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  • 1
    Electronic Resource
    Electronic Resource
    A generalized method for various data processing techniques in gravity interpretation (1976)
    Springer
    Pure and applied geophysics 114 (1976), S. 975-982 
    Details
    ISSN: 1420-9136
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Summary The various data processing techniques (downward continuation, first and second derivatives and their downward continuation) used in gravity interpretation, are analogous to different types of linear filtering operations whose theoretical filter (amplitude) responses can be derived from $$(u^2 + v^2 )^{N/2} \exp (d\sqrt {u^2 + v^2 } )$$ by suitably choosingN andd, whereu andv are angular frequencies in two perpendicular directions,d the height or depth of continuation in unit of grid interval; andN denotes the order of the vertical derivative. By incorporating a mathematical smoothing function, $$e^{ - \lambda (u^2 + v^2 )} $$ (λ being the smoothing parameter) in the theoretical filter response function, it has been possible, by selecting a suitable value of smoothing parameter, to establish an approximate equivalence of the effect of the mathematical smoothing with the inherent smoothing introduced, because of the numerical approximation (approximation error) for practically all data-processing techniques. This approximate equivalence leads to a generalized method of computing sets of weight coefficients for various data-processing techniques from filter response matching method. Several sets of weight coefficients thus have been computed with different smoothing parameter. The amplitude response curves of the various existing sets of weight coefficients have also been calculated for assessing the quality of the approximation in achieving the desired filtering operation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00876196
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  • 2
    Electronic Resource
    Electronic Resource
    Calculation of the second vertical derivative of gravity field (1969)
    Springer
    Pure and applied geophysics 76 (1969), S. 5-16 
    Details
    ISSN: 1420-9136
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Summary Two formulas, using Taylor's series expansion method, have been developed by means of which the second vertical derivative of gravity field may be computed at any point in the horizontal plane of observation. A comparative study of the resolving powers of different approaches by performing numerical and filter response tests suggests that the formulas provide a definite improvement over many existing methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00877833
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  • 3
    Electronic Resource
    Electronic Resource
    Coefficient sets for one dimensional gravity operations using filter theory (1971)
    Springer
    Pure and applied geophysics 88 (1971), S. 5-11 
    Details
    ISSN: 1420-9136
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Summary Analytical expressions for the weight coefficients of the upward and downward continuation, and first and second derivative and their downward continuation operations have been obtained from their corresponding theoretical amplitude response functions in cut off frequency region using filter theory. These expressions, along with the smoothing and shortening operators of Hanning and Hamming types have been utilized to calculate the coefficient sets for each operation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00877887
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  • 4
    Electronic Resource
    Electronic Resource
    Direct gravity interpretation of sedimentary basin using digital computer — Part I (1971)
    Springer
    Pure and applied geophysics 86 (1971), S. 5-12 
    Details
    ISSN: 1420-9136
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Summary A method is developed for rapid gravity interpretation of a sedimentary basin using a digital computer. Assuming a linear variable density contrast (both vertically and horizontally), expressions have been derived for the gravitational attraction of a rectangular strip. An interpretation of the structure of Godavari Valley (India) has been made using these expressions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00875068
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  • 5
    Electronic Resource
    Electronic Resource
    Direct gravity interpretation of sedimentary basin using digital computer — Part II (1971)
    Springer
    Pure and applied geophysics 86 (1971), S. 13-17 
    Details
    ISSN: 1420-9136
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Summary An algorithm, suitable for digital computer application, has been developed for rapid gravity interpretation of sedimentary basin. A discrete linear variable density contrast pattern over the constant density contrast has been preferred to obtain the structural configuration of the basin. The present algorithm, with slight modification, can be used for calculation of isostatic root increment below the mountain. An interpretation of the structure of Godavari Valley, India has been made using this algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00875069
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  • 6
    Electronic Resource
    Electronic Resource
    CALCULATION OF THE VERTICAL GRADIENT OF THE GRAVITY FIELD USING THE FOURIER TRANSFORM (1972)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 20 (1972), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Fourier transform techniques have been used to calculate the theoretical filter (amplitude) response function of Nth order vertical derivative continuation operation. The amplitude response functions of the vertical gradient and its continuation follow from the same. These response functions are subsequently used to calculate the weighting coefficients suitable for two dimensional equispaced data. A shortening operator has been incorporated to limit the extent of the operator. For comparative study, some of the developed coefficient sets and the one presented in this paper are analysed in the frequency domain and their merits and demerits are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2478.1972.tb00647.x
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  • 7
    Electronic Resource
    Electronic Resource
