An anomalous high-velocity layer at shallow crustal depths in the Narmada zone, India

The Narmada zone in central India is a zone of weakness that separates the region of Vindhyan (Meso-Neoproterozoic) deposition to the north from Gondwana (Permo-Carboniferous–lower Cretaceous) deposits to the south. The reinterpretation of analogue seismic refraction data, acquired during the early 1980s, using 2-D ray-tracing techniques reveals a basement (velocity 5.8–6.0 km s⁻¹ ) topography suggesting that the Narmada zone, bounded by the Narmada North and Narmada South faults is a region of basement uplift. A layer of anomalously high velocity (6.5–6.7 km s⁻¹ ) at depths between 1.5 and 9.0 km appears to be present in the entire region. Within the Narmada zone this layer occurs at shallower depths than outside the Narmada zone. At two places within the Narmada zone this layer is at a depth of about 1.5 km. This layer cannot be considered as the top of the lower crust because in this case it should have produced large positive gravity anomalies at the shallowest parts. Instead, these parts correspond to Bouguer gravity lows. Furthermore, lower crust at such shallow depths has not been reported from any other part of the Indian shield. Therefore, this layer is likely to represent the top of a high-velocity mafic body that has different thicknesses in different places.     

An algebraic formulation of geophysical inverse problems

Many geophysical inverse problems derive from governing partial differential equations with unknown coefficients. Alternatively, inverse problems often arise from integral equations associated with a Green's function solution to a governing differential equation. In their discrete form such equations reduce to systems of polynomial equations, known as algebraic equations. Using techniques from computational algebra one can address questions of the existence of solutions to such equations as well as the uniqueness of the solutions. The techniques are enumerative and exhaustive, requiring a finite number of computer operations. For example, calculating a bound to the total number of solutions reduces to computing the dimension of a linear vector space. The solution set itself may be constructed through the solution of an eigenvalue problem. The techniques are applied to a set of synthetic magnetotelluric values generated by conductivity variations within a layer. We find that the estimation of the conductivity and the electric field in the subsurface, based upon single-frequency magnetotelluric field values, is equivalent to a linear inverse problem. The techniques are also illustrated by an application to a magnetotelluric data set gathered at Battle Mountain, Nevada. Surface observations of the electric ( E _y ) and magnetic ( H _x ) fields are used to construct a model of subsurface electrical structure. Using techniques for algebraic equations it is shown that solutions exist, and that the set of solutions is finite. The total number of solutions is bounded above at 134 217 728. A numerical solution of the algebraic equations generates a conductivity structure in accordance with the current geological model for the area.     

Erosional decay of the Yucca Mountain crest, Nevada

A simple numerical landscape evolution model is used to investigate the rate of erosional decay of the Yucca Mountain crest in Nevada, USA — a location proposed as a permanent repository for high level radioactive waste. The model is based on a stream power approach in which we assume that the rate of erosion is proportional to the size of the catchment as a proxy for water flux and to the square of the topographic gradient. The proportionality constants in the model are determined using the structural history of the region: extensional tectonics has dissected the region into a series of well-defined tilt blocks in the last 11 my and the ratio of fault displacement and gully incision during this time is used to scale the model. Forward predictions of our model into the future show that the crest will denude to the level of the proposed site between 500,000 years and 5 my. This prediction is based on conservative estimates for all involved parameters. Erosion may be more rapid if other processes are involved. For example, our model does not consider continuing uplift or catastrophic surface processes as they have been recorded in the region. We conclude that any “total system performance analysis” (TSPA — as has been performed for the Yucca Mountain region to predict geological events inside the ridge) must consider erosion as an integral part of its predictions.     

