Model Of Upper Mantle Research Articles

Assessing the depth resolution of tomographic models of upper mantle structure beneath Iceland

Earlier inversions of body wave delay‐time data recorded during the ICEMELT portable broadband experiment imaged a cylindrical plume‐like low‐velocity anomaly extending to at least 400 km depth beneath Iceland, but the depth extent of the anomaly resolvable by tomography has recently been called into question. We have performed several additional resolution tests to evaluate the depth resolution of tomographic models of the Icelandic upper mantle. The distribution of paths of body waves recorded by ICEMELT can distinguish among three different types of models: (a) a wide and shallow anomaly, (b) a narrow and deep anomaly, and (c) a narrow and shallow anomaly. While tomographic models contain an element of nonuniqueness, these tests illustrate that the depth resolution of passive seismic experiments spanning subaerial Iceland is adequate for distinguishing among alternative geodynamic models.

Regional wave propagation in Tanzania, East Africa

Crust and upper mantle structure under Tanzania, East Africa, is investigated using broadband waveforms and phase travel times collected from regional events recorded by the 1994–1995 Tanzania Broadband Seismic Experiment. Broadband displacement waveforms from the mL 5.9 Rukwa graben earthquake (18 August 1994) are modeled using a wave number integration algorithm and a new “phase time” inversion technique to infer a very simple crustal and upper mantle model that can be used for waveform studies of other regional earthquakes in the area. Displacement amplitudes for all phases in the data are predicted quite well using source parameters determined from a previous study of teleseismic waveforms. The crust is parameterized by a linear gradient in velocity defined by surface and Moho P velocities, Poisson's ratio, and crustal thickness. This simple parameterization is sufficient to explain arrival times and waveshapes of the three‐component waveforms recorded between 200 and 800 km at stations located on the craton and Mozambique belt. The S wave train consists of Sn, multiple Sn, and critically reflected S wave multiples in the crustal waveguide, in addition to the fundamental mode Rayleigh wave. High phase velocity, critical S wave reflections are seen to form the low group velocity Lg phase. Prominent sP depth phases are seen in the regional waveform data which can be used to infer accurate source depths for events in the region. The Tanzania craton and adjacent Mozambique belt crustal structure is simple and laterally homogeneous, showing few effects of rift disruption. High wave velocities in the uppermost mantle suggest little thermal modification from rifting processes of the East African Rift.

Anisotropy in the Australasian upper mantle from Love and Rayleigh waveform inversion

Abstract Records of both Rayleigh and Love waves have been analyzed to determine the pattern of anisotropy in the Australasian region. The approach is based on a two-stage inversion. Starting from a smooth PREM model with transverse isotropy about a vertical symmetry axis, the first step is an inversion of the waveforms of surface waves to produce path specific one-dimensional (1-D) upper mantle models. Under the assumption that the 1-D models represent averages along the paths, the results from 1584 Love and Rayleigh wave seismograms are combined in a tomographic inversion to provide a representation of three-dimensional structure for wavespeed heterogeneities and anisotropy. Polarization anisotropy with SH faster than SV is retrieved in the upper 200–250 km of the mantle for most of Precambrian Australia. In this depth interval, significant lateral variations in the level of polarization anisotropy are present. Locally, the anisotropy can be large, reaching an extreme value of 9% that is difficult to reconcile with current mineralogical models. However, the discrepancy may be explained in part by the presence of strong lateral heterogeneities along the path, or by effects introduced by the simplifying assumption of transverse isotropy for each path. The consistency between the location of polarization and azimuthal anisotropy in depth suggests that both observations share a common origin. The observation of polarization anisotropy down to at least 200 km supports a two-layered anisotropic model as constrained by the azimuthal anisotropy of SV waves. In the upper layer, 150 km thick, anisotropy would be related to past deformation frozen in the lithosphere while in the lower layer, anisotropy would reflect present day deformation due to plate motion.

