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1.
The numerical results of downward continuation (DWC) of point and mean gravity anomalies by the Poisson integral using point, single mean, and doubly averaged kernel are examined. Correct evaluation of the integral in its innermost zone is a challenging task. To avoid instabilities, an analytical planar approximation is used in the innermost integration zone. In addition it is shown that the single mean mode has the minimum discretization error. Downward continuation of point and mean anomalies by singly and doubly averaged kernel are the same mean anomalies on the geoid.  相似文献   

2.
In the evaluation of the geoid done according to the Stokes-Helmert method, the following topographical effects have to be computed: the direct topographical effect, the primary indirect topographical effect and the secondary indirect topographical effect. These effects have to be computed through integration over the surface of the earth. The integration is usually split into integration over an area immediately adjacent to the point of interest, called the near zone, and the integration over the rest of the world, called the far zone. It has been shown in the papers by Martinec and Vaníek (1994), and by Novák et al. (1999) that the far-zone contributions to the topographical effects are, even for quite extensive near zones, not negligible.Various numerical approaches can be applied to compute the far-zone contributions to topographical effects. A spectral form of solution was employed in the paper by Novák et al. (2001). In the paper by Smith (2002), the one-dimensional Fast Fourier Transform was introduced to solve the problem in the spatial domain. In this paper we use two-dimensional numerical integration. The expressions for the far-zone contributions to topographical effects on potential and on gravitational attraction are described, and numerical values encountered over the territory of Canada are shown in this paper.  相似文献   

3.
This paper describes certain procedures for deriving from the apparent resistivity data as measured by the Wenner electrode configuration two functions, known as the kernel and the associated kernel respectively, both of which are functions dependent on the layer resistivities and thicknesses. It is shown that the solution of the integral equation for the Wenner electrode configuration leads directly to the associated kernel, from which an integral expression expressing the kernel explicitly in terms of the apparent resistivity function can be derived. The kernel is related to the associated kernel by a simple functional equation where K1(λ) is the kernel and B1(λ) the associated kernel. Composite numerical quadrature formulas and also integration formulas based on partial approximation of the integrand by a parabolic arc within a small interval are developed for the calculation of the kernel and the associated kernel from apparent resistivity data. Both techniques of integration require knowledge of the values of the apparent resistivity function at points lying between the input data points. It is shown that such unknown values of the apparent resistivity function can satisfactorily be obtained by interpolation using the least-squares method. The least-squares method involves the approximation of the observed set of apparent resistivity data by orthogonal polynomials generated by Forsythe's method (Forsythe 1956). Values of the kernel and of the associated kernel obtained by numerical integration compare favourably with the corresponding theoretical values of these functions.  相似文献   

4.
The physical meaning of the truncated geoid, which is defined by the convolution of gravity anomalies with the Stokes function on a spherical cap of specified radius, has been studied by the authors. They investigated its relation to the density distribution, generating the surface gravity, and its potential use in inversion. Some progress results for simulated studies on point mass anomalies are presented. The behavior of the truncated geoid is controlled by the radius of the integration domain, hereinafter referred to as the truncation parameter, which is treated as a free parameter. The change of the truncated geoid in response to the change of the truncation parameter was studied in the context of the simulated mass distributions. By means of such computer simulations we have managed to demonstrate the clear sensitivity of the truncated geoid to the depths, in addition to the horizontal positions, of point mass anomalies generating the synthetic surface gravity. The objective of this paper is to illustrate, with the help of computer simulation as the method of our study, the contribution of the truncated geoid to the solution of the gravimetric inverse problem. Further work towards employing the truncated geoid in gravity exploration is being conducted.  相似文献   

5.
De Lacy  M.C.  Rodríguez-Caderot  G.  Marín  E.  Ruiz  A.  Borque  M.J.  Gil  A.J.  Biagi  L. 《Studia Geophysica et Geodaetica》2001,45(1):55-66
Two new GPS surveys have been carried out to check the accuracy of an existing gravimetric geoid in a test area located in northern Andalusia (Spain). The fast collocation method and the remove-restore procedure have been used for the computation of the quasigeoid model. The Spanish height system is based on orthometric heights, so the gravimetrically determined quasigeoid has been transformed to a geoid model and then compared to geoid undulations provided by GPS and levelling at benchmarks belonging to the Spanish first-order levelling network. The discrepancies between the gravimetric solution and GPS/levelling undulations amount to ±2 cm for one survey and ±5 cm for another after fitting a plane to the geoid model.  相似文献   

