ALBERT

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Description: Published

Description: 125-127

Description: 3.3. Geodinamica e struttura dell'interno della Terra

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Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 1994

Description: The thesis addresses the applicability of traditional hydraulic theory to an unstable, mid-latitude jet where the only wave present is the Rossby wave modified by shear. While others (Armi 1989, Pratt 1989, Haynes et al.1993 and Woods 1993) have examined specific examples of shear flow "hydraulics", my goal was to find general criteria for the types of flows that may exhibit hydraulic behavior. In addition, a goal was to determine whether a hydraulic mechanism could be important if smaller scale shear instabilities were present. A flow may exhibit hydraulic behavior if there is an alternate steady state with the same functional relationship between potential vorticity and streamfunction. Using theorems for uniqueness and existence of two point boundary value problems, a necessary condition for the existence of multiple states was established. Only certain flows with non-constant, negative dQ(ψ)/dψ have alternate states. Using a shooting method for a given transport and a given smooth relationship between potential vorticity and streamfunction, alternate states are found over a range of beta. Multiple solutions arise at a pitchfork bifurcation as a stability parameter is raised above the stability threshold determined by the necessary condition for instability. The center branch of the pitchfork is unstable to the gravest mode, while the two outer branches do not even have discrete modes. Other pitchfork bifurcations occur as higher meridional modes become unstable. Again, the inner branch is unstable to the next gravest mode, while the outer branches do not support this discrete mode. These results place the barotropic instability problem into a large set of nonlinear systems described by bifurcation theory. However, if the eastward transport across the channel is large enough, the normal modes may stabilize and these waves have a phase speed less than the minimum velocity of the flow. In this case, the flow is analogous to sub-critical hydraulic flow. The establishment of these states and the nature of transitions between them is studied in the context of an initial value problem, solved numerically, in which the zonally uniform jet is forced to adjust to the sudden appearance of an obstacle. The time-dependent adjustment of an initially stable flow exhibits traditional hydraulic behavior such as control and influence in the far-field. However, if the flow is unstable, the instability dominates the evolution. If the topographic slope renders the flow more unstable than the ambient flow, then the resulting adjustment can be understood as a local instability. The thesis has established a connection between hydraulic adjustment and the barotropic instability of the flow. Both types of dynamics arise from adjustments among multiple equilibria in an unforced, inviscid fluid.

Description: This research was supported by National Science foundation grants OCE 91-15359 and OCE 89-16446, and also by a Department of Defense AASERT grant administered under ONR N00014-89-J-1182.

Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and Woods Hole Oceanographic Institution February 1994

