A method has been developed for the measurement, in the laboratory, of the variation of the elastic properties of rocks in the frequency range 40-120 cycles/set. In addition, the observations yield information concerning the internal dissipation of energy over this range. A number of rock specimens have been examined and the results are compared with those of other investigators.The literature devoted to the elastic properties of rocks is extensive and covers the results of observations made under a wide variety of different physical conditions of temperatures and pressures. In the laboratory observations have been made employing a steady load on the specimen and also by dynamic methods using an applied sinusoidal force, whilst, in the field and under the generally justified assumption of isotropy, seismic observations of the velocities of both longitudinal and transverse waves allow the elastic constants to be calculated.The results obtained by various observers differ appreciably, part of the difference being due to experimental errors but, more generally, a greater part being due to differences in the physical states of the specimens and on the methods of observation.Thus, for Rockport granite, Quincy granite and Sudbury diorite, the observations, made by Ide (1936) using a resonance method, gave a value for Young's modulus consistently higher then those determined statically by Zisman (1933). Since both these experiments worked at normal laboratory temperatures and pressures and, in some experiments, Ide was able to use the same rock specimens employed by Zisman, the differrence here can be attributed to the method of observation. As is well known, the difference between a statically determined elastic
In this note the problem of random flights is considered for the case of a small number of vectors, each vector possessing the same constant magnitude. A formula is developed which permits the calculation of the probability function of the sum of N + 1 such vectors if the function of the sum of N vectors is known. The formulae for the probability distributions up to N = 8 are quoted and some of their practical applications mentioned.
Based on simple scaling laws, a method is developed for the routine interpretation of magnetic anomalies arising from uniformly magnetised dykes. The method can be applied to any observed component of the field, i.e. the vertical, horizontal or the total field anomaly and it is applicable for any resultant direction of magnetisation of the dyke itself and for any strike direction. The necessary data for the interpretation are given in the form of curves covering a range from o up to 15 for the ratio of the thickness of the dyke to the depth to its top. It is also shown that, by integrating in a suitable manner the observed anomaly due to inclined bodies having a horizontal upper surface and en-,closed by two pairs of parallel and inclined planes, a curve is obtained which corresponds to a dyke anomaly and which can be interpreted by the same technique.
An analysis of the natural magnetic polarization of the basalt flows of Mull shows that many are adversely magnetized but the mean direction of magnetization of each flow, based on observations of a number of specimens, is not always significant. For such flows measurements of the magnetic stability, response to heat treatment, etc., suggest that the original intensities have been modified by later events. Finally, the observed natural intensities could be acquired by cooling in a field similar in magnitude to that of the Earth's present field.Introduction.-The detailed history of the Earth's magnetic field is only known from observations of the secular variation over a few centuries. Recently efforts have been made to extend this limited knowledge by a study of the natural residual magnetism of both sedimentary and igneous rocks. Thus the study of glacial varves (I) has suggested that the Earth's field has not changed significantly during very recent geological times. Similarly with igneous rocks, the examination of modern lavas has shown that the rocks acquire a residual magnetization in a direction corresponding to that of the Earth's field in which they cool (z), and observations on Quaternary Lavas (3) again indicate little change in the general direction of the Earth's field over the last million years, any small variation in direction comparing with the secular changes which have been observed directly. Many older igneous rocks, and also some older sedimentary rocks, show remarkable directions of magnetization, differing widely from the direction of the present field, and in most cases the direction of polarization is nearly opposite to that of the Earth's present field. Thus, a magnetic survey over the Pilandsberg Dyke System of South Africa (4), which is of age about zoo x 1o6 years, has yielded magnetic anomalies compatible with an adverse magnetization of the whole system. In many other places, e.g. Germany, Iceland, Japan, New Zealand, etc., other igneous rocks show similar characteristics. In particular, the suite of tholeiite dykes of the North of England (5) has been examined at a number of points over an area of some 200 miles by 80 miles. Here the investigations consisted of a determination of the magnetic anomaly in the vertical component of the Earth's field produced by the dykes at a number of sites, and at a selected number of sites oriented rock specimens were collected and their magnetic properties determined in the laboratory. These observations demonstrated that in general the whole of the system possessed adverse magnetization. It is significant here that the magnetic anomaly, predicted on the basis of the properties of the collected specimens, agreed closely with that observed, so that there could be no doubt of the representative nature of the specimens.
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