Research ArticleGEOPHYSICS

Elastic properties of silicate melts: Implications for low velocity zones at the lithosphere-asthenosphere boundary

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Science Advances  13 Dec 2017:
Vol. 3, no. 12, e1701312
DOI: 10.1126/sciadv.1701312
  • Fig. 1 Relationship between density and velocity for silicate crystals, glasses, and melts.

    Dashed lines are lines of constant mean atomic weight (m); the molecular weight is divided by the number of atoms in the chemical formula. Birch’s Law states that for a constant m, there is a linear relationship between density and velocity. One-atm (1-atm) and high-pressure data for crystalline silicates follow Birch’s Law (dashed lines). One-atm data for glasses and melts are shown as labeled fields, with 1-atm data for melts shown as red diamonds [see the studies of Clark et al. (9) and Rivers and Carmichael (26) for further information]. High-pressure data (<6 to 10 GPa) for silicate glasses are shown as symbols with the compositions labeled (9, 15, 35, 36).

  • Fig. 2 Conceptual models of the melt geometry used in these calculations.

    Geometry 1 is based on the studies of Berryman (37, 38). Geometry 2 is modified from Takei (11), Mavko (12), and Schmeling (39). Geometry 3 is modified from Holtzman and coworkers (6, 22). The effect of any intermediate geometry on seismic velocities can be modeled by modifying the aspect ratio (α) in Eqs. 3 and 4 [see the study of Takei (11) for further discussion of the derivation of α].

  • Fig. 3 Bulk modulus (KS) as a function of depth for silicate melt and the crystalline mantle.

    Silicate melts modeled using the NFD model (solid curve) and using the third-order BM EoS (dashed curve). KS for the solid is calculated from the ak135-f 1D global model (dotted curve) (23). Envelopes for the BM EoS model and the NFD model are in green and blue, respectively, and account for variations in density model and elastic properties for the melt phase as reported in the literature. (Inset) Ratio of the solid to liquid bulk moduli (β) as a function of depth for silicate melts modeled using the NFD model and using the third-order BM EoS. The thin curves correspond to variations due to density model (fig. S1) and elastic properties for the melt phase reported herein.

  • Fig. 4 Effect of varying melt fraction and geometry on seismic velocity reductions calculated as a function of depth.

    (A) Reduction in seismic velocity (ΔV) for P and S waves (solid and dashed curves, respectively) as a function for pressure in equilibrated melt texture (geometry 2) for 0.01, 0.03, and 0.05 melt fraction shown as blue, green, and red curves, respectively, using the NFD model for the compressibility of the silicate liquid. (B) ΔV using BM EoS for the silicate liquid compressibility. (C) RSP calculated as a function of depth for the NFD model and BM EoS shown as black and gray curves, respectively. Melt geometry 1, 2, and 3 are shown as dotted, solid, and dashed curves, respectively. For clarity, the curves shown are calculated using the average value in Fig. 3. Curves with analysis for possible variations in density and KS for the melt phase are given in the Supplementary Materials. Boxes indicate the values of ΔV and RSP from recent seismic studies (24). The bold box for ΔV is the reported value, whereas the shaded box is for error. For seismic studies, the assumed transition width (thickness) of the low velocity layer affects the magnitude of ΔV (see the Supplementary Materials for geometries 1 and 3).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/12/e1701312/DC1

    fig. S1. Density of a mafic (basalt) melt as a function of pressure.

    fig. S2. Comparison of velocity profiles for 1D global average models.

    fig. S3. Comparison of model parameters for the ak135-f and PREM 1D global average reference models.

    fig. S4. P and S wave velocity reductions for all melt geometries.

    fig. S5. Analysis of variation in melt properties on the calculated P wave velocity reduction.

    fig. S6. Analysis of variation in melt properties on the calculated S wave velocity reduction.

    fig. S7. Analysis of variation in melt properties on the calculated RSP values.

    Reference (40)

  • Supplementary Materials

    This PDF file includes:

    • fig. S1. Density of a mafic (basalt) melt as a function of pressure.
    • fig. S2. Comparison of velocity profiles for 1D global average models.
    • fig. S3. Comparison of model parameters for the ak135-f and PREM 1D global average reference models.
    • fig. S4. P and S wave velocity reductions for all melt geometries.
    • fig. S5. Analysis of variation in melt properties on the calculated P wave velocity reduction.
    • fig. S6. Analysis of variation in melt properties on the calculated S wave velocity reduction.
    • fig. S7. Analysis of variation in melt properties on the calculated RSP values.
    • Reference (40)

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