Modelling of ground deformation and gravity fields using finite element method: an application to Etna volcano

Elastic finite element models are applied to investigate the effects of topography and medium heterogeneities on the surface deformation and the gravity field produced by volcanic pressure sources. Changes in the gravity field cannot be interpreted only in terms of gain of mass disregarding the ground deformation of the rocks surrounding the source. Contributions to gravity changes depend also on surface and subsurface mass redistribution driven by dilation of the volcanic source. Both ground deformation and gravity changes were firstly evaluated by solving a coupled axisymmetric problem to estimate the effects of topography and medium heterogeneities. Numerical results show significant discrepancies in the ground deformation and gravity field compared to those predicted by analytical solutions, which disregard topography, elastic heterogeneities and density subsurface structures. With this in mind, we reviewed the expected gravity changes accompanying the 1993–1997 inflation phase on Mt Etna by setting up a fully 3-D finite element model in which we used the real topography, to include the geometry, and seismic tomography, to infer the crustal heterogeneities. The inflation phase was clearly detected by different geodetic techniques (EDM, GPS, SAR and levelling data) that showed a uniform expansion of the overall volcano edifice. When the gravity data are integrated with ground deformation data and a coupled FEM modelling was solved, a mass intrusion could have occurred at depth to justify both ground deformation and gravity observations.     

3-D magnetotelluric inversion and model validation with gravity data for the investigation of flood basalts and associated volcanic rifted margins

20 magnetotelluric (MT) soundings were collected on the Isle of Skye, Scotland to provide a high-resolution three-dimensional (3-D) electrical resistivity model of a volcanic province within the framework of a project jointly interpreting gravity, seismic, geological and MT data. The full 3-D inversion of the MT data jointly interpreted with gravity data reveals upper crustal structure. The main features of the model are interpreted in conjunction with previous geological mapping and borehole data. Our model extends to 13 km depth, several kilometres below the top of the Lewisian basement. The top of the Lewisian basement is at approximately 7–8 km depth and the topography of its surface was controlled by Precambrian rifting, during which a 4.5 km thick sequence of Torridonian sediments was deposited. The Mesozoic sediments above, which can reach up to 2.2 km thick, have small-scale depocentres and are covered by up to 600 m of Tertiary lava flows. The interpretation of the resistivity model shows that 3-D MT inversion is an appropriate tool to image sedimentary structures beneath extrusive basalt units, where conventional seismic reflection methods may fail.     

Choice of norm for the density distribution of the Earth

Summary. The determination of the density distribution of the Earth from gravity data is called the inverse gravimetric problem. A unique solution to this problem may be obtained by introducing a priori data concerning the covariance of density anomalies. This is equivalent to requiring the density to fulfil a minimum norm condition. The generally used norm is the one equal to the integral of the square of the density distribution ( L² -norm), the use of which implies that blocks of constant density are uncorrelated. It is shown that for harmonic anomalous density distributions this leads to an external gravity field with a power spectrum (degree-variances) which tends too slowly to zero, i.e. implying gravity anomalies much less correlated than actually observed. It is proposed to use a stronger norm, equal to the integral of the square sum of the derivatives of the density distribution. As a consequence of this, base functions which are constant within blocks, are no longer a natural choice when solving the inverse gravimetric problem. Instead a block with a linearly varying density may be used. A formula for the potential of such a block is derived.     

Regional vertical tectonics in the Eastern Mediterranean

Summary. New gravity observations from a systematic survey of the Eastern Mediterranean Sea and from a reconnaissance land survey in Central and Western Turkey have been compiled with existing data. Lack of sufficient geological and geophysical information precludes an analysis of the local anomalies or crustal structure; however, implications of the topography and gravity field at long wavelengths have been examined. Negative free-air anomalies characterize almost the entire Eastern Mediterranean basin and positive anomalies predominate in Turkey and the Aegean Sea. The change in sign coincides with the northern boundary of the African plate, and the wavelength and amplitude of the gravity variation are of the order of 1000 km and 100 mgal respectively. The lithosphere is probably unable to support such anomalies because the implied shear stresses are too large. The source of the anomalies is concluded to be in the asthenosphere where the low finite strength of material suggests that some sort of flow must exist to maintain the stresses. A good correlation is observed between the gravity and topography at wavelengths greater than 300 km; and the relationship is the same as that observed in the North Atlantic and the Central Pacific, as well as that computed for simple models of mantle convection. The gravity and topography of the Eastern Mediterranean can be explained in terms of flow in the upper mantle. This is the first region of subsidence for which this interpretation has been made.     

