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- Volume 27, Issue 3, 1979
Geophysical Prospecting - Volume 27, Issue 3, 1979
Volume 27, Issue 3, 1979
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REFRACTOR VELOCITY DETERMINATION—CAUSE AND NATURE OF SOME ERRORS*
By B. SJÖGRENAbstractFor detailed determination of refractor velocities of in‐line reversed profiles, two principally different systems have been employed, the ABC method and Hales's method. The two systems differ in the travel‐path arrangements used. The more conventional approach to the problem, the ABC method, makes use of critically refracted rays converging on a common surface position, while Hales's method deals with the common position on the refractor surface from which critically refracted rays diverge towards the ground surface.
Because of the travel‐path system used, Hales's method has proved to be particularly applicable to high‐relief structures and to cases where the refractor lies at considerable depth. Some of the ambiguities in more commonly used interpretation techniques can be solved by Hales's method.
Some attention has also been paid to errors caused by non‐critical refractions and to the diffraction problem.
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MULTIPLE REFLECTIONS AND HEAD WAVES IN THE GULF OF SUEZ*
More LessAbstractInferior 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.
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SYNTHETIC SEISMOGRAMS AT NON‐VERTICAL INCIDENCE*
By E. J. DOUZEAbstractSynthetic seismograms are usually computed for reflections from vertical incidence of P waves for a horizontally layered medium. In actual practice the angle of incidence departs from the vertical, as receivers are usually located at some distance from the source. At angles other than the vertical, the conversion of P‐ to S‐wave energy and changes in the reflection coefficient affect the shape of the synthetic seismograms. The effect of non‐vertical incidence on synthetic seismograms is examined in this paper.
Seismograms at non‐vertical incidence have been computed using the plane‐wave approach of Haskell (1953) for a layered medium. The use of plane waves is an approximation to the actual case of spherical wavefronts from a surface source.
Using plane‐wave theory, the expected wave forms as a function of angle of incidence were computed numerically for several simple models. The results indicate that the synthetic seismograms do not change significantly for angles of incidence between o and 25 degrees. For larger angles the changes in the wave forms may be severe. The effect is more pronounced for high‐velocity layers than for low‐velocity layers.
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TOWARDS UNIFICATION OF GEOPHYSICAL PROBLEMS FOR HORIZONTALLY STRATIFIED MEDIA*
By E. SZARANIECAbstractTheorems and relations describing a system of horizontal layers are considered as the elements of a meta‐system having a layered structure. This implies a layered structure of a solution of geophysical problems for horizontally stratified medium.
Wave equation, Laplace's equation, and Maxwell's equations are the special cases of a more general differential equation. By separation of variables the basic equation for layered structures is obtained.
A multi‐layer medium may result from accumulation of successive layers. The descending or ascending accumulation is possible, depending whether the successive layers are inserted at the top or at the bottom of the medium. The discretization of a basic equation provides two sets of formulas for descending or ascending accumulation, respectively.
The relationship between the mathematical expressions of the seismic transfer function and the magnetotelluric input impedance is derived. The deduction leads to the possibility of converting the magnetotelluric observations into an equivalent synthetic seismogram.
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THE SUPPRESSION OF SURFACE MULTIPLES ON SEISMIC RECORDS*
More LessAbstractA new approach is presented for the suppression of multiples reflected at the surface of a horizontally layered fluid or elastic medium, recorded at non‐zero offsets from the source. The scheme used is to extract the effect of the free surface in the frequency‐wavenumber domain and then to replace this surface by a non‐reflecting boundary. The multiple suppression operator requires a detailed knowledge of the source time function and the elastic properties of the medium between the source and the surface.
For a stratified fluid or a liquid layer overlying a stratified elastic medium, complete multiple suppression can be achieved with noise free data. If only the vertical component is available for an elastic medium an approximate approach may be used which removes most of the multiple energy. Good results may be achieved with this multiple suppression scheme in the presence of noise. The method is designed to be used before records are stacked in a CDP gather.
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NUMERICAL MODELLING OF A NEW MULTI‐FREQUENCY ELECTROMAGNETIC SYSTEM*
Authors T. LEE, R. L. RICHARDSON and K. VOZOFFAbstractThe amplitude of the horizontal magnetic field in the ground between two parallel wires, both carrying an alternating current in the same direction, is likely to have a saddle point if the separation between the wires is small and the frequency is low. The amplitude has a maximum in the vertical direction and a minimum in the horizontal.
Rectangular geological structures in the ground which are centered between the wires have a varying effect on the magnetic fields at the surface. In general, the vertical magnetic field “crosses over” at the center of the structure.
A shallow and flat lying conductor displays a broad flat type of profile when the horizontal magnetic field between the wires is measured. Changing the structure to a narrower but more conducting one at depth will provide a more pointed but still broad profile. The phase of the horizontal field is also increased.
When the structure is a thin vertical dyke, the amplitude of the horizontal magnetic field anomaly due to the dyke rapidly decreases as the depth of the dyke is increased. The phase of the horizontal field is less sensitive to changes in depth of the dyke but is more sensitive to the conductivity ratio of the dyke and the half‐space. The amplitude of the vertical magnetic field anomaly due to the dyke is only slightly influenced by conductivity contrast or the depth of the dyke. The phase of the vertical magnetic field, however, is strongly influenced by the conductivity contrast, particularly if the conductivity frequency product is greater than hundred.
