Lateral Density Variations Research Articles

The impact of lateral density variation model in the determination of precise gravimetric geoid in mountainous areas: a case study of Iran

The existence of topography above the geoid violates the basic assumption of Stokes’ formula for the determination of the geoid. Usually a constant density of 2.67 g cm−3 is used in the determination of the geoid. However, we know that the density of the topographical mass departs by about 10–20 per cent from the actual mean value of the crustal density. Iran has one of the largest relief and density variations in the world and the geoid computation in this area is affected the most by topographical density effects. The influence on the geoid height coming from the actual and Pratt-Hayford's isostatic models are studied. Numerical results show that the differences in the geoid height due to actual and isostatic density models can reach up to 0.22 and 0.29 m, respectively, which is not negligible in a precise geoid determination with centimetre accuracy. Our results suggest that the effect of topographical density lateral variations is significant enough and ought to be taken into account specially in mountainous regions in the determination of a precise geoid model.

A refined conversion from normal height to orthometric height

The difference between orthometric and normal heights (or the height anomaly and the geoid height) is usually approximated by a term consisting of the Bouguer anomaly times elevation divided by normal gravity. We derive an improved formula, which includes a topographic roughness term (terrain correction) and a term due to the lateral variation of topographic density, for the practical application of this conversion. It is shown that for high mountainous areas with rough topography these two terms are of the same order as the Bouguer anomaly related term. Already for elevations of a few hundred metres they could reach the order of a centimetre. In addition, for the more precise computations in high mountainous areas, a term related with the downward continuation of topographic potential from the surface to sea level could be significant.

DNA Bonding to CVD Diamond Probed by Scanning Electron-, Fluorescence-, and Atomic force- Microscopy

ABSTRACTDouble stranded desoxyribonucleic acid (ds-DNA) layers, bonded to hydrogen terminated polycrystalline diamond, are characterized by scanning electron (SEM), fluorescence (FM), and atomic force microscopy (AFM). DNA grafting has been achieved using photochemical bonding of ω-unsaturated 10-amino-dec-1-ene molecules. SEM detects local variations of electron affinities on polycrystalline diamond, revealing distinct grain structures. FM applied on fluorescence labeled ds-DNA show laterally varying intensities of typically 20 %, which resembles also grain structure as detected by SEM. Contact and tapping mode AFM characterization reveal a tilted DNA bonding to diamond, dense layer formation which gives rise to smoothening of surface properties. The lateral density variation of DNA is attributed to local variations of the photo-electron emission efficiency which affects the photochemical attachment chemistry of amine linker molecules to diamond.

Slab dip vs. lithosphere age: No direct function

One paradigm of subduction relates the dip of the slab to the buoyancy of the downgoing lithosphere along subduction zones, with the negative buoyancy proportional to the age of the oceanic lithosphere. We measured the dip of the slab down to depths of 250 km along 164 sections crossing 13 subduction zones and compared it with the age of the subducting oceanic lithosphere both at the trench and at depth. We show here that this relationship is far more irregular than previously suggested, and that it is not possible to simply correlate the increase of the slab dip to the increasing age of the downgoing cooler lithosphere. Younger oceanic lithosphere may show steeper dip than older segments of slabs (e.g., Central America vs. South America), in contrast with predictions of models considering only slab pull. The combination of slab age and subduction rate better accounts for slab dip; however the correlation is not satisfactory (correlation coefficient equal to 0.450). These results suggest that supplemental forces or constraints have to be accounted for, such as thickness and shape of the hangingwall plate, absolute plate velocity, presence of lateral density variations in the hosting upper mantle, effects of accretion/erosion, subduction of oceanic plateaus and slab deformation due to the motion of the mantle relative to the subducting plate.

Propagation of tectonic waves

Mountain building depends on the disequilibrium between boundary stresses, either at the base of the deforming lithosphere or its lateral boundaries, and buoyancy stresses arising form lateral density variations within the lithosphere itself. On the basis of the thin viscous sheet approximation, we propose a model which accounts for both crustal and lithospheric thickness variations. The deformation is controlled by the sum of the moments of density anomalies (i.e. density anomalies times depth) of compositional and thermal origins. The transport of the compositional moment is obtained from the continuity equation while the transport of the thermal moment is obtained from the heat equation. The resulting set of equations controls the coupled behavior of the crust and lithosphere. It shows that various type of solutions can exist: unstable, stable and propagating. When propagation occurs, the crustal and the lithospheric thickness variations are out of phase. The tectonic waves propagate with velocities around 5 mm yr−1 that increase with the crustal thickness and decrease with the lithospheric viscosity. We discuss these solutions and argue that continents may in large part be in a domain of propagating tectonic waves.

