ALBERT

Notes: The decay rate of gamma radiation emitted by a Jamaican mineral spring was measured using portable rate meters. The results of these experiments, supported by auxiliary tests, suggested that the main radioelement causing the radioactivity was radon 222. Fluctuations in the intensity of the radiation were studied in situ. An inverse relation between the intensity and the discharge rate of water was established and the effect of rainfall and of earthquakes was investigated. Some suggestions are made concerning the possible source of radon.

Notes: The iron ores of the Siegerland-district are found in lodes occurring in schists of Lower Devonian age. In the course of the geophysical exploration for these ores, an attempt was also made to clarify the structure and the tectonics of the substratum of the sedimentary rock formations by seismic reflection measurements from the surface. Reflections were recorded in great numbers from layers of Silurian and Devonian age. The form of the folding of the strata derived therefrom corresponds well with that deduced from geological investigations. Beyond that, correlatable reflections were recorded from horizons down to a depth of nearly 25 000 m. It turned out that the iron ore lodes known from the mine workings occur almost vertically above those places where greater dislocations appear in the deepest substratum, and which geologically could be interpreted as fracture zones. The results so far obtained seem to be indicative of the fact that the tectonics of the deepest substratum and the occurrence of ore deposits are related to each other.

Notes: Precision calibration tests carried out with a Worden gravimeter in environment conditions as varied as possible have led to the following conclusions. The secular variation curve of the calibration shows that the secular relative variation has been very appreciable in the first year of life of the instrument, precisely of 1.3 × 10−3 in 13 months, while it has been practically zero in the second year. This must be ascribed to the fact that at the beginning of the operations the gravity-meter had just arrived from the factory with its measuring body renewed.On the other side the effect of 24°C of temperature difference between two series of determinations reveals itself in a variation of 0.0022 of the value of the calibration, so that it can be established that the variation of the calibration is I‰ for each 10°C of temperature variation.

Notes: Due weight must be given to three factors (1) its purpose, (2) the limitations imposed by nature, industry and environment, (3) the effect of errors in auxiliary measurements. Together the last two factors give an estimate of the accuracy which can be achieved. If this is sufficient for the instrument to fulfil its purpose design and construction can proceed. If it is not, a detailed survey of the last two factors is necessary in order to estimate the research effort that will be required when directed into the most effective channels. If the project is considered worth the effort it can proceed. These factors are discussed in relation to a borehole gravimeter. It is shown that the purpose will be served only if the accuracy is comparable with the best surface gravimeters. Borehole versions of some surface instruments are considered and it is concluded that none is suitable without considerable modifications. A successful borehole gravimeter is likely to be a completely new instrument.

Notes: Recently, quite good determinations of interfaces have been made by means of seismic well surveys. These were carried out for various oil companies in Northwest Germany, especially on salt-domes, and in Southern Germany, and in the area of the Upper Rhine Valley. It was the purpose to determine the configuration and position of salt-flanks and important planes of stratification in the neighbourhood of deep wells, and thus to reduce the risk of expensive wells.For the delineation of the boundary surfaces the method described by Gardner in “Geophysics 1949” was applied.The problems arising and the results obtained are discussed in connection with some interesting examples. From them we see, above all, that a knowledge as precise as possible of the seismic velocities of all media involved in the measurement is very important. A good idea of the general stratification in the area of deep wells seismically surveyed will make possible a rational and adequate planning of the survey program and will facilitate the interpretation.

Notes: A method is described in which the major part of gravimetric terrain corrections may be estimated by digital computing methods.

Notes: The electric and magnetic field of a direct-current element, embedded in a space consisting of two halfspaces differing in conductivity and permeability, is given in a form suitable for integration along a cable. From these formulae is obtained the field when one end of a D.C. cable is grounded in a highly conducting, pencilformed ore body, considered as a line electrode with uniform current leakage. Numerical examples are given for a horizontal line electrode. The formulae should be useful as a first approximation to the A.C. case. The validity of this is shortly discussed.

Notes: An analogy is established between the propagation of an electromagnetic field in a horizontally stratified conductive medium and that of currents in a linear electric network. This analogy will allow us to know in which case measurements executed at the surface of the ground can provide information about the properties of deeper layers. The situation is the same as when one tries, by means of impedance measurements at the input terminals, to know the properties of electric lines or lumped networks.A symmetrical linear network establishes between:Voltages V1 and V2 (respectively at input and output terminals)Currents I1 and I2 (respectively at input and output terminals), the relationship 〈displayedItem type="mathematics" xml:id="mu1" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR77:GPR_77_mu1"/〉 is called the “phase constant” and Z the characteristic impedance The table 〈displayedItem type="mathematics" xml:id="mu2" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR77:GPR_77_mu2"/〉 is called “characteristic matrix”If one then takes the horizontal components of an electromagnetic field, one can compare the voltage V with the horizontal electric field E (in volts m-1) and the current I with the horizontal magnetic field H (in Amp m−1)For plane waves in vacuum, one gets (Schelkunoff) Z=C (velocity of light)A layer whose thickness is D has a phase constant⌈= 2 πD/λ (λ= wavelength)For plane waves in a conductive, non magnetic medium whose conductivity is δ, one gets 〈displayedItem type="mathematics" xml:id="mu3" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR77:GPR_77_mu3"/〉 For the system of waves created by a point-source one expresses the solution, since it is classical, as a sum or integral of different modes. For each of these modes, one can still write a bilinear relationship similar to (1), and calculate Z and ⌈.A generalization of this result is given.Boundary conditions that exist at the surfaces of separation are met by writing the continuity of E and H. This condition exactly corresponds to the fact that there one V and one I at the junctions of various sections of lines, or networks.The characteristic matrix of a cascade of networks-or here that of a horizontally stratified ground– is the product of the matrixes of each network. If, in addition, one knows the end impedance–here the conductivity λn of the last layer, supposed to be infinite–one can compute the input impedance Re of the whole system. In electromagnetic prospecting, it is Re that conditions the observable field.Inversely, if measurements were infinitely accurate, the. knowledge of the surface field would give all the thicknesses D and conductivities δ of intermediate layers, in the same way that impedance measurements at the input terminals of a cable would allow to locate any failure. The imperfection of measurements causes the elements located too far away (from the point of view of wave attenuation) to escape detection.

Notes: The attention of everyone has already been drawn to the part which accident reports must play (Geophysical Prospecting, March, 1957, PP- 1 to 8). We intend to show here, with supporting examples, that the systematic analysis of the causes, does allow one to obtain practical conclusions.To begin with, it is advisable to widen the notion of geophysical accident as much as possible. This being done, about 200 reports distributed over a long period and a sufficient number of parties, are dealt with. The collected reports are sufficiently numerous to draw conclusions in a general way bearing on the headings: drilling, transport, outbreaks of fire, explosives, falls, stings, shocks, miscellaneous causes.All the quoted figures are referred to the number of accidents reported. Action must be taken to encourage european geophysicists to study accident reports and to analyse the causes. This may be done in such a way that secret information, such as whereabouts of their personnel, is not disclosed.Efforts to promote “Security” must in the first place bear on the quest for the causes, the definitions of ‘accident’ and of ‘geophysicist’ being taken at their widest possible meaning.

