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1.
The magnetic and gravity field produced by a given homogeneous source are related through Poisson's equation. Starting from this consideration, it is shown that some 2D interpretation tools, widely applied in the analysis of aeromagnetic data, can also be used for the interpretation of gravity gradiometric data (vertical gradient). This paper deals specifically with the Werner deconvolution, analytic signal and Euler's equation methods. After a short outline of the mathematical development, synthesized examples have been used to discuss the efficiency and limits of these interpretation methods. These tools could be applied directly to airborne gravity gradiometric data as well as ground gravity surveys after transformation of the Bouguer anomalies into vertical gradient anomalies. An example is given of the application of the Werner deconvolution and Euler's equation methods to a microgravity survey.  相似文献   

2.
In this paper, I introduce a new approach based on truncated singular value decomposition (TSVD) analysis for improving implementation of grid-based Euler deconvolution with constraints of quasi 2D magnetic sources. I will show that by using TSVD analysis of the gradient matrix of magnetic field anomaly (reduced to pole) for data points located within a square window centered at the maximum of the analytic signal amplitude, we are able to estimate the strike direction and dip angle of 2D structures from the acquired eigenvectors. It is also shown that implementation of the standard grid-based Euler deconvolution can be considerably improved by solving the Euler's homogeneity equation for source location and structural index, simultaneously, using the TSVD method. The dimensionality of the magnetic anomalies can be indicated from the ratio between the smallest and intermediate eigenvalues acquired from the TSVD analysis of the gradient matrix. For 2D magnetic sources, the uncertainty of the estimated source location and structural index is significantly reduced by truncating the smallest eigenvalue.Application of the method is demonstrated on an aeromagnetic data set from the Åsele area in Sweden. The geology of this area is dominated by several dike swarms. For these dolerite dikes, the introduced method has provided useful information of strike directions and dip angles in addition to the estimated source location and structural index.  相似文献   

3.
A simple and fast determination of the limiting depth to the sources may represent a significant help to the data interpretation. To this end we explore the possibility of determining those source parameters shared by all the classes of models fitting the data. One approach is to determine the maximum depth-to-source compatible with the measured data, by using for example the well-known Bott–Smith rules. These rules involve only the knowledge of the field and its horizontal gradient maxima, and are independent from the density contrast.Thanks to the direct relationship between structural index and depth to sources we work out a simple and fast strategy to obtain the maximum depth by using the semi-automated methods, such as Euler deconvolution or depth-from-extreme-points method (DEXP).The proposed method consists in estimating the maximum depth as the one obtained for the highest allowable value of the structural index (Nmax). Nmax may be easily determined, since it depends only on the dimensionality of the problem (2D/3D) and on the nature of the analyzed field (e.g., gravity field or magnetic field). We tested our approach on synthetic models against the results obtained by the classical Bott–Smith formulas and the results are in fact very similar, confirming the validity of this method. However, while Bott–Smith formulas are restricted to the gravity field only, our method is applicable also to the magnetic field and to any derivative of the gravity and magnetic field. Our method yields a useful criterion to assess the source model based on the (∂f/∂x)max/fmax ratio.The usefulness of the method in real cases is demonstrated for a salt wall in the Mississippi basin, where the estimation of the maximum depth agrees with the seismic information.  相似文献   