Flexible computation of teleseismic synthetics for source and structural studies

SUMMARY The modelling of P and S arrivals at teleseismic distances, for shallow sources, requires the consideration of the interaction of the direct arrivals and their surface reflections (pP, sP and pS, sS). A flexible computational scheme has been developed to allow for distinct crustal and upper mantle structures beneath source and receiver with full allowance for reverberation effects. The seismic response to a point moment tensor source is built up from the reflection and transmission properties of portions of the media in the frequency–slowness domain. This allows control of the propagation processes in the shallower parts of the model. A simple representation is used for the contribution from the lower mantle that can also be adapted to include core reflections and refractions. The response at each receiver is calculated using a restricted slowness integral over a bundle of slownesses surrounding the geometric slowness for each group of phases. Thus, for example, P, pP and sP can be calculated together without the cost of a full reflectivity treatment. This teleseismic calculation scheme provides a good representation of the main P or S arrivals at teleseismic distances over a wide range of frequencies and can be used for both source and structural studies. The method is illustrated by showing the influence of regional upper mantle models on the nature of the seismograms. There can be significant changes in the relative amplitudes of the direct and surface-reflected phases, which would modify inferences about source mechanism. An observational example using broad-band P and S arrivals from an event in the Fiji region, recorded at a network of stations in northwestern Australia, illustrates the way in which surface-reflected phases can provide useful constraints on event depth, and also how deviations from the predicted seismograms for a reference model can be used for structural investigations.

Investigation of Crust and Upper-Mantle Structure in the Black Sea with Group-Velocity Data

In this study, crust and upper-mantle structure in the Black Sea have been investigated by measuring the group-velocity dispersion data of seismic surface waves. Structural models for the profiles between Istanbul station (IST) and six earthquakes that occurred near the northeastern coast of the Black Sea have been constructed. These six profiles are approximately in the NE–SW direction and across the Black Sea. Seismograms of Rayleigh waves for four earthquakes and both Love and Rayleigh waves for two earthquakes have been analyzed. Group velocities have been computed with the multiple filter technique (MFT) from the vertical and/or horizontal component records of six selected earthquakes. Crust and upper-mantle structure for each profile has been estimated by trial and error fitting of these group-velocity values. A three-layered crustal model has been determined for all the profiles. Density values of the layers are identical for all models except for profile 1, of which one part lies in Anatolia. Thickness and density values of the layers in the crust and upper-mantle structure models obtained from the analyses of both Love and Rayleigh waves for the same profile (for profiles 2 and 6, individually) are identical. There are small changes in the velocity values. When the profiles are compared among themselves, it is shown that the crust is getting thinner from south to north, i.e., toward the center of the Black Sea basin.

Early formation and long-term stability of continents resulting from decompression melting in a convecting mantle

The origin of stable old continental cratonic roots is still debated. We present numerical modelling results which show rapid initial formation during the Archaean of continental roots of ca. 200 km thick. These results have been obtained from an upper mantle thermal convection model including differentiation by pressure release partial melting of mantle peridotite. The upper mantle model includes time-dependent radiogenic heat production and thermal coupling with a heat reservoir representing the Earth's lower mantle and core. This allows for model experiments including secular cooling on a time-scale comparable to the age of the Earth. The model results show an initial phase of rapid continental root growth of ca. 0.1 billion year, followed by a more gradual increase of continental volume by addition of depleted material produced through hot diapiric, convective upwellings which penetrate the continental root from below. Within ca. 0.6 Ga after the start of the experiment, secular cooling of the mantle brings the average geotherm below the peridotite solidus thereby switching off further continental growth. At this time the thickness of the continental root has grown to ca. 200 km. After 1 Ga of secular cooling small scale thermal instabilities develop at the bottom of the continental root causing continental delamination without breaking up the large scale layering. This delaminated material remixes with the deeper layers. Two more periods, each with a duration of ca. 0.5 Ga and separated by quiescent periods were observed when melting and continental growth was reactivated. Melting ends at 3 Ga. Thereafter secular cooling proceeds and the compositionally buoyant continental root is stabilized further through the increase in mechanical strength induced by the increase of the temperature dependent mantle viscosity. Fluctuating convective velocity amplitudes decrease to below 10 mma −1 and the volume average temperature of the sub-continental convecting mantle has decreased ca. 340 K after 4 Ga. Surface heatflow values decrease from 120 to 40 mW m −2 during the 4 Ga model evolution. The surface heatflow contribution from an almost constant secular cooling rate was estimated to be 6 mW m −2, in line with recent observational evidence. The modelling results show that the combined effects of compositional buoyancy and strong temperature dependent rheology result in continents which overall remain stable for a duration longer than the age of the Earth. Tracer particles have been used for studying the patterns of mantle differentiation in greater detail. The observed ( p, T, F, t)-paths are consistent with proposed stratification and thermo-mechanical history of the depleted continental root, which have been inferred from mantle xenoliths and other upper mantle samples. In addition, the particle tracers have been used to derive the thermal age of the modelled continental root, defined by a hypothetical closing temperature.