Description: Ambient noise in the sea has been observed for over 100 years. Previous studies conclude that the primary source of microseisms is nonlinear interaction of surface gravity waves at the sea surface. Though this source relationship is generally accepted, the actual processes by which the wave generated acoustic noise in the water column couples and propagates to and along the sea floor are not well understood. In this thesis, the sources and propagation of sea floor and sub-sea floor microseismic noise between 0.2 and 10 Hz are investigated. This thesis involves a combination of theoretical, observational and numerical analysis to probe the nature of the microseismic field in the Blake Bahama Basin. Surface waves are the primary mechanism for noise propagation in the crust and fall into two separate groups depending on the relative wavelength/water depth ratio. Asymptotic analysis of the Sommerfeld integral in the complex ray parameter plane shows results that agree with previous findings by Strick (1959) and reveal two fundamental interface wave modes for short wavelength noise propagation in the crust: the Stoneley and pseudo-Rayleigh wave. For ocean sediments, where the shear wave velocity is less than the acoustic wave velocity of water, only the Stoneley interface wave can exist. For well consolidated sediments and basalt, the shear velocity exceeds the acoustic wave velocity of water and the pseudo-Rayleigh wave can also exist. Both interface waves propagate with retrograde elliptic motion at the sea floor and attenuate with depth into the crust, however the pseudo-Rayleigh wave travels along the interface with dispersion and attenuation and "leaks" energy into the water column for a half-space ocean over elastic crust model. For finite depth ocean models, the pseudo-Rayleigh wave is no longer leaky and approaches the Rayleigh wave velocity of the crust. The analysis shows that longer wavelength noise propagates as Rayleigh and Stoneley modes of the ocean+crust waveguide. These long wavelength modes are the fundamental mechanism for long range noise propagation. During the Low Frequency Acoustic Seismic Experiment (LFASE) a four-node, 12- channel borehole array (SEABASS) was deployed in the Blake Bahama Basin off the coast of eastern Florida (DSDP Hole 534B). This experiment is unique and is the first use of a borehole array to measure microseismic noise below the sea floor. Ambient background noise from a one week period is compared between an Ocean Bottom Seismometer (OBS) and SEABASS at sub-bottom depths of 10, 40, 70 and 100 meters below the sea floor. The 0.3 H z microseism peak is found to be nearly invariant with depth and has a power level of 65 and 75 dB rel 1 (nm/ s2)2)/ H z for the vertical and horizontal components respectively. At 100 m depth, the mean microseismic noise levels above 0.7 Hz are 10 dB and 15-20 dB quieter for the vertical and horizontal components respectively. Most of this attenuation occurs in the upper 10 m above 1.0 Hz, however higher modes in the spectra show narrow bandwidth variability in the noise field that is not monotonic with depth. Dispersion calculations show normal mode Stoneley waves below 0.7 Hz and evidence of higher modes above 0.8 Hz. A strong correlation between noise levels in the borehole and local sea state conditions is observed along with clear observation of the nonlinear frequency doubling effect between ocean surface waves and microseisms. Particle motion analysis further verifies that noise propagates through the array as Rayleigh/Stoneley waves. Polarization direction indicates at least two sources; distant westerly swell during quiescent times and local surface waves due to a passing storm. Above 1.0 Hz the LFASE data shows little coherence and displays random polarization. Because of this, we believe scattered energy is a significant component of the noise field in the Blake Bahama Basin. A fully 3-D finite difference algorithm is used to model both surface and volume heterogeneities in the ocean crust. Numerical modeling of wave propagation for hard and soft bottom environments shows that heterogeneities on the order of a seismic wavelength radiate energy into the water column and convert acoustic waves in the water into small wavelength Stoneley waves observed at the borehole. Sea floor roughness is the most important elastic scattering feature of the ocean crust. Comparisons of 2D and 3D rough sea floor models show that out-of-plane effects necessitate the use of 3D methods. The out-of-plane energy that is present in the LFASE data comes from either heterogeneities in the source field (i.e. mixed gravity wave directions) or, equally likely, scattering of the source field from surface or volume heterogeneities in the sea floor.

Description: This research was supported by Office of Naval Research grants N00014-89-C-0018, N00014-89-J-1012, N00014-90-C-0098, N00014-90-J-1493 and N00014-93-1-1352.

Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution August 1995

Description: The problem of estimating boundary and initial conditions for a regional open-ocean model is addressed here. With the objective of mimicking the SYNOP experiment in the Gulf Stream system, a meandering jet is modeled by the fully nonlinear barotropic vorticity equation. Simulated observations of current velocity are taken using current meters and acoustic tomography. Twin experiments are performed in which the adjoint method is used to reconstruct the flow field. The estimated flow is forced to resemble the true flow by minimizing a cost function with respect to some control variables. At the minimum, the error covariance matrix of the estimated control variables can be evaluated from the inverse Hessian of the cost function. The first major scientific objective of this work is the estimation of initial and boundary conditions for the model from sparse interior data. First the vorticity initial conditions are used as control variables and the boundary conditions are kept fixed. The jet-like flow is found to induce strong dependence of the model/data misfit upon the specified boundary conditions. Successively, the boundary values of streamfunction and vorticity are included among the control variables and estimated together with the initial conditions. Experiments are performed with various choices of scaling and first guess for the control variables, and various observational strategies. The first major new result obtained is the successful estimation of the complete set of initial and boundary conditions, necessary to integrate the vorticity equation forward in time. From a time-invariant first guess for the boundary conditions, the assimilation is able to create temporal variations at the boundaries that make the interior flow match well the velocity observations, even when noise is added. It is found that information from the observations is communicated to the boundaries by advection of vorticity and by the instantaneous domain-wide connections in the streamfunction field due to the elliptic character of the Poisson equation. The second major scientific objective is the estimation of error covariances in the presence of strongly nonlinear dynamics. The evaluation of the full error covariance matrix for the estimated control variables from the inverse Hessian matrix is investigated along with its dependence upon the degree of nonlinearity in the dynam1cs. Further major new results here obtained are the availability of off-diagonal covariances, the successful calculation of error covariances for all boundary and initial conditions, and the estimation of errors for the interior fields of streamfunction and vorticity. The role of the Hessian matrix is assessed in gauging the sensitivity of the estimated boundary and initial conditions to the data. Also, the importance is stressed of retaining off-diagonal structure of the Hessian to obtain more accurate error estimates.