6.
Gravity anomaly reference fields, required e.g. in remove-compute-restore (RCR) geoid computation, are obtained from global geopotential models (GGM) through harmonic synthesis. Usually, the gravity anomalies are computed as point values or area mean values in spherical approximation, or point values in ellipsoidal approximation. The present study proposes a method for computation of area mean gravity anomalies in ellipsoidal approximation (‘ellipsoidal area means’) by applying a simple ellipsoidal correction to area means in spherical approximation. Ellipsoidal area means offer better consistency with GGM quasigeoid heights. The method is numerically validated with ellipsoidal area mean gravity derived from very fine grids of gravity point values in ellipsoidal approximation. Signal strengths of (i) the ellipsoidal effect (i.e., difference ellipsoidal vs. spherical approximation), (ii) the area mean effect (i.e., difference area mean vs. point gravity) and (iii) the ellipsoidal area mean effect (i.e., differences between ellipsoidal area means and point gravity in spherical approximation) are investigated in test areas in New Zealand and the Himalaya mountains. The impact of both the area mean and the ellipsoidal effect on quasigeoid heights is in the order of several centimetres. The proposed new gravity data type not only allows more accurate RCR-based geoid computation, but may also be of some value for the GGM validation using terrestrial gravity anomalies that are available as area mean values.  相似文献   

7.
A new formulation is proposed for the electrical potential developed inside a horizontally‐layered half‐space for a direct current point‐source at the surface. The recursion formula for the kernel coefficient in the potential integral is simpler than the generally used two‐coefficient recursion. The numerical difficulties that may occur during the computation of the integrals and near the source axis are examined and solutions are proposed. The set of equations permits a stable and accurate computation of the tabular potential everywhere in the medium.  相似文献   

8.
A method for splitting sea surface height measurements from satellite altimetry into geoid undulations and sea surface topography is presented. The method is based on a combination of the information from altimeter data and a dynamic sea surface height model. The model consists of geoid undulations and a quasi-geostrophic model for expressing the sea surface topography. The goal is the estimation of those values of the parameters of the sea surface height model that provide a least-squares fit of the model to the data. The solution is accomplished by the adjoint method which makes use of the adjoint model for computing the gradient of the cost function of the least-squares adjustment and an optimization algorithm for obtaining improved parameters. The estimation is applied to the North Atlantic. ERS-1 altimeter data of the year 1993 are used. The resulting geoid agrees well with the geoid of the EGM96 gravity model.  相似文献   

9.
As plates move across the surface of the earth they change their curvature in response to the changing curvature of the earth and as a consequence membrane stresses are generated. At any particular point within a plate the stress generated will be proportional to the change in radius of curvature at that point.The rate of change of curvature of the geoid is latitude dependent, consequently the calculation of latitude-generated stress (σγ) is relatively straightforward. For a point moving from an initial latitude of γ0 to a latitude of γ:σλ∝ (sin2λ0?sin2λ)By determining the stress generated at a sequence of points within a plate during set time intervals, membrane stress domains can be defined and used to predict the way in which a plate would deform.In West Africa two phases of compression (Coniacian-Santonian and Palaeocene-Eocene) have been observed within the Lower Benue Rift, followed by a phase of extension (starting about 25 m.y. ago and continuing to the present day) across the Cameroun Volcanic Line. Membrane stress domain theory offers an explanation not only for the timing of all three phases of deformation but is also closely in agreement with the best available information for the extent of deformation.The Red Sea Rift and the rift between Madagascar and the rest of the African continent were both initiated in domains of very high membrane stress generation.  相似文献   

10.
This paper deals with a method for detection of local geoid deformations; as a consequence, the methods main application concerns geoid adjustment to GPS/levelling points. This is based on the fact that these points should present no local geoid deformation to avoid errors in the adjustments. These type of miscalculations would lead to an incorrect adjustment and result in further errors in subsequent studies with GPS in the proximity at the point with local deformation.The method proposed is based on predictions of gravity disturbance from geoid undulations using Poisson integral with modified kernel, and its comparison with the gravity disturbance from GPS and gravimetric observations.The use of gravity disturbance instead of gravity anomalies has been chosen since gravity disturbance is a quantity derived from GPS and not from levelling. The loss of accuracy arising with a local height reference system is therefore theoretically avoided as far as the differences in geodetic reference systems regarding positions of gravity measurements and coefficients of the global models are accounted for.Extended numerical tests using computed geoidal undulations and the corresponding gravity disturbances obtained from the geopotential model GPM98cr computed up to degree 720 illustrate the validity of the proposed method and its usefulness as local geoid deformations detection tool.Finally, the method is tested using real GPS/Gravimetric data and geoid models IBERGEO95 and EGG97 with good results.  相似文献   