A geometrical interpretation of ideal body problems

Summary. For linear geophysical inverse problems, the exercise of finding a greatest lower bound on the uniform norms of positive solutions fitting N data, is shown to have a geometrical counterpart in the N- dimensional space of N -tuples of real numbers. By application of the Fenchel Duality Theorem, we demonstrate that the problem is equivalent to the discovery of a particular hyperplane tangent to a convex set in this space. As examples in the case of two data, the new formulation is applied to the problems of recovering density information from planetary mass and moment of inertia, and from two vertical gravity anomalies.     

Tidal gravity in Britain: tidal loading and the spatial distribution of the marine tide

Summary. Tidal gravity measurements have been made at six sites in Britain with two nulled LaCoste and Romberg Earth tide gravitymeters. The M ₂ observations from these and two further sites are compared with calculations of the tidal loading from the seas around the British Isles and the major oceans. Models of the M ₂ marine tides are convolved with Green's functions for appropriate radially stratified Earth models. The differences between the M ₂ observations and the theoretical calculations are less than 0.6 μ gals and it is shown that these differences contain further information concerning the errors in the marine tide models. The M ₂ marine tides on the north-west European continental shelf are reasonably well known and this allows a useful test of the feasibility of using tidal gravity measurements for the inverse ocean tide problem in areas where the ocean tides are less well known. The differential gravity loading signal between pairs of gravity stations is shown to be important for considerations of the uniqueness and accuracy of the inverse problem. M ₂ tidal gravity loading maps for the British Isles and Europe have been produced which are of use in making corrections to various geodetic measurements.     

Lithoprobe southern Canadian Cordilleran transect: Rocky Mountain thrust belt to Valhalla gneiss complex

Summary. LITHOPROBE has acquired nearly 270 km of crustal seismic reflection data across the eastern portion of the southern Canadian Cordillera, These reflection profiles, obtained during the Fall of 1985, extend from the Rocky Mountain thrust and fold belt, across the Rocky Mountain Trench, Purcell anticlinorium, Kootenay Arc, Nelson batholith and Valhalla gneiss complex. North American basement and its overlying foreshortened miogeoclinal rocks can be traced westward to the Kootenay Arc. The Purcell anticlinorium is carried by a series of west dipping thrust faults which emerge east of the anticlinorium and converge downward and merge with a detachment surface above autochthonous North American basement. Proterozoic supracrustal rocks, thickened by folding and thrusting, occupy the core of the anticlinorium. Steeply dipping surface structures of the western Purcell anticlinorium and Kootenay Arc appear to be truncated at 3 - 4 s (9-12 km) by a gently east-dipping reflection that may delineate the upper boundary of an allochthonous wedge inserted between the near surface rocks and autochthonous basement below. Beneath the Kootenay Arc, at a travel time of 9–10 s (27–30 km), the North American basement seems to be truncated by the major east-dipping Slocan Lake fault zone, which can be traced from its surface exposure at the east edge of the Valhalla gneiss complex eastward to near the base of the crust. A high amplitude, west-dipping reflection underlies the Valhalla complex and may be related to a major compressional shear zone.     

