Lateral heterogeneity in the convecting mantle

Jarvis, Gary T.; Peltier, W. R.

doi:10.1029/jb091ib01p00435

Cited by 59 publications

(20 citation statements)

References 48 publications

(37 reference statements)

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“…This result is in accordance with earlier observations by Jarvis and Peltier (1986). This decrease in the rms temperature fluctuations with Rayleigh number has a profound effect on the convergence of the numerical methodology.…”

Section: Flow Structure and Basic Statisticssupporting

confidence: 94%

High rayleigh number convection at infinite prandtl number with weakly temperature-dependent viscosity

Balachandar

Yuen

Reuteler

1996

Geophysical & Astrophysical Fluid Dynamics

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The effects of high Rayleigh number convection for temperature-dependent viscosity at infinite Prandtl number are studied with three-dimensional direct numerical simulations (using a fully spectral method) in a wide box with dimensions 5 x 5 x 1. The form of the temperature-dependent viscosity decreases exponentially with the temperature. Solutions for an volumetrically averaged Rayleigh numbers up to 6.25 x lo6 have been obtained for a viscosity contrast of 25. Both models with and without viscous dissipation and adiabatic heatings have been considered. There is a distinct difference in the plume dynamics between models with a dissipation number D = 0 and D = 0.3. At zero dissipation number the hot plumes extend up to the top, while plumes at D = 0.3 are cooled due to adiabatic expansion and do not extend throughout the entire layer. The cold descending flows occur in sheets and they form longer wavelength networks and can reach the bottom, regardless of the value of D. A time-varying depth-dependent mean horizontal flow is produced from the correlation between the laterally varying viscosity field and the velocity gradients. At high Rayleigh number there is also a change in the surface toroidal velocity field to a coherent network of river-like structures and compact vortices. Viscous dissipation is found to increase with the Rayleigh number and is particularly strong in regions of downwelling flows. In the context of mantle convection, these localized heat sources are observed to be strong with local magnitudes in some places exceeding what Earth-like radioactive heating would be by more than an order of magnitude.

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Section: Flow Structure and Basic Statisticssupporting

confidence: 94%

High rayleigh number convection at infinite prandtl number with weakly temperature-dependent viscosity

Balachandar

Yuen

Reuteler

1996

Geophysical & Astrophysical Fluid Dynamics

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“…While at Ra = lo7 he found that by harmonic degree 50 the thermal variance had only decreased by a factor of 2. This is qualitatively similar to the results of the much simpler 2-D convection models of Jarvis & Peltier (1986).…”

Section: Comparisons To Convection Modelssupporting

confidence: 88%

Spectra of mantle shear wave velocity structure

Davies¹,

Guðmundsson²,

Clayton

1992

Geophysical Journal International

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S U M M A R YWe applied the stochastic method of Gudmundsson, Davies & Clayton (1990) (which was applied to ISC P-wave data) to teleseismic ISC S-wave data to obtain an independent estimate of mantle structure. We inverted the variance of S-wave traveltime residuals of bundles of rays to obtain a description of the spectrum of lateral heterogeneity as a function of depth through the mantle. The technique yields robust estimates of the traveltime scattering power (the product of a characteristic scalelength of heterogeneity and the mean square of slowness perturbations). We can estimate the characteristic scalelength (half-width), from the autocovariance; which can be reconstructed from the spectra. Hence by division, we can estimate the root mean square slowness. By extrapolating the variance of bundles of rays to bundles of zero cross-sectional area we can also estimate the scale-incoherent signal (which is a plausible estimate of the noise in the data), which is removed from the data.We find that most of the structure generating shear wave traveltime residuals is located in the uppermost mantle. About half of the structure is short scale (harmonic degree 1 > 50). The large-scale structure (1 < 50) has a half-width of about 500 km in the upper half of the mantle. This S-wave half-width is consistent with the P-wave half-widths determined by Gudmundsson et al. (1990). The S-wave half-width in the lower half of the mantle is poorly constrained. It varies from 500 to 3000km, which spans the better constrained value of 1200 km found by Gudmundsson et al. (1990) for P-waves. The incoherent scatter suggests that the signal-to-noise ratio of the S-wave data set is around 1.5.Assuming that the compressional and shear wave velocity variations are correlated then the signal weighted value of the ratio d In ( y . ) l d In (y,) is =2, as also found in normal mode studies. This is much larger than the value of ~0 . 8 -1 . 4 suggested by laboratory experiments undertaken at atmospheric pressure. There is no evidence of periodicity in the traveltime autocovariance; this suggests little or no periodicity in the underlying convection. The short half-width through most of the mantle suggests high Rayleigh number convection, with its attendant small-scale structures. The power decreases by an order of magnitude or more in going from the upper mantle to the lower mantle, the same as found by Gudmundsson et al. (1990) for P-waves. This large difference suggests either a change in convective regime and/or a difference in the temperature sensitivity of elastic constants in both layers. The increased short-scale structure at the top of the mantle suggests that a large part of the seismic signature at this boundary is compositional, since one would expect a red spectrum for a thermal boundary layer. The derived spectra between 1 = 10 and I = 50 are similar in shape to spectra from the mantle convection simulations of Glatzmaier (1988) with a Rayleigh number of 106-107, which would suggest layered convection, if the comparison is valid.

