Numerical modelling of a mantle plume: the plume head–lithosphere interaction in the formation of an oceanic large igneous province
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Mantle plume
Lithospheric flexure
Lithospheric flexure
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SUMMARY The (effective) elastic thickness of the lithosphere defines the strength of the lithosphere with respect to a load on it. Since the lithosphere is buoyant on a viscous mantle, its behaviour with respect to a load is not fully elastic, but rather viscoelastic. Fennoscandia is a well-known area in the world where the lithosphere has not yet reached its isostatic equilibrium due to the ongoing uplift after the last glacial period at the end of the Pleistocene. To accommodate for this changing property of the lithosphere in time, we present the flexural model of isostasy that accommodates temporal variations of the lithospheric flexure. We then define a theoretical model for computing the elastic thickness of the lithosphere based on combining the flexural and gravimetric models of isostasy. We demonstrate that differences between the elastic and viscoelastic models are not that significant in Fennoscandia. This finding is explained by a relatively young age of the glacial load when compared to the Maxwell relaxation time. The approximation of an elastic shell is then permissible in order to determine the lithospheric structure and its properties. In this way, the elastic thickness can be estimated based on combining gravimetric and flexural models of isostasy. This approach takes into consideration the topographic and ocean-floor (bathymetric) relief as well as the lithospheric structural composition and the post-glacial rebound. In addition, rheological properties of the lithosphere are taken into consideration by means of involving the Young modulus and the Poisson ratio in the model, both parameters determined from seismic velocities. The results reveal that despite changes in the Moho geometry attributed to the glacial isostatic adjustment in Fennoscandia are typically less than 1 km, the corresponding changes in the lithospheric elastic thickness could reach or even exceed ±50 km. The sensitivity analysis confirms that even small changes in input parameters could significantly modify the result (i.e. the elastic thickness estimates). The reason is that the elastic thickness estimation is an inverse problem. Consequently, small changes in input parameters can lead to large changes in the elastic thickness estimates. These findings indicate that a robust estimation of the elastic thickness by our method is possible if comprehensive information about structural and rheological properties of the lithosphere as input parameters are known with a relatively high accuracy. Otherwise, even small uncertainties in these parameters could result in large errors in the elastic thickness estimates.
Isostasy
Lithospheric flexure
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Lithosphere subjected to an externally derived horizontal stress undergoes creep in the lower lithosphere resulting in the decay of lower lithosphere stress and the associated amplification of stress within the upper lithosphere. This stress response of lithosphere has been investigated for a lithosphere model with power-law stress and temperature dependent viscoelastic properties. The rate and extent of stress decay and associated stress amplification is greatly dependent on the lithosphere geotherm. Oceanic lithosphere subject to an applied stress of ± O.1 kb undergoes upper lithosphere stress amplification of × 1.5, × 1.8 and × 2.0 at 104, 106 and 108 yr respectively. At 106 yr the effective lithosphere thickness is reduced to approximately 40 km. The stress decay and amplification proceeds more rapidly for an applied stress of ± 1.0 kb and in the case of a tensile applied stress results in some upper lithosphere fracture. For continental and Basin and Range type lithosphere the comparable stress amplification at 106 yr, for a stress of ± 0.1 kb, is × 2.0 and × 6.5 with effective lithosphere thicknesses of 60 and 20 km respectively. The large values of stress amplification for the Basin and Range lithosphere result in complete upper lithosphere fracture which gives rise to a cyclic process of upper lithosphere faulting and lower lithosphere creep in which extensive lithosphere deformation can occur. The stress amplification process also occurs for stresses generated by lateral density contrasts. For an isostatically compensated plateau uplift structure, deviatoric stresses of the order of 1 kb can be generated in the upper lithosphere by this process and are sufficient to cause tensile fracture of the upper lithosphere. The response of viscoelastic lithosphere to constant geometry bending stresses has also been examined and results in substantial but not complete reduction of the bending stresses.
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SUMMARY The rise of mantle plumes to the base of the lithosphere leads to observable surface expressions, which provide important information about the deep mantle structure. However, the process of plume–lithosphere interaction and its surface expressions remain not well understood. In this study, we perform 3-D spherical numerical simulations to investigate the relationship between surface observables induced by plume–lithosphere interaction (including dynamic topography, geoid anomaly and melt production rate) and the physical properties of plume and lithosphere (including plume size, plume excess temperature, plume viscosity, and lithosphere viscosity and thickness). We find that the plume-induced surface expressions have strong spatial and temporal variations. Before reaching the base of the lithosphere, the rise of a plume head in the deep mantle causes positive and rapid increase of dynamic topography and geoid anomaly at the surface but no melt production. The subsequent impinging of a plume head at the base of the lithosphere leads to further increase of dynamic topography and geoid anomaly and causes rapid increase of melt production. After reaching maximum values, these plume-induced observables become relatively stable and are more affected by the plume conduit. In addition, whereas the geoid anomaly and dynamic topography decrease from regions above the plume centre to regions above the plume edge, the melt production always concentrates at the centre part of the plume. We also find that the surface expressions have different sensitivities to plume and lithosphere properties. The dynamic topography significantly increases with the plume size, plume excess temperature and plume viscosity. The geoid anomaly also increases with the size and excess temperature of the plume but is less sensitive to plume viscosity. Compared to the influence of plume properties, the dynamic topography and geoid anomaly are less affected by lithosphere viscosity and thickness. The melt production significantly increases with plume size, plume excess temperature and plume viscosity, but decreases with lithosphere viscosity and thickness.