Crustal density structure in the Spanish Central System derived from gravity data analysis (Central Spain)

Shallow and deep sources generate a gravity low in the central Iberian Peninsula. Long-wavelength shallow sources are two continental sedimentary basins, the Duero and the Tajo Basins, separated by a narrow mountainous chain called the Spanish Central System. To investigate the crustal density structure, a multitaper spectral analysis of gravity data was applied. To minimise biases due to misleading shallow and deep anomaly sources of similar wavelength, first an estimation of gravity anomaly due to Cenozoic sedimentary infill was made. Power spectral analysis indicates two crustal discontinuities at mean depths of 31.1 ± 3.6 and 11.6 ± 0.2 km, respectively. Comparisons with seismic data reveal that the shallow density discontinuity is related to the upper crust lower limit and the deeper source corresponds to the Moho discontinuity. A 3D-depth model for the Moho was obtained by inverse modelling of regional gravity anomalies in the Fourier domain. The Moho depth varies between a mean depth of 31 km and 34 km. Maximum depth is located in a NW–SE trough. Gravity modelling points to lateral density variations in the upper crust. The Central System structure is described as a crustal block uplifted by NE–SW reverse faults. The formation of the system involves displacement along an intracrustal detachment in the middle crust. This detachment would split into several high-angle reverse faults verging both NW and SE. The direction of transport is northwards, the detachment probably being rooted at the Moho.

Earth gravity up to second order in topography and density

The gravity potential of a planet is usually expanded up to first order only as a linear function of topography and lateral variations of density. In this article, we extend these expressions up to second order and we estimate the magnitude of the new non-linear terms. We find that they are not negligible when compared to observed values: tens of metres for height anomalies and tens of milligals for gravity anomalies. Therefore, second-order expressions should be taken into account when inverting global gravity data.

Analogue modelling of the initiation of subduction

We report the results of experiments on the initiation of subduction, using stratified analogue models in a large centrifuge, where the experiments are driven only by the enhanced gravity of the centrifuge without the effect of external lateral stresses. The scaled density of the stratified components resembles that of the asthenosphere and the continental and oceanic lithospheres. The experiments demonstrate that under the effect of enhanced gravity, the layers simulating the oceanic lithosphere detach from the front of the ‘continental lithosphere’ and plunge under it, pushing the more pliable asthenosphere downwards. Simultaneously, the ‘continental lithosphere’ is thrust over the downgoing slab; where friction is low, the ‘continental lithosphere’ extends considerably so that the ‘ductile continental lithosphere’ is exposed in some places. The rate of thrusting of the experimental continental slab over the oceanic one, as well as the amount of extension of the overriding slab and the extent of the rollback of the subduction zone that follows the initial lithospheric detachment, are controlled by friction and density differences between the subducting and the overthrust slabs. The analogue experiments emphasize the role of lateral density variations in incipient subduction and the effect of differential seismic friction along the subduction plane on the evolution of subduction zones, their shape and the evolution of their backarc basins. The morphological resemblance of the experimental results to various subduction systems seems to support their applicability to real subduction systems.

The effect on the geoid of lateral topographic density variations

Gravimetric geoid determination by Stokes’ formula requires that the effects of topographic masses be removed prior to Stokes integration. This step includes the direct topographic and the downward continuation (DWC) effects on gravity anomaly, and the computations yield the co-geoid height. By adding the effect of restoration of the topography, the indirect effect on the geoid, the geoid height is obtained. Unfortunately, the computations of all these topographic effects are hampered by the uncertainty of the density distribution of the topography. Usually the computations are limited to a constant topographic density, but recently the effects of lateral density variations have been studied for their direct and indirect effects on the geoid. It is emphasised that the DWC effect might also be significantly affected by a lateral density variation. However, instead of computing separate effects of lateral density variation for direct, DWC and indirect effects, it is shown in two independent ways that the total geoid effect due to the lateral density anomaly can be represented as a simple correction proportional to the lateral density anomaly and the elevation squared of the computation point. This simple formula stems from the fact that the significant long-wavelength contributions to the various topographic effects cancel in their sum. Assuming that the lateral density anomaly is within 20% of the standard topographic density, the derived formula implies that the total effect on the geoid is significant at the centimetre level for topographic elevations above 0.66 km. For elevations of 1000, 2000 and 5000 m the effect is within ± 2.2, ± 8.8 and ± 56.8 cm, respectively. For the elevation of Mt. Everest the effect is within ± 1.78 m.

