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- Volume 33, Issue 8, 1985
Geophysical Prospecting - Volume 33, Issue 8, 1985
Volume 33, Issue 8, 1985
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TUTORIAL LINEAR INVERSE FILTERS IN ORTHOGONAL COORDINATES*
By E. J. DOUZEAbstractThe linear filter is used extensively in exploration geophysics, and is usually computed using the least squares normal equations. In the general field of time series, the inverse problem is often solved through eigenvalue expansion solutions to integral equations.
The normal equations can be solved in terms of the eigenvalues and eigenvectors of the autocorrelation matrix. It has been suggested that a spectral expansion technique should be used which computes the inverse directly without explicit use of the normal equations. If all possible spiking positions are calculated using the normal equations, the spiking operator matrix is obtained. The matrix operator obtained from the spectral expansion is closely related to the spiking operator matrix. Thus, it is possible to compute the spectral expansion filter using the normal equations. Therefore, it is possible to use the best features of both methods, i.e. obtaining the optimum filter with the normal equations, and discarding the poorly determined parts of the solution based on spectral expansion.
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A NUMERICAL STUDY OF LAMB'S PROBLEM*
By M. J. KUHNAbstractThis paper considers propagation of elastodynamic waves in an imperfectly elastic half‐space. Two different excitation modes are investigated: a buried source of compressional waves and a vertically directed areal load applied to the surface. Numerical integration of the analytical solution of the wave equation allows study of the vertical and horizontal components of displacement and/or particle velocity anywhere in the half‐space. One case of particular interest concerns the examination of particle displacement and velocity at the surface in a circular area above the source. In another application seismograms generated by an explosive buried source are contrasted with seismograms generated by the transient application of a vertically directed load to the free surface. Still another application of considerable practical interest concerns the study of the nongeometrical pS—wave, in particular its characteristics as functions of range and depth. Finally, in the last application the behavior of a rarely observed wave (denoted here by the letter U) is studied in both elastic and visco‐elastic half‐spaces.
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WAVE FIELD EXTRAPOLATION TECHNIQUES FOR INHOMOGENEOUS MEDIA WHICH INCLUDE CRITICAL ANGLE EVENTS. PART I: METHODS USING THE ONE‐WAY WAVE EQUATIONS*
Authors C. P. A. WAPENAAR and A. J. BERKHOUTAbstractPart I of this series starts with a brief review of the fundamental principles underlying wave field extrapolation. Next, the total wave field is split into downgoing and upgoing waves, described by a set of coupled one‐way wave equations. In cases of limited propagation angles and weak inhomogeneities these one‐way wave equations can be decoupled, describing primary waves only. For large propagation angles (up to and including 90°) an alternative choice of sub‐division into downgoing and upgoing waves is presented. It is shown that this approach is well suited for modeling as well as migration and inversion schemes for seismic data which include critical angle events.
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IS IT POSSIBLE TO INCREASE THE RESOLUTION IN SEISMIC EXPLORATION FOR COAL BY USING HIGH FREQUENCY SIGNALS?*
Authors H. RÜTER and R. SCHEPERSAbstractIn seismic exploration for coal data resolution is a fundamental problem. Modeling helps to understand those details of the geology that can be interpreted from the seismic image. For single seam exploration, the vertical resolution of a seismic section is defined by the bandwidth of the signals. If there are several seams, each seam acts as a high‐pass filter for reflections and as a low‐pass filter for transmitted waves. Synthetic seismograms show that reflections from deep seams have a low frequency content.
Within a layered sequence of coal seams, many multiples are generated which disturb later primary reflections. The ratio of primaries to multiples depends on the frequency content of the seismic data and on the number of overlying seams. The multiple problem is more severe with high frequencies.
Primary reflections from deep coal seams within a sequence can be detected only if low‐frequency signals are used. However, the use of low‐frequency signals reduces the resolution of the deeper data.
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ON TIMING THE VSP FIRST ARRIVAL*
Authors P. B. DILLON and V. A. COLLYERAbstractThe advent of signal energy on a VSP or check‐shot trace may be defined as the first break. An accurate pick of this first break would be possible in the absence of noise. However, real data traces are inevitably corrupted by noise and this leads to difficulty in identifying a break because the signal‐to‐noise ratio is low in its neighbourhood.
Under such conditions, an obvious alternative is to pick “troughs” where the local signal‐to‐noise ratio is likely to be much higher. Although trough picking is an effective way to minimize the noise problem, it is sensitive to signal properties (such as absorption and multiple reflections) which have no effect upon the accuracy of break picks. Thus, trough picking is signal‐sensitive and break picking is noise‐sensitive.