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“…Some of our results may be used to make qualitative inferences about mantle dynamics. In the steady state Benard convection scenario, Jarvis & Peltier (1986) find that the convective boundary layers have a very narrow low-degree spectrum of lateral temperature variations, while the interiors of convection cells possess a relatively broad spectrum. This contradicts our finding of a decrease in correlation length towards the extremes of the mantle.…”

Section: Discussion a N D Conclusionmentioning

confidence: 99%

Stochastic analysis of global traveltime data: mantle heterogeneity and random errors in the ISC data

Guðmundsson

Davies

Clayton

1990

Geophysical Journal International

133

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Analysis of global traveltime data has been formulated in terms of the stochastic properties of the Earth's heterogeneity pattern and random errors in the data. The formalism relates the coherency of traveltime residuals within bundles of rays (summary rays) of varying size to the spherical harmonic power spectrum of the slowness field of the medium. It has been applied to mantle P-wave data from the ISC catalogue. The measure of coherency is the variance within summary rays. It is estimated within bins in source depth, epicentral distance and the scale size of the area defining a summary ray. The variance at infinitesimal scale length represents the incoherent component of the data (random errors). The variation of the variance with scale length contains information about the autocorrelation function or power spectrum of slowness perturbations within the Earth. The variation with epicentral distance reflects the depth variation of the spectrum. The formalism accounts for the uneven distribution (clustering) of stations and events.We find that estimates of random errors correlate well with complexities on the traveltime curve of P-waves. The variance peaks at 1.0-2.0 s2 at A = 20", where triplications occur on the traveltime curve, drops to 0.15-0.8 s2 at teleseismic distances, and rises to 0.4-1.3 s2 approaching the core shadow, where the traveltime curves of P-waves and PcP-waves merge. These estimates should be considered upper bounds for the random error variance of the data. The signal to random noise ratio in the teleseismic ISC P-wave data is about SIN = 2.Inversion of the scale-dependent structural signal in the data yields models that concentrate heterogeneity strongly in the upper mantle. The product of correlation length and power drops by about two orders of magnitude from the surface of the Earth to the lower mantle. About half of this quantity in the upper mantle is due to small-scale features (<300 km). The lower mantle is devoid of small-scale structure. It contains 0.1 per cent velocity variations at a characteristic scale of about lo00 km. This corresponds to a spectral band-width of 1~7 .The D" layer at the bottom 100-200 km of the mantle shows up as a distinct layer in our results. It has 0.3 per cent velocity variations at a characteristic scale of 350 km. The top of the lower mantle contains 0.3 per cent velocity variations on a scale of 500 km and also contains some srnall-scale power.These results are compatible with previous deterministic lower mantle studies, although some details differ. The strength of heterogeneity in the upper mantle may obscure attempts to model the Earth's deep interior.

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Lateral heterogeneity in the convecting mantle

Cited by 59 publications

References 48 publications

High rayleigh number convection at infinite prandtl number with weakly temperature-dependent viscosity

High rayleigh number convection at infinite prandtl number with weakly temperature-dependent viscosity

Spectra of mantle shear wave velocity structure

Stochastic analysis of global traveltime data: mantle heterogeneity and random errors in the ISC data

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