Notes: Seismic model experiments are described in which long strips of plexiglass were used as models. One end of the strip was sawn off at an oblique angle and, at the opposite end, the strip was excited by means of a barium titanate transducer. The experiments showed that, if the width of the strip was sufficiently small, an anomalous reflection against the oblique end occurred which travelled in the longitudinal direction of the strip. This anomalous reflection did not occur when the width of the strip was large. These results are explained on the basis of Fresnel's theory. It is inferred that, in the subsurface, refracted waves may be reflected against fault planes without the law of reflection being satisfied, provided that the refracted wave is propagated in a sufficiently thin high velocity layer.

Notes: Changes of shape of seismic waves provide information on the properties of the material in which the waves propagate. Ricker (1953) has attempted to explain the changes of shape on the basis of a simple viscoelastic theory. His conclusions are at variance with those of others who find a dependence of the attenuation on frequency which could be explained only by a much more complicated linear theory or by nonlinear theories.To provide a basis for discussion, the essentials of the theory of viscoelasticity are briefly reviewed. If a relaxation spectrum, rather than one or very few relaxation times, is admitted, a great variety of experimental results can be described by the linear theory of viscoelasticity. A linear theory is indicated when no obvious violations of the principle of superposition occur.Ricker's theory is presented with some modifications which allow for a finite duration of the initial pulse and for the approximate character of his basic assumptions. There do not appear to be serious discrepancies between his theory and his experimental results. Some of the objections to his theory can be met by assuming a finite duration of the initial pulse. However, more direct measurements made under similar circumstances by McDonal et al. (1958) at the same location lead to a conclusion on the nature of the material not in accordance with Ricker's. This casts doubt on the sensitivity of his method.Laboratory measurements usually yield results which are not explainable in terms of simple viscoelastic models. Whether a linear theory with a relaxation spectrum or a nonlinear theory should apply depends much on the experimental conditions. We must also consider the possibility of nonlinear mechanisms which are active at small amplitudes. No stand is taken in this controversy, but it is pointed out that the question linear or nonlinear could be decided experimentally without considering the details of the theories.

Notes: A method of refraction computing is described which establishes the two points of incidence at the surface of the ray-paths from any point on the refractor when observed from opposing directions. The distance between these points is used to determine the radius and the centre of a circle to which the refractor must be tangential. The matching of forward and reverse data is intrinsic in the method so that the resulting profile is automatically positioned in depth. It is shown that if the effects of dip are neglected, errors are introduced in the derived radius and also in the position of the centre but these errors are shown to cancel each other almost exactly.

Notes: The wells Parentis 10 and 12 which are located on the eastern edge of the Parentis anticline were found to be considerably lower at the top of the reservoir series than had been expected.Unfortunately the village of Parentis is located in this important zone and no more seismic results could be obtained which might help locate faults and give a better picture of the area. To help in our understanding of the area, we attempted to investigate the subsurface conditions surrounding the wells by shooting shaped charges or primacord in the well and recording the returning seismic energy along profiles located on the surface. Thus far, we have used this method in three wells: Parentis 10, Parentis 12 and Lugos 2.With the data given by a velocity survey in each well, time-distance curves have been calculated for several typical possibilities: horizontal layers, dipping layers and the effect of a fault. A comparison of the calculated and experimental curves shows anomalies which correspond to a change of the average velocity along the travel path, which can correspond to geological changes such as: a sudden change of dip, a fault or a thickening of the section.The anomalies have been studied on the different profiles from each well and a possible interpretation of the subsurface conditions has been given. The directions of the major accidents determined by this method are in general agreement with those found by the regular seismic shooting.

Notes: The directional sensitivities of an array of geophones depend as much on the size of the array as on the directional sensitivities of the single geophones forming the array. In a former paper (Celminš 1956) the effect of the size of the array was investigated. In addition to this the influence of the directional sensitivities of the individual geophones on the sensitivities of an array of geophones is investigated here.In δ 2 some general formulae for the directional sensitivities are derived. In addition the directional sensitivities of a single geophone according to P- and S-waves are investigated (δ3 and δ4). In δ5 the'directional sensitivities for the most important cases of arrays of parallel geophones are computed. The results of the computation (shown in fig. 4 and 5) give an idea of the types of directional sensitivities which occur in the use of geophone arrays.

Notes: Non-explosive seismic sources, notably the falling weight and the eccentric machine, have occasionally proved advantageous in experimental and practical seismology in spite of their relative feebleness.Another alternative is the pulsed vibrator, which offers the advantage of a completely controllable waveform. Recent theory shows that such a source is quite well adapted to the radiation of high frequency waves from the surface of the ground; it is estimated, for example, that in typical circumstances reflections should be obtainable from depths of the order of 200 metres. The theory also shows how resonances may be avoided so as to radiate the impulsive waveform unimpaired.

Notes: Book review in this articleGedenkboek F. A. Veiling Meinesz, Verhandelingen van het Koninklijk Nederlandsch Geologisch-Mijnbouwkundig Genootschap, Geologische Serie, Vol. XVIII, May, 1957.

Notes: A brief description of the procedure usually adopted for ascertaining the accuracy o aeromagnetic data is given as a background to the discussion of factors which affect this accuracy. These factors fall mainly into two groups: spatial positioning, i.e. relation to the ground surface, and effects contributing to the observed relative magnetic values. The evaluation of the observed anomalies in terms of the most probable causes and the anomalies themselves are directly influenced by the amount of the available control of factors mentioned above. The effects of various factors, such as plan positioning, height keeping, diurnal drift, are discussed, the arguments being based on theoretical and practical premises.

Notes: The effect of the composition of the tank walls on apparent resistivity determinations made in model experiments has been investigated for the two extreme cases of an insulating and a perfectly conducting tank wall: The resulting errors have been determined both by calculation and by experiment.Experiments are described which demonstrate that the magnitude of the effect can be considerably reduced by specially constructed tank walls.

Notes: Amplitude measurements have been made of the height of the first peak of an arrival refracted from a shallow refractor. If the amplitude is assumed to decay as the inverse mth power of the distance, the least squares value for m is found to be 2.16 ± .04. Because of this value and because of the character of the recorded event it is concluded that the arrival is a simple critical refraction. After applying the theoretical ‘spread’ factor for critical refraction there remains a residual attenuation of 1.96 ± 0.28 decibels per 1000 feet. The predominant frequency in the pulse is about 20 c.p.s. and this attenuation agrees with the losses found for such a frequency by extrapolation of the published results of other workers. Although no evidence could be seen on the records for a change of pulse frequency with distance, the quoted result would be consistent with a dependence of residual attenuation on the first power of the frequency, and would be inconsistent with a dependence on the second power of the frequency.It is concluded that studies of the amplitudes of refracted events will give useful estimates of the attenuation factors of rocks.

Notes: A method of constructing depth contour maps of arbitrarily curved horizons obtained from seismic reflection surveys is discussed. This method takes into account three dimensional refraction, avoiding the construction of seismic cross sections of any kind. It requires little work even if refraction at several horizons is taken into account. The multiple layer problem is traced back to the single layer case. Discontinuities in velocity are also taken into account.