4.
In this paper, we present a case study on the use of the normalized source strength (NSS) for interpretation of magnetic and gravity gradient tensors data. This application arises in exploration of nickel, copper and platinum group element (Ni‐Cu‐PGE) deposits in the McFaulds Lake area, Northern Ontario, Canada. In this study, we have used the normalized source strength function derived from recent high resolution aeromagnetic and gravity gradiometry data for locating geological bodies. In our algorithm, we use maxima of the normalized source strength for estimating the horizontal location of the causative body. Then we estimate depth to the source and structural index at that point using the ratio between the normalized source strength and its vertical derivative calculated at two levels; the measurement level and a height h above the measurement level. To discriminate more reliable solutions from spurious ones, we reject solutions with unreasonable estimated structural indices. This method uses an upward continuation filter which reduces the effect of high frequency noise. In the magnetic case, the advantage is that, in general, the normalized magnetic source strength is relatively insensitive to magnetization direction, thus it provides more reliable information than standard techniques when geologic bodies carry remanent magnetization. For dipping gravity sources, the calculated normalized source strength yields a reliable estimate of the source location by peaking right above the top surface. Application of the method on aeromagnetic and gravity gradient tensor data sets from McFaulds Lake area indicates that most of the gravity and magnetic sources are located just beneath a 20 m thick (on average) overburden and delineated magnetic and gravity sources which can be probably approximated by geological contacts and thin dikes, come up to the overburden.  相似文献   

5.
The calculable magnitudes of the anomalous magnetic field from simple 2D sources and their gradients and Laplacians appear as ratios that can be synthesized in functional forms, corresponding to the different source shapes. Field components and first‐order derivatives are involved in the inversion procedures presented. The structural index and source depth are estimated independently of each other. The applied functions allow magnetic profiles and magnetic maps to be shape‐ and depth‐converted with immediate imaging of the inversion results. The contours of these functions outline elongated loops around the 2.5D anomaly axis on magnetic maps. The width of the loops reflects the depth and structural index N of the source in the scale units of the inverted map. Model and field tests illustrate the effectiveness of this approach for fast automatic inversion of large sets of magnetic data for depth, shape, length and location of simple sources.  相似文献   

6.
Based on ion distribution function found from the dynamic equation, the density distribution of He+ ions originating from the polar ionosphere and up-flowing along the magnetic field line is studied during quiet and weakly disturbed geomagnetic conditions. The results show the following. (1) The ionospheric up-flowing He+ ions mainly reside in the inner magnetosphere and their density has a negative radial gradient. (2) The ionospheric up-flowing He+ ion distributions along the magnetic field line are mainly controlled by gravity and the geomagnetic field configuration. Larger the gravity, larger is the ion density. Smaller the intensity of magnetic field, smaller is the ion density. (3) If the geomagnetic activity index Kp is high, more up-flowing He+ ions will enter the magnetosphere and the region where the up-flowing ions are dominant will grow. This is consistent with observations of ionospheric up-flowing ions. Some features of the geopause can be understood based on our theoretical results.  相似文献   

7.
A key non-linear mechanism in a strong-field geodynamo is that a finite amplitude magnetic field drives a flow through the Lorentz force in the momentum equation and this flow feeds back on the field-generation process in the magnetic induction equation, equilibrating the field. We make use of a simpler non-linear?α?2-dynamo to investigate this mechanism in a rapidly rotating fluid spherical shell. Neglecting inertia, we use a pseudo-spectral time-stepping procedure to solve the induction equation and the momentum equation with no-slip velocity boundary conditions for a finitely conducting inner core and an insulating mantle. We present calculations for Ekman numbers (E) in the range 2.5× 10?3 to 5.0× 10?5, for?α?=α 0cos?θ?sin?π?(r?ri ) (which vanishes on both inner and outer boundaries). Solutions are steady except at lower E and higher values of?α?0. Then they are periodic with a reversing field and a characteristic rapid increase then equally rapid decrease in magnetic energy. We have investigated the mechanism for this and shown the influence of Taylor's constraint. We comment on the application of our findings to numerical hydrodynamic dynamos.  相似文献   

8.
Information on the mass and the spatial location of an arbitrary source body can be obtained by performing suitable integrations of 3D gravity and magnetic data along an infinite straight line. No assumptions on the density/magnetization distribution or the shape and location of the source are required. For an oblique borehole, a relationship between the lower limit of the source mass and the distance to the body is obtained. The mass contrast and the magnetic moment of the source can also be estimated. For a vertical borehole, both gravity and vertical magnetic component anomalies have equal areas to the left and right of the depth axis. The particular case of a horizontal gallery not intersecting the body is also studied. If the source is intersected, a lower limit is estimated for the maximum thickness of the body along the gallery. Information on the vertical coordinate of the centre of mass of the source can also be obtained. Numerical tests with synthetic gravity data support the theoretical results.  相似文献   