Description: Funding for this research was provided by Office of Naval Research (ONR) Grant N00014-90-J-1481 and, since 1/1/95, ONR Grant N00014-95-1-0226.

Description: Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution August 1991

Description: Using a semi-geostrophic, reduced gravity thin jet model, we analytically study the evolution of initial meanders into pinched-off rings. The model used is similar to the path equation developed by Flierl and Robinson {1984) for vertically coherent meanders. However, in the present model, the meanders are baroclinic, and a stretching term arises due to the motion of the interface. It can be shown that the equation governing the time-dependent meander of this jet (Pratt, 1988) can be transformed into the Modified Korteweg- deVries (MKdV) equation in intrinsic coordinates. The MKdV equation admits two types of solitary wave solutions, loop solitons and breathers. The breathers are permanent meanders which propagate on the path , and some are able to form rings. Using the inverse scattering transform , we can predict breather and ring formation for simple initial meanders. The inverse scattering t ransform is applied to S and Ω shaped meanders with piecewise constant and continuous curvature. S shaped meanders, or steps, must be multi-valued to form breathers, and must have very steep angles in order to form rings. Due to integral constraints, Ω shaped meanders, or lobes, are unable to pinch together to form rings unless they are wide enough so that the two side flanks of the lobe act as two independent steps. The numerical solutions indicate that the breathers predicted by the inverse scattering is a very good approximation to the full solution.

Description: This work has been supported by NSF contract number OCE 89-16446 and ONR contract number N00014-S9-J-1182.

Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution March 1992

Description: Rotating baroclinic and barotropic boundary currents flowing around a corner in the laboratory were studied in order to discover the circumstances under which eddies were produced at the corner. Such flows are reminiscent of oceanic coastal flows around capes. When the baroclinic currents, which consisted of surface flows bounded by a density front, encountered a sharp corner, immediately downstream of the corner an anticyclone grew in the surface layer for an angle of greater than 40 degrees. Varying the initial condition of the flow or the depth of the lower layer did not noticeably affect the gyre's properties except for its growth speed, which was greater when the lower layer was shallower. The barotropic currents were pumped along a sloping bottom, and also formed anticyclonic gyres which quickly attained an approximately steady state. For a given topography, the size of the gyre was proportional to the inertial radius u/f. Volume flux calculations based on the surface velocity revealed vertical shear which increased with gyre size. Hydraulic models were also applied to flow around gently curving topography to determine the critical separation curvature as a function of upstream parameters.

Description: This work was supported by the National Science Foundation grant OCE 89-15408.

Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution April 1992

Description: A pair of simple models representing the interaction of a continuously stratified f-plane quasigeostrophic lens with a uniform external shear flow is examined. The study is motivated by the desire to understand the processes that affect Mediterranean Salt Lenses and other mesoscale lenses in the ocean. The first model represents the eddy as a pair of quasigeostrophic 'point potential vortices' in uniform external shear, where the two point vortices are imagined to represent the top and bottom of a baroclinic eddy. While highly idealized, the model succeeds in qualitatively reproducing many aspects of the behavior of more complex models. In the second model the eddy is represented by an isolated three dimensional patch characterized by quasigeostrophic potential vorticity linear in z, in a background flow with constant potential vorticity. The boundary of the lens may be deformed by interactions with a uniform background shear. A family of linearized analytical solutions representing such a vortex is discussed in Chapter 3. These solutions represent lens-like eddies with trapped fluid cores, which may propagate through the surrounding water when there is external vertical shear. The analysis predicts the possible forms of the boundary deformation in a specified external flow, and the precession rate of normal mode boundary perturbations in the absence of external flow. The translation speed of the lens with respect to the surrounding fluid is found to be a simple function of the external vertical shear and the core baroclinicity. A numerical algorithm which is a generalization of the contour dynamics technique to stratified quasigeostrophic flow is used to extend the linear results into the nonlinear regime. This numerical analysis allows a determination of the range of environmental conditions (e.g., the maximum shear and/ or core baroclinicity) in which coherent vortex solutions can be found, and allows the stability of the steadily translating solutions to be examined directly. It is found that the solutions are stable if neither the external shear nor the core baroclinicity is too large, and that the breakdown of the unstable solutions is characterized by the loss of an extrusion of core fluid to the surrounding waters. The translation speeds of the large amplitude numerical solutions are found to have the same functional dependence on the external vertical shear and the core baroclinicity that was found in the linear analysis, and it is demonstrated that the solutions translate at a rate which is equal to the background flow speed at the center of potential vorticity of the lens. As a test of the model results, new data from a recent SOFAR float experiment are presented and compared with the model predictions. The data show that the cores of two different Mediterranean Salt Lenses are tilted, presumably as a result of interactions with external flows. Both the sense of the tilt and its relation to the translation of the lens are in qualitative agreement with the model solutions.

Description: I am happy to acknowledge the support of the Office of Naval Research (grant N00014-89-J-1182) and the National Science Foundation (grants OCE 8916446 and OCE 87-00601).

Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 1992

Description: This study concerns the barotropic interactions between a mesoscale eddy and a straight monotonic bottom topography. Through simple to relatively complicated modeling effort, some of the fundamental properties of the interaction are investigated. In chapter two, the fundamental aspects of the interaction are examined using a simple contour dynamics model. With the simplest model configuration of an ideal vortex and a step topography, the basic dynamical features of the observed oceanic eddy-topography interaction are qualitatively reproduced. The results consist of eddy-induced cross-topography exchange, formation of topographic eddies, eddy propagation and generation of topographic waves. In chapter three, a more complicated primitive equation model is used to investigate a mesoscale eddy interacting with an exponential continental shelf/slope topography on both f and β-planes. The f-plane model recasts the important features of chapter two. The roles of the eddy size and strength and the geometry of topography are studied. It is seen that the multiple anticyclonic eddy-slope interactions strongly affect the total cross-slope volume transport and the evolution of both the original anticyclone and the topographic eddy. Since a cyclone is trapped at the slope and eventually moves on to the slope, it is most effective in causing perturbation on the shelf and slope. The responses on the shelf and slope are mainly wavelike with dispersion relation obeying that of the free shelf-trapped wave modes. On the β-plane, the problem of an eddy colliding onto a continental shelf/slope from a distance with straight or oblique incident angles is investigated. It is found that the straight eddy incident is more effective in achieving large onslope eddy penetration distance than the oblique eddy incident. The formation of a dipole-like eddy pair consisting of the original anticyclone and the topographic cyclone acts to suppress the eddy decay due to long Rossby wave radiation. A weak along-slope current near the edge of the slope is found, which is part of a outer slope circulation cell originated from the Rossby wave wake trailing the propagating eddy. Model-observation comparisons in_chapter four show favorable qualitative agreement of the model results with some of the observed events in the eastern U.S. continental margins and in the Gulf of Mexico. The model results give dynamical interpretations to some observed features of the oceanic eddy-topography interactions and provide enlightening insight into the problem.

Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 1992

Description: Variations in the abundances of elements and radiogenic isotopes in mantle derived peridotites and volcanic rocks are chemical integrals over time, space, and process, which ultimately contain information about the role of convection in the earth's mantle in creating, maintaining, and destroying geochemical heterogeneities. Successful inversion of these integrals requires extensive knowledge of the geochemical behavior of elements, the length scales of chemical variability, the evolution with time of geologic systems, the physical properties of mantle rocks, and the driving forces of phenomena which govern heat and mass transport in a dynamic earth. This dissertation attempts to add to this knowledge by examining the trace element and isotope geochemistry of mantle peridotites and oceanic island basalts, and by studying aspects of the flow of viscous fluids driven by thermal buoyancy. The trace element and isotopic systematics of peridotites and associated mafic layers from the Ronda Ultramafic Complex, southern Spain (Chapter 2), provides information bearing on the geochemical behavior of the highly incompatible elements U, Th, and Pb in the mantle, and on the length scales of geochemical variability in a well exposed peridotite massif. Garnet is demonstrated to be a significant host for U in the mantle, and together with clinopyroxene, these two minerals control the abundances and partitioning relationships of U and Th during the melting of anhydrous peridotite. Clinopyroxene, plagioclase, and to a lesser extent garnet are hosts for Pb in mantle peridotite; however, the role of trace sulfide may exert some control over the abundance and partitioning of Pb in some samples. Due to the possibility that Pb is partitioned into sulfide, the U/Pb, Th/Pb, and Ce/Pb ratios measured in clinopyroxene are likely to be higher than the bulk rock. U-Pb age systematics of garnet-clinopyroxene pairs from Ronda peridotites and mafic layers indicate Pb isotopic equilibrium in these samples up to 20-50 Ma ago. The Pb-Pb systematics of garnet- and spinel-facies peridotites and mafic layers indicate a heterogeneity on the order of 3 Ga old. This Pb isotope signature may have been created within the massif 3 Ga ago, or may have been metasomatically imprinted on the massif 1.3 Ga ago by basaltic melts with island arc affinities. The isotopic evolution of Ronda is consistent with at 1.3 Ga ago, and was subsequently incorporated into the subcontinental lithosphere. The very low U, Th, and Pb concentrations in depleted peridotite indicate that recycled crustal materials, with U-Th-Pb concentrations 102-104 times higher than peridotite, will have a larger influence on the isotopic composition of Pb in the mantle than on the Sr and Nd isotopic composition. An investigation of the trace element and isotopic compositions of clinopyroxenes in peridotite xenoliths from Savaii, Western Samoa and Tubuai, Austral Islands (Chapter 3) reveals geochemical signatures which are not present in basalts from these islands, due to the inherent averaging of melting processes. The data indicate similarities in the melting and melt segregation processes beneath these isotopically extreme islands. Samples with LREE depleted clinopyroxenes, with positive Zr and negative Ti anomalies, are the result of poly baric fractional melting of peridotite in the garnet- and spinel lherzolite stability fields, with the Savaii samples having experienced a larger mean degree of melting than the Tubuai samples. The extreme fractionation of HREE in the Savaii samples requires that they have melted to the clinopyroxene-out point (about 20%) while retaining residual garnet; the low concentrations ofHREE in these same samples requires a further 10-20% melting in the spinel lherzolite stability field. The extremely high total degrees of melting experienced by the Savaii samples (33-42%), as well as the high degree of melting in the garnet lherzolite stability field, suggests a mantle plume origin for these xenoliths. A large majority of the xenolith clinopyroxenes from both Savaii and Tubuai are LREE enriched to varying degrees, and many samples display significant intergrain trace element heterogeneity. This highly variable yet systematic heterogeneity was the result of metasomatism by percolating melts undergoing chromatographic trace element fractionation. The trace element compositions of some LREE enriched clinopyroxenes are consistent with the percolating melt being typical oceanic island basalt. The clinopyroxenes with the highest LREE concentrations from both islands, which also have very low Ti and Zr concentrations and large amounts of grain-boundary hosted Ba, require that the percolating melt in these cases had the trace element signature of carbonatite melt. The isotopic composition