Mantle layering from ScS reverberations: 2. The transition zone

Abstract

Based on multiple long-period ScS reverberations, Revenaugh and Jordan [1991] infer a 10-20 km peak-to-peak topography on the 410-and 660-kin discontinuities which is negatively correlated. They draw conclusions about lateral thermal variations in the transition zone from these observa- tions. We show that the correlation on which this result of Revenaugh and Jordan [1991] is based is severely influencedby the processing method used. The untouched correlation is too weak as to support any such conclusions. In the notation of Revenaugh andJordan [1991] T410, T•60, and rs•cs are observed (and corrected) two-way travel times of reflections from the 410-and 660-km discontinuities and of the whole mantle, respectively. Other notations used are ! I I ! rTZ = r•60 --r•0 and rLM = r%s--r660. In Figure 6 of Revenaugh and Jordan [1991], rl•o and r•z are shown as a ' -r • diagram correctly displays function of %•,. The r•0 the correlation of the 410-and 660-km discontinuities. The correlation coefficient is given as +0.35, indicating no significant correlation between the two discontinuities. The correlation coefficient from the ' -r' and r' ' 7'TZ LM TZ --r4•0 diagrams is -0.78 and -0.65, respectively (Figure 6 and Table 2). These apparently improved values seem to provide the basic argument for the inferred anticorrelated topography. The variables r•a and r•1o can be considered statistically in-! I dependent. However, the pair rUM and and also the pair rTZ r•lf, and r•z is by definition statistically dependent. This was recognized by Revenaugh and Jordan qualitatively but not taken into account quantitatively. In the following, we show that the correlation coefficients p== and pyz of the random variables z,y and z are not zero, when z and y are statistically independent random variables and z is defined as z := z -y. Proof The probability distributions of z and y are given as p=(z) and Pu(Y), respectively. The joint probability distribution q(z,z) for z and z is = Hence the second-order central moment/z=z results in : f f (z-•)(z-•)q(z,z)dzdz = f/(z --e)(z --•)p=(z)py(z --z)dzdz = ...= ti• y!O. The second-order central moment /z•z is equal to the variance of the distribution p•(z) and is therefore not zero. Analoguous computations yield I•yz = --•Lyy I•zz = lazz q-I•yy From the definition of the correlation coefficient, it follows that Pyz --Furthermore, if the probabilities p•(z) and py(y) have the same variance g = g=• = g•, the correlations can be reduced to 1 Pzz =--Pyz-V/• = 0.707... That means in this case the correlation coefficient of z and z (or y and z) is a constant and independent from the actual probability distributions p•(z) and pu(y). The obtained value is even very close to the values given by Revenaugh and Jordan [1991] in Table 2. As an example, Figure 1 shows a set of 30 random numbers in the z-y plane. The numbers are uniformly distributed within a circle of radius 1 centered at (2,2). The correlation coefficient of this set evaluates to 0.02, indicating independence of z and y probabilities. Figure ...

Global mapping of topography on transition zone velocity discontinuities by stacking SS precursors

“…The 520 impedance contrast is less than half that seen for the 410 [e.g., Revenaugh and Jordan, 1991;Shearer, 1996]; this is apparent in the waveform stacks where the 520 peak has a relatively low amplitude. However, the visibility of the 520- …”

“…Modeling results have shown that a compositional boundary at 660 km associated with layered convection would be displaced several hundred kilometers or more by subducting slabs [e.g., Hager and Raefsky, 1981; Christensen and Yuen, 1984]. Subsequent observations that the amplitude of 660 topography is of the order of tens of kilometers provide strong evidence against a purely compositional origin for the 660-km discontinuity [e.g., Revenaugh and Jordan, 1991;Shearer, 1991]. It is now generally accepted that most, if not all, of the velocity and density changes across the 410-and 660-km discontinuities result from phase changes, which mineral physics experiments predict will occur near these depths.…”

Topography of the transition zone seismic discontinuities

“…Shearer [1990] used transition zon e discontinuity reflection precursors to SS and PP (S410S, S660S, P410P, P660P) to investigate global 410-and 660-km discontinuity depths. This study provided the discontinuity depth estimates of 410, 520, and 660 km that now name them (though the estimates reportedly first appeared in a dissertation [Revenaugh, 1989] [1997], all using subduction zone earthquakes to look downward at the underlying discontinuities with either S660P, S410P, or both (Figure 2 and Figure 3b). The principal uncertainties in these studies are the earthquake depths themselves (with up to _+ 10 km depth uncertainty), the typical assumption that the discontinuity is horizontal (which affects the interaction geometry), and the velocity structure near the slab (which distorts ray paths and modifies travel times near the interaction point).…”

Thermal, hydrous, and mechanical states of the mantle transition zone beneath southern Africa

“…The positive and negative Clapeyron slopes of the 410-and 660-km discontinuities, in that order, dictate a thinning of the mantle transition zone in the presence of thermal upwelling. For the same reason, a cold thermal anomaly penetrating the transition zone induces a thicker-than-normal transition zone [19]. Compositional variations in the transition zone, such as water content, may also a¡ect the transition zone structure.…”