9.
A method is presented for determining bounds of the properties of axial symmetric bodies from a finite number of gravity and magnetic observations based on Parker's theory of ideal bodies. Bounds on the density contrast and the intensity of magnetization are calculated as a function of depth to the top of the anomalous source, restricting the range of smallest possible solutions to fit the data. The model studied is approximated by an array of vertical annuli cylinders, each of uniform density and magnetization. Linear programming algorithms based on the ideal body theory were used to calculate the distribution of these parameters within the body. Simultaneous inversion of gravity and magnetic data is performed assuming a constant ratio between the density contrast and the intensity of magnetization and that a common body is responsible for both observed fields. The parameter k(|J|/δp) provides information about the rock type of the structure. Interpretation of gravity and aeromagnetic data from Darnley Bay, NWT, Canada, indicated the presence of a shallow ultrabasic intrusion.  相似文献   

10.
The voluminous gravity and magnetic data sets demand automatic interpretation techniques like Naudy, Euler and Werner deconvolution. Of these techniques, the Euler deconvolution has become a popular choice because the method assumes no particular geological model. However, the conventional approach to solving Euler equation requires tentative values of the structural index preventing it from being fully automatic and assumes a constant background that can be easily violated if the singular points are close to each other. We propose a possible solution to these problems by simultaneously estimating the source location, depth and structural index assuming nonlinear background. The Euler equation is solved in a nonlinear fashion using the optimization technique like conjugate gradient. This technique is applied to a published synthetic data set where the magnetic anomalies were modeled for a complex assemblage of simple magnetic bodies. The results for close by singular points are superior to those obtained by assuming linear background. We also applied the technique to a magnetic data set collected along the western continental margin of India. The results are in agreement with the regional magnetic interpretation and the bathymetric expressions.  相似文献   

11.
《水文科学杂志》2013,58(4):700-712
Abstract

The groundwater flow equation governing the elevation (h) of the steady-state phreatic surface in a sloping aquifer fed by constant recharge over a bi-circular sector is rhh′ ? r 2 Bh′ + Pr 2 ? PR 2 = 0, where r is the radial coordinate, P is a constant involving recharge and aquifer properties, and B is the slope of the aquifer—bedrock boundary. The derived flow equation describes radially convergent flow through a sloping aquifer that discharges to a water body of fixed head. One important simplification is that in which the width of the bi-circular sector is constant, and the draining land becomes a rectangular aquifer. The bi-circular sector and rectangular-strip groundwater flow problems are solved in terms of implicit equations. The solutions for the steady-state phreatic surfaces depend on the ratio of recharge to hydraulic conductivity, the slope of the aquifer-bedrock, and the downstream constant-head boundary. Computational examples illustrate the application of the solutions.  相似文献   

12.
Abstract

Bayly (1993) introduced and investigated the equation (? t + v·▽-η ▽2)S = RS as a scalar analogue of the magnetic induction equation. Here, S(r, t) is a scalar function and the flow field v(r, t) and “stretching” function R(r, t) are given independently. This equation is much easier to handle than the corresponding vector equation and, although not of much relevance to the (vector) kinematic dynamo problem, it helps to study some features of the fast dynamo problem. In this note the scalar equation is considered for linear flow and a harmonic potential as stretching function. The steady equation separates into one-dimensional equations, which can be completely solved and therefore allow one to monitor the behaviour of the spectrum in the limit of vanishing diffusivity. For more general homogeneous flows a scaling argument is given which ensures fast dynamo action for certain powers of the harmonic potential. Our results stress the singular behaviour of eigenfunctions in the limit of vanishing diffusivity and the importance of stagnation points in the flow for fast dynamo action.  相似文献   

