One-dimensional modeling of multiple scattering in the upper inner core: Depth extent of a scattering region in the Eastern Hemisphere

Abstract

Attenuation of PKP(DF) in the Eastern Hemisphere is examined in terms of multiple scattering to simultaneously explain a puzzling relationship, a relatively fast velocity anomaly corresponding to strong attenuation. Reflectivity synthetics with one-dimensional random velocity fluctuations are compared with observations of PKP(DF)/PKP(Cdiff) amplitude ratios and differential travel times of PKP(Cdiff)-PKP(DF) for the equatorial paths. A Gaussian distribution of P-wave velocity fluctuations with the standard deviations of 5%, 6%, and 7% in the uppermost 200 km of the inner core is superimposed on the velocity structure that is slightly faster than the typical structure in the Eastern Hemisphere, which is likely to explain both the travel time and amplitude data as far as only the one-dimensional structure is considered. Further examinations of the statistic characteristic of scatterer distribution in two and three-dimensions are required to obtain a realistic conclusion.

Keywords

seismology / the inner core / attenuation / scattering

References

[1] Braginsky S J. Structure of the F Layer and Reasons for Convection in the Earth’s Core. Dokl. Akad. Nauk SSSR, 1963, 149: 8-10.

[2] Calvet M, Margerin L. Constraints on Grain Size and Stable Iron Phases in the Uppermost Inner Core from Multiple Scattering Modeling of Seismic Velocity and Attenuation. Earth Planet. Sci. Lett., 2008, 267(1–2): 200-212.

[3] Cao A, Romanowicz B. Hemispherical Transition of Seismic Attenuation at the Top of the Earth’s Inner Core. Earth Planet. Sci. Lett., 2004, 228(3–4): 243-253.

[4] Cormier V F, Li X, Choy G L. Seismic Attenuation of the Inner Core: Viscoelastic or Stratigraphic. Geophys. Res. Lett., 1998, 25(21): 4019-4022.

[5] Cormier V F, Li X. Frequency-Dependent Seismic Attenuation in the Inner Core 2. A Scattering and Fabric Interpretation. J. Geophys. Res., 2002, 107(B12): ESE 14-1-ESE 14-15.

[6] Cormier V F. Texture of the Uppermost Inner Core from Forward- and Back-Scattered Seismic Waves. Earth Planet. Sci. Lett., 2007, 258(3–4): 442-453.

[7] Deguen R. Structure and Dynamics of Earth’s Inner Core. Earth Planet. Sci. Lett., 2012, 333–334: 211-225.

[8] Hollerbach R, Jones C. Influnece of the Earth’s Inner Core on Geomagnetic Fluctuations and Reversals. Nature, 1993, 365: 541-543.

[9] Kennett B L N. Doornbos D J. Systematic Approximations to the Seismic Wavefield. Seismological Algorithms: Computational Methods and Computer Programs, 1988 London: Academic Press, 237-259.

[10] Knuth D E. Seminumerical Algorithms, 1997, 3rd ed. Reading, Massachusetts: Addison-Wesely, 762.

[11] J. Geophys. Res., 2007, 112 B5

[12] Li X, Cormier V F. Frequency-Dependent Seismic Atteunuation in the Inner Core, 1. A Viscoelastic Interpretation. J. Geophys. Res., 2002, 107(B12): ESE 13-1-ESE 13-20.

[13] Lister J, Buffett B. The Strength and Efficiency of Thermal and Compositional Convection in the Geodynamo. Phys. Earth Planet. Inter., 1995, 91: 17-30.

[14] Liu H P, Anderson D L, Kanamori H. Velocity Dispersion due to Anelasticity Implications for Seismology and Mantle Composition. Geophys. J. Int., 1976, 47: 41-58.

[15] Monnereau M, Calvet M, Margerin L, . Lopsided Growth of Earth’s Inner Core. Science, 2010, 328(5981): 1014-1017.

[16] Montagner J P, Kennett B L N. How to Reconcile Body-Wave and Normal-Mode Reference Earth Models. Geophys. J. Int., 1996, 125(1): 229-248.

[17] Morelli A, Dziewonski A M, Woodhouse J H. Anisotropy of the Inner Core Inferred from PKIKP Travel-Times. Geophys. Res. Lett., 1986, 13(13): 1545-1548.

[18] Müller G. The Reflectivity Method—A Tutorial. J. Geophys. Res., 1985, 58(1–3): 153-174.

[19] Press W H, Teukolsky S A, Vetterling W T, . Numerical Recipes in C: The Art of Scientific Computing, 1988 Cambridge: Cambridge Unversity Press, 994.

[20] Ryberg T, Tittgemeyer M, Wenzel F. Finite Difference Modeling of P-Wave Scattering in the Upper Mantle. Geophys. J. Int., 2000, 141(1): 787-800.

[21] Sato H, Fehler M. Seismic Wave Propagaion and Scattering in the Heterogeneous Earth, 1997 Berlin: Springer, 308.

[22] Song X D, Richards P G. Seismological Evidence for Differential Rotation of the Earth’s Inner Core. Nature, 1996, 382(6588): 221-224.

[23] Song X D, Helmberger D V. Seismic Evidence for an Inner Core Transition Zone. Science, 1998, 282(5390): 924-927.

[24] Souriau A, Romanowicz B. Anisotropy in Inner Core Attenuation: A New Type of Data to Constrain the Nature of the Solid Core. Geophys. Res. Lett., 1996, 23: 1-4.

[25] Souriau A. Romanowicz B, Dziewonski A M. Deep Earth Structure—The Earth’s Cores. Treatise on Geophysics, Vol. 1, Seismology and Structure of the Earth, 2007 Amsterdam: Elsevier, 655-693.

[26] Sumita I, Bergman M. Olson P. Inner-Core Dynamics. Treatise on Geophysics, Vol. 8, Core Dynamics, 2009 Amsterdam: Elsevier, 299-318.

[27] Tanaka S, Hamaguchi H. Degree One Heterogeneity and Hemispherical Variation of Anisotropy in the Inner Core from PKP(BC)-PKP(DF) Times. J. Geophys. Res., 1997, 102(B2): 2925-2938.

[28] Tanaka S. Depth Extent of Hemispherical Inner Core from PKP(DF) and PKP(Cdiff) for Equatorial Paths. Phys. Earth Planet. Inter., 2012, 210–211: 50-62.

[29] Tittgemeyer M, Wenzel F, Fuchs K, . Wave Propagation in a Multiple-Scattering Upper Mantle—Observations and Modeling. Geophys. J. Int., 1996, 127(2): 492-502.

[30] Tkalčić H. Large Variations in Travel Times of Mantle-Sensitive Seismic Waves from the South Sandwich Islands: Is the Earth’s Inner Core a Conglomerate of Anisotropic Domains?. Geophys. Res. Lett., 2010, 37 L14312.

[31] Watanabe T, Natori M, Oguni T. Numerical Calculation Softwares with Fortran77 (in Japanese). Maruzen, Tokyo, 1989, 325.

[32] J. Geophys. Res., 2002, 107 B11

[33] Woodhouse J H, Giardini D, Li X D. Evidence for Inner Core Anisotropy from Free Oscillations. Geophys. Res. Lett., 1986, 13(13): 1549-1552.

[34] J. Geophys. Res., 2005, 110 B2

[35] Yu W C, Wen L. Seismic Velocity and Attenuation Structures in the Top 400 km of the Earth’s Inner Core along Equatorial Paths. J. Geophys. Res., 2006, 111 B7 B07308