Extremal inversion of static earth displacements due to volume sources

Summary. The inverse problem of using static displacements observed at the surface to infer volume changes within the Earth is considered. This problem can be put in a form such that the method of ideal bodies and the method of positivity constraints may both be applied. Thus all of the techniques previously developed for the gravity inverse problem can be extended to the static displacement problem. Given bounds on the depth, the greatest lower bound on the fractional volume change can be estimated, or, given bounds on the fractional volume change, the least upper bound on the depth can be estimated. Methods of placing bounds on generalized moments of the perturbing body are also developed, and techniques of handling errors in the data are discussed.
Examples are given for both two- and three-dimensional problems. The ideal body method is suited for both 2- and 3-D problems when only two data points are considered, but is unwieldy for more data points. The method of positivity constraints is more versatile and can be used when there are many data points in the case of 2-D problems, but it may lead to an excessive amount of computation in 3-D problems.     

Plan-view curvature of foreland basins and its implications for the palaeostrength of the lithosphere underlying the western Alps

In zones of continental collision, three methods can be used to calculate the strength of the underthrust lithosphere: (1) a forward model approach to the Bouguer gravity field, (2) an inverse model of the gravity and topography using admittance techniques, or (3) a forward model of the stratigraphic infill of the foreland basin to estimate the cross-sectional profile of the downflexed plate. The use of reconstructed stratigraphy has the potential to yield values for the equivalent elastic thickness (T_e) of the cratonic lithosphere at varying slices in geological time, and hence enable an insight into the longer term (10–50 Myr) mechanical behaviour of the continental lithosphere. Calculations of T_e based on isopachs of foreland basin stratigraphy use sea level as a reference line to estimate the basement deflection, and therefore are limited to using stratigraphy which records shallow marine or coastal sedimentation. A new empirical approach is applied to evaluating ancient T_e values using the reconstructed palaeocurvature of the basin in plan view. The radius of curvature of 12 curvilinear foreland basins is plotted against their documented T_e values and shows a linear relationship. The maximum T_e value for a given radius of curvature can also be plotted as a straight line. The palaeocurvature of reconstructed basins can then be compared with the plots, and estimates of likely maximum T_e values may be obtained. During Eocene times, the underfilled foreland basin of the Alps was characterized on its cratonic edge by the deposition of Nummulite-rich limestones. Palaeogeographical reconstructions of the Nummulitic Limestones enable estimates of the palaeocurvature of the cratonic margin of the Alpine foreland basin during the Eocene. By comparing this value with the curvature of documented basins, it is possible to suggest that the European lithosphere underlying the western Alps had an effective elastic thickness of no greater than 17 km during the Eocene. It has been suggested that the transition in the depositional state of the Alpine foreland basin from an underfilled to a filled state during middle Oligocene times was linked to a thickening of the continental lithosphere associated with the effective ramp of the Tethyan passive margin. The T_e value of less than 17 km during the underfilled stage combined with a value of 10±5 km for the later filled stage at 17 Ma does not lend support to this hypothesis.     

内蒙古牙克石市秧草沟铅锌银钼矿化探特征及找矿意义

秧草沟铅锌银钼矿位于植被覆盖严重、基岩裸露零星的大兴安岭林区,该铅锌银钼矿床是在1︰1万土壤测量及其所圈定的化探异常查证基础上,通过地表槽探工程揭露、中深部钻探工程验证发现的,现已圈定矿体27个,初步概算铅锌银、钼资源量已达中型矿床规模。该矿区的找矿经验对在地表覆盖厚、基岩裸露稀少的林区开展找矿工作具有指导意义。     

The reduction of aliasing in gravity anomalies and geoid heights using digital terrain data

