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1.
Summary. A method is outlined to determine the dynamic behaviour of a phase boundary in the Earth when non-uniform time-varying pressure and temperature conditions are assumed at the Earth's surface. An integral equation describing the phase boundary motion is derived and it is solved under a linearizing assumption. The solution is obtained in the form of a double integral transform. Short and long time-expansions of the solution can be obtained from series expansion and integration of the Laplace transform along a branch cut. The method is illustrated by considering a stepwise change in surface pressure conditions.
For short times, the solution exhibits the same type of time dependence (i.e. the first-order term is in t 1/2) as the one obtained in the one-dimensional case (i.e. uniform pressure perturbation at the Earth's surface).
For long times, it is shown that the time dependence of the phase boundary motion is almost identical to the one derived for the one- dimensional case if the wavenumber k L of the surface excitation is such that κ k 2Lτ≤ 1 (where τ is the relaxation time associated with the one-dimensional phase boundary motion and κ is the thermal diffusivity). If κ k 2Lτ > 1, then the relaxation time for the phase boundary motion in two dimensions is of the order of κ−1 k −2L.
When considering parameters that would be appropriate for a basalt to eclogite phase transition at Moho depth, the latter situation is met only when the load wavelength is smaller than 35 km.  相似文献   

2.
Summary. The thermal effect of a rapid injection of hot magmas into the lower part of the lithosphere is modelled as an increase in heat production through the invaded region. The change in surface heat flow and the uplift resulting from the thermal expansion are determined in three-dimensional axially symmetric geometry: they are expressed as the space time convolutions of a Green's function with the anomalous heat production.
The anomalies with shorter wavelength (compared to the lithospheric thickness) are attenuated. This filtering affects the surface uplift more than the heat flow anomaly; the attenuation effect is larger when only the lower part of the lithosphere is invaded.
The uplift time constant is of the same order as the heat conduction time if the lower lithosphere is invaded by magmas at a moderate rate (i.e. the rate of injection does not exceed the equivalent of 0.1 per cent of the lithospheric volume in 106yr). Fifty per cent of the total uplift takes place in about 80 × 106yr for a lithosphere 100 km thick. The uplift is slightly faster when the whole lithosphere is invaded. The heat flow anomaly is delayed when the lower part of the lithosphere is invaded.
The spatial extent and the timing of the uplift and heat flow anomalies are critical in determining the mechanism's feasibility. Magma injections explain rapid uplifts [> 100 m (106 yr)−1] only if the magma is supplied at a very high rate (i.e. at least 10 per cent of the lithosphere volume per 106yr). It is a feasible mechanism for uplifts that occur over longer periods of time (≊ 30 × 106yr) such as those that seem to have occurred when the African plate came to rest with respect to the mantle.  相似文献   

3.
Summary. The ascent of a hot spherical body through a fluid with a strongly temperature-dependent viscosity has been studied using an axisymmetric finite element method. Numerical solutions range over Peclet numbers of 10−1– 103 from constant viscosity up to viscosity variations of 105. Both rigid and stress-free boundary conditions were applied at the surface of the sphere. The dependence of drag on viscosity variation was shown to have no dependence on the stress boundary condition except for a Stokes flow scaling factor. A Nusselt number parameterization based on the stress-free constant viscosity functional dependence on the Peclet number scaled by a parameter depending on the viscosity structure fits both stress-free and rigid boundary condition data above viscosity variations of 100. The temperature scale height was determined as a function of sphere radius. For the simple physical model studied in this paper pre-heating is required to reduce the ambient viscosity of the country rock to less than 1022 cm2 s−1 in order for a 10 km diapir to penetrate a distance of several radii.  相似文献   

4.
Surface velocities in parts of the India–Asia collision zone are compared to velocities calculated from equations describing fluid flow driven by topographically produced pressure gradients. A good agreement is found if the viscosity of the crust is ∼1020 Pa s in southern Tibet and ∼1022 Pa s in the area between the Eastern Syntaxis and the Szechwan Basin. The lower boundary condition of the flow changes between these two areas, with a stress-free lower boundary in the area between the Szechwan basin and the Eastern Syntaxis, and a horizontally rigid but vertically deformable boundary where strong Indian lithospheric material underlies southern Tibet. Deformation maps for olivine, diopside and anorthite show our findings to be consistent with laboratory measurements of the rheology of minerals. Gravitationally driven flow is also suggested to be taking place in the Indo–Burman Ranges, with a viscosity of ∼1019–1020 Pa s. Flow in both southern Tibet and the Indo–Burman Ranges provides an explanation for the formation of the geometry of the Eastern Himalayan Syntaxis. The majority of the normal faulting earthquakes in the Tibetan Plateau occur in the area of southern Tibet which we model as gravitationally spreading over the Indian shield.  相似文献   

