摘要:

AbstractI.IntroductionIn this section the problem is stated, its physical and mathematical difficulties are indicated, and the way the authors try to overcome them are briefly outlined.Made up of a few measurements of limited accuracy, an electrical sounding does not define a unique solution for the variation of the earth resistivities, even in the case of an isotropic horizontal layering.Interpretation (i.e. the determination of the true resistivities and thicknesses of the ground‐layers) requires, therefore, additional information drawn from various more or less reliable geological or other geophysical sources. The introduction of such information into an automatic processing is rather difficult; hence the authors developped a two‐stage procedure:a) the field measurements are automatically processed, without loss of information, into more easily usable data;b) some additional information is then introduced, permitting the determination of several geologically conceivable solutions.The final interpretation remains with the geophysicist who has to adjust the results of the processing to all the specific conditions of his actual problem.II.Principles of the procedureIn this section the fundamental idea of the procedure is given as well as an outline of its successive stages.Since the early thirties, geophysicists have been working on direct methods of interpreting E.S. related to a tabular ground (sequence of parallel, homogeneous, isotropic layers of thicknesseshiand resistivitiesρi). They generally started by calculating the Stefanesco (or a similar) kernel function, from the integral equation of the apparent resistivity:whereris the distance between the current source and the observation point, S0the Stefanesco function, ρ(z) the resistivity as a function of the depthz, J1the Bessel function of order 1 and λ the integration variable. Thicknesses and resistivities had then to be deduced from S0step by step. Unfortunately, it is difficult to perform automatically this type of procedure due to the rapid accumulation of the errors which originate in the experimental data that may lead to physically impossible results (e.g. negative thicknesses or resistivities) (II. 1).The authors start from a different integral representation of the apparent resistivity:whereK1is the modified Bessel function of order I. Using dimensionless variablest = r/2h0andy(t)=ζ (r)/ρ1and subdividing the earth into layers of equal thicknesses h0(highest common factor of the thicknesseshi), ø becomes an even periodic function (period 2π) and the integral takes the form:The advantage of this representation is due to the fact that its kernel ø (function of the resistivities of the layers), if positive or null, always yields a sequence of positive resistivities for all values of θ and thus a solution which is surely convenient physically, if not geologically (II.3). Besides, it can be proved that ø(θ) is the Fourier transform of the sequence of the electric images of the current source in the successive interfaces (II.4).Thus, the main steps of the procedure are: a) determination of a non‐negative periodic, even function ø(θ) which satisfies in the best way the integral equation of apparent resistivity for the points where measurements were made; b) a Fourier transform gives the electric images from which, c) the resistivities are obtained. This sequence of resistivities is called the “comprehensive solution”; it includes all the information contained in the original E.S. diagram, even if its too great detail has no practical significance.Simplification of the comprehensive solution leads to geologically conceivable distributions (h, ρ) called “particular solutions”. The smoothing is carried out through the Dar‐Zarrouk curve (Maillet 1947) which shows the variations of parameters (transverse resistanceRi= hi.ρi–as function of the longitudinal conductanceCi=hi/ρi) well suited to reflect the laws of electrical prospecting (principles of equivalence and suppression). Comprehensive and particular solutions help the geophysicist in making the final interpretation (II.5).III.Computing methodsIn this section the mathematical operations involved in processing the data are outlined.The function ø(θ) is given by an integral equation; but taking into account the small number and the limited accuracy of the measurements, the determination of ø(θ) is performed by minimising the mean square of the weighted relative differences between the measured and the calculated apparent resistivities:minimum with inequalities as constraints:wheretlare the values oftfor the sequence of measured resistivities andplare the weights chosen according to their estimated accuracy.When the integral in the above expression is conveniently replaced by a finite sum, the problem of minimization becomes one known as quadratic programming. Moreover, the geophysicist may, if it is considered to be necessary, impose that the automatic solution keep close to a given distribution (h, ρ) (resulting for instance from a preliminary interpretation). If φ(θ) is the ø‐function corresponding to the fixed distribution, the quantity to minimize takes the form:where:The images are then calculated by Fourier transformation (III.2) and the resistivities are derived from the images through an algorithm almost identical to a procedure used in seismic prospecting (determination of the transmission coefficients) (III.3).As for the presentation of the results, resorting to the Dar‐Zarrouk curve permits: a) to get a diagram somewhat similar to the E.S. curve (bilogarithmic scales coordinates: cumulativeRandC) that is an already “smoothed” diagram where deeper layers show up less than superficial ones and b) to simplify the comprehensive solution.In fact, in arithmetic scales (RversusC) the Dar‐Zarrouk curve consists of a many‐sided polygonal contour which múst be replaced by an “equivalent” contour having a smaller number of sides. Though manually possible, this operation is automatically performed and additional constraints (e.g. geological information concerning thicknesses and resistivities) can be introduced at this stage. At present, the constraint used is the number of layers (III.4).Each solution (comprehensive and particular) is checked against the original data by calculating the E.S. diagrams corresponding to the distributions (thickness, resistivity) proposed. If the discrepancies are too large, the process is resumed (III.5).IV.ExamplesSeveral examples illustrate the procedure (IV). The first ones concern calculated E.S. diagrams, i.e. curves devoid of experimental errors and corresponding to a known distribution of resistivities and thicknesses (IV. 1).Example I shows how an E.S. curve is sampled. Several distributions (thickness, resistivity) were found: one is similar to, others differ from, the original one, although all E.S. diagrams are alike and characteristic parameters (transverse resistance of resistive layers and longitudinal conductance of conductive layers) are well determined. Additional informations must be introduced by the interpreter to remove the indeterminacy (IV.1.1).Examples 2 and 3 illustrate the principles of equivalence and suppression and give an idea of the sensitivity of the process, which seems accurate enough to make a correct distinction between calculated E.S. whose difference is less than what might be considered as significant in field curves (IV. 1.2 and IV. 1.3). The following example (number 4) concerns a multy‐layer case which cannot be correctly approximated by a much smaller number of layers. It indicates that the result of the processing reflects correctly the trend of the changes in resistivity with depth but that, without additional information, several equally satisfactory solutions can be obtained (IV. 1.4).A second series of examples illustrates how the process behaves in presence of different kinds of errors on the original data (IV.2).A few anomalous points inserted into a series of accurate values of resistivities cause no problem, since the automatic processing practically replaces the wrong values (example disturbed (IV.2.1).However, the procedure becomes less able to make a correct distinction, as the number of erroneous points increases. Weights must then be introduced, in order to determine the tolerance acceptable at each point as a function of its supposed accuracy. Example 6 shows how the weighting system used works (IV.2.2).The foregoing examples concern E.S. which include anomalous points that might have been caused by erroneous measurements. Geological effects (dipping layers for instance) while continuing to give smooth curves might introduce anomalous curvatures in an E.S. Example 7 indicates that in such a case the automatic processing gives distributions (thicknesses, resistivities) whose E.S. diagrams differ from the original curve only where curvatures exceed the limit corresponding to a horizontal stratification (IV.2.3).Numerous field diagrams have been processed (IV. 3). A first case (example 8) illustrates the various stages of the operation, chiefly the sampling of the E.S. (choice of the left cross, the weights and the resistivity of the substratum) and the selection of a solution, adapted from the automatic results (IV.3.1). The following examples (Nrs 9 and 10) show that electrical prospecting for deep seated layers can be usefully guided by the automatic processing of the E.S., even when difficult field conditions give original curves of low accuracy. A bore‐hole proved the automatic solution proposed for E.S. no 10, slightly modified by the interpreter, to be correc