Seismic waveform modeling and surface wave tomography in a three-dimensional Earth: asymptotic and non-asymptotic approaches

We investigate the impact of the theoretical limitations brought by asymptotic methods on upper-mantle tomographic models deduced from long-period surface wave data (period >80 s), by performing a synthetic test using a non-asymptotic formalism. This methodology incorporates the effects of back and multiple forward scattering on the wave field by summing normal modes computed to third order of perturbations directly in the 3D Earth, and models the sensitivity to scatterers away from the great-circle path. We first compare the methods we used for the forward problem, both theoretically and numerically. Then we present results from the computation of 7849 synthetic Love waveforms in an upper mantle model consisting of two heterogeneities with power up to spherical harmonic degree 12. The waveforms are subsequently inverted using a 0th order asymptotic formalism (equivalent to a path-average approximation in the surface waves domain). We show that the main structures are retrieved, but that the theoretical noise on the output model is of the same order as the noise due to the path-coverage and a priori constraints.

The significance of shear heating in continental delamination

Most numerical models of continental delamination processes, up to now, have not considered the effects of viscous heating in the thermo-mechanics of a geological system with both thermal and compositional buoyancies. We have studied the influence of viscous heating in the continental delamination problem using a two-dimensional finite-difference model with markers to delineate the distribution of crustal and mantle rheologies and the compositional buoyancy forces. This upper-mantle model consisting of a two-component crust and an olivine mantle is driven by both thermal and compositional buoyancy forces. For the advection of the different crust and mantle components, we have used 180 000 markers for the lower resolution, and up to 1.5 million markers for the highest resolution. A quasi-brittle rheology is employed in the lithosphere. The ductile rheology is non-Newtonian in the crust and mantle. We have employed a high resolution grid of up to 201×401 finite difference points for the momentum equation in order to resolve the fine features associated with viscous heating. The spatial resolution for the temperature grid is four times higher, being as fine as 840 m, while the densest grid for the streamfunction is 3.35 km. The effective thermal Rayleigh number hovers around O(10 6) and the chemical Rayleigh number is slightly larger. Comparison has been conducted between models with and without shear heating. Noticeable differences in the thermal fields, up to several hundred degrees, are found in certain localized areas, adjacent to the descending continental root, which can go down to around 300 km depth. There are greater thermal fluctuations in the regions with pronounced amounts of viscous dissipation. We found that there is a spatial correlation between the regions with a significant release of gravitational potential energy due to the varying large undulations of the crust–mantle interface and regions with significant viscous heating in the crust. The timescales of the dynamics, O(10 4a), are considerably reduced during the intense shear-heating episodes, as revealed by the dramatic increase in the number of time-steps needed for maintaining a proper temporal resolution.

Body waveform modeling of east Mediterranean earthquakes at intermediate distances (17°–30°) with a Gaussian beam summation method

We study eastern Mediterranean earthquakes in the magnitude range 5.5–6.5 by body waveform modeling at distances between 17° and 30°. We compute synthetics at these distances using the Gaussian beam summation (GBS) method, taking into account all waves refracted and reflected by the upper mantle discontinuities. Modeling depends crucially on the choice of an appropriate upper mantle model. Using the well‐known May 13, 1995, Kozani‐Grevena event in Greece, we choose a representative column of the 3SMAC upper mantle model as an average velocity structure for modeling eastern Mediterranean earthquakes recorded in Europe. We studied three events with different tectonic settings, location, and magnitude. For the July 20, 1996, Dodecanese earthquake we determined a depth of 12.5 km, a source duration of 6 s, and a seismic moment of 1.20×1018 Nm. Most of the seismograms for this event are very well modeled. Using only seismograms recorded at the epicentral range 17°–30°, we modeled the October 1, 1995, Turkey event. We find a depth of 9 km and a normal fault mechanism in agreement with the regional tectonic setting. Finally, we studied the February 23, 1995, earthquake in Cyprus for which we retrieved depth, source time function, and a seismic moment of 2.04×1018 Nm. The upper mantle phases for all these events are well identified and modeled. We conclude that GBS can be used to model seismograms at intermediate distances, retrieving information about both fault plane solution, depth and source time functions. Propagation effects are also observed, but they can not be inverted with this limited data set.