5.
We use annual GPS observations on the Reykjanes Peninsula (RP) from 2000 to 2006 to generate maps of surface velocities and strain rates across the active plate boundary. We find that the surface deformation on the RP is consistent with oblique plate boundary motion on a regional scale, although considerable temporal and spatial strain rate variations are observed within the plate boundary zone. A small, but consistent increase in eastward velocity is observed at several stations on the southern part of the peninsula, compared to the 1993–1998 time period. The 2000–2006 velocities can be modelled by approximating the plate boundary as a series of vertical dislocations with left-lateral motion and opening. For the RP plate boundary we estimate left-lateral motion  18+4−3 mm yr−1  and opening of  7+3−2 mm yr−1  below a locking depth of  7+1−2 km  . The resulting deep motion of  20+4−3 mm yr−1  in the direction of  N(100+8−6)°E  agrees well with the predicted relative North America–Eurasia rate. We calculate the areal and shear strain rates using velocities from two periods: 1993–1998 and 2000–2006. The deep motion along the plate boundary results in left-lateral shear strain rates, which are perturbed by shallow deformation due to the 1994–1998 inflation and elevated seismicity in the Hengill–Hrómundartindur volcanic system, geothermal fluid extraction at the Svartsengi power plant, and possibly earthquake activity on the central part of the peninsula.  相似文献   

6.
Summary. A systematic approach is suggested for modelling the development of sedimentary basins. The theory, which partitions basin formation into initiating and isostatic adjustment processes, is applicable to all modes of basin formation if these processes are linear, or can he represented with sufficient accuracy in an incrementally linear form.
The dynamics of regional isostatic adjustment are characterized by the Heaviside space-time Green functions for the response of elastic and viscoelastic (Maxwell) thin plate models of the lithosphere. It is shown, by convolving the Heaviside—Green functions with cylindrical surface loads, that the rate of isostatic adjustment on a viscoelastic lithosphere is a function of the wavelength of the surface load, long wavelengths being compensated most rapidly.
Six archetypal initiating processes for sedimentary basin development are presented. These processes are those responsible for the subsidence of the Earth's surface which creates a depression in which water and sediments collect. Isostatic amplification of subsidence by sediment and water loads is cast in the form of an integral equation with isostatic Heaviside—Green functions as kernel.
Specific examples, the basins that result from a graben initiating process, are compared with the largest scale structure of the North Sea Basin, a basin that is known to be underlain by a graben system. A model, in which a 50-km wide graben subsides exponentially with a time constant of 5 × 107yr during the interval 180–100 Myr bp , is shown to be consistent with the largest scale structure of the North Sea Basin if the underlying lithosphere is viscoelastic with a flexural rigidity of ∼5 × 1025 Nm and relaxation time constant ∼ 106 yr.  相似文献   

7.
We compare the present-day sediment discharge (solid phase) of some of the largest rivers in Asia to the average discharge deduced from the mass accumulated in several sedimentary basins during the Quaternary. There is a very good correlation, especially for the largest rivers: the Ganges–Brahmaputra, the Changjiang, the Huanghe and, to a lesser extent, the Indus and the Zhujiang. This suggests that present-day average discharge at the outlet has remained constant throughout the Quaternary at least for very large rivers (drainage area of the order of 105–106 km2). This, in turn, suggests either that continental denudation of large Asian catchments has remained on average constant, implying a strong tectonic control on erosion during the Quaternary, or that the river network has the ability to buffer changes in hillslope erosion or in sea-level in order to conserve the total discharge at the outlet. We show how this buffering capacity relies on the characteristic reaction time-scale of Asian alluvial plains (of the order of 105–6 years), that is, much higher than the time-scales of the Quaternary climate oscillations (of the order of 104 years). A short-term perturbation originating in hillslopes will be diluted by the floodplain. At the outlet the signal should have a longer time span and a smaller amplitude. In the same manner, an alluvial plain should not instantaneously react to a 104-year sea-level drop because of its inertia. Along with long-term tectonic control we infer this buffering to be the main cause for the average constancy of sediment yield of large Asian rivers during the Quaternary.  相似文献   

