A NOTE ON CONVOLUTION AND PADDING FOR TWO-DIMENSIONAL DATA*

Gupta , V. K., and Ramani , N., 1978, A Note on Convolution and Padding for Two-Dimensional Data, Geophysical Prospecting 26, 214–217. Filtering of gridded data by means of two-dimensional generalized convolution results in a loss of data along the edges of the map. This loss can be counteracted by ‘padding’– filling the surrounding of the input map with some kind of data. Padding by algebraic extrapolation is assumed to be better than surrounding the maps with zeroes. A Føsrtran IV routine for padding by algebraic extrapolation is available from the authors.     

A NOTE ON THE USE OF A NOMOGRAM FOR SELF-POTENTIAL ANOMALIES*

A nomogram has been devised for situations, in which the source of a self-potential anomaly can be approximated by an obliquely polarized sphere or horizontal cylinder embedded in a homogeneous half space. The nomogram can be used for rapid determination of three parameters of the target: (1) depth to the centre, (2) angle between the axis of polarization and the horizontal, (3) shift of the point vertically above the centre of the body from zero potential value. The nomogram has been tested and the parameters determined for SP results obtained over ore bodies Weiss and Süleymanköy in the Ergani Copper district, Turkey. The curves computed for the estimated parameters match the field curves well.     

A NOTE ON THE USE OF NOMOGRAMS FOR APPARENT RESISTIVITY COMPUTATION*

Nomograms are presented for the purpose of rapid computation of the apparent resistivity functions from the field data for symmetrical and unsymmetrical linear electrode arrays.     

FITTING OBSERVED PROFILES TO A MAGNETIZED DYKE OR FAULT-STEP MODEL*

The symmetry shown, by the function describing the magnetic anomaly due to a dyke or vertical fault step leads to a method by which an observed profile may be adjusted to conform with that symmetry. By making these adjustments a minimum the ideal dyke or fault profile closest to the observations is constructed. In three of four possible situations this is interpreted by simple geometry. Parallelpiped models may be transformed into two dykes for symmetry analysis. Depth limited models are not so amenable, even in special cases.     

A NOTE ON THE LINEAR FILTER METHOD OF INTERPRETING RESISTIVITY SOUNDING DATA*

In the linear filter method of interpreting resistivity sounding data, as developed by Ghosh (1971), it appears that the filter function in the x-domain approaches an oscillating function for both large positive and large negative abscissa values. In the present note the reason for this oscillating behaviour is derived, and a possible practical application is indicated.     

A NOTE ON SIGNAL DISTORTION DUE TO DYNAMIC (NMO) CORRECTIONS*

By applying dynamic corrections a seismic trace recorded at a distance x from the energy source should be varied in such a way as to obtain a trace which would be recorded at zero-distance, i.e. at the source itself. Only such a zero-offset-trace contains the correct sequence of reflection coefficients (reflectivity function), whilst all other traces contain a distorted reflectivity function. In the simplest case, the reflectivity function is compressed over a shorter time whereas in more complicated cases a partial inversion of the reflectivity function results. This happens when some of the reflection hyperbolae intersect one another. The reconstruction of the true zero-offset reflectivity function by the application of dynamic corrections can only be an approximative process. In the first case mentioned we must expect a decrease in accuracy of the corrected trace in comparison with a zero-offset-trace. In the second case, where intersections of the hyperbolae occur, accurate reconstruction is clearly impossible. The problems are discussed with the help of theoretical and practical examples.     

A NOTE ON THE LINEAR FILTER METHOD OF COMPUTING ELECTROMAGNETIC SOUNDING CURVES *

The values of the filter coefficients used for the computation of electromagnetic sounding curves are studied in conjunction with the values of the input function to the filter, or the range of values which the input function may assume, and the filters are broken off at such a place that the error in the sum of the products of filter coefficient and input function does not exceed a prescribed value. This analysis is carried out for the horizontal coils system, the perpendicular coils system, and the vertical coplanar coils system. The lengths of the filters so derived depend on the layer parameters, the frequency and the coil spacing. Even in the most unfavourable cases the filters are shorter than the filters published by Koefoed, Ghosh, and Polman (1972).     

A NOTE ON THE GHYBEN-HERZBERG FORMULA

Abstract

By considering a conveniently chosen schematization of the flow regime in an unconfined coastal aquifer of large depth a generalization of the Ghyben-Herzberg formula, accounting for the discharge of fresh water towards the sea, is derived.     