Notes: 1. A Worden gravity meter has been tested for sinusoidal variations in the external temperature, by determining simultaneously the corresponding variations of temperature inside the Dewar vacuum bottle, and the variations in the readings.A second Worden gravimeter has been tested for rapid variations in external pressure.

Notes: The results of field and laboratory methods of density determination on a series of Coal Measure, Permian and Triassic rooks are presented and the different methods compared. It is concluded that the most satisfactory method is that of measuring the vertical change of gravity in a mine shaft. Nettleton's method is unsatisfactory to us, due to weathering of the rocks (particularly Magnesian Limestone) and possible effects from drift. Laboratory measurements are of variable value depending on the lithology and source of the samples.A method adopted to solve the problem of finding the true densities for use in a local gravity survey in N.E. England is given.

Notes: The iron ores of the Siegerland district are found in lodes occurring in schists of Lower Devonian age. These lodes, normally dipping almost perpendicularly, could be traced only by seismic reflection measurements underground, up to distances of approximately 500 m. The geophones were attached to the walls of the galleries. The frequencies of the recorded longitudinal and transverse waves ranged from 200 to 500 c.p.s. By this method a new siderite lode was discovered.

Notes: Book Reviewed in this article:Lehrbuch der angewandten Geophysik, Teil II, H. Haalck.

Notes: A series of repeat observations during a period of 5 years reveal a variation with time of the Worden gravimeter No. 142 small dial spring system. A possible change in the gravity difference concerned is ruled out. It is shown that the small dial scale factor has diminished by about 0.25 % within the last two years against about 0.5 % four to five years ago. The ratio of L.D. to S.D. has been analysed and the results obtained show confirmation of the change in the small dial system and prove a consistency in the large dial system.

Notes: A study is made of the possibility of calculating electric potentials, and therefore of interpreting apparent resistivity measurements, when the ground presents structural conditions more complicated than plane, parallel stratification.For this work a schematic type of structure has been chosen, in which the discontinuity planes for electric resistivity are both parallel and perpendicular to the level of the ground.The problem has been examinated in its general aspect, and then some criteria for the numerical calculation have been indicated.Some calculated examples are presented, relevant to vertical electric soundings accomplished by conventional technique, for particular types of structure.

Notes: The elastic impulse-from an explosion is propagated through the earth as an expanding shell bounded by the wavefront. This wavefront and its motion are a physical reality while rays or trajectories are much less sharply defined and cannot actually be observed because the wavelengths involved in seismic processes are too long. This means that the visualization and the interpretation of seismic processes can be carried out in a more satisfactory, simple and comprehensible way with wavefronts than with rays.H. R. Thornburgh (1930) introduced the very lucid and simple method of interpreting seismic refraction sections, using Huygen's principle to construct wavefronts from two symmetrical shotpoints by working back from their observed arrival times at the surface. The depths are found first with only a knowledge of the velocities down to the refractor and after that the velocities in the refractor can be determined.The pattern of the two wavefronts at equal time intervals, obtained when carrying out Thornburgh's construction, leads to the very simple, approximative “Plus-Minus” method. The additions of the travel times from two symmetrical shotpoints to-each geophone give the relative depths and their subtractions give the velocities of the refractor. The method extrapolates exact quantities from the refractor boundary up to the surface by the “Plus”- and “Minus” lines. This extrapolation introduces errors that can, more or less, be corrected for. A number of hypothetical cases are presented to give an insight into the applicability and reliability of the “Plus-Minus” method. Its main applications are for fairly shallow refraction investigations and for determining weathering corrections for refraction and reflection work.

Notes: Major savings for operators of seismic parties have been achieved by the use of prilled ammonium nitrate as a substitute for gelatin dynamite in areas where shot holes are dry. Pound for pound, the prills appear to have the same energy yield as 60% gelatin dynamite, and some improvement of records has been noted where prills are used. Safety problems are less with ammonium nitrate than with dynamite, and the development of efficient field handling techniques prevents the loss of production.

Notes: Some mathematical inequalities are proved and their relevance to the interpretation of local magnetic and gravity anomalies is discussed. They can be applied to the readings of either a vertical magnetometer or a total field magnetometer or a gravimeter and yield a maximum possible value for the depth below the earth's surface of the top surface of the body producing the anomaly.

Notes: In order to eliminate the effect of smoothing due to the use of a finite number of grid points, the second derivative is computed by integrating the product of g with a convenient continuous function, which yields the second derivative to the extent to which the first terms of the Taylor expansion of g represent its value correctly. By applying this method to the anomaly caused by an isolated mass, and to that caused by a homogeneous half plane, it is shown that, if the result obtained is interpreted as if it really were a second derivative, erroneous values for the depth and the mass are obtained. If the real depth of the mass is small, a too large apparent depth is obtained. In the case of a half plane the use of a system of grid points gives the same result. These considerations permit the rational choice of the method of computing the second derivative, such that the effects of too shallow mass irregularities are attenuated.

Notes: From gamma ray absorption the density of soil to a depth of i m. can be determined in situ, without taking samples, by a method which has been described in a previous paper (Wendt 1954) and which has been checked with satisfactory results (mean error about 1%). A nearly vertical steel rod with a gamma ray source at its lower end is pushed into the ground, and the gamma radiation is measured at the surface with two counters placed symmetrically with respect to the rod.As a first step in interpreting the observed effects, the assumption had been made that counters are infinitesimally small. This paper shows how a theory can be developed without this assumption, the finite dimensions of the counters being taken into account by an integral expression. For this purpose a determination of the dependence of the counting rate on the angle of incidence of the gamma rays is required. A comparison of the experimental results with the theoretical ones demonstrates that the integral expression is correct.The influence of deviations from the normal geometry of the arrangement (e.g. caused by bending of the probe) on the results is investigated, as well as the influence of variations of the density with depth.The treatment of the basic problems has been carried through in such a manner that the results obtained can be applied to other absorption methods as well.

Notes: In this paper an attempt has been made to evaluate the possibilities of determining subsurface features from temperature measurements made at shallow depths. The temperatures at the observation depth used are subject to seasonable variations. The amount of this variation differs, and these differences have been attributed to structural features. Local differences in temperature are also caused by surface factors such as the thermal conductivity of the soil, the vegetation and the micro-climate. The differences in temperature due to surface factors are so great that the variation in heat flow caused by differing thermal conductivities of the rocks at depth cannot be detected at the surface. It is not possible therefore to use this method to determine the position of subsurface structures such as domes, anticlines or horsts.It is also shown that concentrations of radioactive elements in the rocks do not provide any measurable heating.The method has been successfully applied to the problem of finding fissures, cracks and similar features provided that convective heat transport from depth to the surface has taken place along these features. In order to compute the area through which a given amount of water at a given depth must pass to give a specific temperature increase a model has been considered. From the shape of the temperature anomaly above a fissure carrying such heated water, the places at which the rising water enters the groundwater stream can be seen immediately. It is possible to estimate the amount of rising water by computing the amount of heat energy transferred to the surface.The method is particularly suitable for determining the position of steam deposits in regions of recent vulcanicity. In such a region a location, hitherto unknown, was found where steam rising from depth condenses beneath the surface.The area and form of the anomaly indicate the extent in depth of this steam bearing zone. By means of observations made at the individual points, it was also possible to compute approximately the energy being released at the surface. This value can give an indication of the extent to which the steam deposits regenerate themselves.Finally it has been shown that percolating canal water can be detected thermally near the canal banks. Such anomalies are dependent on the season.