13.
Abstract

The singular differential equations for finite temperature relativistic magnetohydrodynamic (MHD) winds integrate to two algebraic equations when the source magnetic field is a monopole. This simplification enables an extensive characterization of the asymptotic wind solutions in terms of source parameters. We will consider only the critical solutions-those that pass smoothly through both an intermediate (Alfvenic) and a fast MHD critical point and expand to zero pressure at infinite radial distance from the source. Because the constants of motion must be specified to extremely high accuracy, the critical solutions cannot be found analytically. Synopsis of many numerical solutions reveals a uniform parametric characterization of the asymptotic wind in terms of one combination of source parameters, Z, the mean source particle energy divided by mc2[sgrave]½, where [sgrave] is a generalization of Michel's (1969) cold relativistic wind strength parameter. Cool winds, with Z<1, behave asymptotically much as Michel's cold wind minimum torque solution; Z1 hot winds have quite different, but simply characterized, asymptotic solutions. Thus, the strength of magnetized relativistic outflows can depend critically upon the temperature of the source.  相似文献   

14.
A time domain boundary element in a cylindrical coordinate system is developed for the analysis of wave propagation in a half space. The integral formulation is based on Graffi's dynamic reciprocal theorem and Stokes' fundamental solutions. The field quantities (displacements and tractions) are expressed as products of Fourier series in the tangential direction and linear polynomials in the other spatial directions. Gaussian integration is used to integrate the non-singular parts of the integral equations, whereas the integration of the singular components, which are either of order 1/r or 1/r2, is handled by special numerical schemes. In the time marching aspect, the field quantities are assumed to vary linearly in the temporal direction as well. Examples for wave propagation due to various forms of surface excitations are reported to demonstrate the accuracy of the method.  相似文献   

15.
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16.
In this study, a Markov Random Field (MRF) approach is used to locate source boundary positions which are difficult to identify from Bouguer gravity and magnetic maps. As a generalized form of Markov Chains, the MRF approach is an unsupervised statistical model based algorithm and is applied to the analysis of images, particularly in the detection of visual patterns or textures. Here, we present a dynamic programming based on the MRF approach for boundary detection of noisy and super-positioned potential anomalies, which are produced by various geological structures. In the MRF method, gravity and magnetic maps are considered as two-dimensional (2-D) images with a matrix composed of N1 × N2 pixels. Each pixel value of the matrix is optimized in real time with no a priori processing by using two parameter sets; average steering vector (θ) and quantization level (M). They carry information about the correlation of neighboring pixels and the locality of their connections. We have chosen MRF as a processing approach for geophysical data since it is an unsupervised, efficient model for image enhancement, border detection and separation of 2-D potential anomalies. The main benefit of MRF is that an average steering vector and a quantization level are enough in evaluation of the potential anomaly maps. We have compared the MRF method to noise implemented synthetic potential field anomalies. After satisfactory results were found, the method has been applied to gravity and magnetic anomaly maps of Gelibolu Peninsula in Western Turkey. Here, we have observed Anafartalar thrust fault and another parallel fault northwest of Anafartalar thrust fault. We have modeled a geological structure including a lateral fault, which results in a higher susceptibility and anomaly amplitude increment. We have shown that the MRF method is effective to detect the broad-scale geological structures in the Gelibolu Peninsula, and thus to delineate the complex tectonic structure of Gelibolu Peninsula.  相似文献   

