TY - JOUR

T1 - Convective mixing and the fine structure of mantle heterogeneity

AU - Olson, Peter

AU - Yuen, David A.

AU - Balsiger, Derick

PY - 1984/12/30

Y1 - 1984/12/30

N2 - A simple theoretical model is presented for the statistical distribution of small-scale, passive heterogeneity in a convecting mantle. The important new variables used to characterize the anomaly field are the autocorrelation function R and its Fourier transform, the energy spectrum E. The anomaly variance, the sample variance (i.e., the anomaly variance as filtered by the sampling process) and the mixing time scale are expressed in terms of E. Equations governing the time evolution of R and E are derived, starting with the transport-diffusion equation. The energy spectrum equation is solved for deformation models with homogeneous normal and shear strain components. The predictions from these models are compared with results of numerical experiments on mixing of slab-shaped heterogeneities by Bénard convection. Both the numerical experiments and the theory indicate that compositional heterogeneity subjected to convective flow becomes drawn into thin sheets oriented subparallel to the transport direction. Re-mixing of subducted slabs produces a laminated mantle. The energy spectrum of the laminate is highly anisotropic. Where the transport direction is predominantly horizontal, the energy at high wave numbers is in the vertical; the low wave number energy is in the horizontal plane. The shape of the energy spectrum contains information on mean mantle strain rates, age of the anomalies, and solid state diffusion rates.

AB - A simple theoretical model is presented for the statistical distribution of small-scale, passive heterogeneity in a convecting mantle. The important new variables used to characterize the anomaly field are the autocorrelation function R and its Fourier transform, the energy spectrum E. The anomaly variance, the sample variance (i.e., the anomaly variance as filtered by the sampling process) and the mixing time scale are expressed in terms of E. Equations governing the time evolution of R and E are derived, starting with the transport-diffusion equation. The energy spectrum equation is solved for deformation models with homogeneous normal and shear strain components. The predictions from these models are compared with results of numerical experiments on mixing of slab-shaped heterogeneities by Bénard convection. Both the numerical experiments and the theory indicate that compositional heterogeneity subjected to convective flow becomes drawn into thin sheets oriented subparallel to the transport direction. Re-mixing of subducted slabs produces a laminated mantle. The energy spectrum of the laminate is highly anisotropic. Where the transport direction is predominantly horizontal, the energy at high wave numbers is in the vertical; the low wave number energy is in the horizontal plane. The shape of the energy spectrum contains information on mean mantle strain rates, age of the anomalies, and solid state diffusion rates.

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U2 - 10.1016/0031-9201(84)90053-0

DO - 10.1016/0031-9201(84)90053-0

M3 - Article

AN - SCOPUS:0021570115

VL - 36

SP - 291

EP - 304

JO - Physics of the Earth and Planetary Interiors

JF - Physics of the Earth and Planetary Interiors

SN - 0031-9201

IS - 3-4

ER -