11.
Summary A summation method of upward continuation of gravity data has been considered under the assumption that observations are available at regular intervals. The upward continued value has been obtained as the sum of products of individual gravity values and corresponding theoretical coefficients. Besides the usual parameter involving horizontal and vertical distances, the theoretical coefficients have been generalized to be dependent also on i) the order of a low order polynomial assumed to represent the gravity variation around a grid point and ii) the weights assigned to the gravity values at the nearest four grid points used for least-squares determination of the polynomial. Since the observations in practical cases are available over a finite area only, the effect of truncation of the area of the integration has also been discussed separately. The method has been programmed and tested on a three-dimensional model, whose true gravity effects were computed at various levels over a finite area. Upward continued values have been computed under various assumptions about the gravity field in the outside region. Comparisons of these results with the true values indicate that the truncation effect becomes increasingly important for larger values of the ratio of elevation to grid separation and/or when the gravity field is not a local one. It has also been found that the greater is the above ratio, the less important is the effect of weights on the theoretical coefficients and practically vanishes(<10 –4 ) when the ratio is greater than5.0.  相似文献   

12.
Calculating topographic gravitational potential (GP) is a time-consuming process in terms of efficiency. Prism, mass-point, mass-line, and tesseroid formulas are generally used to calculate the topographic GP effect. In this study, we reformulate the higher-order formula of the tesseroid by Taylor series expansion and then evaluate the fourth-order formula by numerical tests. Different simulation computations show that the fourth-order formula is reliable. Using the conventional approach in numerical calculations, the approximation errors in the areas of the north and south poles are extremely large. Thus, in this study we propose an approach combining the precise numerical formula and tesseroid formulas, which can satisfactorily solve the calculation problem when the computation point is located in the polar areas or areas very near the surface. Furthermore, we suggest a “best matching choice” of new combination approach to calculate the GP precisely by conducting various experiments. Given the computation point at different positions, we may use different strategies. In the low latitude, we use a precise numerical formula, the fourth-order tesseroid formula, the second-order tesseroid formula, and the zero-order formula, in the 1° range (from the computation point), 1° to 15° range, 15° to 40° range, and the range outside 40°, respectively. The accuracy can reach 2 × 10?5 m2 s?2. For the high latitude, we use the precise numerical formula, fourth-order tesseroid, second-order tesseroid, and zero-order tesseroid formulas in the ranges of 0° to 1°, 1° to 10°, 10° to 30°, and the zones outside 30°, respectively. However, if an accuracy level of 2 × 10?5 m2 s?2 is required, the zero-order tesseroid formulas should not be used and the second-order tesseroid formula should be used in the region outside 15° for the low latitude and in the region outside 10° for the high latitude.  相似文献   

13.
The community structure of zooplankton was studied in relation to physico-chemical characteristics of the river Chambal polluted by industrial effluents and domestic sewage near Nagda. Thirtytwo species of zooplankton of five main groups, viz. Protozoa, Rotifera, Cladocera, Copepoda and Ostracoda were observed at pre-pollution sampling stations. The abundance, distribution, total population, group percentage and species diversity were studied and correlated with pollution-indicating parameters. Species diversity values indicated a decrease from the sampling station near a pre-effluent point to an effluent discharge channel and an increase at a post-effluent discharge point revealing a slight recovery zone. Keratella tropica and Kellicottia sp. were identified as pollution tolerant taxa.  相似文献   