Notes: The following assumptions are made in the mathematical treatment of the problem. Below a plane earth's surface there is a three-layered elastic medium the interfaces of which are parallel to the earth's surface. The uppermost layer represents the weathered layer in which the velocity of propagation of seismic waves increases linearly with depth. The two lower layers, the so-called intermediate layer and the substratum each have a constant velocity. The surface of the earth is acted on simultaneously by a normal pressure N in the form of a Heaviside pulse. The seismic wave thus generated is propagated through the elastic media.The aim of the investigation is to study the shape of the wave1) in the intermediate layer, after the wave has entered it the first time2) at the earth's surface, after the wave has been reflected once at the interface between the intermediate layer and the substratum.The mathematical solutions can in both cases be expressed as series of Bessel functions. Some numerical examples illustrate the quasi-periodic nature of the solutions. The pseudo-frequency is determined by the gradient of velocity in the uppermost layer; it assumes a value of approximately 50 c.p.s. for a gradient of appr.〈inlineGraphic alt="inline image" href="urn:x-wiley:00168025:GPR328:GPR_328_mu1" location="equation/GPR_328_mu1.gif"/〉

Notes: The President of the E.A.E.G. Safety Committee has stated that European geophysicists fail to attach sufficient importance to accident statistics. Nevertheless these statistics are the best means at our disposal for the study of the factors influencing the number and severity of accidents.It appears essential that two points should be stressed, firstly that the accident reports must be completed correctly, and secondly that the interpretation of each report and of the statistical data must be done systematically.If these conditions are fulfilled it should be possible to create, at all levels, a technical and psychological atmosphere which would do much to protect geophysicists against accidents.

Notes: 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.

Notes: When gravimetric prospecting is concerned with a region featuring broken relief the calculation of topographical corrections becomes vitally important, for these rectify apparent anomalies completely. It is essential that they should be calculated as exactly as possible. By the classic method this takes an extremely long time and may in the long run involve an outlay actually higher than that expended on operations on the terrain.It has thus been felt necessary to seek methods which would speed up calculation, and, bearing that in mind, the use of a polar integrator has been envisaged. With this the contour lines of a map can be followed between two fixed radii, the pole corresponding to the location of the position. Two integrator roulettes will give the values of the first two terms of the expansion in terms of the quotient of the height divided by the distance, the second of the terms resulting from the curvature of the earth. Unless there are escarpments very close to the position, the use of these two terms will be sufficient.Polar integration will deal successively with different contour lines and a subsidiary graph will be plotted, giving the value of each of the integrals in terms of the height. By means of this subsidiary graph the values of the corrections will be obtained with a planimeter and a moment integrator. It is envisaged that the same operation could be repeated in the case of two maps with different scales, for instance, 1–20,000 and 1–200,000 the effect of the areas in the immediate neighbourhood of the position being taken into account by the observer. It is hoped that in this way the calculation of topographical corrections will be made quicker, more exact and less laborious.

Notes: The problems connected with reflexion surveys in areas of rough topography consist of choosing proper equipment and of making careful near-surface corrections. This paper illustrates some solutions to these problems that have been adopted in a survey which has recently started in a hily coastal area, in Southern Italy.As the area is characterized by a youthful and very actively eroded topography of Post-Miocene clays and litoral clastic sediments, both rotary and percussion drilling were necessary whilst all the seismic equipment had to be light to allow straight lines to be shot as far as possible. Details are given of the truckmounted, light equipment which has been designed for this special purpose.In connection with the youthful topography of the area being surveyed, the criteria for the proper computation of the near-surface corrections is discussed. The great differences in elevation, combined with variations in the surface and near-surface materials, necessitated a careful analysis before deciding the thickness of the correction zone. The results are shown of the preliminary tests carried out in order to determine the average thickness of the low-velocity zone. The solution adopted for drawing the reference surface determining the base of the correction zone for the whole of the area is subseqently explained.Reference datum is drawn so as to follow gently, and with segments of constant slopes, the general features of the rough topographic relief at a depth ranging from 30 to 60 metres from the surface. Criteria for the routine checking of velocity variations in the correction zone are illustrated. Such checks are based on both uphole time analyses and refraction “first breaks” plots, with deeper shot holes at constant intervals.Unsatisfactory results necessitate longer spreads for “low velocity tests” and uphole shooting from deeper holes and the reference datum is deepened for the particular area where this becomes necessary.The final cross-sections are shown and although, as yet, no deep holes, are available to check the seismic data, the general appearance of the cross-sections seems to indicate that subsurface data are free from the influence of topography and of the velocities in the near-surface formations.

Notes: The paper describes the determination of the chlorine content of deep ground water by means of the direct resistivity method using the Wenner electrode configuration. The purpose was to investigate the distribution of salinity in the brackish waters within a permeable sand of thickness 250 metres and which forms the deeper subsoil of the Ysselmeer areas.Such a knowledge is of great value, firstly because the seepage of salt water into the proposed deep “polders” may reduce the crop yield, and secondly because it allows areas, where potable waters may occur, to be delineated.To test the method, measurements were made near existing boreholes which extended to a depth of 350 metres. From these borings water samples from various depths were collected and it was found that the resistivity pl of the porewater was closely related to their chlorine content. The resistivity p of the saturated sand was determined from the geo-electrical measurements. It was found that the resistivity p was given by p= 4, 5 pl. From this relation, which is independent of the salinity, the chlorine content of the porewater could be estimated. These results are in close agreement with those of other observers. In the area p varied from 1 to 200 ohmmetres corresponding to a chlorine content changing from 12.000 to 15 mg per litre.The method was adapted for working over water. Each of fourteen insulated conductors in a special cable terminated in an electrode, and these electrodes were spaced along the cable so that nine different Wenner spacings could be selected. The electrode separations varied from 44 metres up to 306 metres.

Notes: 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.

Notes: Specific electrical resistivity of natural waters contains information on their genesis. The authors propose to conduct mass and regime observations of this parameter in river and stream beds.The electrical resistivities in streams flowing from under a glacier reveal details formed at the same time as the glacier. Observations in the beds of big rivers show a gradual increase in water salinity overlain by reductions by inflowing glacial waters.The diurnal and annual trend of changes in the electrical conductivity of water associated with the change in the balance of glacial and ground waters has been established near to glaciers.Resistivity observations help to locate discharge sites of sub-permafrost waters, for water.