The deep structure of the Australian continent from surface wave tomography

We present a new model of 3-D variations of shear wave speed in the Australian upper mantle, obtained from the dispersion of fundamental and higher-mode surface waves. We used nearly 1600 Rayleigh wave data from the portable arrays of the Skippy project and from permanent stations (from Agso, Iris and Geoscope). Agso data have not been used before and provide better data coverage of the Archean cratons in western Australia. Compared to previous studies we improved the vertical parameterization, the weighting scheme that accounts for variations in data quality and reduced the influence of epicenter mislocation on velocity structure. The dense sampling by seismic waves provides for unprecedented resolution of continental structure, but the wave speed beneath westernmost Australia is not well constrained. Global compilations of geological and seismological data (using regionalizations based on tectonic behavior or crustal age) suggest a correlation between crustal age and the thickness and composition of the continental lithosphere. However, the age and the tectonic history of crustal elements vary on wavelengths much smaller than have been resolved with global seismological studies. Using our regional upper mantle model we investigate how the seismic signature of tectonic units changes with increasing depth. At large wavelengths, and to a depth of about 200 km, the inferred velocity anomalies corroborate the global pattern and display a progression of wave speed with crustal age: slow wave propagation prevails beneath the Paleozoic fold belts in eastern Australia and wave speeds increase westward across the Proterozoic and reach a maximum in the Archean cratons. The high wave speeds associated with Precambrian shields extend beyond the Tasman Line, which marks the eastern limit of Proterozoic outcrop. This suggests that parts of the Paleozoic fold belts are underlain by Proterozoic lithosphere. We also infer that the North Australia craton extends off-shore into Papua New Guinea and beneath the Indian Ocean. For depths in excess of 200 km a regionalization with smaller units reveals that some tectonic subregions of Proterozoic age are marked by pronounced velocity highs to depths exceeding 300 km, but others do not and, surprisingly, the Archean units do not seem to be marked by such a thick high wave speed structure either. The Precambrian cratons that lack a thick high wave speed “keel” are located near passive margins, suggesting that convective processes associated with continental break-up may have destroyed a once present tectosphere. Our study suggests that deep lithospheric structure varies as much within domains of similar crustal age as between units of different ages, which hampers attempts to find a unifying relationship between seismic signature and lithospheric age.

SV-wave azimuthal anisotropy in the Australian upper mantle: preliminary results from automated Rayleigh waveform inversion

The pattern of azimuthal anisotropy for SV waves in the upper mantle beneath Australia has been determined using a two-stage tomographic procedure for Rayleigh waves. The inversion exploits an automated procedure based on the waveform inversion method of Cara & Lévêque (1987) to allow the analysis of 668 vertical-component seismograms within a few weeks. The automated procedure provides an effective choice of the secondary observables used in the waveform inversion for both fundamental and higher modes, allowing the construction of a set of radially stratified upper-mantle models which represent the average structures on paths criss-crossing the Australian continent. The 668 path-average models are then combined in a 3-D velocity model which describes the lateral variation of the SV velocity and its azimuthal anisotropy. The lateral variations in wave speed show a good overall agreement with previous results for shear wave-speed variations in Australia but are accompanied by significant azimuthal anisotropy. At 150 km depth the anisotropy displays a simple pattern with most of the directions of fast SV velocities dominated by a north–south component close to the present-day absolute plate motion. Nevertheless, in the regions with the highest shear wave speed, anisotropy is not aligned with the current plate motion, suggesting a local resistance to mantle flow.

