdP amplitudes are reduced by 1 to 2% for a 10-km interval (compared with a sharp discontinuity), 3 to 7% for a 20-km interval, 6 to 13% for a 30-km interval, and 11 to 22% for a 40-km interval. The effect is largest where the velocities near the discontinuity are the smallest (that is, for S410S) and smallest where the velocities are the largest (that is, for P660P), although the S versus P difference is lessened in our case by the higher frequency content in the PP stack (the SS data have a dominant period of 30 s; the PP data are peaked at a 21-s period). Nonlinear gradients, which may occur for mantle phase transitions (14), will produce smaller amplitude reductions for reflected pulses than linear gradients over the same depth interval. Thus, these numbers represent upper bounds; the actual amplitude reductions may be smaller.
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31
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0344533769
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note
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Values of the incoherent stacking parameter ranging from σ = 0 s (perfect coherence) to 1.6 times larger than our preferred values (for example, σ = 4 s for SdS waves and σ = 2.7 s for PdP waves) resulted in adjusted amplitudes that varied by less than 20% from our computed amplitudes.
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0345396144
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The shear impedance is the product of the shear velocity and density; thus, the shear impedance contrast is given by the sum of the S velocity and density jumps.
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36
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0033153647
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J. B. Gaherty, Y. Wang, T. H. Jordan, D. J. Weidner, Geophys. Res. Lett. 26, 1641 (1999). This paper contains the changes in density and S velocity at 410 km for pyrolite and piclogite models. Corresponding values for the changes in P velocity were obtained from J. B. Gaherty (personal communication).
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(1999)
Geophys. Res. Lett.
, vol.26
, pp. 1641
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Gaherty, J.B.1
Wang, Y.2
Jordan, T.H.3
Weidner, D.J.4
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38
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0344102442
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note
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Weidner and Wang (24) computed density and velocity profiles through the 660-km discontinuity for several different models of mantle composition (with differing Al content) and temperature (1700, 1900, and 2100 K). The points labeled "Pyr" in Fig. 3B are for their 5% Al model at 1700 K; for this model, the velocity and density jumps occur across an interval of less than 20 km. Some of the other models have more gradual gradients that cannot be directly converted to points on Fig. 3. We tested to see if these models might fit our data by computing synthetic seismograms based on the profiles in Fig. 4 of Weidner and Wang (24). All of these models grossly overpredict our observed S660S and P660P amplitudes and lie outside the error bars plotted in Fig. 2.
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0344682181
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S. M. Ridgen et al., ibid. 354, 143 (1991).
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(1991)
Nature
, vol.354
, pp. 143
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Ridgen, S.M.1
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41
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0344102441
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note
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This work was supported by NSF grants EAR93-15060, EAR95-07994, EAR96-14350, and EAR96-28020. M.P.F. was supported by an NSF Postdoctoral Fellowship and the Cecil H. and Ida M. Green Foundation. J. Gaherty and J. Vidale provided constructive reviews of an earlier version of this report.
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