Notes: The VLF response of laterally inhomogeneous and anisotropic models is calculated numerically using the finite element method.Some results are presented for a slab model in terms both of the polarization parameters, i.e., the tilt angle and ellipticity of the magnetic polarization ellipse, and the amplitude ratio |Hz/Hx|.On the basis of both the ellipticity and the tilt angle, it is possible to discriminate between a poor conductor and a good one. The direction of the dip can be determined from the anomaly profiles of all diagnostic parameters. The effect of the conductive overburden is most noticeable on the ellipticity profile: one observes attenuation for a poor conductor and “negative attenuation” for a good conductor. The anomaly profiles for anisotropic cases are consistent with the ones of the isotropic cases.

Notes: Master curves are presented for three-layer earth-sections, the electrical resistivity in the intermediate layer of which has a linear variation with depth. A new approach is proposed to interpret the sounding data with the help of RMS difference in apparent resistivity values.

Notes: Basic Laterolog devices employ a measure-current focusing technique to provide well logs of formation resistivity that feature sharp vertical definition combined with a depth of investigation much improved over those of normals of comparable spacings.To develop the concept of measure-current focusing, a disk-electrode arrangement analogous to a guard-ring capacitor is considered first, leading finally to consideration of a real sonde in a cylindrical borehole. In the latter, auxiliary currents are adjusted to maintain substantially at zero the vertical potential gradients above and below the central measure-current electrode; this has the effect of focusing the measure-current beam.However, prediction of sonde responses on the basis of current patterns can in some cases be misleading. Indeed, for a given Laterolog array, one may use a (reciprocalmode) current pattern radically different from the one defined by the basic (direct-mode) measure-current focusing scheme and still obtain the same resistivity measurement. This feature is illustrated for Laterolog 3 by use of transfer impedances, and demonstrated for certain more general cases using the reciprocity theorem.Comparisons of Laterolog responses across typical thin beds, both non-invaded and invaded, with those of normal devices of a comparable range of spacings illustrate the improved vertical resolution obtained with Laterolog devices. The examples also show the different magnitudes of the auxiliary currents (thenceforth designated “bucking”- or “focusing” currents) used in the direct and reciprocal modes and illustrate how these currents must continuously vary in order to maintain the focused condition as the sonde moves through the bed.Finally, briefly considering possible applications of Laterolog-type arrays in surface prospecting, it is shown that a one-dimensional array laid out on the surface does not provide the same degree of measure-current focusing as is obtained in a borehole. Some improvement is obtained with a combination of two crossed linear arrays. Much more is obtained using a circular array.

Notes: Inferior reflection quality in the Gulf of Suez at the target depth interval is attributable in part to surficial multiple reflections. An excellent example of the latter is observed on a typical seismic line in the northern portion of the Gulf. An increase in prominence of the multiple reflections appears associated with decreasing depth to a dipping highvelocity layer.Inversion of a second-order polynomial time-distance function, fitted to the observed refraction onset time-distance values, gives the velocity-depth function for sediments between the water bottom and a high-velocity layer. Velocities thus determined increase non-linearly with depth from a value near water velocity at the water bottom. Depths to the high-velocity layer are obtained from the associated head-wave linear time-distance function and by ray tracing in the overlying sediments.As the high-velocity layer approaches the water bottom from sub-water depths exceeding 0.6 km to a depth of 56 m, intensity of the multiple reflections increases to the extent of completely dominating individual records to a time of at least 3 s. The estimated plane-wave normal-incident reflection coefficient at the top of the high-velocity layer increases with decreasing depth to this layer, approaching 0.5 at the shallowest depth. This strong reflection coefficient further substantiates the existence of multiple reflections between the high-velocity layer and water layer. However, existence of water-layer multiples cannot be ruled out. The estimated water-bottom reflection coefficient is approximately 0.3, a substantial value. Multiple reflections of considerably less intensity are apparent where the high-velocity layer is deepest, and it is likely that such are waterlayer multiple reflections. Unfortunately, water-layer multiple reflections and multiple reflections between the water surface and high-velocity layer cannot be separated by their coincidence with time-distance (normal moveout) curves, the configuration of each visibly matching the curves equally well.

Notes: Seismic exploration techniques which have been developed for oil prospecting contribute a valuable means for surveying coal measures. Since the object is to detect minor faults within the first 1500 m, rather than structural features at great depth, the new technique requires much higher resolution in the early part of the traditional seismic cross-section.Higher resolution means broader bandwidth, which must be obtained by extending the high frequency end of the spectrum. This is achieved (a) by scaling down the explosive charge size and using single geophones instead of groups, and (b) by reducing the sampling interval in space and time. Noise which does not scale down includes static anomalies and ground-roll. The consideration of statics, ground-roll, and the high-cut filtering effect of the near surface layers forces the use of deep shot holes and, where possible, deep detectors. This approach is confirmed by experiments and has been implemented on a regular basis in production.It is demonstrated that the present technique will clearly resolve faults with a vertical throw of about 5 m at 800 m depth.

Notes: Correlations between longitudinal velocities and rock mechanic parameters such as fracture frequencies and “Rock Quality Designation” (RQD) values have been studied, based upon velocity data from various rock types and different geographical locations.The dispersion of values at different sites studied is on average ± 0.8 cracks per meter and for the RQD values ± 3.5%. Within sites the dispersion of individual values relative to the average for the site is ± 1.0 – 2.0 cracks per meter and ± 2 – 6% for the RQD values.The deviations are rather moderate, especially when considering the variation of rock type involved in the studies: amphibolite, granite, gneiss, meta-anorthosite, pegmatite, porphyry, quartzite, and mylonite. The studies thus confirmed earlier assumptions that there is a strong correlation between longitudinal velocity and fracturing and that the velocities can be used to give rather accurate predictions of the quality of rock masses for construction purposes. The accuracy of the predictions increases if the velocity level of the more competent rock is taken into account.The correlation between velocity and fracturing is related to jointed but unweathered igneous and metamorphic rock and cannot be applied without introducing serious errors to a site where the rocks present a higher degree of alteration and weathering.Comparisons between rock permeability and longitudinal velocity proved that a more reliable general correlation is not likely to be found.By comparing the elastic moduli Edyn, μ, and k with ø, Vp/V8, and k/μ, indications have been obtained where the optimum rock conditions for a certain site are to be encountered. This has been verified by a similar comparison where the elastic moduli have been replaced by fracturing values.The value of the longitudinal velocity as a means to evaluate rock quality increases if the position of the velocity in the range of the Poisson's ratio has been established.The average relationships between longitudinal velocities and the corresponding elastic moduli proved to be:The values from each site differ from the average values with about ± 2 GPa for Edyn and about ± 1 GPa for μ and k.It was confirmed that in igneous and metamorphic rocks longitudinal velocities ≤ 4000 m/s generally indicate rock masses where heavier tunnel support will be needed. This velocity limit corresponds to an average fracture frequency of about 10 cracks per meter and a RQD value of about 65 %. The prediction of the tunnel reinforcements needed at a particular site will, however, be improved if the general velocity level of the more competent rock is considered.