Preliminary models of upper mantle P and S wave velocity structure in the western South America region

Upper mantle P and S wave velocities in the western South America region are obtained at depths of foci from an analysis of travel time data of deep earthquakes. The inferred velocity models for the Chile–Peru–Ecuador region reveal an increase of P velocity from 8.04 km/s at 40 km to 8.28 km/s at 250 km depth, while the S velocity remains almost constant at 4.62 km/s from 40 to 210 km depth. A velocity discontinuity (probably corresponding to the L discontinuity in the continental upper mantle) at 220–250 km depth for P and 200–220 km depth for S waves, with a 3–4% velocity increase, is inferred from the velocity–depth data. Below this discontinuity, P velocity increases from 8.54 km/s at 250 km to 8.62 km/s at 320 km depth and S velocity increases from 4.81 km/s at 210 km to 4.99 km/s at 290 km depth. Travel time data from deep earthquakes at depths greater than 500 km in the Bolivia–Peru region, reveal P velocities of about 9.65 km/s from 500 to 570 km depth. P velocity–depth data further reveal a velocity discontinuity, either as a sharp boundary at 570 km depth with 8–10% velocity increase or as a broad transition zone with velocity rapidly increasing from 560 to 610 km depth. P velocity increases to 10.75 km/s at 650 km depth. A comparison with the latest global average depth estimates of the 660 km discontinuity reveals that this discontinuity is at a relatively shallow depth in the study region. Further, a velocity discontinuity at about 400 km depth with a 10% velocity increase seems to be consistent with travel time observations from deep earthquakes in this region.

Seismic structure of the upper mantle beneath the western Philippine Sea

We investigate the seismic structure of the western Philippine Sea using two sets of seismological observations: ScS reverberations, which provide the layering framework for a regional upper mantle model, and observations of frequency-dependent phase delays for direct S waves, surface-reflected phases ( sS, SS, sSS), and surface waves ( R 1, G 1), which constrain the velocity and anisotropy structure within the layers. The combined data set, comprising 17 discontinuity amplitudes and layer travel times from the ScS-reverberation stack and more than 1000 frequency-dependent phase delays, was inverted for a path-averaged, radially anisotropic model. Mineralogical estimates of the bulk sound velocity and density are incorporated as complementary constraints. The final model, PHB3, is characterized by a 11.5-km thick crust, an anisotropic lid bounded by a sharp negative G discontinuity at 89 km, an anisotropic low-velocity layer extending to 166 km, a subjacent high-gradient region, and transition-zone discontinuities at depths of 408 km, 520 km and 664 km. The lid is slower than in a comparable model for the Tonga–Hawaii corridor (PA5), but also significantly thicker, requiring a compositional variation between the two regions. We explore the hypothesis that the thickness of the oceanic lid is controlled by the melting depth at the spreading centers during crust formation, and that the thicker crust and lid in the Philippine Sea results from deeper melting owing to a higher potential temperature and perhaps a higher water content in the upper mantle.

Melting relations of hydrous and dry mantle compositions and the genesis of komatiites

The hydrous phase relations of primitive upper mantle model compositions in the CaO‐MgO‐Al2O3‐SiO2‐H2O system with 1, 2 and 5 wt.% H2O have been investigated with a multianvil high pressure apparatus at 6.5 GPa and temperatures from 1550°C to 2050°C. Liquidus temperatures decrease by about 100°C and the temperature interval to produce about 60% partial melting reduces to less than 50°C in the 1–2 wt.% H2O‐bearing systems. At an H2O content of about 5 wt.%, garnet is the first dissolved phase and the stability field of orthopyroxene expands. Aluminum undepleted komatiite magmas can be formed by melting at 200 km depth in a hydrous mantle at significantly lower temperatures than under dry conditions. Thus, komatiite magmas cannot constrain temperatures in the Archean mantle. In addition, cratonic peridotites may have formed as residues of partial melting under various H2O contents.