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Asthenosphere
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The heights of hotspot volcanoes are modeled by assuming isostatic equilibrium between the magma column and the adjacent lithosphere. The depth to the level of compensation is assumed to be related to the thickness of the lithosphere after it has been reheated and thinned by a hotspot. There is a square‐root relationship between volcano height and lithospheric age. Relationships between volcano height and lithospheric thickness and between reheated thickness and age of the lithosphere can be constrained within the limits imposed by uncertainties in lithospheric and magma densities. If the reheated thickness determined from the isostatic model can be compared with lithospheric thickness determined from thermal models of the lithosphere, then a relationship between the thickness of the lithosphere before and after reheating can be derived. Combining the upper limit on the reheated thickness/age relationship with a theoretical expression, derived by S. T. Crough, which relates swell height to lithospheric age, reset thickness, and physical constants, yields a swell‐height/age relationship that is in good agreement with empirical swell‐height data. This agreement supports the assumption that the lithospheric thickness defined isostatically by volcano heights is closely related to the thermal thickness of the lithosphere, a result that, in turn, supports the thermal origin of hotspot swells.
Lithospheric flexure
Hotspot (geology)
Swell
Asthenosphere
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Lithospheric flexure
Flexural rigidity
Thermal subsidence
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The earth's lithosphere and asthenosphere are modeled as a thin elastic sheet and a fluid substratum, respectively; the physical principles involved are briefly described. The flexural rigidity of the lithosphere is deduced from observations of the wavelength and amplitude of bending in the vicinity of supercrustal loads. Data from Lake Bonneville given by M. D. Crittenden, Jr., are reinterpreted to give a value for the flexural rigidity of the lithosphere in the Basin and Range province of the western United States of 5×1022 Newton meters. Observations of loading in Canada give values for the flexural rigidity of greater than 3×1020N m for the Caribou Mountains in Northern Alberta; about 4×1023 N m for the topography over the Interior Plains; about 1023 N m for the Boothia uplift in arctic Canada; and about 1025 N m for the bending of the beaches of Pleistocene Lakes Agassiz and Algonquin. The flexure of the lithosphere at Hawaii and the bending of the oceanic lithosphere near island arcs give values of about 2×1023 N m. For short-term loads (103–104 years) the flexural rigidity of the continental lithosphere is almost two orders of magnitude larger than for long-term loads, indicating nonelastic behavior of the lithosphere with a viscous (about 1023 N sec m−2) as well as an elastic response to stress. From the values of the flexural rigidity, the thickness of the continental lithosphere is inferred to be about 110 km and that of the oceanic lithosphere about 75 km or more. The anomalously low flexural rigidity of the lithosphere of the Basin and Range province may be due to a very thin lithosphere, only about 20 km thick, with hot, lower crustal material acting as an asthenosphere.
Lithospheric flexure
Flexural rigidity
Asthenosphere
Tectonophysics
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Mantle plume
Lithospheric flexure
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Under gravitational loading, a volcanic edifice deforms, and the underlying lithosphere downflexes. This has been observed on Earth, but is equally true on other planets. We use finite element models to simulate this gravity-driven deformation at Olympus Mons on Mars. Eleven model parameters, including the geometry and material properties of the edifice, lithosphere and underlying asthenosphere, are varied to establish which parameters have the greatest effect on deformation. Values for parameters that affect deformation at Olympus Mons, Mars, are constrained by minimising misfit between modelled and observed measurements of edifice height, edifice radius, and flexural moat width. Our inferred value for the Young's modulus of the Martian lithosphere, 17.8 GPa, is significantly lower than values used previously, suggesting that the Martian lithosphere is more porous than generally assumed. The best-fitting values for other parameters: edifice density (2111 – 2389 kg.m–3) and lithosphere thickness (83.3 km) are within ranges proposed hitherto. The best-fitting values of model parameters are interdependent; a decrease in lithosphere Young's modulus must be accompanied by a decrease in edifice density and/or an increase in lithosphere thickness. Our results identify the parameters that should be considered within all models of gravity-driven volcano deformation; highlight the importance of the often-overlooked Young's modulus; and provide further constraints on the properties of the Martian lithosphere, namely its porosity, which have implications for the transport and storage of fluid throughout Mars' history.
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Asthenosphere
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Stratigraphic, petrological and geophysical studies suggest that the Late Permian (~ 260 Ma) Emeishan Large Igneous Province in southern China may be formed by mantle plume activity. However, the plume impingement hypothesis remains controversial since interpretations based on volcano-stratigraphic analyses around plume induced domal uplift/inner zone suggest that the volcanism occurred under submarine environment rather than elevated sub-aerial (above sea level) conditions, usually associated with the dynamic topography effects of the ascending mantle plumes. Here, 2-D numerical and 3-D scaled laboratory (analogue) plume experiments are used to explore the coupled dynamics of plume-mantle-lithosphere interaction and their evolution of surface topography characteristics. Experimental results show that the initial (plume incubation) phase is characterized by rapid, transient domal uplift above the plume axis, subsequently, as plume head flattens, there is short wavelength topographic variation (ie. subsidence and uplift occurs synchronously) due to the shear stress imposed onto the base of the lithosphere and loss of gravitational potential energy. The surface depressions predicted by the plume models, next to the plume axial/inner/uplift zone, may explain the deposition of submarine volcanics at Lake Erhai, Dali in the western side and Xiluo and Daqiao in the eastern side, which may resolve the plume controversy for the formation of Emeishan Large Igneous Province. Notably, while experimental results from these two different techniques show some differences, (e.g much bigger plume head for the laboratory experiment), the overall characteristics of the predictions have robust similarities. For instance, the extension above the plume axis may explain the enigmatic cause of the Panxi rift system, in the middle of the inner zone where giant dyke swarms radiate from, and mafic magma underplatings in the lower crust has been described by seismological studies.
Mantle plume
Large igneous province
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