Observations of gravity can be aliased by virtue of the logistics involved in collecting these data in the field. For instance, gravity measurements are often made in more accessible lowland areas where there are roads and tracks, thus omitting areas of higher relief in between. The gravimetric determination of the geoid requires mean terrain-corrected free-air anomalies; however, anomalies based only on the observations in lowland regions are not necessarily representative of the true mean value over the topography. A five-stage approach is taken that uses a digital elevation model, which provides a more accurate representation of the topography than the gravity observation elevations, to reduce the unrepresentative sampling in the gravity observations. When using this approach with the Australian digital elevation model, the terrain-corrected free-air anomalies generated from the Australian gravity data base change by between 77.075 and −84.335 mgal (−0.193 mgal mean and 2.687 mgal standard deviation). Subsequent gravimetric geoid computations are used to illustrate the effect of aliasing in the Australian gravity data upon the geoid. The difference between 'aliased' and 'non-aliased' gravimetric geoid solutions varies by between 0.732 and −1.816 m (−0.058 m mean and 0.122 m standard deviation). Based on these conceptual arguments and numerical results, it is recommended that supplementary digital elevation information be included during the estimation of mean gravity anomalies prior to the computation of a gravimetric geoid model.     

Mechanisms for the formation of ridge-axis topography atslow-spreading ridges: a lithospheric-plate flexural model

The seafloor topography of a slow-spreading ridge shows a number of well-documented regularities at the ridge segment scale as the result of the complex interplay between ridge-axis magmatic and tectonic processes. This paper describes the results of a detailed analysis of the seafloor topography of the Mid-Atlantic Ridge near the Atlantis transform, where marine gravity data provide independent, although non-unique, constraints on subseafloor density structure. Using a combined topography and gravity data set, we identified the specific contributions of subseafloor density structure to the seafloor topography. We show that the observed along-axis deepening (0.3–0.8 km) from the midpoint of a ridge segment towards the non-transform offsets in the study area can be explained by the vertical deflection of a zero-age plate in response to along-axis crustal thickness variations. However, this effect can only account for 50–60 per cent of the observed 1.5–1.7 km deepening towards the Atlantis transform, suggesting the presence of significant stresses in the lithosphere near a transform. Results of plate flexural calculations also predict a more elevated rift flank at the inside corner of the ridge–transform intersection than at the conjugate outside corner. Such an asymmetry in rift flank topography is calculated to be greatest near a transform fault with a significant volume of deep transform valley and when adjacent plates across the transform fault are mechanically decoupled or only weakly coupled. Together these results illustrate the complex interplay between various tectonic processes at a slow-spreading ridge.     

The multibody space-time geodetic boundary value problem and the Honkasalo term

Summary. The geodetic boundary value problem is solved by taking temporal changes of geometry and gravity into account. It is aimed to get complete information about the mechanical response of the Earth to an external tidal force which is only imperfectly known. The information is used to solve the inverse Love-Shida problem, e.g. by computing the Love -Shida operators. The general solution (4.25), (4.26) is specialized for a perfectly known external gravity field and for a free fixed boundary of the Earth.     

Small-scale mantle flows and induced lithospheric stress near island arcs

Summary. This paper explores the middle ground between complex thermally-coupled viscous flow models and simple corner flow models of island arc environments. The calculation retains the density-driven nature of convection and relaxes the geometrical constraints of corner flow, yet still provides semianalytical solutions for velocity and stress. A novel aspect of the procedure is its allowance for a coupled elastic lithosphere on top of a Newtonian viscous mantle. Initially, simple box-like density drivers illustrate how vertical and horizontal forces are transmitted through the mantle and how the lithosphere responds by trench formation. The flexural strength of the lithosphere spatially broadens the surface topography and gravity anomalies relative to the functional form of the vertical flow stresses applied to the plate base. I find that drivers in the form of inclined subducting slabs cannot induce self-driven parallel flow; however, the necessary flow can be provided by supplying a basal drag of 1–5 MPa to the mantle from the oceanic lithosphere. These basal drag forces create regional lithospheric stress and they should be quantifiable through seismic observations of the neutral surface. The existence of a shallow elevated phase transition is suggested in two slab models of 300 km length where a maximum excess density of 0.2 g cm⁻³ was needed to generate an acceptable mantle flow. A North New Hebrides subduction model which satisfies flow requirements and reproduces general features of topography and gravity contains a high shear stress zone (75 MPa) around the upper slab surface to a depth of 150 km and a deviatoric tensional stress in the back arc to a depth of 70 km. The lithospheric stress state of this model suggests that slab detachment is possible through whole plate fracture.     