Eurasian surface wave tomography: Group velocities

This paper presents the results of a study of the dispersion characteristics of broadband fundamental surface waves propagating across Eurasia. The study is broader band, displays denser and more uniform data coverage, and demonstrates higher resolution than previous studies of Eurasia performed on this scale. In addition, the estimated group velocity maps reveal the signatures of geological and tectonic features never before displayed in similar surface wave studies. We present group velocity maps from 20 s to 200 s period for Rayleigh waves and from 20 s to 125 s for Love waves. Broadband waveform data from about 600 events from 1988 through 1995 recorded at 83 individual stations across Eurasia have produced about 9000 paths for which individual dispersion curves have been estimated. Dispersion curves from similar paths are clustered to reduce redundancy, to identify outliers for rejection, and to assign uncertainty estimates. On average, measurement uncertainty is about 0.030–0.040 km/s and is not a strong function of frequency. Resolution is estimated from “checker‐board” tests, and we show that average resolutions across Eurasia range from 5° to 7.5° but degrade at periods above about 100 s and near the periphery of the maps. The estimated maps produce a variance reduction relative to the Preliminary Reference Earth Model (PREM) of more than 90% for Rayleigh waves below 60 s period but reduce to about 70% between 80 and 200 s period. For Love waves, variance reductions are similar, being above 90% for most periods below 100 s and falling to 70% at 150 s. Synthetic experiments are presented to estimate the biases that theoretical approximations should impart to the group velocity maps, in particular source group time shifts, azimuthal anisotropy, and systematic event mislocations near subducting slabs. The most significant problems are probably caused by azimuthal anisotropy, but above 100 s the effect of source group time shifts may also be appreciable. These effects are probably below the signal levels that we interpret here, however. Many known geological and tectonic structures are observed in the group velocity maps. Of particular note are the signatures of sedimentary basins, continental flood basalts, variations in crustal thickness, backarc spreading, downgoing slabs, and continental roots. Comparison of the estimated group velocity maps with those predicted by CRUST5.1/S16B30 is qualitatively good, but there are significant differences in detail which provide new information that should help to calibrate future crustal and upper mantle models of Eurasia.

Lithosphere-asthenosphere system in shield areas of North America and Europe

In previous papers surface dispersion data have been combined with the results of deep seismic refraction data to derive a regionalization of the lithosphere-asthenosphere system and to investigate the presence of significant heterogeneity down to depths of 350 km along two profiles in the North European Fennoscandian area; a regionalized upper mantle model for the whole area down to more than 400 km is given as cross sections. We have extended that approach to North America. The older part of the shield shows lid thickness up to more than 100 km with, if any, weak shear velocity contrast to the underlying layer. The surrounding areas are characterized by a thinner lid; a stronger low-velocity zone to lid contrast may be found in peripheral areas. A map of the lithosphere-asthenosphere system has been derived, permitting a better regional resolution of the shear-wave velocity distribution with depth beneath different regions of North America. The correlation between the lithosphere-asthenosphere system structure and other geophysical data is commented as well as the results for North America and those obtained for the corresponding North European area, in order to outline the geophysical characteristics of shield areas that might give useful constraints for the geodynamic behaviour of the plates to which they belong.

Modelling surface waves in anisotropic structures II: Examples

Surface waves in several anisotropic geological settings are studied by numerical simulation. Asymptotic point-source synthetic seismograms are obtained using formulas from a companion paper, the group velocities and mode-excitation factors being evaluated via variational integrals. Some alternative waveform approximations and ray-path effects are explored and the possible significances of peculiarities of anisotropy, such as wavefront folding, are at least partially assessed. Model one is a 5-layer oceanic environment with ±5.6% aligned vertical-crack S-wave anisotropy in the upper crust. The 2–3 s waveforms often have highest group velocities at 45° to the cracks and there are very strong transverse components from a vertical source. Maslov and ray/WKBJ waveforms agree well, even though for some modes and frequencies azimuthal group-velocity variations imply the latter is suspect. The Maslov-integral end-point signals mean that it too requires care and the so-called quasi-WKBJ approximation is a viable alternative. Periods approaching 1 s and/or high crack densities lead to very complicated group-velocity geometry indeed. The second model has ±2% upper-mantle mineral-alignment anisotropy, with its isotropic component constrained to agree with model ak135. The 20–30 s waveforms from a transversely-isotropic source force have fundamental ‘Rayleigh’ and ‘Love’ packets showing clear azimuthal phase anomalies but surprisingly standard polarizations and amplitudes. Only higher modes show such variable amplitudes and phases that they might be identified as likely due to anisotropy. Around 10-s period the higher-mode family has an interesting banded group-velocity structure and as the period is lowered further, two modes separate out and the band tightens in what may be a characteristic feature. Two candidate models of mantle-plume anisotropy show distinct azimuthal dependencies of mode velocities. Point-source surface-wave rays tracked in one plume model display shadows and focusing and show how initially folded wavefronts can unfold in the lateral variations. The upper-mantle models are numerically taxing. R/T coefficients and mode slownesses can be found using double-precision arithmetic, but depth profiles and variational-integrals sometimes require greater accuracy. We find that while displacements near the stack top and bottom may be obtained quite easily, as frequency increases it becomes increasingly difficult to compute those at mid-depth. We find no reason to believe that the Kennett invariant-embedding scheme has lesser accuracy than others.