8.
Summary. The viscoelastic response of the Earth to the mass displacements caused by late Pleistocene deglaciation and concomitant sea level changes is shown to be capable of producing the secular motion of the Earth's rotation pole as deduced from astronomical observations. The calculations for a viscoelastic Earth yield a secular motion in the direction of 72° W meridian which is in excellent agreement with observed values. The average Newtonian viscosity and the relaxation time obtained from polar motion data are about (1.1 ± 0.6)1023 poise (P) and 104 (1 ± 0.5) yr. The non-tidal secular acceleration of the Earth can also be attributed to the viscoelastic response to deglaciation and results in an independent viscosity estimate of 1.6 × 1023 P with upper and lower limits of 1.1 × 1023 and 2.8 × 1023 P. These values are in agreement with those based on the polar drift analysis and indicate an average mantle viscosity of 1–2 × 1023 P.  相似文献   

9.
Observations of ice movements across the British Isles and of sea-level changes around the shorelines during Late Devensian time (after about 25 000 yr BP) have been used to establish a high spatial and temporal resolution model for the rebound of Great Britain and associated sea-level change. The sea-level observations include sites within the margins of the former ice sheet as well as observations outside the glaciated regions such that it has been possible to separate unknown earth model parameters from some ice-sheet model parameters in the inversion of the glacio-hydro-isostatic equations. The mantle viscosity profile is approximated by a number of radially symmetric layers representing the lithosphere, the upper mantle as two layers from the base of the lithosphere to the phase transition boundary at 400 km, the transition zone down to 670 km depth, and the lower mantle. No evidence is found to support a strong layering in viscosity above 670 km other than the high-viscosity lithospheric layer. Models with a low-viscosity zone in the upper mantle or models with a marked higher viscosity in the transition zone are less satisfactory than models in which the viscosity is constant from the base of the lithosphere to the 670 km boundary. In contrast, a marked increase in viscosity is required across this latter boundary. The optimum effective parameters for the mantle beneath Great Britain are: a lithospheric thickness of about 65 km, a mantle viscosity above 670 km of about (4-5) 1020 Pa s, and a viscosity below 670 km greater than 4 × 1021 Pa s.  相似文献   

10.
Summary. Temperatures of CaAl2Si2O8 (anorthite glass) shocked to pressures between 48 and 117 GPa have been measured in the range from 2500 to 5600 K, using optical pyrometry techniques. The pressure dependence of the shock temperatures deviates significantly from predictions based on a single high-pressure phase. Either a variable specific heat, or the existence of three phase transitions, at pressures of about 55, 85 and 100 GPa and with transition energies of about 0.5 MJ kg−1 each (∼ 1.5 MJ kg−1 total) can explain the shock-temperature data. The proposed phase transition at 100 GPa can possibly be identified with the stishovite melting transition. Theoretical models of the time dependence of the thermal radiation from the shocked anorthite based on the geometry of the experiment and the absorptive properties of the shocked material yield good agreement with observations, indicating that it is not necessary to invoke intrinsic time dependences to explain the data in many cases. Observed time dependences were used to calculate absorption coefficients of the shocked material of from about 2 mm−1 to greater than 24 mm−1– an increasing function of shock pressure. The assumption that the shocked material radiates as a black body is supported by the theoretical model, and by the close agreement between measured and calculated black body spectral radiance as a function of wavelength.  相似文献   

11.
The generalized ray method in a vertically inhomogeneous model is formulated without any approximation by homogeneous layers. The solution is obtained as an infinite series in multiply 'reflected' waves. Each term can be solved using the exact method or the plane-wave, first-motion or geometrical approximations. It is shown that the first-motion approximation of the series converges rapidly, the ratio of successive terms in the infinite series being-(2 l + 1)(2 l )(6/π)2.
In addition it is shown that the first-motion approximation, which reduces to the geometrical approximation when the latter is valid, is a useful alternative to geometrical ray theory, being more generally valid and being almost as simple to compute.  相似文献   