Notes: The Minimum Entropy Deconvolution (MED) technique of Wiggins (1977) represents a breakthrough in deconvolution and will undoubtedly find wide application in many fields. MED does not require any phase assumptions about the disturbing function and seeks a deconvolved output which consists of the smallest number of large spikes consistent with the input data.The efficiency of MED is much improved when an exponential transformation is incorporated into the algorithm. This is particularly true when the input traces contain additive noise. In this case the noise suppression characteristics of MED are considerably enhanced by the transformation and the identification of smaller spikes is improved. This paper also presents a kurtosis criterion of simplicity rather than the varimax norm introduced by Wiggins. It appears that for a multiple trace input the kurtosis measure leads to improved results.

Notes: Long leg multiples can be suppressed by a method which provides an alternative to weighted common-depth-point stacking and multichannel stacking filtering. The suppression is achieved by coherency weighting whereby the time-dependent weighting factor decreases as the semblance of the multiple reflections increases.The algorithm of the method is described. Its efficiency is discussed in relation to the input data and results of its application to marine seismic data are presented.For practical application, the stacking velocity of the multiples has to be known. As the process is based on stacking velocities, different types of multiples can be handled, for instance water-bottom multiples or internal multiples. The parameter analysis shows that the degree of multiple suppression can easily be controlled by adapting the parameters of the procedure to the field conditions.During the suppression of multiples, the primaries are saved according to the moveout differences between the two. The non-linear behaviour of the process causes signal suppression and distortion effects, which have to be corrected by AGC normalization and low-pass filtering.Among the various applications available, only the suppression of long leg water-bottom multiples is treated here. The results show that their suppression on the basis of moveout differences is efficient even when standard length streamers are used in regions with water depth of up to 1500 m and more, if the stacking velocity of the primaries is about 10 to 20% higher than that of the multiples. Even if those parts of the primaries which are masked by the multiples are suppressed in the individual common-depth-point gathers by the procedure, the remaining primaries in the AGV stacked section are largely uncovered by the multiple suppression.

Notes: Investigation of fluctuating earth-currents has led to a simple method of eliminating the noise superimposed on the signal in geoelectrical resistivity surveys. The similarity of the potential fluctuations, simultaneously measured at different locations, is used to calculate the direction and magnitude of the potential gradient. Contour maps of equipotential lines were made, both from disjointed gradient measurements using a numerical approximation method and from a network of measured potential differences. These contour maps were compared with potential fields calculated for simple homogeneous models. A good fit was obtained with the field of a conducting plate. When this is subtracted from the measured field, the result is a map that shows anomalies that can be correlated with geological structures.

Notes: The calculation of potential field anomalies on different levels below the measuring level permits to localize the singular points related to the sources of anomalies.It is possible to achieve considerable improvement of the resolution of this method〈list xml:id="l1" style="custom"〉1) filtering of analytical downward continuation,2) the use of the magnitude of the gravitational vector,3) calculation of physe changes.The numerical examples confirm these assumptions.

Notes: The method of finite differences is applied to the computation of multi-dimensional synthetic seismograms. This paper gives a study of the mathematical and numerical formulations of the problem, the boundary conditions, the convergence conditions and how to simulate the source in both one solid or a liquid. It is shown that the numerical formulation chosen is valid both for direct and inverse problems (i.e. for modeling and migration). This formulation makes it possible to use the normal incidence reflection coefficients for P and S waves, whether they travel horizontally or vertically. The examples shown have been chosen on purpose in order to be easily interpreted. They do not give a full idea of the possibilities of the algorithm which allows to consider non-planar interfaces, except close to the vertical axis.

Notes: Finite difference migration has been developed and popularized by J. F. Claerbout of Stanford University and is now widely used in seismic processing. For most sections finite difference migration gives results comparable to those obtained by conventional Kirchhoff migration and, where events are not dipping too much, a cleaner appearance is often apparent. However, there are two practical limitations to the method, and these occur in regions of very steep dip and where there is a large variation of the velocity in the lateral direction.It is possible to develop successively more accurate equations to deal with the steep dip problem, but above third order these schemes become prohibitively expensive to implement. The finite difference method itself introduces errors and so imposes further limitations on the angle of dip. For the effective treatment of steeply dipping beds there appears to be no method available in the time domain which does not suffer from dispersion inaccuracies. However, by developing wavenumber migration, an exact one-way wave equation can be used, and this eliminates any error except that caused by finite sampling.The other difficulty with wave migration is the correct migration in regions with lateral velocity variation. A number of approaches are possible of which three are discussed here. The first uses an exact theory, the second is based on the deviation from a depth stratified model, and the third uses a transformation to a depth co-ordinate system. All methods are discussed with their advantages and limitations. Finally, some examples are shown of wave migration applied to synthetic and real data.

Notes: In seismic refraction surveys, in particular those using first arrival recording techniques, the hidden layer problem occurs where energy from a refractor of higher velocity arrives at the surface before energy from an overlying refractor. The maximum thickness of the hidden layer is referred to as the blind zone.Hypothetically, every recorded refractor has an associated blind zone which may or may not contain a hidden layer. For an assumed earth model of plane constant-velocity layers and stepwise increase of velocity with depth, the effect of a blind zone on an interpreted depth section may be evaluated by defining an intercept time for a blind zone of assumed or known velocity and by using standard time-term equations for layer thicknesses and depths.The treatment covers an arbitrary number of blind zones embedded within a multilayer sequence of horizontal or dipping refractors. Model calculations affirm the benefits of this approach compared with previous methods which, in general, have been restricted to the case of two horizontal layers with one intermediate blind zone.

Notes: For a thin highly-conducting layer with given longitudinal conductance the recurrence formulae for an n-fold horizontally stratified subsoil are established for d.c. resistivity and magnetotelluric soundings. Similarly, a thin low conductivity layer with given transverse resistance is treated in the d.c. case and a non-conducting intermediate bed in magnetotellurics. Model curves for a thin high- or low-conductivity intermediate layer in the three-layer case have been carried out, which may serve as an extension of the well-known three-layer diagrams for a Schlumberger configuration. The corresponding model curves in magnetotellurics are given.By numerical comparison of these curves with real three-layer curves some diagrams have been developed to show the allowed thicknesses of the intermediate layer in the Schlumberger case and in the case of magnetotelluric sounding.

Notes: Four radar systems at three different frequencies are described which are useful in probing into salt for finding information of interest to miners. Ranges in salt to (a) the edge of a salt dome, (b) the top of the salt dome, (c) boreholes in salt, or (d) faults or hazards ahead of mining can be determined using one or more of these radar systems. Radar wave velocities in salt are determined by radar probing through pillars of known length, and then used to determine ranges in salt to timed radar reflections. Radar probing results are shown obtained in different salt mines probing upwards and downwards. Enclosed areas in the mine are the best radar station locations to probe into salt as air reverberation of radar energy is shortened.

Notes: A simple extension of our previous work in which digital filters were developed to transform dipole resistivity measurements over layered earth to Schlumberger ones leads us to the development of filters for transforming the latter to the former. As in the previous work we use a sampling interval of 1/6 In 10 in designing the filters that are both accurate and fast in operation.