A NOTE ON DAMAGE-BASED INELASTIC SPECTRA

When a structure is subjected to moderate to severe ground motions, a few excursions of the response yield level may take place following the reductions usually enforced in the design forces. These excursions are associated with progressive damage in the structure. Thus, a choice of the design level has to be suitably based on the maximum damage to be allowed in the structure. In this paper, a stochastic technique of developing damage-based non-linear spectra has been proposed for the aseismic design of those structures which can be idealized through Single-Degree-Of-Freedom (SDOF) oscillators. The proposed technique has been illustrated by obtaining the non-linear spectra which can possibly be used for a damage-based design. Along with the spectra, allowable ductility demand which should be supplied through proper sizing and detailing of the members and is compatible with the damage has also been specified. The non-linear SDOF oscillators have been approximated for this purpose by equivalent linear oscillators using a new stochastic linearization technique. The proposed linearization technique has been validated through simulation results in the case of an idealized, non-hysteretic, Elasto-Plastic (EP) model.     

A NOTE ON THE INTERPRETATION OF MAGNETIC ANOMALIES OF INFINITE THIN SHEETS BY USING RELATION FIGURES*

The concept of relation figures is utilized in the case of a thin infinite sheet for identification and determination of the causative source geometry, and its various parameters. The plot of ?T versus ?V is a conic, the plots between the respective symmetric components and the respective asymmetric components are straight lines, and the resulting diagram between the first horizontal versus the first vertical derivative of either ?T or ?V is a cardioid. The authors are grateful to Shri V. Babu Rao and Dr R. K. Verma for their encouragement. They would like to thank the Director of the N. G. R. I. for permission to publish this paper. The neat drawing of Sri P. Sundara Rao is appreciated.     

POISSON'S CONSTANT WITH DRY SEDIMENTS AND WITH PACKINGS OF SPHERES*

In order to find a relation between Poisson's constant of dry sediments and the porosity, it is necessary to consider the elastic behavior of the sediment's initial state and the final state during the process of consolidation. Sand and other loose materials of more or less granular substances represent the initial state. As substitute for this zone, elastic constants of simple cubic and hexagonal packing are examined. Supposed is the adhesion for the planes of contact. Besides of Hertz's formula for the contact area of spheres, an elastic function of displacement due to a tangential force for the contact area of the spheres is used. This function has been derived. With the aid of these two. elements, the constants of the mentioned packing are calculated. Poisson's constant will then be calculated from the formula being valid for isotropic solids for three different directions of the sound. The mean value is lying at . With the known equation of Poisson's constant of rock having a small porosity, a third-degree polynomial is formed. This polynomial agrees well with the average values of known measurements, and therefore can serve as a guide for the calculation of Poisson's constant of water-saturated sediments.     

关于提高微震事件自动识别效率的一个注记

利用美国国家地震信息中心的地震早期警报系统，通过对数字化地震记录的分析，针对各种可能出现的情况，对微震的自动识别和计算机实时处理进行了讨论。有关结论对地震的自动识别和震源参数的计算测定精度的提高，有重要的参考意义。     

关于逆转方法B解的不唯一性

讀了魏鼎文同志的文章以后,我們想提出以下两点不同的看法,与魏鼎文同志商榷。 1.文献[1]中用两个实例表明,在目前实驗精度內,方法B得不出大气臭氧垂直分布的精細結构,这点对于如何利用方法B的結果是很有参考价值的。不过,我們认为,不能把精細結构方面的某种不定性,看成是方法B解不唯一的証明。     

A NOTE ON INEXPENSIVE TELEMETRY OF RIVER SEDIMENT CONCENTRATIONS

Synopsis

An inexpensive method for continuous monitoring of suspended sediment concentrations in rivers has recently been developed at the University of Natal. The instrument uses newly available solid state electronic circuitry and has been thoroughly laboratory-tested. The circuitry and the operation of the instrument are described in general terms.     

关于逆转方法B解的不唯一性

讀了魏鼎文同志的文章以后,我們想提出以下两点不同的看法,与魏鼎文同志商榷。 1.文献[1]中用两个实例表明,在目前实驗精度內,方法B得不出大气臭氧垂直分布的精細結构,这点对于如何利用方法B的結果是很有参考价值的。不过,我們认为,不能把精細結构方面的某种不定性,看成是方法B解不唯一的証明。