17.
Nonparametric inverse methods provide a general framework for solving potential‐field problems. The use of weighted norms leads to a general regularization problem of Tikhonov form. We present an alternative procedure to estimate the source susceptibility distribution from potential field measurements exploiting inversion methods by means of a flexible depth‐weighting function in the Tikhonov formulation. Our approach improves the formulation proposed by Li and Oldenburg (1996, 1998) , differing significantly in the definition of the depth‐weighting function. In our formalism the depth weighting function is associated not to the field decay of a single block (which can be representative of just a part of the source) but to the field decay of the whole source, thus implying that the data inversion is independent on the cell shape. So, in our procedure, the depth‐weighting function is not given with a fixed exponent but with the structural index N of the source as the exponent. Differently than previous methods, our choice gives a substantial objectivity to the form of the depth‐weighting function and to the consequent solutions. The allowed values for the exponent of the depth‐weighting function depend on the range of N for sources: 0 ≤N≤ 3 (magnetic case). The analysis regarding the cases of simple sources such as dipoles, dipole lines, dykes or contacts, validate our hypothesis. The study of a complex synthetic case also proves that the depth‐weighting decay cannot be necessarily assumed as equal to 3. Moreover it should not be kept constant for multi‐source models but should instead depend on the structural indices of the different sources. In this way we are able to successfully invert the magnetic data of the Vulture area, Southern Italy. An original aspect of the proposed inversion scheme is that it brings an explicit link between two widely used types of interpretation methods, namely those assuming homogeneous fields, such as Euler deconvolution or depth from extreme points transformation and the inversion under the Tikhonov‐form including a depth‐weighting function. The availability of further constraints, from drillings or known geology, will definitely improve the quality of the solution.  相似文献   

18.
Checking the predictive worth of an environmental model inevitably includes a goodness of fit metric to quantify the degree of matching to recorded data, thereby giving a measure of model performance. Considerable analysis and discussion have taken place over fit indices in hydrology, but a neglected aspect is the degree of communicability to other disciplines. It is suggested that a fit index is best communicated to colleagues via reference to models giving unbiased predictions, because unbiased environmental models are a desirable goal across disciplines. That is, broad recognition of a fit index is aided if it simplifies in the unbiased case to a familiar and logical expression. This does not hold for the Nash–Sutcliffe Efficiency E which reduces to the somewhat awkward unbiased expression E = 2 – 1/r2, where r2 is the coefficient of determination. A new goodness of fit index V is proposed for model validation as V = r2/(2‐E), which simplifies to the easily communicated V = r4 in the unbiased case. The index is defined over the range 0 ≤ V ≤ 1, and it happens that V < E for larger values of E. Some synthetic and recorded data sets are used to illustrate characteristics of V in comparison to E. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

19.
The local reach gradient of small gravel bed rivers (drainage area 0-8-110 km2) in the Eifel, West Germany, is adjusted to transport the river bed sediments. Transport of gravel becomes possible under high flow conditions (Shields entrainment factor ≈-03). Mean bed material size for riffle sections increases with distance downstream. For small drainage areas channel slope is a negative exponential function of drainage area, while for the larger region the additional influence of bedload size has to be considered. Good agreement with Hack's data (1957) for Virginia and Maryland, U.S.A., is achieved (S = 0.0066 (D50/A)- 40., r = 0.67).  相似文献   

20.
Abstract

In this paper we analyse the stationary mean energy density tensor Tij = BiBj for the x 2-sphere. This model is one of the simplest possible turbulent dynamos, originally due to Krause and Steenbeck (1967): a conducting sphere of radius R with homogeneous, isotropic and stationary turbulent convection, no differential rotation and negligible resistivity. The stationary solution of the (linear) equation for Tij is found analytically. Only Trr , T θθ and T φφ are unequal to zero, and we present their dependence on the radial distance r.

The stationary solution depends on two coefficients describing the turbulent state: the diffusion coefficient β≈?u2?τc/3 and the vorticity coefficient γ ≈ ?|?×u|2?τc/3 where u(r, t) is the turbulent velocity and c its correlation time. But the solution is independent of the dynamo coefficient α≈??u·?×u?τc/3 although α does occur in the equation for Tij . This result confirms earlier conclusions that helicity is not required for magnetic field generation. In the stationary state, magnetic energy is generated by the vorticity and transported to the boundary, where it escapes at the same rate. The solution presented contains one free parameter that is connected with the distribution of B over spatial scales at the boundary, about which Tij gives no information. We regard this investigation as a first step towards the analysis of more complicated, solar-type dynamos.  相似文献   

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