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Causality and Its Implications for the Interpretation of Seismological Observations on the Upper Mantle
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DOI：10.1029/2024JB030639.png)
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Abstract
En 中文
Seismic wave velocities in the hot mantle are affected by non-elastic, time-dependent deformation and hence depend on frequency ( V S , P ( ω ) ${V}_{S,P}(\omega )$ ). We show that the principle of causality leads to a seismological Kramers-Kronig relation log V S , P ( ω ) V S , P ( ∞ ) ≅ − Δ V S , P V S , P ( ∞ ) = − 1 π ∫ log ω ∞ Q − 1 ( ξ ) · dlog ξ $\log \left[\frac{{V}_{S,P}\,(\omega )}{{V}_{S,P}\,(\infty )}\right]\mathit{\cong }-\frac{{\Delta }{V}_{S,P}}{{V}_{S,P}(\infty )}=-\frac{1}{\pi }\int \nolimits_{\log \,\omega }^{\infty }{Q}^{-1}(\xi )\mathit{\cdot }\text{dlog}\xi $ where Q − 1 ( ω ) ${Q}^{-1}(\omega )$ is attenuation caused by non-elastic deformation. This relation indicates that the frequency dependence of seismic wave velocity comes from Q − 1 ( ω ) ${Q}^{-1}(\omega )$ (attenuation) integrated over all frequencies above the frequency at which the wave velocity is measured. A frequently used relation Δ V S , P V S , P ( ∞ ) ≅ Q − 1 ( ω ) $\frac{{\Delta }{V}_{S,P}}{{V}_{S,P}(\infty )}\mathit{\cong }{Q}^{-1}(\omega )$ can be derived from this relation if Q − 1 ( ω ) ∝ ω − α ${Q}^{-1}(\omega )\mathit{\propto }{\omega }^{-\alpha }$ (with α ≅ $\alpha \mathit{\cong }$ 0.3 for ω L < ω < ω H ${\omega }_{L}< \omega < {\omega }_{H}$ ) but Q − 1 ( ω ) = 0 ${Q}^{-1}(\omega )=0$ for ω > ω H $\omega > {\omega }_{H}$ . The validity of this relation is tested using seismologically estimated seismic wave velocities and attenuation in the asthenosphere. We find that Δ V S , P V S , P ( ∞ ) ≫ Q − 1 ( ω ) $\frac{{\Delta }{V}_{S,P}}{{V}_{S,P}(\infty )}\mathit{\gg }{Q}^{-1}(\omega )$ , that is, the above relation ( Δ V S , P V S , P ( ∞ ) ≅ Q − 1 ( ω ) ) $(\frac{{\Delta }{V}_{S,P}}{{V}_{S,P}(\infty )}\mathit{\cong }{Q}^{-1}(\omega ))$ is not consistent with the seismological observations on the asthenosphere. This implies that there is a mechanism of attenuation at high frequencies ω > ω H $\left(\omega > {\omega }_{H}\right.$ ) that causes substantial (∼5%) velocity reduction (such as elastically accommodated grain-boundary sliding (EAGBS)). Consequently, even when one uses low-frequency seismic wave velocities to understand the Earth structure, the influence of high-frequency anelasticity on seismic wave velocity needs to be included to infer properties related to anelasticity (e.g., temperature). Experimental results on EAGBS in olivine are reviewed and we conclude that EAGBS results in substantial velocity reduction when olivine contains a large amount of water (>100 ppm wt water) but not under water-poor conditions. The reported large velocity reduction at the lithosphere-asthenosphere boundary therefore suggests that the asthenosphere contains a substantial amount of water.
Keywords:
causality
Kramers-Kronig relation
velocity anomalies
seismic attenuation
grain-boundary sliding
water
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J
IF:
4.1
Papers:
1.4W
Citations:
6.4W
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