In this paper a new, efficient method is worked out for the interpretation of self-potential field data. Interpretation of location, depth and dip of the ore body is made, using a pattern of equipotential lines. The negative center and the positive maximum of the potential are found and also the socalled " mid-value" point. The dip a, can be determined accurately for values between 5° and 85°. The method cannot be used for vertical polarization. The depth and location can be found with rela tive accuracy for <*> io°. The main advantage of this new method is the ease of interpretation and a greater accuracy for the high-dip angles.It should be stressed that, for correct and accurate interpretation, the positive maximum is as important as the negative center. Therefore, it should be carefully sought during the field work, and mapped to its full extent. INTRODUCTIONT he existing m ethods of interpretation of self-potential data, obtained from prospecting for ore bodies, are cumbersome and com m only involve a large am ount of guesswork.An elaborate theory for the surface distribution of potentials was worked out b y A. P etro vsk i.1 T he method of interpretation given b y P etro vsk i uses the cur rent densities, which are proportional to the derivatives of the potential curves for a fixed direction of traverse. T h is ob viates taking into account a base-line potential.A later method given b y W. Stern2 is based on form ulas derived from assuming the ore body to be a polarized bar. The potentials m easured in the field are used as such, which gives inaccuracies due to the absence of a fixed base line, relative to which the potentials are defined. In the theory the potential at a large distance is assumed to be zero. In the field, how ever, the zero-potential is difficult to obtain due to the presence of spurious potentials caused b y vegetation and percolation. It is also difficult to predetermine how fa r one has to go to find the " infinitypotential" for practical purposes, as the positive m axim um caused b y the ore can be far from the center of the ore body for low-dip angles.The interpretation here presented is based on P etro vsk i's theory, assum ing the ore body to be a polarized sphere. A " m id -valu e" point is introduced which elim inates the zero-line difficulties and does not require the use of current densities, saving much work and minimizing errors in the interpretation. 600T he " m id-value" point is an im provem ent on the " h alf-valu e" point idea which was outlined b y C. A. H eiland,3 for a vertica lly polarized sphere.A s only three points are used for the interpretation, all of which are well de fined b y the equipotential pattern, inaccuracies due to distortion b y topography are kept to a minimum. Figure 1 represents a hidden polarized sphere in a semi-infinite isotropic medium, and its image at equal distance above the fiat boundary surface. THE THEORY OF IN TERPR ETATIO NThe vertical plane through the plus and minus pole is called the plane of A N E W M ETH O D OF IN T E R P R E T A...
A detailed analysis of truncation errors in the Stokes formula integration, using Molodenskii's method, shows the mode of dependence of the errors on the spherical harmonic components of Ag of different order. The results indicate that significant reduction in the truncation errors can be achieved by adopting a reference model for normal gravity of higher order than that based on the International Ellipsoid. Particularly, the use of a seventh order reference model combined with truncation at the first zero crossing of the Stokes kernel function appears very promising. The treatment of truncation errors for deflection of the vertical as given by Molodenskii et al. and Hirvonen & Moritz yields results for deflections as derivatives of geoidal heights explicitly obtained from Stokes formula. These errors can be reduced by the same techniques as suggested for the Stokes integration. The truncation error behaviour of the Vening Meinesz formulae is shown to be different. An adaptation of Molodenskii's approach using an expansion of the truncated deflection of the vertical kernel function in terms of associated Legendre polynomials of first order provides a means for spherical harmonic analysis of the truncation errors in the Vening Meinesz formulae. 449 1
Published in Petroleum Transactions, AIME, Volume 204, 1955, pages 103–110. Abstract A review is given of the principles on which recently proposed methods of electric log interpretation in shaly sands are based and of the evidence brought up in support of the theoretical derivations. It is pointed out that the qualitative techniques suggested to date have a tendency to be too pessimistic in the prediction of the presence of commercial hydrocarbon accumulation. In the quantitative treatment, a new concept is introduced, namely that of strongly reduced activity of the double layer counter ions which are present near the negatively charged rock surfaces. This lemma when applied to the calculation of the equilibrium concentrations of interstitial waters yields a set of very simple relations. The resulting expressions for electrochemical potentials across rock samples appear in satisfactory agreement with laboratory experiments. The formulae obtained for the electrical conductivity of shaly formations are of the same form as those arrived at empirically by previous workers. Combination of the expressions for potentials and conductivities gives a direct proof of the Tixier relation which states that for shaly water sands the product of apparent formation water resistivity and apparent formation factor equals the resistivity of the sand 100 per cent saturated with formation water and which was verified by the work of Wyllie and Perkins and their co-workers. The relations for the resistivities and spontaneous potentials have been extended to the case of hydrocarbon bearing shaly formations, thus laying a formal basis forthe quantitative interpretation of electric logs in shaly oil sands. Introduction The presence of disseminated clays in porous rocks saturated with electrolytic solutions has a strong influence on the transference of ions taking place under electrical or chemical potential gradients. Both the electrochemical emf's in evidence on the SP curves of electric logs and the electrical conductivity measured on resistivity logs are directly dependent on the ionic transference in the interstitial waters of the formations traversed by boreholes.
True nnd False must be enclosed in braces if they have interred punctuation. If nothing is to be done for"one of etm alternatives, |he punctuation is used without: an enclosed opec'rod. In this simplified compiler, the Matrix Subroutines set End of Program and End of Subroul:inc to non-zero values when the appropriate operators OCCUF,
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