Geophysical Prospecting - Volume 3, Issue 4, 1955

Velocity functions can be grouped into families, any One of which results, in seismic pictures differing among themselves only in their scales of time and distance but similar in all other respects. For any one of these families it follows that curves drawn on logarithmic scales of time and distance to represent a particular relationship between seismic quantities will be similar in shape. This leads to the use of templates with logarithmic scales for fitting a smooth velocity function to a set of seismic data. Suitable templates for fitting refraction and reflection data to velocity distributions linear with either depth or vertical time are presented. An insight into the uncertainties involved is obtained with the aid of numerical examples.

The problem is considered of how to determine, from dip shooting data, the position in space of a reflecting horizon located underneath a refracting interface between two media of different velocities.

The author proposes a combination between a geometric solution and an analytic one, to obtain the quickest result.

The authors develop an optimum filtering theory for seismic reflection recording. A criterion of record improvement is applied to a mathematical model consisting of a set of wavelets superimposed on a random noise backgruond. This leads to the design of electrical filters and geophone and shot‐hole patterns with optimum filtering characteristics.

For the first time a method of observing the effects of hammering and of small blasts has been applied in a series of experiments on various soils, using a three component set of small mechanical leaf spring seismographs. The seismograms have been subjected to a thorough harmonic analysis. By means of these experiments, the theoretical concept of Rayleigh waves generated in a layer overlying a semi infinite medium has been confirmed. The dispersion curves resulting from different experiments correspond well with theoretical dispersion curves.

It may be. concluded that every seismic pulse generates a specific Rayleigh wave mechanism in loose layers. The depth of penetration of the Rayleigh wave mechanism and its frequency spectrum depend upon the delivery of energy and upon the consistence of the particular soil.

Most of the energy delivered is transformed into surface‐waves, and it is obvious that the direct reading of pulses in seismograms effects mainly group velocities of the Rayleigh wave mechanism. Thus, all endeavours to procure information about near surface layers of loose soils by refraction seismic work, as the present investigations show, meet with far more difficulties than has been assumed in the past.

With regard to the determination of the critical frequencies of the generated surface waves, the method of harmonic analysis of seismograms is superior to the usual dynamic method of soil mechanics, since rotating weights do not give the characteristic phase velocities and transversal wave velocities necessary for judging the consistency of loose soils.

Finally, a method of determining the absorption of surface waves is discussed.

Calculations are presented of reflection coefficients of plane longitudinal waves incident at oblique angles on boundary planes between elastic media. It is shown that the manner in which these reflection coefficients vary with the angle of incidence is strongly affected by the values of the Poisson's ratios of the two media. It appears that, contrary to a conclusion arrived at by Muskat and Meres, the reflection coefficient may vary appreciably with the angle of incidence in the range between O° and 30°. Possibilities of practical application of this phenomenon are discussed.

This paper deals with the four electrode method of electrical resistivity prospecting using direct current. It is shown that three resistances can be measured for any four electrode configuration, and a simple relation between them is derived. The particular case of the Wenner electrode configuration is discussed and a further relation derived between the three apparent resistivities corresponding to the three resistances. The practical value of the ‐resistance relation as a means of avoiding experimental errors is indicated.

In general the three apparent resistivities are different in magnitude although there are certain particular cases where they are equal to one another. Their actual values are determined for a number of simple problems and the possibility of having a negative apparent resistivity is illustrated.

Finally, examples of field tests are given in which the three resistances were measured, and it is concluded that the method can often provide a simple way of distinguishing between the effects of lateral and vertical resistivity variations.

The paper discusses the variations of Elevation Correction Factors (E.C.F.) across various stratigraphical and structural occurrences with particular reference to the dipping bed, fault and horst. Graphs are prepared giving E.C.F. variations for various angles of dip and a method is suggested for application in the field. Errors in the linear variation that is commonly used for small angles of dip are discussed.

The second part of the paper consists of the application to interpretation of (I) Change of gravity dip and (2) The gravity inversion. It is shown how from a gravity map the dip, position of outcrop and thickness of a dipping bed can be determined. The last part shows how anticlines can give rise to negative anomalies and that in the direction of dip similar structures can at one point have no surface expression and afterwards invert to positive anomalies. The danger of attempting to predict the size of structures in such areas is emphasised.