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1970.tb02102.x

出版商:Blackwell Publishing Ltd    

年代:1970

数据来源: WILEY

摘要:

AbstractA simple measure, the association parameter, is proposed for directly comparing the results of two electrical soundings. The use of this measure to classify field results and to gain some insight into geological structure before extensive depth interpretation is discussed. In particular it is shown that when used with soundings conducted using the tripotential technique the combined use of association parameter arid lateral inhomogeneity index can allow structural patterns to be discerned where otherwise they might be obscured.Possible extension of the technique is considered.

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1970.tb02103.x

出版商:Blackwell Publishing Ltd    

年代:1970

数据来源: WILEY

摘要:

AbstractThis paper describes certain procedures for deriving from the apparent resistivity data as measured by the Wenner electrode configuration two functions, known as the kernel and the associated kernel respectively, both of which are functions dependent on the layer resistivities and thicknesses. It is shown that the solution of the integral equation for the Wenner electrode configuration leads directly to the associated kernel, from which an integral expression expressing the kernel explicitly in terms of the apparent resistivity function can be derived. The kernel is related to the associated kernel by a simple functional equationwhereK1(λ) is the kernel andB1(λ) the associated kernel.Composite numerical quadrature formulas and also integration formulas based on partial approximation of the integrand by a parabolic arc within a small interval are developed for the calculation of the kernel and the associated kernel from apparent resistivity data. Both techniques of integration require knowledge of the values of the apparent resistivity function at points lying between the input data points. It is shown that such unknown values of the apparent resistivity function can satisfactorily be obtained by interpolation using the least‐squares method. The least‐squares method involves the approximation of the observed set of apparent resistivity data by orthogonal polynomials generated by Forsythe's method (Forsythe 1956). Values of the kernel and of the associated kernel obtained by numerical integration compare favourably with the corresponding theoretical values of these func

