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 Volume 12, Issue 4, 1964
Geophysical Prospecting  Volume 12, Issue 4, 1964
Volume 12, Issue 4, 1964


CORRELATION TECHNIQUES –A REVIEW*
By N. A. ANSTEYABSTRACTCorrelation techniques are in the process of passing from the research laboratory to the field. This paper seeks to aid the transition. The three main sections of the paper have these objects:
 1 To state in words the basic principles on which correlation techniques are based, and the connection between these principles and more familiar concepts which are already among the tools of the exploration geophysicist.
 1 To review briefly the published applications of correlation techniques in science generally.
 1 To discuss some of the additional applications which are now emerging in exploration geophysics.
The treatment is graphical and illustrative, rather than rigorous. The paper is addressed to the practising exploration geoscientist and to the newcomer to correlation techniques. A list of about 150 references is given.



REFRACTION SEISMICS WITH AN ANISOTROPIC OVERBURDEN: A GRAPHICAL METHOD OF INTERPRETATION*
By K. HELBIGABSTRACTAn analytical expression for the time‐distance curve of seismic waves travelling in a medium consisting of intrinsically anisotropic layers with arbitrarily dipping plane interfaces can be given in terms of the “co‐ordinates” of the interfaces (length h of the perpendicular from the shotpoint to the interface, strike ν and dip α of the interface) if for each layer the velocity is given as a function of the orientation of the wave normal. The interpretation of the time‐distance curve is understood as the inverse process, namely finding an expression for the co‐ordinates in terms of some characteristics of the time‐distance curve, e.g. intercept times and apparent velocities. In addition, it is useful to know where the “limiting ray”, which is the ray connecting shotpoint and last geophone, enters and leaves a specific layer, for it is only on the medium between these two points that information can be obtained by interpretation. As ray and wave normal do not generally coincide in anisotropic media, the location of these points cannot be calculated from the co‐ordinates and the direction of the wave normal without recourse to the functional dependence between the directions of ray and wave normal.
An analytical solution of this problem would involve the solution of a number of equations, implicitly containing several parameters. Successive approximation would be rather cumbersome. Instead, a graphical method is proposed which yields all pertinent information without calculation.



CRITICAL‐ANGLE EFFECTS IN SEISMIC EXPLORATION*
By J. PH. POLEYABSTRACTIn the case where a medium of velocity α1 is underlain by a medium of higher velocity α2, no propagation of compressional elastic wave energy into the lower medium takes place at angles of incidence exceeding a certain critical value. This so‐called critical angle –which is a measure of the actual velocity‐contrast –is furthermore marked by a sharp increase in the amount of reflected compressional energy. An investigation has been made to find out whether this critical‐angle effect might be usable as a velocity‐contrast indicator in seismic exploration.
Model experiments confirmed the expectation that this effect should be manifest at the surface under ideal conditions.
Two small‐scale field set‐ups showed that the effect is actually measurable in the field (in one case after applying corrections for planting variations).
Finally a seismic line along the shore of the North Sea provided the data for contrast analysis over a considerable distance along the base of the Tertiary. Comparison of the measured changes in contrast and subcrop velocities obtained at those locations where subsurface data from independent sources were available, showed good agreement.
It is concluded that critical‐angle shooting may be used to indicate subcrop changes along a reflector, or even to obtain the same sub‐stratum velocity as is sought in conventional refraction work, at considerably shorter operating distances.



A NEW TECHNIQUE FOR THE MEASUREMENT OF GEOPHONE PARAMETERS UNDER FIELD CONDITIONS*
By B. A. PALMERAbstractNormally only operational checks are made on geophones in the field because of the lack of suitable test equipment. The test method described here was developed to enable accurate (better than 1 %) measurements to be made, in the field, of all geophones in common use which have natural frequencies of i c/s or greater.
The portable field instrument is simple to operate and can be used to test refraction and reflection geophones, either singly or in series strings.



ON THE CORRELATION OF GRAVITY WITH TIDAL ANOMALIES*
By E. GROTENAbstractTidal deformations of the solid earth show remarkable regional fluctuations. Mean gravity anomalies reveal strong positive correlation with the regional variations in the vertical tide component, if the effect of topography on the gravity field is reduced by isostatic proceedings. The correlation of these “tidal anomalies” with the lower harmonics of the gravity field is weaker. Heterogenities of the upper mantle may be a source of these differences in the deformations.