Regional three‐dimensional gravity modelling of the NE Atlantic margin

AbstractA series of three‐dimensional models has been constructed for the structure of the crust and upper mantle over a large region spanning the NE Atlantic passive margin. These incorporate isostatic and flexural principles, together with gravity modelling and integration with seismic interpretations. An initial isostatic model was based on known bathymetric/topographic variations, an estimate of the thickness and density of the sedimentary cover, and upper mantle densities based on thermal modelling. The thickness of the crystalline crust in this model was adjusted to equalise the load at a compensation depth lying below the zone of lateral mantle density variations. Flexural backstripping was used to derive alternative models which tested the effect of varying the strength of the lithosphere during sediment loading. The models were analysed by comparing calculated and observed gravity fields and by calibrating the predicted geometries against independent (primarily seismic) evidence. Further models were generated in which the thickness of the sedimentary layer and the crystalline crust were modified in order to improve the fit to observed gravity anomalies. The potential effects of igneous underplating and variable upper mantle depletion were explored by a series of sensitivity trials. The results provide a new regional lithospheric framework for the margin and a means of setting more detailed, local investigations in their regional context. The flexural modelling suggests lateral variations in the strength of the lithosphere, with much of the margin being relatively weak but areas such as the Porcupine Basin and parts of the Rockall Basin having greater strength. Observed differences between the model Moho and seismic Moho along the continental margin can be interpreted in terms of underplating. A Moho discrepancy to the northwest of Scotland is ascribed to uplift caused by a region of upper mantle with anomalously low density, which may be associated with depletion or with a temperature anomaly.

Synchrotron X-ray Diffraction and Reflection Studies of a Polymacromonomer Monolayer at the Air−Water Interface: Transition from Aligned Single Molecules to Homogeneous Layer

Monolayers of polymacromonomers with poly(vinyl)pyridine side chains of different lengths, polyPVP20.8 and polyPVP46.7, are studied at the air/water interface. Combination of reflection data and diffraction peaks allows the establishment of a structural model. In the expanded phase at pressures below approximately 15 mN/m, the side chains are adsorbed to the air/water interface, causing polymer backbone stretching and alignment of the single molecules. The in-plane peaks are due to the lateral electron density variation above and below the adsorption layer. The diameter of the flattened cylindrical molecules corresponds to twice the contour length of the side chains (25 and 12.5 nm, respectively) and decreases on monolayer compression by approximately 20%, due to side chain desorption. Additionally, side chain desorption causes monolayer thickening. Above the phase transition, the lateral order disappears. Obviously, the side chains of adjacent molecules mix and the monolayer is homogeneous.

Constraining large-scale mantle heterogeneity using mantle and inner-core sensitive normal modes

Attempts to resolve density heterogeneity within the mantle using normal-mode data revealed an unexpected feature near the core-mantle boundary: regions of strong sheer velocity reduction, known as superplumes, are characterized by heavier than average material [Science 285 (1999) 1231]. Thus far, free-oscillation studies of mantle structure have relied upon modes which sample only the mantle (e.g., [ J. Geophys. Res. 96 (1991) 551; Science 285 (1999) 1231; J. Geophys. Res. 104 (1999a) 993; Geophys. J. Int. 143 (2000b) 478; Geophys. J. Int. 150 (2002) 162]). In order to better constrain mantle heterogeneity, we add inner-core sensitive modes to our data set, and invert for mantle structure and inner-core anisotropy simultaneously. The additional modes do not alter the pattern of the density anomalies relative to model SPRD6 [Geophys. J. Int. 145 (2001) 77]. However, they help constrain the amplitude of lateral variations in density. In a previous study, obtaining a density model with reasonable amplitudes required supplemental gravity data, which are not included in the current study. Nonetheless, the new density model is generally weaker, especially at the bottom of the mantle. The root-mean square (RMS) amplitude of the model exhibits two maxima around 600 and 2300 km depth. Experiments indicate that these are robust components of the model and neither artifacts of the choice of radial basis functions nor the damping scheme. Comparisons of the density model with shear- and compressional-velocity models show negative or nearly zero correlation in the transition zone and near the base of the mantle, where the root-mean square density amplitude is high. Finally, the anomalous features near the core-mantle boundary are confirmed: strong anti-correlation between shear and bulk-sound velocities, and increased density at the locations of superplumes.