of one of these "carbonatitic" samples from Tubuai is similar to basalts from this island. The isotopic composition of clinopyroxene in a "carbonatitic" sample from Savaii records 87Sr/86Sr and l43Nd/l44Nd values of .71284 and .512516 respectively, far in excess of the most extreme Samoa basalt values (87Sr/86Sr=.70742, 143Nd/l44Nd=.51264). These "carbonatitic" signatures indicate the presence of volatilerich, isotopically extreme components in the mantle beneath Tubuai and Savaii, which likely have their origins in recycled crustal materials. The Re-Os isotope systematics of oceanic island basalts from Rarotonga, Savaii, Tahaa, Rurutu, Tubuai, and Mangaia are examined (Chapter 4). Os concentration variations suggest that olivine, or a low Re/Os phase associated with olivine, controls the Os concentration in basaltic magmas. The Savaii and Tahaa samples, with high 87Sr/86Sr and 207Pb/204Pb ratios (EMII), as well as basalts from Rarotonga, have 1870s/1860s ratios of 1.026-1.086, within the range of estimates of bulk silicate earth and depleted upper mantle. The basalts from Rurutu, Tubuai, and Mangaia (Macdonald hotspot), characterized by high Pb isotope ratios (HIMU), have 1870sfl860s ratios of 1.117-1.248, higher than any estimates for bulk silicate earth, and higher than Os isotope ratios of metasomatized peridotites. The high 1870s/1860s ratios indicate the presence of recycled oceanic crust in the mantle sources of Rurutu, Tubuai, and Mangaia. Inversion of the isotopic data for Mangaia (endmember HIMU) indicate that the recycled crustal component has Rb/Sr, Sm/Nd, Lu/Hf, and Th/U ratios which are very similar to fresh MORB glasses, and U/Pb and Th/Pb ratios which are within the range of MORB values, but slightly higher than average N-MORB. These results indicate that the low-temperature alteration signature of altered oceanic crust may be largely removed during subduction, and that oceanic crust was recycled into to the lower mantle source of the Macdonald hotspot plume. Furthennore, the high 187Os/l86Os ratios of the Tubuai and Mangaia basalts indicates that percolation through depleted mantle peridotite (187Os/186Qs=1.00-1.08), observed to occur in the Tubuai xenoliths, had little influence on the composition of the erupted basalts. A fluid dynamic model for mantle plumes is developed (Chapter 5) by examining a vertical, axisymmetric boundary layer originating from a point source of heat, and incorporating experimentally constrained rheological and physical properties of the mantle. Comparison of linear (n=l) and non-Newtonian (olivine, n=3) rheologies reveals that non-Newtonian plumes have narrower radii and higher vertical velocities than corresponding Newtonian plumes. The non-Newtonian plumes also exhibit "plug flow" at the conduit axis, providing a mechanism for the transport of deep mantle material, through the full depth of the mantle, in an unmixed state. Plumes are demonstrated to entrain ambient mantle via the horizontal conduction of heat, which increases the buoyancy and lowers the viscosity of mantle at the plume boundary. Streamlines calculated from the fluid dynamic model demonstrate that most of the entrained mantle originates from below 1500 km depth. Parameterization of the entrainment mechanism indicates that the factional amount of entrained mantle is lower in stronger, hotter plumes due to their higher vertical velocities. Examination of the global isotopic database for oceanic island basalts reveals the presence of a mantle component (FOZO), common to many hotspots worldwide, characterized by depleted 87Sr/86Sr and 143Nd/l44Nd, radiogenic 206,207,208Pb/204Pb, and high 3He/4He. This component is isotopically distinct from the source of MORB; thus, with the exception of ridge centered hotspots such as Iceland and the Galapagos, upper mantle does not appear to be a component in most hotspots, in agreement with entrainment theory. The combined fluid dynamic and isotopic results indicate that both FOZO and the enriched mantle components (EMI, EMil, and HIMU) are located in the lower mantle. Furthermore, high 3He/4He in FOZO precludes an origin for FOZO-bearing plumes in a thermal boundary layer at 670 km depth in the mantle. Since a 670 km thermal boundary layer would be replenished by the downward motion of the upper mantle, an origin for FOZO at 670 km would require either 1) a high 3He/4He signature in the MORB source, or 2) entrainment of MORB mantle into intraplate plumes, neither of which is observed in the OIB isotope data. This indicates that the 670 km discontinuity is not a barrier to mantle convection. The preservation of isotopically different upper and lower mantles does not require layered convection, but is probably the result of an increasing residence time with depth in the mantle, possibly caused by an increase in the mean viscosity of the mantle with depth.