12.
A series of sensitivity analyses using dielectric, mixture and microwave scattering models is presented. Data from the Seasonal Sea Ice Monitoring and Modeling Site (SIMMS) in 1990 and 1991 are used to initialize the models. The objective of the research is to investigate the role of various geophysical and electrical properties in specifying the total relative scattering cross section (ρ') of snow covered first-year sea ice during the spring period.
The seasonal transition period from the Winter SAR scattering season to Early Melt was shown to signal a transition in dielectric properties which caused the snow volume to become a factor in the microwave scattering process. The effect of the thermal insulation of a snow cover on sea ice was shown to be significant for both ε' and ε'. Higher atmospheric temperatures caused proportionally greater changes in the dielectric properties of the sea ice at the base of the snow cover. Model ρ0 was computed for a range of sensor, sensor-earth geometry, and geophysical properties. In the Winter season the surface roughness terms (ohand L) were shown to have a significant impact on ρ0 when the ice surface was the primary scattering mechanism. Once the snow cover began to warm and water was available in a liquid phase, the ice surface became masked because of the decrease in microwave penetration depths. During this period the water volume variable dominated ρ0, both from its impact on ρv0, and due to its control over the dielectric mismatch created at the air/snow interface.  相似文献   

13.
Summary. We give the analytical formulation for calculating the transient displacement of fields produced by earthquakes in a stratified, selfgravitating, incompressible, viscoelastic earth. We have evaluated the potential of viscous creep in the asthenosphere in exciting the Chandler wobble by a four-layer model consisting of an elastic lithosphere, a two-layer Maxwell viscoelastic mantle, and an inviscid core. The seismic source is modelled as an inhomogeneous boundary condition, which involves a jump condition of the displacement fields across the fault in the lithosphere. The response fields are derived from the solution of a two-point boundary value problem, using analytical propagator matrices in the Laplace-transformed domain. Transient flows produced by post-seismic rebound are found to be confined within the asthenosphere for local viscosity values less than 1020P. The viscosity of the mantle below the low-viscosity channel is kept at 1022P. For low-viscosity zones with widths greater than about 100 km and asthenospheric viscosities less than 1018P, we find that viscoelasticity can amplify the perturbations in the moment of inertia by a factor of 4–5 above the elastic contribution within the time span of the wobble period. We have carried out a comparative study on the changes of the inertia tensor from forcings due to surface loading and to faulting. In general the global responses from faulting are found to be much more sensitive to the viscosity structure of the asthenosphere than those produced from surface loading.  相似文献   

14.
The deglaciation history of Balsfjord, northern Norway, and post-glacial mass movement events were investigated. Radiocarbon dates indicate that the Balsfjord glacier retreated from the Tromsø–Lyngen moraines about 10.4 14C Ky BP. Between ca. 10.3 14C Ky BP and 9.9 14C Ky BP, deposition of a distinct end moraine–the Skjevelnes moraine–in the central part of Balsfjord occurred. The transition from glacimarine to open marine sedimentary environment took place before 9.6 14C Ky BP. Between ca. 9.5 14C Ky BP and 8.4 14C Ky BP, at least one local and three regional mass movement events occurred. After this period, no gravity flow activity is preserved in the cores. The high frequency of mass movements in the early post-glacial period is presumed to be due to fast sea level changes and/or tectonic activity induced by rapid isostatic uplift.  相似文献   

15.
Previous investigations of the causal relationship between postglacial rebound and earthquakes in eastern Canada have focused on the mode of failure and the observed timing of the pulse of earthquake/faulting activity following deglaciation. In this study, the observational database has been extended to include observed orientations of the contemporary stress field and the rotation of stress since deglacial times. It is shown that many of these observations can be explained by a realistic ice history and a viscoelastic earth with a uniform 1021 Pa s mantle.
The effects of viscosity structure on the above predictions are also examined. It is shown that, since most of the above observations are found within the ice margin, they are not very sensitive to lithospheric thickness. Also, the inclusion of a 25 or 50 km ductile layer within the lithosphere will not decouple the seismogenic upper crust. High viscosity (1022 Pa s) in the lower mantle is rejected by the stress orientation and rotation observations. A low-viscosity (6 times 1020Pa s) upper mantle with 1.6 times 1021 Pa s in the upper part of the lower mantle and 3 times 1021 Pa s in the lower part of the lower mantle below 1200 km depth has been found to give predictions that are in general agreement with the observations.  相似文献   