Discussion of Mean Gravity Along the Plumbline

According to the definition of the orthometric height, the mean value of gravity along the plumbline between the Earth's surface and the geoid is defined in an integral sense. In Helmert's (1890) definition of the orthometric height, a linear change of the gravity with depth is assumed. The mean gravity is determined so that the observed gravity at the Earth's surface is reduced to the approximate mid-point of the plumbline using Poincare-Prey's gravity gradient. Niethammer (1932) and later Mader (1954) took into account the mean value of the gravimetric terrain correction within the topography considering the constant topographical density distribution along the plumbline (for more details see Heiskanen and Moritz, 1967). Vanicek et al. (1995) included the effect of the lateral variation of the topographical density into the definition of Helmert's orthometric height. Recently, Hwang and Hsiao (2003) discussed the influence of the vertical gradient of disturbing gravity on the orthometric heights. In this paper, the mean integral value of gravity along the plumbline within the topography is defined so that the actual topographical density distribution and the change of the disturbing gravity with depth are taken into account. Based on the definition of the mean gravity, the relation between the orthometric and normal heights is discussed.

Scales of spatial heterogeneity for perennial and seasonal snow layers

AbstractLocal observations of snow layers are used as the basis for spatial extrapolation of snow properties and for establishing a time record of snow deposition, yet significant lateral variations in layer thickness, density and microstructure are well documented. Here we examine the nature of layer heterogeneity over distances of 10– 100 000 m using data from primarily flat locations in Alaska, Antarctica and Greenland. We find that at a scale of 10 m or less, perennial snow layers on glaciers and ice sheets are more uniform and laterally continuous than seasonal layers, which, in addition to heterogeneity introduced by wind and water percolation, are also affected by local topography and vegetation. At a scale of about 100 m, heterogeneity of seasonal and perennial snow layers converges and approaches a peak value. At larger scales (103–105m), local (order 100 m) forcing continues to produce most of the layer heterogeneity, with synoptic-scale variations adding small amounts. Cross-correlation at these larger scales is based on recognizing distinctive layer sequences or matching a few key layers of snow. Many layers cannot be correlated because they pinch out or change at scales (i.e. 100 m) smaller than the spacing between snow pits.

Superstructures and coincidences of a thin oxide film on a metallic substrate: A STM study

An alumina thin film, grown at 1000 K on a ${\mathrm{Ni}}_{3}\mathrm{Al}(111)$ substrate, is investigated using low-temperature scanning tunneling microscopy. Depending on the (positive) voltage applied to the sample, two superstructures are imaged. Using tunneling spectroscopy, this effect is traced back to a lateral variation of the local density of states within the apparent unit cell of the oxide thin film. In the vicinity of the conduction-band edge, the density of empty states for tunneling electrons is locally enhanced over characteristic points of the unit cell. A coincidence lattice between film and metallic substrate, with a unit cell of same size and symmetry, is proposed as the origin of this modulation of the oxide electronic structure.

On the origins of band topography, Europa

We use stereo-derived topography of extensional bands on Europa to show that these features can be elevated by 100–150 m with respect to the surroundings, and that the positive topography sometimes extends beyond the band margins. Lateral variations in shell thickness cannot maintain the observed topography for timescales greater than ∼0.1 Myr. Lateral density variations can maintain the observed topography indefinitely; mean density contrasts of 5 and 50 kg m −3 are required for shell thicknesses of 20 and 2 km, respectively. Density variations caused by temperature contrasts require either present-day heating or that bands are young features (<1 Myr old). Stratigraphic analyses suggest that these mechanisms are unlikely. The observation that bands form from ridges may be explained by an episode of shear-heating on ridges weakening the ridge area, and leading to strain localization during extension. Fracture porosity is likely to persist over Myr timescales in the top one-third to one-quarter of the conductive part of the ice shell. Lateral variations in this porosity (of order 20%) are the most likely mechanism for producing band topography if the ice shell is thin (≈2 km); porosity variations of 2% or less are required if the shell is thicker (≈20 km). If the ice shell is thick, lateral variations in salt content are a more likely mechanism. Warm ice will tend to lose dense, low-melting temperature phases and be buoyant relative to colder, salt-rich ice. Thus, lateral density variations will arise naturally if bands have been the sites of either localized heating or upwelling of warm ice during extension.