In essence, the field behaves like that of the conventional vertical loop source, but the fields are uniform over much larger areas. This suggests the possibility of using dip angle measurements for rapid reconnaissance.
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CALCULATION OF GALVANIC EFFECTS BY MEANS OF THE METHOD OF SUB‐AREAS*
By L. ESKOLAAbstractA numerical method is proposed for solving the problem of steady current flow. The electrodynamic model is replaced by the equivalent stationary charge distribution obtained by Poisson's analysis, in which the surface integral equation for field intensity is reduced to a set of simultaneous linear algebraic equations by means of the method of sub‐areas. The solution of the set allows the calculation of an approximation for the charge density distribution on the discontinuity surfaces of conductivity.
The method is valid for complex conductivities, whereby the apparent phase shift of IP can be calculated from the complex potential or field intensity. The phase shift anomaly calculated as an application is very similar to the corresponding frequency effect anomaly.
The method allows the calculation of the mise‐à‐la‐masse effect as a solution to a potential problem, in which the primary current electrode is located within the body to be surveyed.
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DEFINITION AND APPLICATION OF THE FREQUENCY ‐EFFECT TRANSFORM FUNCTION TO THE INTERPRETATION OF IP SOUNDINGS*
By D. PATELLAAbstractThis paper deals with a new method of quantitative interpretation of induced polarization soundings in the frequency‐domain. From the general expression of the apparent frequency‐effect for soundings carried out on a multi‐layered earth the application of Hankel's inversion theorem allows to introduce a new function, called here the “frequency‐effect transform”. The new interpretation method consists of two steps: 1) the inversion of field data to obtain the frequency‐effect transform graph and 2) the analysis of this graph to derive the layering parameters. The first step is performed by means of a slightly revised version of a simple numerical procedure, previously suggested by the author for the inversion of d.c. resistivity sounding data. The second step is carried out by a complete curve‐matching procedure, applied directly on the transform graph. This implies suitable master curves, whose preparation doesn't meet all the mathematical difficulties which are present when preparing master curves of the apparent frequency‐effect function.
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THEORETICAL AND EXPERIMENTAL INVESTIGATIONS FOR CAVITY RESEARCH WITH GEOELECTRICAL RESISTIVITY METHODS*
Authors H. MILITZER, R. RÖSLER and W. LÖSCHAbstractThe exact localization of subterranean cavities and the determination of their dimensions is very important for the planning of geotechnical and mining activities. It is a complicated geophysical task often at the limit of detection. Nevertheless geophysical investigation is the only alternative to a dense and expensive grid of boreholes. This report tests the usefulness of geoelectrical resistivity methods for cavity detection under some new aspects. The basis for evaluation was a theoretical analysis of different conventional and focussing measuring arrays and of special arrays for a geoelectrical research between two boreholes.
The limit of detectability of a cylindrical cavity of defined cross‐section and depth was calculated for the different measuring arrays on the basis of computation of the apparent resistivity ρa. Furthermore, the influence of possible errors (current supply of the electrodes and the distance between the electrodes) is discussed for focussed systems.
The second part of the article is directed at the behaviour of the apparent resistivity ρa, the disturbing potential δVd caused by the cavity and the normal potential δV0 of the measuring array all in relation to a homogeneous earth. Some new results are presented.
In the last part of the article theoretical results are compared with some field measurements.
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Volumes & issues
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Volume 72 (2023 - 2024)
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Volume 71 (2022 - 2023)
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Volume 70 (2021 - 2022)
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Volume 69 (2021)
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Volume 68 (2020)
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Volume 67 (2019)
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Volume 66 (2018)
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Volume 65 (2017)
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Volume 64 (2015 - 2016)
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Volume 63 (2015)
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Volume 62 (2014)
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Volume 61 (2013)
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Volume 60 (2012)
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Volume 59 (2011)
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Volume 58 (2010)
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Volume 57 (2009)
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Volume 56 (2008)
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Volume 55 (2007)
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Volume 54 (2006)
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Volume 53 (2005)
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Volume 52 (2004)
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Volume 51 (2003)
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Volume 50 (2002)
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Volume 49 (2001)
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Volume 48 (2000)
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Volume 47 (1999)
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Volume 46 (1998)
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Volume 45 (1997)
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Volume 44 (1996)
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Volume 43 (1995)
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Volume 42 (1994)
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Volume 41 (1993)
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Volume 40 (1992)
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Volume 39 (1991)
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Volume 38 (1990)
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Volume 37 (1989)
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Volume 36 (1988)
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Volume 35 (1987)
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Volume 34 (1986)
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Volume 33 (1985)
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Volume 32 (1984)
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Volume 31 (1983)
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Volume 30 (1982)
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Volume 29 (1981)
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Volume 28 (1980)
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Volume 27 (1979)
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Volume 26 (1978)
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Volume 25 (1977)
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Volume 24 (1976)
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Volume 23 (1975)
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Volume 22 (1974)
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Volume 21 (1973)
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Volume 20 (1972)
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Volume 19 (1971)
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Volume 18 (1970)
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Volume 17 (1969)
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Volume 16 (1968)
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Volume 15 (1967)
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Volume 14 (1966)
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Volume 13 (1965)
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Volume 12 (1964)
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Volume 11 (1963)
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Volume 10 (1962)
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Volume 9 (1961)
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Volume 8 (1960)
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Volume 7 (1959)
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Volume 6 (1958)
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Volume 5 (1957)
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Volume 4 (1956)
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Volume 3 (1955)
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Volume 2 (1954)
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Volume 1 (1953)