    SEPARATION OF REGIONAL AND RESIDUAL ANOMALIES BY LEAST-SQUARES ORTHOGONAL POLYNOMIAL AND RELAXATION TECHNIQUES: A PERFORMANCE EVALUATION (1992)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 40 (1992), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: The performances of least-squares orthogonal polynomial and relaxation techniques in the separation of regional and residual anomalies have been evaluated with a view to minimizing personal biasing. The advantage of orthogonal over nonorthogonal polynomials is their ability to estimate an optimum order of polynomial to represent the predominant regional trend in the data using an approximate 2D difference table, the Z-matrix. The correlation coefficients between residuals of two consecutive orders also give the same result. In the relaxation technique, a linear trend is assumed within each cell of the mesh of a square grid. A set of such linear segments can approximate any complicated regional trend. The performances of these two techniques have been evaluated using simulated gravity anomalies produced by 2D and 3D complex regional structures superimposed on residual fields due to cylinders and prismatic bodies, as well as three field examples taken from the published literature. The analyses have revealed that the relaxation technique produces excellent results when an optimum polynomial order rather than an arbitrary fixed one is used for computing the boundary conditions along the periphery of the map. Analyses have revealed that such boundary conditions provide minimum distortion near the two ends of the profile.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2478.1992.tb00368.x
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  • 8
    Electronic Resource
    Electronic Resource
    MAPPING OF CRUSTAL DISCONTINUITIES BY WAVELENGTH FILTERING OF THE GRAVITY FIELD (1992)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 40 (1992), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: A statistical technique, based on the concept of a 1D energy density spectrum of the observed gravity field, has been used to compute ensemble average depths to various horizons containing causative sources of random geometric shape, size, density, etc. The plot of the logarithm of the energy of the observed Bouguer anomaly versus the angular frequency can be approximated, over a certain frequency band, by a linear segment whose slope is related to an average ensemble depth around which a random distribution of numerous anomalous sources exists. Suitable matched filters, based on the computed values of intercepts and slopes of several linear segments approximating the spectrum, have been used to deconvolve the gravity effects associated with the causative sources, occurring around their respective mean depths. The individual deconvolved gravity effects thus separated out have been modelled using the sin x/x method by assuming a fluctuating interface between two formations.The applicability of the present method has been assessed using two observed Bouguer anomaly profiles: one from Ujjain to Mahan, and the other from Jhansi to Mandla where Deep Seismic Sounding (DSS) results are available. The proposed geological crustal models along these two profiles exhibit reasonably good agreement with those obtained from DSS results. A geologically plausible model of the crust in a virgin region has been presented along a Bouguer anomaly profile from Jaipur to Raipur.The following main conclusions have been drawn from the present analysis: (1) The depths to the Moho and Archaean basement interfaces fluctuate between 33.2 and 36.8 km and between 4.6 and 7.0 km respectively. (2) The Narmada-Son Lineament (NSL) does not coincide exactly with the Moho upwarp beneath it. However, this offset is greater in the eastern part of the NSL rather than in the western part. (3) The development of the Satpura horst structure is due to a rise in the Moho interface in a compressional regime. (4) The intrabasement feature (depth from 5 to 12 km) represents a hybrid massif possibly formed due to an admixture of sialic and simatic crust under a tensional regime in the Ujjain-Mahan section.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2478.1992.tb00553.x
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  • 9
    Electronic Resource
    Electronic Resource
    A COMPARATIVE STUDY OF THE SHORTENING OPERATORS USED IN VARIOUS DATA PROCESSING TECHNIQUES IN GRAVITY INTERPRETATION (1977)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 25 (1977), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Discrete Fourier transform analysis provides an infinite number of weight coefficients for filters like upward and downward continuation. For practical applicability, the lengths of such filters have been reduced to a manageable number by various shortening operators, viz. those by Peters, Martin, Mufti, v. Hann, Hamming, and the truncation operator. A comparative study for choosing an operator which approximates the theoretical filter response best has indicated that Martin's shortening operator and the truncation operator are best, respectively, for normalized and non-normalized sets of weight coefficients.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2478.1977.tb01149.x
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  • 10
    Electronic Resource
    Electronic Resource
    EFFECTS OF DATA ERRORS AND ACCURACY IN SECOND DERIVATIVE COMPUTATION BY RATIONAL APPROXIMATION (1975)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 23 (1975), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: The effects of systematic (constant) and random errors in the observed data have been investigated analytically for rational approximation method of computing second derivative involving a summation of the products of the averages of the gravity field with the corresponding weight coefficients, both in numerator as well as in denominator. A theoretical gravity anomaly over three spheres has been analyzed to demonstrate the high accuracy in the approximation. Since the sums of the weight coefficients in numerator and denominator are zero and one respectively, the regional gravity anomaly, even though approximated by a constant value over the entire area under computation, can produce substantially large error in the calculated derivative value. This is happening because of the contribution of the regional field in the denominator. Thus, inspite of the high accuracy in rational approximation, the method has limited application to field cases where a combined gravity field consisting of regional and residual anomalies is usually used. Master curves are presented for the constant and random errors by which a rough estimate of the percentage of error in second derivative computation can be made provided one has some idea of the magnitudes of the regional field and random error.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2478.1975.tb00687.x
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