The strength of the lunar lithosphere

A self-gravitating, elastic, spherical thick shell model is used to derive the present state of the lateral variations of density and stress differences within the lunar lithosphere. The model is allowed to deform under the load of an initial surface topography and internal density distribution, such that the resulting deformed body gives rise to the observed surface topography and gravity specified by the spherical harmonics of degree up to 70. Two main models are considered, Model A and Model B, with elastic lithospheres of thickness 300 and 210 km, respectively. Model A displays density perturbations of generally less than ±200 kg/m 3 within the crustal layers, reducing rapidly to less than ±20 kg/m 3 at the base of the lithosphere. The density perturbations in Model B are similar in the crust and marginally higher at the base of the lithosphere. The major stress differences in the mantle are associated with the mascon basins and are found to reach maximums of 8–10 MPa within the lower lithosphere (150–270 km) of Model A and maximums of 12–16 MPa at 150 to 180 km depth for Model B. A moderate correlation exists between the modeled stress distributions and shallow moonquake epicenters. However, the overall results of this study imply that other remnant stresses, due to processes other than density perturbations, exist and play a critical role in the large shallow moonquakes.

An integrated geophysical investigation of the upper crust in the epicentral area of the 1980, Ms=6.9, Irpinia earthquake (Southern Italy)

In this paper, we investigate the upper crustal structure of the Irpinia region, Southern Apennines thrust belt, Italy, through analysis and joint interpretation of gravity data, seismic reflection lines and subsurface information from many deep wells. The investigated region includes the epicentral area of the 1980 ( M s=6.9) Irpinia earthquake and is one of the Italian regions with the highest seismic hazard. The upper crustal structure is imaged by modeling a series of 15 SW-trending gravity profiles, spaced about 5 km apart, plentifully constrained by seismic reflection lines and wells, thus reducing the inherent ambiguity of the gravity modeling. Despite of the complexity of the modeled Bouguer anomalies, the application of a calibrating procedure to constrain the range of variability of the density values, as well as the use of geometric constraints, results in a good level of stability in the final density cross-sections, which in fact appear coherent both in the density values and in the geometrical features. The inferred model shows important lateral density variations that can be mostly related to NW-trending geologic structures. High-density bodies delineate carbonate platform thrust sheets and broad antiforms involving Mesozoic basinal rocks, while low-density shallow bodies are associated with Pliocene basins. In addition, important density (i.e. lithological) variations are evident along the strike of the range, the most relevant being an abrupt deepening of the Apulia Carbonate Platform in the southeastern part of the investigated region. In the epicentral region of the 1980 event, we find that the geometry of the high-density, high-velocity carbonates of the Apulia Platform appears correlated with the distribution of the aftershocks and with the P-wave velocity anomaly pattern as inferred from a previous local earthquake tomography. The structural highs of the Apulia Platform correspond to high-velocity regions, where aftershocks and coseismic slip of the mainshock are concentrated. This correlation suggests that the Apulia Carbonate Platform geometry played an important role in the rupture propagation and in the aftershock distribution.

Insights into orogenesis: getting to the root of a continent–ocean–continent collision, Southern Urals, Russia

The Ural mountains preserve a late Palaeozoic collision that forms a 2500 km suture in the world's largest landmass, Eurasia. Several features of the mountain belt, in particular a well-preserved crustal root, are uncharacteristic of other Palaeozoic orogens such as the Appalachians and Caledonides. Previous interpretations of the Southern Uralian root suggested that it is composed of East European Craton crust derived from the west. A new potential field data model, considered in conjunction with published seismic, heat-flow and geological data, indicates that the root is composed mainly of mafic granulite, which we interpret as oceanic arc crust originally accreted from the east, subducted eastward, and metamorphosed. A load caused by crustal lateral density variations, combined with topography, isostatically compensates root buoyancy and is thus the main cause of its preservation.

Correction to “Correction to ‘Origin of lateral variation of seismic wave velocities and density in the deep mantle’ by Shun‐ichiro Karato and Bijaya B. Karki”

Correction to “Correction to ‘Origin of lateral variation of seismic wave velocities and density in the deep mantle’ by Shun‐ichiro Karato and Bijaya B. Karki”