CALCUL DU GRADIENT VERTICAL DU CHAMP DE GRAVITE ou DU CHAMP MAGNETIQUE MESURE A LA SURFACE DU SOL*

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In a previous paper by the first author a method has been presented for computing the first vertical derivative of the gravity field or of the magnetic field. In the present paper an analysis is given of the errors in the first vertical derivative that result when the. latter is computed by the above method. Two sorts of errors are considered. Firstly, the. error in the first vertical derivative that results from the errors in interpolating between isogam lines on the Bouguer anomaly map. Secondly, the error in the first vertical derivative that results from the approximations upon which the computation method is based. The conclusion is reached that both sorts of err,or are only of minor importance.This paper is a redly to a question asked by Mr. Thomas A. Elkins from Mr. V. Baranov. Mr. T. A. Elkins writes:"Your vertical gradient paper (Baranov, 1953) describes an ingenious method of treating some important but difficult problems. I would have been interested in your including a mathematical discussion, if such is practical, of the effect of the approximation of the curve by pieces of biquadratic parabolas on the accuracy of final formulas".This question may possibly be of general interest and it might be useful to express our ideas on the subject. The method of calculation employed requires two stages : I) Plotting of canonical values on the gravimetric map, 2) Calculating the product of each of these values by a coefficient and adding all these products. The possible errors are naturally divided into two groups: I) Errors of plotting due to necessary interpolation in the reading of each canonical value, 2) Errors in the calculation of the coefficients.The two sources of errors are independent and will be dealt with separately.

“…-0 -g'fn 4 h For h = 2 (example given in the paper presented in Hanover, Baranov 1953) we obtain the upper limit 5,s %. Of course, the actual error is smaller: it is only 2,1 %.…”

Section: Some Examplesmentioning

confidence: 97%

Some Remarks on the Errors in the Calculation of the Vertical Gradient of Gravity*

Баранов

Tassencourt

1954

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confidence: 99%

“…For years magnetic interpreters have derived vertical magnetic gradients from total field observations (Baranov, 1953). The development of optically pumped magnetometers like rubidium vapor, cesium vapor, and other varieties, made it possible to actually observe vertical magnetic gradients in aeromagnetic surveys.…”

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confidence: 99%

A New Parameter for Aeromagnetic Surveying*

Thyssen-Bornemisza¹

1967

The author proposes the parameter ATz/ATl for possible application in aeromagnetic surveying making use of already available gradiometer systems equipped with sensors separated vertically.For years magnetic interpreters have derived vertical magnetic gradients from total field observations (Baranov, 1953). The development of optically pumped magnetometers like rubidium vapor, cesium vapor, and other varieties, made it possible to actually observe vertical magnetic gradients in aeromagnetic surveys. Hood (1965) recently pointed out the value of this new magnetic exploration technique, and discussed the application of Euler's differential equation in the form @AT/ah) max = -(nATnm)/h (1) as useful for the interpretation of results. The left side term expresses the amplitude of vertical magnetic gradient anomaly measured directly by gradiometer according to (AT2 -ATl)/Ah, where two sensing devices separated by the vertical interval of Ah furnish the required difference between two total field values. The sensitivity of a total field channel is generally better than 0.2 gamma while the sensitivity of the gradiometer itself may exceed 0.0006 gamma per meter.The parameters n and h in the right hand side of relation (I) denote the fall-off exponent and the depth of the causative body or structure going down from the airborne system. Finally, AT max represents the amplitude of the total magnetic field anomaly which can be measured by one of the two sensors.The fall-off exponent or the exponential attenuation of the magnetic effect can be computed when "z" the depth to the source is known, or is being approximated by conventional magnetic methods or by borehole information.

“…Amongst these, the second derivative method has been put to maximum use. The first derivative (gradient) method, inspite of certain subtle advantages over the second derivative (Evjen 1936;Baranov 1953 ;and Henderson 1960) has received little attention. And except Baranov (1953) and Henderson (1960) not much work has been done to develop practical schemes for the computation of the gradient.…”

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confidence: 99%

“…The first derivative (gradient) method, inspite of certain subtle advantages over the second derivative (Evjen 1936;Baranov 1953 ;and Henderson 1960) has received little attention. And except Baranov (1953) and Henderson (1960) not much work has been done to develop practical schemes for the computation of the gradient. This state of affairs seems to be largely due to the fact that the mathematical analysis needed for gradient computation is more complicated than that needed for the second derivative (Baranov 1953) *The mathematical analysis of Baranov (1953) and Henderson (1960) requires the use of upward continuation integral which is valid only for z < o and is singular at .z = o, with the z-axis positive downwards.…”

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confidence: 99%

Calculation of the Vertical Gradient of the Gravity Field Using the Fourier Transform*

Agarwal

Lal

1972

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.