Frequency-dependent effects on travel times and waveforms of long-period S and SS waves

The spectral properties of upper-mantle velocity perturbations are dominantly determined from regional and global tomographic models. In this paper we study frequency-dependent effects of l3ng-period S and SS waves of SH-type through random upper-mantle models with specified spectral properties. In particular, we investigate the information content of the power spectra of travel time perturbations as a function of model spectrum and frequency band. Wave propagation is simulated by a finite-difference (FD) approximation to the axi-symmetric wave equation in spherical coordinates. For global models with cylindrical symmetry and constant angular increment Δθ, the use of spherical coordinates leads to an effective lateral grid spacing (arc length) decreasing with depth. This is contrary to the requirements of global models with low velocities at the top of the mantle, which necessitate a dense grid spacing at small depths and a wider grid spacing at the base of the mantle. We introduce a grid with depth-dependent lateral grid spacing to overcome this inconsistency. Our main findings are that (1) the properties of spatial power spectra of travel time fluctuations are frequency-dependent; (2) power spectra of models obtained from long-period tomography may underestimate the power at intermediate scales; (3) frequency-dependent effects on the waveform are sensitive to the scales and amplitudes of perturbations present in the upper mantle.

Effect of anisotropy on oceanic upper mantle temperatures, structure, and dynamics

Olivine and orthopyroxene crystals composing the oceanic upper mantle align under progressive simple shear strain. Because the thermal diffusivities (κ) and viscosities of these minerals are anisotropic, mineral alignment affects vertical heat flow and upper mantle dynamics. The vertical thermal diffusivity of upper mantle peridotite decreases with progressive simple shear strain, leading to higher temperatures in the shallow upper mantle than predicted by an isotropic half‐space cooling model. This, in turn, causes higher surface heat flow, shallower ocean basins, weaker asthenosphere, and slightly thinner lithosphere. Viscosity associated with an oriented simple shear strain (ηsh), such as that caused by plate motion, also evolves with progressive strain, though ηsh at high strains has not been characterized. Regardless of the evolution of ηsh with strain, the effects of thermal diffusivity anisotropy on upper mantle temperatures, surface heat flow, lithosphere thickness, asthenosphere viscosity and shear stress at the plate bottom remain evident. Shear heating elevates the geotherm by more than κ anisotropy except in the youngest ocean and in cases with significant shear weakening or a slowly moving plate (less than ∼3 cm/yr). The magnitude of shear heating effects depends on how ηsh increases or decreases at high strains. For models in which ηsh increases as a function of strain, shear heating elevates temperatures beyond reasonable upper mantle estimates (i.e., above 1400°C), suggesting that such strain induced viscosity increases are not likely. We present a model for ocean upper mantle cooling and deformation that includes upper mantle thermal diffusivity anisotropy and shear heating. This model predicts heat flow, shear wave split times, lithosphere thicknesses, and basin depths which are consistent with observations but suggests that basal tractions on ocean plates are lower than previously thought.

Numerical models of mantle convection with secular cooling

SUMMARY A 2-D time-dependent finite-difference numerical model is used to investigate the thermal character and evolution of a convecting layer which is cooling as it convects. Two basic cooling modes are considered: in the first, both upper and lower boundaries are cooled at the same rate, while maintaining the same temperature difference across the layer; in the second, the lower boundary temperature decreases with time while the upper boundary temperature is fixed at 0 C. The first cooling mode simulates the effects of internal heating while the second simulates planetary cooling as mantle convection extracts heat from, and thereby cools, the Earth's core. The mathematical analogue between the effects of cooling and internal heating is verified for finiteamplitude convection. It is found that after an initial transient period the central core of a steady but vigorous convection cell cools at a constant rate which is governed by the rate of cooling of the boundaries and the viscosity structure of the layer. For uppermantle models the transient stage lasts for about 30 per cent of the age of the Earth, while for the whole mantle it lasts for longer than the age of the Earth. Consequently, in our models the bulk cooling of the mantle lags behind the cooling of the coremantle boundary. Models with temperature-dependent viscosity are found to cool in the same manner as models with depth-dependent viscosity; the rate of cooling is controlled primarily by the horizontally averaged variation of viscosity with depth. If the Earth's mantle cools in a similar fashion, secular cooling of the planet may be insensitive to lateral variations of viscosity.