16.
This paper extends our earlier examinations of the utility of various approximations for treating the dynamics of the Earth's liquid core on time-scales of the order of 104 to 108 s. We discuss the effects of representing the response of the mantle and inner core by static (versus dynamic) Love numbers, and of invoking the subseismic approximation for treating core flow, used either only in the interior of the liquid core (SSA-1) or also at the boundaries (SSA-2). The success of each approximation (or combinations thereof) is measured by comparing the resulting surface gravity effects (computed for a given earthquake excitation), and (for the Slichter mode) the distribution of translational momentum, with reference calculations in which none of these approximations is made. We conclude that for calculations of the Slichter triplet, none of the approximations is satisfactory, i.e. a full solution (using dynamic Love numbers at elastic boundaries and no core flow approximation) is required in order to avoid spurious eigenfrequencies and to yield correct eigenfunctions (e.g. conserving translational momentum) and surface gravity. For core undertones, the use of static Love numbers at rigid boundaries is acceptable, along with SSA-1 (i.e. provided the subseismic approximation is not invoked at the core boundaries). Although the calculations presented here are for a non-rotating earth model, we argue that the principal conclusions should be applicable to the rotating Earth. Shortcomings of the subseismic approximation appear to arise because both SSA-1 and SSA-2 lower the order of the governing system of differential equations (giving rise to a singular perturbation problem), and because SSA-2 overdetermines the boundary conditions (making it impossible for solutions to satisfy all continuity requirements at core boundaries).  相似文献   

17.
Seismic sources with observable glut moments of spatial degree two   总被引：1，自引：0，他引：1  
Let ζΛ and r Λ. be the hypocentral position and time of an extended indigenous seismic source. Backus showed that the force moment tensors of the source, Γ( m +1, n )(ζΛ, r Λ), determine and are determined by the motion which the source produces. For small m + n , only the long-period motion is relevant. The glut moment tensor Λ( m,n ) (ζΛ, r Λ.) can be calculated uniquely from γ( m +1, n )(ζΛ r Λ) only if m = 0 or m = 1. The tensor G =Λ(2,0)(ζΛ) gives the spatial variance tensor WΛ of the source, and WΛ. roughly describes the size, shape and orientation of the source region. Therefore the failure of the observed F =Γ(3,0)(ζΛ) to determine G uniquely is of seismological interest. In the present paper we show that F determines G uniquely if we assume the source to be a simple straight line source (SSLS) or an ideal fault in an isotropic medium with isotropic prestress (IFIMIP). We give tests on F which determine whether it can come from a SSLS, from an IFIMIP or from a simple plane surface source (SPSS). If we assume the source to be a SPSS then knowing F and the fault plane determines G to within an unknown scalar multiple of a certain tensor tangent to the fault plane. Moreover F determines the fault plane uniquely unless F can come from a SSLS. If it can, then F determines this virtual source line uniquely, and F permits the fault plane to be any plane containing the virtual source line.  相似文献   

18.
The deformation at the core–mantle boundary produced by the 2004 Sumatra earthquake is investigated by means of a semi-analytic theoretical model of global coseismic and postseismic deformation, predicting a millimetric coseismic perturbation over a large portion of the core–mantle boundary. Spectral features of such deformations are analysed and discussed. The time-dependent postseismic evolution of the elliptical part of the gravity field ( J 2) is also computed for different asthenosphere viscosity models. Our results show that, for asthenospheric viscosities smaller than 1018 Pa s, the postseismic J 2 variation in the next years is expected to leave a detectable signal in geodetic observations.  相似文献   

19.
Micromonas pusilla (Butcher) Manton & Parke appears to be a prominent member of the Barents Sea picoplankton community as revealed by the serial dilution culture method. Cell numbers frequently exceeded 107 cells 1−1, though they usually varied between 103and 106 cells l−1. A number of other identified and unidentified taxa were recorded and quantified. Distribution relative to the marginal ice zone is reported.  相似文献   

20.
A geomagnetic precursor to the 1979 Carlisle earthquake   总被引：3，自引：0，他引：3  
Summary. A study of horizontal field transfer functions, in the period range 10–104s, has been made for the 2 yr period preceding the 1979 Carlisle earthquake (magnitude 5). The study using two sites, local to and remote from the earthquake epicentre, reveals that a precursory effect is observed at short periods (<102s) some 35 km from the main epicentre. The results indicate a change from two-dimensional geolectric anisotropy to a more conductive three-dimensional geoelectric configuration during the period immediately preceding the earthquake.  相似文献   

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