THE KÖNIGSBERGER RATIO AND THE DIPPING‐DYKE EQUATION*
By PETER HOODABSTRACTThis article deals with the effect that the Königsberger ratio, the ratio of remanent to induced magnetization, has in modifying the dipping‐dyke equation. Many reversed dykes are found on aeromagnetic maps and their presence indicates that remanent magnetism must often play a significant part in the magnetic expression of normally‐polarized dykes. The methods for the measurement of remanent magnetization and susceptibility (k) are outlined, and the relationship between k and volume % magnetite (V) is discussed. It is proposed that a good approximation is k= 0.15 (x^{−1} ‐ x), where x=1‐V/100. The general equation for the dipping dyke, which includes the contribution of remanent magnetization, is given. A method of obtaining k from the magnetic map is also derived.



LONG, HORIZONTAL CYLINDRICAL ORE BODY AT ARBITRARY DEPTH IN THE FIELD OF TWO LINEAR CURRENT ELECTRODES*
More LessAbstractThe electric potential distribution when an infinitely long, horizontal cylinder is embedded in an otherwise homogeneous earth with a flat surface, and the current is supplied by two infinitely long electrodes on the surface, parallel to the axis of the cylinder, can be readily found by solving Laplace's equation in bipolar coordinates. The expression for the apparent resistivity (in the sense of Schlumberger) can be obtained after differentiating the expression for the surface potential. This, like the expression for the potentials themselves, involves infinite series in the general case. For the particular case of a cylinder with zero resistivity the apparent resistivity (ρa) can, however, be expressed in terms of the Jacobian elliptic functions cs (2Kμ/π) and the trigonometrical functions cot u where K is the complete elliptic integral of the first kind. The value of K depends upon the radius‐to‐depth ratio of the cylinder. For a cylinder of infinite resistivity the logarithmic derivative of the theta function replaces cs (2Kμ/π). Excellent tabulations exist from which the cs and the cotangent functions can be easily computed.
A set of 36 apparent resistivity curves have been computed for the particular case of a perfectly conducting horizontal cylinder midway between the electrodes (but at arbitrary depth), from which a number of interesting conclusions emerge.
It is found that the resistivity anomaly (departure of apparent resistivity from its normalized value 1) vertically above the cylinder axis increases with the electrode separation (2L) but attains a maximum value only when the electrodes are at infinity, that is, when the normal electric field is homogeneous. The optimum electrode separation for detecting a cylinder at any depth whatever would therefore appear to be infinity.
However, the resistivity anomaly at infinity, which will be called the asymptotic anomaly Δρa(o), in contrast to the central anomaly Δρa(o) directly above the cylinder, is zero when the electrodes are at infinity and increases as they approach each other. The asymptotic anomaly attains a maximum value when 2L is vanishingly small, that is, when the current source is a (linear) electric dipole. Its value is then exactly the same as that of the central anomaly for infinite electrode separation. The optimum electrode separation if the asymptotic anomaly were to be measured would be zero.
It is interesting to note that a cylinder of finite radius‐to‐depth ratio (not equal to zero) alters the electric field even at infinity by a finite amount.
In general for any 2L, with the single exception of , where h is the depth to the cylinder axis and a is the cylinder radius. In this case the two are equal.
Between the central and the asymptotic resistivities for any electrode separation, there exists the relation where m1is the complementary modulus of the elliptic functions. Since K and m1are not independent, the product is a function of the ratio a/h only. The value of the central resistivity for infinite electrode separation is also given by and this fact could be used for finding the a/h ‐ratio of a horizontal cylinder by Schlumberger electric drilling above it.
It is also found that the variation of the resistivity anomaly of a horizontal cylinder, in a homogeneous field, with change in depth or radius, follows very nearly an inverse 2nd power law, as for the magnetic anomaly of a cylinder in a homogeneous magnetic field.
The paper discusses computations involving elliptic functions in some detail because such computations do not seem to be reported in geophysical literature.



BOOK REVIEWS
Book Review in This Article:
Robert L. Miller and James Steven Kahn
Ye. P. Fedorov, Nutation and Forced Motion of the Earth's Pole. Translated from the Russian by Bertha Swirles Jeffreys, Foreword by Sir Harold Jeffreys.

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