Notes: Seismic facies analysis makes use of different seismic parameters in order to get other than structural information. A review is given of possibilities and usefulness of seismic facies analysis in oil exploration.A seismic facies unit can be defined as a sedimentary unit which is different from adjacent units in its seismic characteristics. Parameters that should be taken into consideration in the seismic facies analysis are as follows: reflection amplitude, dominant reflection frequency, reflection polarity, interval velocity, reflection continuity, reflection configuration, abundance of reflections, geometry of seismic facies unit, and relationship with other units.Interpretation of seismic facies data may be either direct or indirect. The purpose of the direct interpretation is to find out geological causes responsible for the seismic signature of a seismic facies unit. So, the direct interpretation may be aimed at predicting lithology, fluid content, porosity, relative age, overpressured shales, type of stratification, geometry of the geological body corresponding to the seismic facies unit and its geological setting. The indirect interpretation is intended to reach some conclusions on depositional processes and environments, sediment transport direction, and some aspects of geological evolution (transgression, regression, subsidence, uplift, erosion).The results of the seismic facies analysis may be shown on seismic facies cross-sections and seismic facies maps. Depending on the available seismic data and geological conditions in the area under consideration, the seismic facies maps may be of different types such as general seismic facies maps showing distribution of different seismic facies units, sand-shale ratio maps, direction of cross-bedding and paleo-transport maps etc.Several kinds of seismic facies units and their geological interpretation are discussed as examples of seismic facies analysis.

Notes: The reflectivity method for computing synthetic seismograms can be applied to seismic prospecting problems with special focus on coal-mining problems. The method allows the calculation of reflected waves for point-source excitation and non-vertical incidence. It automatically includes all possible conversions of wave types and all inner multiple reflections. Synthetic horizontal- and vertical-component seismogram sections are given for a simple two-seam model and for a realistic seam sequence which is represented by 48 layers; the source-receiver distances range from 100 m to 1000 m. These seismograms show prominent PS reflections already at moderate source-receiver distances. These waves complicate the vertical-component records by producing arrivals of similar strength as the PP reflections. From this it is concluded that PS reflections in strongly layered media can cause problems in routine CDP stacking. On the horizontal-component records the PS reflections are dominant. Because of the lower velocities of S waves the time resolution of PS reflections is better than that of PP reflections. This suggests that horizontal-component recording may be useful in the investigation of subsurface regions with strong velocity contrasts, even with conventional energy sources producing mainly P waves.

Notes: Expressions for the I. P. activity coefficient for an inhomogeneous sphere with the conductivity increasing/decreasing from the core towards the periphery according to a power law have been derived.In certain geometrical situations of the electrode configurations a negative I. P. signal is obtained. The negative I. P. may be understood as due to modifications in the discharge current from the polarized medium during the discharge process.The results of the investigation may be useful for more accurate interpretation of I. P. anomalies due to isometric inhomogeneous bodies.

Notes: Magneto-telluric experiments were performed in August 1974 in the Muhos Jotnian sedimentary formation and the Koillismaa Precambrian basement complex by the Centre de Recherches Géophysiques, Garchy, and the Department of Geophysics, University of Oulu, employing the “Résistivimètre magnéto-tellurique”, an instrument which permits apparent resistivity values to be observed at eight pre-selected frequencies between 8–1700 Hz.Preliminary soundings were made on the Muhos formation and on its surroundings, after which a magneto-telluric profile was measured involving eleven sites on a line 13 km long extending across the formation. Some further soundings were made at certain sites of known stratigraphy. The resistivity values in the sedimentary formation were found to vary between 10 ωm and 200 ωm, while those in the basement were markedly higher. This resistivity contrast suggests that the method seems to be suitable for delimiting the sedimentary formation.Soundings made on the basement at Koillismaa show apparent resistivity values in the range 1000–20000 ωm. The interpretation of these soundings was in agreement with other, independently obtained geophysical results.

Notes: Multispectral recordings used for remote sensing are not without analogy with seismic records from CDP field set-ups. These seismic data may be regarded as “photographs’ of deep regions of the earth taken from various angles.The Karhunen-Loève (K.L.) transformation is commonly used for multispectral data processing, where it helps emphasize some features of remote sensing information. The same method may be applied to seismic data processing. Signal-to-noise ratio is improved on synthetic or field examples when K.L. transformation is applied instead of conventional CDP stacking. Residual statics seem to be diminished by a significant factor.

Notes: A horizontally layered non-absorptive system of homogeneous layers may be specified by giving the reflection coefficients at each interface. Provided the layers have equal vertical travel time and a perfect reflector as a free surface, the reflection coefficients are generally reconstructed from the reflected pulses by way of solving simultaneous equations of the Toeplitz matrix form with the Levinson recursion method. There exists an alternative approach to solving this problem which by simple reasoning immediately turns out the (Levinson) recursion scheme. The method is based on formulas that relate to solving the forward problem. It resembles Kunetz's (1962) original inverse solution in as much as the computation of the reflection coefficients is based on the idea of separating the contribution of a primary from the sum of all multiples.

Notes: The magneto-telluric and telluric-telluric profiling techniques are presented, and then a new method which combines these two techniques for mapping a parameter defined as the “apparent pseudo-resistivity”.The results obtained for the uranium structures in the Cluff Lake district (Saskatchewan Canada) indicate the use of these different techniques in the detection of zones of conduction for surface zones and for deeper zones, and demonstrate the advantages of these methods over the usual electrical methods in problems of structural research.

Notes: The accuracy of the two most common arrival time functions used in seismic velocity estimation is investigated. It is shown that the hyperbolic arrival time function is more accurate than the parabolic arrival time function for a horizontally layered elastic medium. An upper bound on the difference between the two arrival time functions is given.A maximum-likehood detector for estimating the arrival time of the signals is given. For the signal-in-noise model that is used the maximum-likelihood detector is equivalent to a least-squares detector which corresponds to using the signal energy as coherency measure. The semblance coefficient corresponds to a normalized least-squares detector. The semblance coefficient is very similar to a filter performance measure that is used in least-squares filter design.

Notes: The proposed system works as follows:〈list xml:id="l1" style="custom"〉1By a trial-and-error procedure using a graphic display terminal a geologically relevant layer sequence with parameters (ρj, dj) is adjusted to yield roughly the measured curve.2The resulting layer sequence is used as starting model for an iterative least squares procedure with singular value decomposition. Minimization of the sum of the squares of the logarithmic differences between measured and calculated values with respect to the logarithms of the resistivities and thicknesses as parameters linearizes the problem to a great extent, with two important implications:〈list xml:id="l2" style="custom"〉a) a considerable increase in speed (the number of iterations goes down), thus making it cheap to achieve the optimum solution;b) the confidence surfaces in parameter space are well approximated by the hyper-ellipsoids defined by the eigenvalues and eigenvectors of the normal equations.Since these are known from the singular value decomposition we do in fact know all possible solutions compatible with the measured curve and the geological concept.〈list xml:id="l3" style="custom"〉3It is possible to “freeze” any combination of parameters at predetermined values. Thus extra knowledge and/or hypotheses are easily incorporated and can be tested by rerunning step (2). The overall computing time for a practical case is of the order of 10 sec on a CDC 6400.