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1970.tb02104.x

出版商:Blackwell Publishing Ltd    

年代:1970

数据来源: WILEY

摘要:

AbstractThe paper deals with the early stages of development of a convenient form of electromagnetic induction method of sounding referred to as ‘Central Frequency Sounding’ and abbreviated as CFS. The method is introduced as a rapid and useful technique for investigation of shallow engineering and hydro‐geological problems. Sets of theoretical two‐layer master curves, suitable for interpretation of field data involving measurement of the vertical magnetic component of the field induced at the center of a loop placed on a two‐layer earth, have been presented.The approximate but reasonably accurate solutions for a two‐layer earth of any arbitrary resistivity contrast have been considered for the purpose and expressed in a form suitable for computation. The computed results have been presented in sets of curves useful for interpretation of

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1970.tb02105.x

出版商:Blackwell Publishing Ltd    

年代:1970

数据来源: WILEY

摘要:

AbstractA high sensitivity thermometer using a thermistor sensing element was designed for practical measurements in the field.The most suitable procedures for the elimination of diurnal and seasonal variation of temperature, the influence of vegetation cover and of other effects were investigated.Positive results of geothermic measurements have been acquired on sulfide deposits. By far the most important results of geothermic measurements have been obtained in hydrogeological problems, e.g. the investigation of circulation of underground water. In the case of prospection for cold mineral waters the combination of geothermic measurements with gasometric analyses is very useful. As the classical domain for geothermic investigation, prospection for hot water is to be mentioned.

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1970.tb02106.x

出版商:Blackwell Publishing Ltd    

年代:1970

数据来源: WILEY

摘要:

AbstractWater seepage from reservoirs causes appreciable anomalies of natural electric fields. The possibility of mapping leakage places by means of the SP method has been discussed by the authors in an earlier report. Further work has shown that detailed measurements of the natural electric field allow to determine the seepage rates from individual areas of a water reservoir in relative units. If data on the total discharge from a water reservoir are available, the conventional seepage units can be converted into absolute ones. Using this technique on a water reservoir in Armenia has permitted to control the change of the leakage rate as hydroinsulation operations were in progress. It has been established that as a result of shielding the bottom with clay material leakage from the central part of the reservoir has stopped. On the other hand, construction of cement seepage‐proof protection has had so far no appreciable positive effec

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1970.tb02107.x

出版商:Blackwell Publishing Ltd    

年代:1970

数据来源: WILEY

摘要:

SummaryIt is pointed out that after identifying reflection events from the same horizon on two records obtained on the same spread from two different shotpoints, one can simultaneously estimate parameters of reflection events and relative static corrections. The parameters of reflection events are treated as quantities to compute whereas relative static corrections are treated as quantities to minimize by the least squares method. Static corrections obtained from different horizons for the same point on the spread are averaged.The case of more than one pair of records for the same spread (or part of the spread), vital for multiple coverage, is also discussed.

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1970.tb02108.x

出版商:Blackwell Publishing Ltd    

年代:1970

数据来源: WILEY

摘要:

AbstractTwo alternative types of diagrams are shown which allow the direct conversion of readings taken by certain types of proton magnetometers into magnetic field strength. The accuracy of these diagrams is discussed and found to satisfy the requirements.

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1970.tb02109.x

出版商:Blackwell Publishing Ltd    

年代:1970

数据来源: WILEY

摘要:

AbstractThe conditions for creating and recording converted waves in the area of the Panonien basin are considered. Comparison between the characteristics of converted waves recorded in the field and characteristics of converted waves calculated for the model which approximately corresponds to lithophysical conditions of the area is made.The comparative interpretation of the crustal structure along the profile, using different types of waves, is given.

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1970.tb02110.x

出版商:Blackwell Publishing Ltd    

年代:1970

数据来源: WILEY

摘要:

AbstractThe seismometer‐ground system is represented by a damped oscillatory system. Relatively simple approximation formulas are derived to express the coupling between ground and seismometer. These expressions are applicable in seismic exploration. The coupling is that of a mass, suspended by a spring, to the surface that the ground would have in absence of the seismometer. It results in a low‐pass filtering of the ground motion, which is due to the presence of the seismometer. This effect is expressed in a unit‐impulse response. It appears that, over a sufficiently homogeneous ground and for low frequencies, one has a true coupling between ground and seismometer. To obtain a sufficiently large pass‐band, a low seismometer housing‐mass together with a not too small housing radius are

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1970.tb02111.x

出版商:Blackwell Publishing Ltd    

年代:1970

数据来源: WILEY