14.
When comparing solutions for the propagation of SH waves in plane parallel layered elastic and viscoelastic (anelastic) media, one of the first things that becomes apparent is that in the elastic case the location of the saddle points required to obtain a high frequency approximation are located on the real p axis. This is true of the branch points also. In a viscoelastic medium this is not typical. The saddle point corresponding to an arrival lies in the first quadrant of the complex p-plane as do the branch points. Additionally, in the elastic case the saddle point and branch points lie on a straight line drawn through the origin (the positive real axis in the complex p-plane), while in the viscoelastic case this is generally not the case and the saddle point and branch points lie in such a manner as to indicate the degree of their complex values.In this paper simple SH reflected and transmitted particle displacement arrivals due to a point torque source at the surface in a viscoelastic medium composed of a layer over a half space will be considered. The path of steepest descent defining the saddle point in the first quadrant will be parameterized in terms of a real variable and the high frequency solutions and intermediate analytic results obtained will be used to formulate more specific constraints and observations regarding saddle point location relative to branch point locations in the complex p-plane.As saddle point determination for an arrival is, in general, the solution of a non-linear equation in two unknowns (the real and imaginary parts of the complex saddle point p 0), which must be solved numerically, the use of analytical methods for investigating this problem type is somewhat limited.Numerical experimentation using well documented solution methods, such as Newton's method, was undertaken and some observations were made. Although fairly basic, they did provide for the design of algorithms for the computation of synthetic traces that displayed more efficient convergence and accuracy than those previously employed. This was the primary motivation for this work and the results from the SH problem may be used with minimal modifications to address the more complicated subject of coupled P-SV wave propagation in viscoelastic media.Another reason for revisiting a problem that has received some attention in the literature was to approach it in a fairly comprehensive manner so that a number of specific observations may be made regarding the location of the saddle point in the complex p-plane and to incorporate these into computer software. These have been found to result in more efficient algorithms for the SH wave propagation and a significant enhancement of the comparable software in the P-SV problem.  相似文献   

15.
The combination of Stokes formula and an Earth Gravity Model (EGM) for geoid determination has become a standard procedure. However, the way of modifying Stokes formula vary from author to author, and numerous methods of modification exist. Most methods are deterministic, with the primary goal of reducing the truncation bias committed by limiting the area of Stokes integration around the computation point, but there are also some stochastic methods with the explicit goal to reduce the global mean square error of the geoid height estimator stemming from the truncation bias as well as the random errors of the EGM and the gravity data. The latter estimators are thus, at least from a theoretical point of view, optimal in a global mean sense, but in a local sense they may be far from optimality.Here we take advantage of the error variance-covariance matrices of the EGM and the terrestrial gravity data to derive the modification parameters of Stokes kernel in a local least-squares sense. The solution is given for the unbiased type of modification of Stokes formula of Sjöberg (1991).  相似文献   

16.
The EGM08 geopotential model complete to degree and order 2159 was used in a remove-compute-restore (RCR) method for the geoid computation in the State of Rio de Janeiro, Brazil. Terrain and indirect effect corrections were computed using a 6-arcsec resolution DTE, derived from the TOPODATA Project (Shuttle Radar Topography Mission data) raised by the National Institute for Space Research. INPE, Brazil. We applied Voronoi/Delaunay discretisations for discrete Stokes integration. In these schemes, target area is partitioned into polygons/triangles, respectively, and the computation is carried out by point-wise numerical integration and no gridding is mandatory. For both procedures, the cells were produced using either observed gravity data combined with gridded Bouguer derived information. Particularly in Delaunay scheme, as the gravity anomalies are interpolated into the triangular cells, and geoid undulations are computed for their vertices, Stokes function singularity was gone. Externally estimated errors resulting from a comparison with GPS/leveling data were presented for both the schemes and classical ones, as well as for the EGM08 undulations. They yielded RMS differences equal to 0.105 m, 0.110 m, 0.110 m, 0.115 m and 0.228 m, respectively, for Voronoi, Delaunay, Voronoi/Delaunay with gridded-data alone and EGM08, computed between 32 GPS/leveling points.  相似文献   

17.
A digitised tectonic model, initially built up for regionalization of Rayleigh waves, is applied to the geoid in order to define the mean geoid heights of the following regions: 3 oceanic regions, namely young oceans (0–30 Ma) middle-aged oceans (30–80 Ma) and old oceans (> 80 Ma); trenches and subduction zones; mountains; and shields. The relative importance of the deep sources is damped or enhanced by progressively removing or adding the lower or higher degrees of the geoid. A statistical approach allows us to quantify the success of the correlation between tectonics and these filtered geoids.Significant variations are observed in these correlations for oceanic regions (including subduction zones) with a cut-off between degree-2 and higher degrees. For degrees ? 3, a well-known trend is observed: high values correspond to young oceans (ridges) and low values to old oceans, high values are also obtained for subduction zones. On the contrary, and unexpectedly, for the degree-2 alone a trend reversal is observed: geoid lows are observed over ridges and geoid highs over old oceans; trenches give the same geoid amplitude than old oceans. Clearly this denotes a degree-2 convection pattern connected to plate tectonics. In addition it is shown that the minimum and maximum inertia axes of the surface distribution of young oceans, and independently of old oceans and trenches, coincide with the Earth's equatorial inertia axes (74°E and 164°E), i.e., with the equatorial extremes of the degree-2 geoid.Plate tectonics is uncorrelated with the polar anomaly of the degree-2 geoid, namely the flattening which is not accounted for by Earth rotation. A north-south axisymmetric convection with a degree-2 pattern is proposed to explain this extra flattening; this model is supported by the latitude dependence of the depth of oceanic ridges.  相似文献   

