On the nature of the P-wave velocity gradient in the inner core beneath Central America

Abstract

We conduct an experiment to investigate whether linearity in the observed velocity gradient in the volume of the inner core sampled by the PKP ray paths beneath Central America is a robust approximation. Instead of solving an optimization problem, we approach it within the Bayesian inference. This is an ensemble approach, where model specification is relaxed so that instead of only one solution, groups of reasonable models are acceptable. Furthermore, in transdimensional Bayesian inference used here, the number of basis functions needed to model observations is by itself an unknown. Our modeling reveals that in the ensemble of models, the most likely are those containing only 2 nodes (linear trend). Thus our result justifies the assumption used for the determination of inner core rotation with respect to the rest of the mantle that the observed gradient is constant in its nature (linear). Recent observations in seismology suggest that it is likely that the spatial variability in elastic parameters is a widespread phenomenon in the inner core. Future array observations will further constrain spatial extent and magnitude of velocity changes and show whether there is a significant difference between these observations in the two quasi-hemispheres of the inner core.

Keywords

solid earth physics / deep geophysics

References

[1] Bayes T. An Essay towards Solving a Problem in the Doctrine of Chances. Phyl. Trans., 1763, 53: 370-418.

[2] J. Geophys. Res., 2012, 117 B2

[3] Bréger L, Tkalčić H, Romanowicz B. The Effect of D” on PKP(AB-DF) Travel Time Residuals and Possible Implications for Inner Core Structure. Earth Planet. Sci. Lett., 2000, 175: 133-143.

[4] Calvet M, Chevrot S, Souriau A. P-Wave Propagation in Transversely Isotropic Media II. Application to Inner Core Anisotropy: Effects of Data Averaging, Parametrization and a Priori Information. Phys. Earth Planet. Inter., 2006, 156: 21-40.

[5] Creager K C. Inner Core Rotation Rate from Small-Scale Heterogeneity and Time-Varying Travel Times. Science, 1997, 278: 1284-1288.

[6] Denison D G T, Holmes C, Mallick B, . Bayesian Methods for Nonlinear Classification and Regression, 2002 Hoboken: John Wiley & Sons

[7] Deguen R, Alboussière T, Brito D. On the Presence and Structure of a Mush at the Inner Core Boundary of the Earth. Phys. Earth Planet. Inter., 2007, 274: 1887-1891.

[8] Garcia R, Tkalčić H, Chevrot S. A New Global PKP Data Set to Study Earth’s Core and Deep Mantle. Phys. Earth Planet. Int., 2006, 159: 15-31.

[9] Gallagher K, Bodin T, Sambridge M, . Inference of Abrupt Changes in Noisy Geochemical Records Using Bayesian Transdimensional Change Point Models. Earth Planet. Sci. Lett., 2011, 311: 182-194.

[10] Green P. Reversible Jump MCMC Computation and Bayesian Models Selection. Biometrika, 1995, 82: 711-732.

[11] Green P. Trans-dimensional Markov Chain Monte Carlo. Highly Structured Stochastic Systems, 2003, 27: 179-198.

[12] Hastings W. Monte Carlo Simulation Methods Using Markov Chains and Their Applications. Biometrika, 1970, 57: 97-109.

[13] Irving J C E, Deuss A. Hemispherical Structure in Inner Core Velocity Anisotropy. J. Geophys. Res., 2011, 116 B04307

[14] Kennett B L N, Engdahl E R, Buland R. Constraints on Seismic Velocities in the Earth from Travel Times. Geophys. J. Int., 1995, 122: 108-124.

[15] Leykam D, Tkalčić H, Reading A M. Core Structure Re-Examined Using New Teleseismic Data Recorded in Antarctica: Evidence for, at Most, Weak Cylindrical Seismic Anisotropy in the Inner Core. Geophys. J. Int., 2010, 180(3): 1329-1343.

[16] Lindner D, Song X D, Ma P, . Inner Core Rotation and Its Variability from Nonparametric Modeling. J. Geophys. Res., 2010, 115 B14 4307

[17] Mäkinen A M, Deuss A. Global Seismic Body-Wave Observations of Temporal Variations in the Earth’s Inner Core, and Implications for Its Differential Rotation. Geophys. J. Int., 2011, 187: 355-370.

[18] McSweeney T J, Creager K C, Merrill R T. Depth Extent of Inner Core Seismic Anisotropy and Implications for Geomagnetism. Phys. Earth Planet. Inter., 1997, 101: 131-156.

[19] Metropolis N, Rosenbluth A W, Rosenbluth M N, . Equations of State Calculations by Fast Computational Machine. J. Chem. Phys., 1953, 21: 1087-1091.

[20] Romanowicz B, Tkalčić H, Breger L. On the Origin of Complexity in PKP Travel Time Data from Broadband Records. AGU Volume on Inner Core and Lower Mantle. AGU Geodynamics Series, 2003, 31: 31-44.

[21] Sambridge M, Bodin T, Gallagher K, . Transdimensional Inference in Geosciences. Phil. Trans. R. Soc. A, 2013, 371 20110547

[22] Song X D. Joint Inversion for Inner Core Rotation, Inner Core Anisotropy, and Mantle Heterogeneity. J. Geophys. Res., 2000, 105: 7931-7943.

[23] Stroujkova A, Cormier V F. Regional Variations in the Uppermost 100 km of the Earth’s Inner Core. J. Geophys. Res., 2004, 109 B10307

[24] 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: 2925-2938.

[25] Tkalčić H, Romanowicz B, Houy N. Constraints on D” Structure Using PKP(AB-DF), PKP(BC-DF) and PcP-P Traveltime Data from Broadband Records. Geophys. J. Int., 2002, 149: 599-616.

[26] 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.

[27] Tkalčić H, Young M, Bodin T, . The Shuffling Rotation of the Earth’s Inner Core Revealed by Earthquake Doublets. Nature Geoscience, 2013, 6: 497-502.

[28] Waszek L, Deuss A. Distinct Layering in the Hemispherical Seismic Velocity Structure of Earth’s Upper Inner Core. J. Geophys. Res., 2011, 116 B12313

[29] Zhang J, Song X D, Li Y, . Inner Core Differential Motion Confirmed by Earthquake Waveform Doublets. Science, 2005, 309: 1357-1360.

[30] Zhao D, Lei J. Seismic Ray Path Variations in a 3D Global Velocity Model. Phys. Earth Planet. Sci. Inter., 2004, 141: 153-166.