Walsh spectra of gravity anomalies over some simple sources

Walsh transform of gravity anomalies over a point mass, a horizontal and a vertical line mass have been computed to obtain a cyclic shift invariant differential energy density (DED) function. Quantitative relations between DED spectral characteristics with depth to centroid/top of the source have been established. The effects of profile length, sampling interval, random noise and zero padding have been investigated. Applicability of the proposed method has been evaluated through two field examples.     

Inversion of gravity and magnetic anomalies over some bodies of simple geometric shape

The general expression for gravity and magnetic anomalies over thin sheets and sloping contacts may be expressed as a polynomial of the formFx ²+C₁Fx+C₂F+C₃x³+C₄x²+C₅x+C₆. The initial parameters of the source are obtained from the coefficientsC ₁, C₂,..., C₆ which may be solved by inverting a 6×6 matrix. The initial parameters are modified by successive iteration process using the difference formula until the root mean square error between the observed and calculated anomalies is a minimum. The regional background which may be in the form of a polynomial is estimated by the computer itself. This method is applied on a number of field anomalies and is found to yield reliable estimates of depth and other parameters of the source.     

On the problem of determining the vertical gradients of gravity anomalies

Summary Green's theorem on harmonic functions makes it possible to determine the integral relationship between the harmonic function and its derivative with respect to the normal on a closed Lyapunov surface. The conditions of solvability are given by Fredholm's theory of integral equations. The solution for a sphere was presented by Molodenskii[3] and the general solution with the help of Molodenskii's parameter k by Ostach[4]. The present paper indicates a possibility of solving this problem with the help of a system of linear algebraic equations, a simplified modification of the Ostach-Molodenskii solution and, finally, a method, based on Eremeev's solution of the fundamental integral equation[5].     

Long-wavelength gravity anomalies and intraplate seismicity

Anomalously high mid-plate and Mid-Oceanic Ridge seismicity apparently characterizes the flanks of the regional free-air gravity and topographic high roughly centered on the postulated Iceland hot spot; anomalously high mid-plate seismicity also occurs around the deep free-air gravity low centered just south of India. Although the correlation between gravity and seismicity is still somewhat inconclusive, it seems to suggest active asthenosphere flow associated with the regional gravity anomalies. Added to other stresses in the plate, the stress transmitted to the plate by this flow would encourage its fracture.     

Satellite orbit computations using gravity anomalies

Summary A typical geodetic satellite orbit has been computed by numerical integration for a period of thirty hours. The gravitational potential of a standard orbit was represented by the SAO 1969 Standard Earth potential coefficients taken to degree 18. Other orbits were generated using the generalized Stokes' equations and the coating method applied to gravity anomalies and surface densities, in 5°, 10°, 15° and 30° equal-area blocks, derived from the given potential coefficients. The differences between these orbits yield the position differences to be expected when representing the potential field by using gravity data instead of potential coefficients. Using 10°, 15°, and 30° blocks and the generalized Stokes' equations, the position error at the end of thirty hours was 89 meters, 224 meters, and 2060 meters respectively. This error is primarily due to the integration error in computing the gravitational field by summation over a finite number of areas.     

On calculation of the vertical deflection and the geoid undulation from gravity anomalies

Specific features of the calculation of the vertical deflection and the geoidal undulation in the Arctic from gravity anomalies are discussed. Basic requirements to the initial model of the anomalous field are described. The technique of calculating the vertical deflection with arbitrarily fine detail is proposed. The ways for improving the models of gravity anomalies for solving the stated problems are suggested.     

Inversion of gravity anomalies over spreading oceanic ridges

Models of spreading ocean ridges are derived by Bayesian gravity inversion with geophysical and geodynamic a priori information. The aim is to investigate the influence of spreading rate, plate dynamics and tectonic framework on crust and upper mantle structure by comparing the Mid Atlantic Ridge (MAR), the Indian Ocean Ridge (IND) and the East Pacific Rise (PAC). They differ in mean spreading rate, dynamic settings, as attached slabs, and plume interaction. Topography or bathymetry, gravity, isostasy, seismology and geology, etc. are averaged along the ridges and guide the construction of initial 2D models, including features as mean plumes, i.e. averaged along the ridge. This is a gross simplification, and the results are considered preliminary.Three model types are tested: (a) the temperature anomaly; (b) asthenospheric rise into thickening lithosphere; (c) a crustal root as had been anticipated before seafloor spreading was discovered. Additional model components are a mean plume, a non-compensated ridge uplift, an under-compensated asthenospheric rise, e.g. of partially molten material, and seismic velocity models for P and S waves. Model type (c), tends to permute to model type (b) from thick crust to thin axial lithosphere. Model type (a) renders ‘realistic’ values of the thermal expansivity, but is insufficient to fit the gravity data; partial melt may disturb the simple temperature effect. A combination of (a) and (b) is most adequate. Exclusive seismic velocity models of S or P waves do not lead to acceptable densities nor to adequate gravity fitting. The different ridges exhibit significant differences in the best models: ATL and IND show an axial mass excess fostering enhanced ridge push, and ATL, in addition, suggests a mean plume input, while PAC shows an axial mass deficit reducing ridge push, most probably due to dominance of slab pull in the force balance.Goodness of the gravity fit alone is no justifiable criterion for goodness of model, indeed minor modifications to each model within the uncertainties of the assumptions can make the fit arbitrarily good. Goodness of model is quantified exclusively by a priori information.     