Notes: Ott and Meder's prediction error filter can be rederived so that it correctly handles input noise vectors which are of smaller dimension than the state vector. The poor performance obtained by Ott and Meder for their example can be explained by means of the error covariance matrix for the prediction error filter.

Notes: The geological sequence rock-coal-rock represents a seismic low-velocity channel. Channel waves generated in a coal seam and their reflections from discontinuities can be used for proving the minability of the seam. To investigate the process of reflection, two-dimensional models of the sequence rock-coal-rock have been investigated by means of the ultrasonic transducer technique. Two-dimensional models have the advantage that the wave field can be observed at an arbitrarily chosen point of the model plate. Thus, by means of these models the direct and the reflected Rayleigh channel wave can be observed along their path of propagation.From the geophysical point of view the various types of discontinuities of a coal seam can be divided into two basic types: one is restricted to the seam, the other includes in addition a fractured zone in the adjoining rock.The investigation of the symmetrical Rayleigh channel wave reflected by a discontinuity yields the following results:For dip angles γ between approximately 90° and approximately 60° the reflectivity is virtually independent of the type of discontinuity. This does not hold for the limiting case of γ= 90° (vertical dip) for which the reflectivity increases with increasing influence of the fractured zone. For dip angles γ between approximately 60° and approximately 40° the reflectivity is still independent of the fractured zone but the shape of the reflected wave deteriorates with increasing influence of the fractured zone.For dip angles γ below approximately 40° the reflected wave deteriorates such that the application of the in-seam seismic reflection method will be difficult or even impossible.The conversion of the direct wave of the symmetrical fundamental mode into a reflected wave of the antisymmetrical fundamental mode has been observed.

Notes: Analytical solutions exist for the potential of a Point Source in media with depth dependent conductivity of the form σ(z) =σ0(1 +αz)n.Of particular importance is the case of the linear gradient (n= 1). More general distributions of conductivity with depth can be approximated by equivalent sequences of homogeneous layers. Comparison between such approximations and the analytical solution for media with linear gradient of conductivity indicates that already a coarse step function yields a reasonably good approximation.

Notes: The contribution of electromagnetic phase comparison techniques to distance measuring is reviewed in an historical context. Special emphasis is accorded the new class of near infra-red electro-optic instruments suited to the measurement of distances under 2 km with an accuracy of a few millimetres. Principles of operation, sources of error, and practical applications are discussed.

Notes: A magnetotelluric digital equipment has been designed and built for operation in geophysical and applied geophysical research. The five components of the natural electromagnetic field can be digitized in the frequency range 1/1000 Hz (magnetic sensor's response limits) to some tens Hz.The magnetotelluric (MT) data are directly digitized in the field and stored in a cassette tape recorder.

Notes: An electromagnetic frequency sounding experiment with a rigid horizontal transmitter coil carrying a stabilized oscillating current was carried out in South Tunesia.The field data were interpreted in terms of the mutual impedance ratio in the horizontal coils system. Where the measurements were sufficiently accurate they generally could be interpreted to a high degree of fit. It is concluded that a vehicle-mounted electromagnetic frequency sounding system is suitable for a fast survey.

Notes: The application of approximate rules, whereby apparent resistivity space sections for two dimensional structures can be composited from spaces derived for elementary features is extended to a complex example drawn from a field survey over a fluorite mineral vein.A quantitative solution for the observed resistivity space is presented and the computational sequence involved in matching the observed space is given in detail.The interpreted results are examined in relation to the known geology, supplemented by the results of excavation, and to model tests conducted using a tank analogue.The example also illustrates how successive compositions can be employed in estimating the form of resistivity space in a relatively complex situation.

Notes: The sampling theorem in two dimensions univocally defines a surface, provided that its values are known at points disposed on a regular lattice. If the data are irregularly spaced, the usual procedure is first to interpolate the surface on a regular grid and then to contour the interpolated data: however, the resulting surface will not necessarily assume the prescribed values on the irregular grid.One way to obtain this result is to introduce a transformation of the coordinates such that all the original data points are transferred into part of the nodes of a regular grid. The surface is then interpolated in the points correspondent to the other crosspoints of the regular grid; the contour lines are determined in the transformed plane and then, using the inverse coordinate transformation, are transferred back to the original plane where they will certainly be congruent with the original data points.Nonetheless, the resulting surface is very sensitive to the interpolation method used: two algorithms for that are analyzed. The first (harmonization) corresponds to the determination of the potential of an electrical field whose contour conditions are those defined by the data points. The second method consists in two dimensional statistical estimation (krigeing); in particular, the effects of different choices for the data auto-covariance function are discussed.The solutions are compared and some practical results are shown.

Notes: Optimum stacking filters based on estimates of trace signal-to-uncorrelated noise ratios are assessed and compared in performance with conventional straight stacking. It is shown that for the trace durations and signal bandwidths normally encountered in seismic reflection data the errors in estimating signal/noise ratios largely counteract the theoretical advantages of the optimum filter. The more specific the filter (e.g. the more frequency components included in its design) the more this is true. Even for a simple weighted stack independent of frequency, the performance is likely to be better than a straight (equal weights) stack only for relatively high signal/noise ratios, when the performance is not critical anyway.

Notes: An approximate method of interpretation of resistivity sounding is presented, which may be described as a very crude manner of application of the exact direct interpretation method. The accuracy of this method is fairly low, the errors being in the order of 25%. The method is very fast in application and well suited for application to multilayer cases. The main advantage of the method is that it is in close and clear relation to the exact theory.

Notes: Electromagnetic coupling in grounded electrical prospecting systems has been studied over four decades. Recently, advanced digital electronic systems have been developed which permit both magnitude and phase measurements over four frequency decades (10−2— 102 Hz). This development has stimulated theoretical studies demonstrating behavior of EM coupling for the more commonly-used electrical prospecting arrays a wide frequency range. A comparison is made between field and theoretical results which demonstrates the validity of the fundamental assumptions involved. Additionally electromagnetic coupling is used successfully as a deep-sounding technique in a highly-conductive sedimentary basin environment.

Notes: A polygonal ray path connects the seismic source and detector positions when the intervening medium consists solely of constant velocity layers with plane interfaces which may have arbitrary orientation. The coordinates of the ray vertices satisfy a system of coupled equations resulting from the requirement that Fermat's principle be satisfied along the ray path. Solving the system of equations is equivalent to tracing the ray numerically. A notable feature of this approach is that a ray which is critically refracted over a segment of its path requires no special handling.

Notes: A satisfactory attenuation of the multiples in marine seismic may be obtained by the application of the principle of “Antiaveraging”.This principle in a first step consists in getting the model of the organized noise, which one tries to eliminate by using an averaging method, and in a second step to subtract that model from the initial information.Obviously the elimination of the model should not simultaneously cause the elimination of useful signals.The model may be obtained if the considered organized noise keeps a constant shape or if its time-space deformation is known. Besides one has to assume the time-distance curve of the organized noise can be determined. Thus noise arrivals may be detected on the records.The “antiaveraging” is very often efficient when organized noises are stronger than signals or when a signal, once identified, exploited and then considered as an organized noise, can be attenuated in order to make the detection of the other signals easier.