Clearly, an ideal first‐arrival picking scheme would combine the noise‐tolerant features of trough picking with the signal‐tolerant features of break picking. This ideal may be approached by exploiting known properties of the VSP trace using conventional signal processing techniques. The result of such processing is to reduce the problem to that of picking a trough correctly centered about the true break time.
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COMPUTER REPRESENTATION OF COMPLEX 3‐D GEOLOGICAL STRUCTURES USING A NEW “SOLID MODELING” TECHNIQUE*
Authors H. GJØYSTDAL, J. E. REINHARDSEN and K. ÅSTEBØLAbstractDuring our recent work with 3‐D dynamic ray‐tracing and velocity inversion problems, a new 3‐D model generation system has been developed using a so‐called “solid modeling” technique. The term “solid modeling” refers to the fact that the logical system governing the internal geometrical properties of the model describes the model as a combination of “solids” or “volumes” in 3‐D space. In each of these volumes the physical parameters (such as seismic velocity, density) vary continuously. Discontinuous changes occur only across the model interfaces separating the volumes.
The model is constructed by firstly forming a number of “simple volumes” from the given interfaces and then combining these simple volumes into more complex volumes which represent the physical volumes of the model. It is easy to make changes to the model, by adding volumes or subtracting volumes and perform more composite operations, all by simple use of Boolean expressions. Every time a model has been specified (or changed), the internal logic automatically carries out a check of physical consistency of the 3‐D model space (no overlapping volumes, no holes).
By including various types of coordinate transformations, different kinds of complex structures can be handled, such as salt domes and vertical and near vertical faulting.
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FIRST ARRIVAL PICKING ON COMMON‐OFFSET TRACE COLLECTIONS FOR AUTOMATIC ESTIMATION OF STATIC CORRECTIONS*
By F. COPPENSAbstractThe increase in the number of geophone groups in production records during recent years and the requirement for accurate basic static corrections for high resolution records have made it necessary to develop sufficiently accurate automatic techniques for the determination of static corrections.
A fully automatic method is presented which makes use of the delay‐time method in order to compute static corrections at each shot position. Delay times, weathering and subweathering velocities are determined from automatic picks of the first arrivals on common‐offset trace collections.
It is assumed that the weathering is a single layer and that the dip of the subweathering layer under the geophone groups is small.
The picking routine is fully automatic and successful in most cases, provided the signal‐to‐noise ratio is sufficiently high.
The subsequent filtering of erroneous values for picked times is performed by means of statistical techniques, using curves of picked times on common‐offset trace collections. If the distance between receivers and shot‐points on the profile is sufficiently short, one can expect only little change in the picked times of two contiguous traces.
The method is well adapted to end‐on spreads with a great number of traces, where distances between geophone groups are short.
Examples are presented showing the possibilities of the method for the determination of long wavelength as well as short wavelength components of static corrections.
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THE APPLICATION OF VHF MEASUREMENTS TO EARTHQUAKE PREDICTION*
Authors R. P. SINGH and D. RANKINAbstractThe use of Very High Frequency measurements applied to the detection of the variation in dielectric constant as a precursor to earthquakes is examined. It is concluded that such a technique is feasible and that the installation of source and sensor in separate deep boreholes provides a suitable environment for this type of study. The boreholes could also be used for a considerable range of other types of instrumentation.
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INTERPRETATION AND DEPTH OF INVESTIGATION OF GRADIENT MEASUREMENTS IN DIRECT CURRENT GEOELECTRICS*
By R. SCHULZAbstractGradient measurements in a homogeneous electrical primary field can easily be interpreted for simple models. The simplified solution (conducting or resistant body in a homogeneous space in a homogeneous electrical field) is often sufficiently accurate, as comparisons with the exact solution (body of finite resistivity in a homogeneous half‐space in a quasihomogeneous electrical field) show. The exact geometry of the body cannot be determined by gradient measurements; the same anomaly of apparent resistivity can be caused by different bodies. In particular, the similarity between a sphere and a cube of the same volume is very high.
There is a distinct influence of the resistivity of the overburden: the higher this resistivity is, the stronger is the effect caused by a buried body.
If a deviation of 10% of the apparent resistivity is assumed as the lower boundary at which a buried body can be detected by gradient measurements, the depth of investigation for a three‐dimensional body is approximately equal to its width; in the two‐dimensional case the thickness of the overburden can be twice the width. If the overburden has a resistivity which is higher than the resistivity of the substratum, these depths are greater. The greatest possible depth is approximately three times the width of the body.
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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 18 (1970 - 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 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)