The Canary Islands swell: a coherence analysis of bathymetry and gravity

The Canary Archipelago is an intraplate volcanic chain, located near the West African continental margin, emplaced on old oceanic lithosphere of Jurassic age, with an extended volcanic activity since Middle Miocene. The adjacent seafloor does not show the broad oceanic swell usually observed in hotspot-generated oceanic islands. However, the observation of a noticeable depth anomaly in the basement west of the Canaries might indicate that the swell is masked by a thick sedimentary cover and the influence of the Canarian volcanism. We use a spectral approach, based on coherence analysis, to determine the swell and its compensation mechanism. The coherence between gravity and topography indicates that the swell is caused by a subsurface load correlated with the surface volcanic load. The residual gravity/geoid anomaly indicates that the subsurface load extends 600 km SSW and 800 km N and NNE of the islands. We used computed depth anomalies from available deep seismic profiles to constrain the extent and amplitude of the basement uplift caused by a relatively low-density anomaly within the lithospheric mantle, and coherence analysis to constrain the elastic thickness of the lithosphere ( T_e ) and the compensation depth of the swell. Depth anomalies and coherence are well simulated with T_e =28–36 km, compensation depth of 40–65 km, and a negative density contrast within the lithosphere of ∼33 kg m⁻³. The density contrast corresponds to a temperature increment of ∼325°C, which we interpret to be partially maintained by a low-viscosity convective layer in the lowermost lithosphere, and which probably involves the shallower parts of the asthenosphere. This interpretation does not require a significant rejuvenation of the mechanical properties of the lithosphere.     

Inference of the Lateral Heterogeneity of the Earth from the Eigenfrequency Spectrum: a Linear Inverse Problem

Summary
We consider the problem of inferring information about the lateral heterogeneity of the Earth's physical properties given certain measurements of the eigenfrequency splitting of the elastic-gravitational normal mode multiplets. We show that this problem can be formulated as a series of exactly linear inverse problems; the data which are relevant to at least the first two of these linear inversions can be measured without having to resolve fully the normal mode multiplets.     

Structure and geological history of the Congo Basin: an integrated interpretation of gravity,magnetic and reflection seismic data

The stratigraphic, paleogeographic and tectonic evolution of the intracratonic Congo Basin in Central Africa has been revised on the basis of an integrated interpretation of gravity, magnetic and reflection seismic data, together with a literature review of papers sometimes old and difficult to access, map compilation and partial reexamination of outcrop and core samples stored in the Royal Museum for Central Africa (RMCA). The Congo Basin has a long and complex evolution starting in the Neoproterozoic and governed by the interplay of tectonic and climatic factors, in a variety of depositional environments.This multidisciplinary study involving 2D gravity and magnetic modeling as additional constraints for the interpretation of seismic profiles appears to be a powerful tool to investigate sedimentary basins where seismic data alone may be difficult to interpret. The tectonic deformations detected in the Congo Basin after the 1970–1984 hydrocarbon exploration campaign in the Democratic Republic of Congo (DRC) have been attributed to crustal contraction and basement uplift at the center of the basin, following a transpressional inversion of earlier graben structures. Two‐dimensional gravity and magnetic models run along key seismic lines suggest the presence of evaporite sequences in some of the deeper units of the stratigraphic succession, in the lateral continuity with those observed in the Mbandaka and Gilson exploration wells. The poorly defined seismic facies that led to the previous basement uplift interpretation of the crystalline basement is shown to correspond to salt‐rich formations that have been tectonically de‐stabilized. These features may be related to vertical salt‐tectonics connected to the near/far‐field effects of the late Pan‐African and the Permo‐Triassic compressive tectonic events that affected this African part of Gondwana.