Numerical behaviour of the downward continuation of gravity anomalies

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.     

Interpretation of gravity anomalies of dykes by pseudo-magnetic transformation

Summary A simple transformation called pseudo-magnetic transformation is introduced in which the horizontal derivatives of the observed gravity anomalies of any body will be calculated. These horizontal derivatives, called the pseudo-magnetic anomalies, are proportional to the vertical magnetic anomalies of the same body assumed to be polarised horizontally. It is shown that the interpretation of gravity anomalies of dykes is not unique except by computing the pseudo-magnetic anomalies, which will be interpreted by the logarithmic curve fitting technique indicated earlier [5]²).     

利用余弦变换计算重力异常的向上延拓

利用余弦变换计算重力异常的向上延拓是一种新方法.根据余弦变换的基本性质,推导了二度、三度体异常向上延拓余弦变换谱理论公式,采用离散余弦变换实现了该法的数值计算;研究了无限长水平圆柱体的补偿因子中主频段的特性,给出了二度体的线性补偿方式;补偿后的理论模型异常向上延拓具有较高的计算精度,除边部几个数据因数据的离散和有限截断使误差较大外（最大误差为6.23%）,其余数据的误差均在1%以内,理论值和计算值曲线基本重合.这说明,与Fourier变换相比,离散余弦变换在数值计算中,受非周期性深度因子的影响小,补偿方式易于选择,其计算方法优于Fourier变换.     

重磁弱异常评价与提取技术

本文阐述了重磁弱异常概念,提出了当代采集方式下重磁弱异常可信度的判断标准,并提出针对重磁弱异常的处理新技术,该技术由消除干扰处理技术和弱异常提取技术组成,实际应用效果显著。随着地质勘探向精细方向发展,重磁弱异常将得到更加广泛的关注。     

Atmospheric effects in the derivation of geoid-generated gravity anomalies

Parameters of the gravity field harmonics outside the geoid are sought in solving the Stokes boundary-value problem while harmonics outside the Earth in solving the Molodensky boundary-value problem. The gravitational field generated by the atmosphere is subtracted from the Earth’s gravity field in solving either the Stokes or Molodensky problem. The computation of the atmospheric effect on the ground gravity anomaly is of a particular interest in this study. In this paper in particular the effect of atmospheric masses is discussed for the Stokes problem. In this case the effect comprises two components, specifically the direct and secondary indirect atmospheric effects. The numerical investigation is conducted at the territory of Canada. Numerical results reveal that the complete effect of atmosphere on the ground gravity anomaly varies between 1.75 and 1.81 mGal. The error propagation indicates that precise determination of the atmospheric effect on the gravity anomaly depends mainly on the accuracy of the atmospheric mass density distribution model used for the computation.     

Future of the interpretation theory of gravity and magnetic anomalies

The general methodology of the interpolation theory of potential fields (gravity and magnetic anomalies), and, primarily, the three fundamental ideas underlying this methodology—(I) approximation, (II) linearization, and (III) optimization-are the matter of the utmost importance. The rationale of these ideas and the ways of their practical implementation are discussed in this paper.     

普光气田重力异常的视密度反演

普光气田是我国近年发现的最大气田．根据气田储层和盖层的岩石密度,估算普光气田上约有零点几毫伽量级的重力异常．但由于区域场和其他岩石的影响,气田的负异常受到严重的干扰．我们使用基于位场切割分离和位场大深度向下延拓的视密度反演新方法,在普光气田上得到明显的负密度异常．在川东北其他一些气田上,也得到负密度异常．根据视密度反演结果,对川东北的含气远景区做了预测．     

A new concept in Euler deconvolution of isolated gravity anomalies

Euler's homogeneity equation has been used to develop a new technique to interpret the gravity anomalies over some simple geometrical sources, namely a finite horizontal line/vertical line, a finite vertical ribbon, a semicircular dome/basin and an isosceles triangle approximating an anticline/syncline. A linear over-determined system of equations has been solved to compute the depth, the horizontal location and the structural index, all treated as free parameters. The concept of a variable structural index provides better depth estimates and helps to identify the source geometry. Nomograms have been prepared to compute an additional model parameter, namely the horizontal/vertical extent of a line, the vertical extent of a ribbon and the radius of a dome/basin. The efficacy of the proposed method has been evaluated using two real field examples.