18.
Fine resolution series from three equatorial ionosondes of the IEEY network in West Africa have revealed small-scale daytime peak F2 structures, superposed on the slowly varying minimum or –trough distribution in the ±5° magnetic latitude zone. We report this new morphology, concentrating on foF2 enhancements of two types: near-equatorial crests (which travel either northwards or southwards) and magnetic field-aligned domes, whose onsets last only tens of minutes. Both types are observed to start at mid-morning or early afternoon hours. We relate their occurrence with the available variations of Vz = E × B upward drift which feeds the equatorial plasma fountain. We suggest the foF2 enhancements to be triggered by brief slow-downs of the Vz velocity near F2 peak altitude in our West African sector. Their short latitude extent differentiates them from the larger-scale tropical crest system. Further analysis of these features should lead to weather-like models of the low latitude ionosphere variations, where unstable local coupling between processes seems to be the trigger.  相似文献   

19.
Least-squares collocation technique was used to process regional gravity data of the SE South American lithospheric plate in order to map intermediate (10–2000 km) wavelength geoid anomalies. The area between 35–10° S and 60–25° W includes the Paraná CFB Province, the Southern São Francisco Craton and its marginal fold/thrust belts, the Brazilian continental margin and oceanic basins. The main features in the geoid anomaly map are: (a) Paraná CFB Province is characterized by a 1000 km long and 500 km wide, NE-trending, 9 m-amplitude negative anomaly which correlates with the distribution of sediments and basalts within the Paraná basin. (b) A circular (600–800 km in diameter) positive, 8 m-amplitude geoid anomaly is located in the southern S. Francisco craton and extends into the northeastern border of the Paraná CFB Province. This anomaly partially correlates with Alto Paranaíba Igneous Province (APIP), where alkalic volcanism and tholeiitic dikes of ages younger than 80 Ma are found and where a low-velocity zone in the mantle has been mapped using seismic tomography. This positive geoid anomaly extends towards the continental margin at latitude 21° S and joins a linear sequence of short wavelength positive geoid anomalies associated with Vitoria–Trindade seamounts. (c) A NE-trending, 1000 km long and 800 km wide, 4 m-amplitude, positive geoid anomaly, which is located along the southeastern coast of Brazil, from latitude 24 to 35° S. The northern part of this anomaly correlates with the Ponta Grossa Arch and Florianopolis dyke swarm provinces. The age of this intrusive volcanism is 130–120 Ma. (d) A circular positive anomaly with 9 m of amplitude, located over the Rio Grande and Uruguay shields and offshore Pelotas basin. Few alkaline intrusives with ages between 65 and 80 Ma are found in the region and apatite fission track ages in basement rocks indicates cooling at around 30 Ma. A semi-quantitative analysis of the observed geoid anomalies using isostatic considerations suggests that the mechanism which generated Paraná CFB Province did not change, in a significant manner, the lithospheric thermal structure, since the same geoid pattern observed within this province continues northward over the Neoproterozoic fold/thrust belts systems separating the São Francisco and Amazon cratons. Therefore, this observation favours Anderson’s idea of rapid basaltic outpouring through a pull-apart mechanism along a major suture zone. A thermal component may still be present in the Southern São Francisco Craton and in the Rio Grande Shield and contiguous continental margins, sites of Tertiary thermal and magmatic reactivations.  相似文献   

20.
An attempt is made to use the barotropic vorticity equation in spectral form in order to study barotropic instability when the basic current has east-west quasi-stationary asymmetries on the scale of long waves. This is done by expressing the spectral equations in three different ways. In the first experiment a 9-component system is integrated and the long waves are allowed to propagate freely. In the second experiment the long waves are constrained to propagate slowly and in the third experiment, they are removed altogether.The motivation behind the present investigation is due to observations made in the motion fields of the tropics. These are characterized by quasi-stationary long waves and very energetically active and propagating short waves.The presence of quasi-stationary long waves seems to enhance the energy exchanges between the short waves and the mean zonal current and also allow for larger energy values for the short waves. Long term integration (90 days) shows a 6-day mode in thev time spectra at latitude 10°N and a 15-day mode in theu time spectra at individual grid points in the equatorial latitudes. Any possible connection between this peak and the observed peak of 15 days in the completely different physics of Kelvin waves is left as a conjecture.  相似文献   

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