Li Li and Donald J. Weidner
Mineral Physics Institute & Department of Geosciences, Stony Brook University, Stony Brook, NY 11794-2100, USA
The velocities of seismic waves are governed by the response of the constituent mineral assemblage to perturbations in pressure and stress. The effective bulk modulus is significantly lowered if the pressure of the seismic wave drives a volume reducing phase transformation [1]. A comparison between the amount of time required by phase transitions to reach equilibrium and the sampling period thus becomes crucial in order to define the softening and attenuation of P waves within a two-phase zone [2]. Such phenomena are difficult to assess experimentally since data at earth conditions are required. Here we show synchrotron based experimental data that demonstrate softening of the bulk modulus within the two-phase loop of olivine-ringwoodite at a time scale of 100 seconds. Scaling the amplitude of the pressure perturbation and grain size to those expected in the Earth, the P wave velocities within the discontinuities at 410, 520, and possibly 660 km are likely significantly lower than otherwise expected. The generalization of these observations to Al controlled phase transitions open the possibility of large velocity perturbations throughout the upper 1000 km of the mantle.
Figure 1.
Calculated P-wave velocities (VP) versus depth in the Earth using pyrolite composition and adiabatic gradient8. a, Here the measurement time is much less than the shortest characteristic time (which we estimate to be ~10 -2 s for P waves). b , Here we assume total phase equilibrium for olivine phases (green line; the blue line is the same as in a ). c , Same as b except total equilibrium for pyroxene–garnet–perovskite transitions is also assumed (red line). The preliminary reference Earth model3
(PREM) is included. Plots in b and c are calculated from the depth derivative of the density model. The density model is derived from the phase equilibria and equations of state for pyrolite minerals10.

, olivine;

, wadsleyite;

, ringwoodite; pv, perovskite; px, pyroxene; gt, garnet.
The current view of the radial seismic structure of the mantle consists of smooth velocity variations punctuated by discontinuities at 410, 520, and 660 km [3], which are thought to be caused by the olivinewadsleyite-ringwoodite-perovskite phase transitions [4, 5]. However, complexities arise from the possible relaxation of the bulk modulus caused by phase transitions [1] in regions of coexisting high and low pressure phases. The olivine phase transitions have finite widths owing to the partitioning of Fe and Mg between coexisting phases [6, 7]. Some of the ‘smooth’ zones consist of coexisting high- and low-pressure phases of pyroxene-garnet-perovskite which tend to have broad two phase zones that are controlled by the partitioning of Al between coexisting phases [8]. In the regions with coexisting high and low pressure phases, the

2 equilibrium bulk modulus, K eq
, will be considerably relaxed because a pressure change will induce a volume change that is the result of the pressure induced phase transformation:
-δV/V = -δP/ΔP tran
(ΔV/V) tran
+ δP/K elas
= δP(1/K tran
+ 1/K elas
) = δP/K eq where ΔP tran
is the width of the two phase zone, (ΔV/V) tran
is the proportional volume change associated with the transformation, and K elas
is the elastic unrelaxed bulk modulus of the two phase aggregate when no phase transition occurs. Whether K eq
or K elas
defines the P-wave velocity depends on whether the kinetics of the transformation are faster or slower than the period of the seismic wave. Figure 1(a-c) illustrates the effect on the P velocity of transition induced relaxation for a pyrolitic Earth [9, 10] with an adiabatic temperature gradient [11]. Figure 1a illustrates the unrelaxed elastic system. Figure 1b shows the relaxed system with only the olivine transforming. Figure 1c is similar to Figure 1b but both olivine and pyroxene reaching equilibrium. Also illustrated in Figure 1c is PREM. It is noteworthy that PREM lies between the relaxed and unrelaxed system and is closest to the unrelaxed velocity in regions where no phase transitions occur.
Based on our experimental results, we argue that the Earth most likely samples a significant fraction of the relaxed system resulting in a reduced P velocity, but with little bulk attenuation.
We report here experiments with an olivine sample, composition of Fa70. The experiments were performed (in X17B2-NSLS) at high pressure and temperature (up to 15 GPa and 1700 K) to define characteristic time of phase transition and the attenuation at the same conditions. Meanwhile the relaxations of the elastic modulus of the sample before-during-after the phase transitions were monitored. The characteristic time of the phase transition from alpha to gamma phase is ~4000 seconds. This is consistent with diffusion as the controlling process with a value for D of 10
-15
m
2 s
-1
for Fe – Mg exchange [12] and a characteristic length of 2 microns which would suggest about half of the material going through the transformation (with 10 micron grains). This is consistent with the model described above and with previous studies on olivine phase kinetics[13]. The energy loss for the olivine-ringwoodite mixed phase region was found to be considerably larger than for the single phase region. The small amplitude of stress in the seismic wave may move the characteristic time to a much smaller value and thus move the attenuation peak to much higher frequencies than that sampled by seismic waves, which is further confirmed by the oscillation tests at various strain amplitude and frequencies.
The data presented here imply that phase transitions reduce P wave velocities in the Earth’s mantle.
While the relaxed and unrelaxed velocities are easy to calculate, the actual velocity will lie between these values, but the exact amount of softening is not yet known. Whether or not the associated bulk attenuation occurs requires more investigations of the time scales. This suggestion alters the essential ingredients that are needed to create a seismic profile from mineral physics data. More experiments and directed seismic observations are needed to define the impact of the process presented here.
ACKNOWLEDGEMENTS We wish to thank Liping Wang and Don Lindsley for support for this project.
Support from the NSLS and COMPRES with financial support by the U. S. DoE, under contract No. DE-
AC02_98CH10886, by the NSF EAR-0711365, EAR652887, EAR 01-35554. MPI publication No. 466.
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3
PUBLICATION
Li, Li, Donald, J. Weidner (2008): Effect of phase transitions on compressional-wave velocities in the Earth's mantle, Nature , 454, 985-986.
FOR MORE INFORMATION
Li Li
Mineral Physics Institute, Stony Brook University, Stony Brook, NY, 11794, USA
Email: lilli@ic.sunysb.edu