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- Volume 32, Issue 6, 1984
Geophysical Prospecting - Volume 32, Issue 6, 1984
Volume 32, Issue 6, 1984
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LINEARIZED INVERSION OF SEISMIC REFLECTION DATA*
By A. TARANTOLAAbstractThis is the first of a series of papers giving the solution of the inverse problem in seismic exploration. The acoustic approximation is used together with the assumption that the velocity field has the form
. The forward problem is then linearized (thus neglecting multiple reflected waves) and the inverse problem of estimating δ is set up. Its rigorous solution can be obtained using an iterative algorithm, each step consisting of a classical Kirchhoff migration (hyperbola summation) plus a classical forward modeling step (circle summation).
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VELOCITY ANALYSIS IN THE p—x‐PLANE FROM A SLANT STACK WAVEFIELD*
Authors R. TANG, A. CARSWELL and WOOIL MOONAbstractClassical methods of interpretation of reflection seismic data are such that interpretation and processing usually occur in the “collected” frame of reference. However, in recent times other data planes have gained increasing acceptance in seismology as a viable alternative. Through linear transformations applied to a record section, both the t—p‐ and p—x‐planes can be produced. The r—p‐domain may be obtained from the t—x‐plane by a transformation known as slant stacking. Normal practice has been to do most of the data processing in the t—x‐plane and then transforming to the r—p‐plane. However, many of the procedures used in the t—x‐domain can be modified for use in the t—p‐plane to increase the coherence.
Velocity inversion may be carried out either in the r—p‐domain or further transformed to the p—x‐plane where the modified Herglotz‐Wiechert inversion may be applied. To perform the inversion, the t—p‐wavefield is converted to a p—x‐representation by the use of a new linear transformation technique, the cross‐stack. By a simple sampling process along a particular p—x‐trajectory, the Herglotz‐Wiechert method can be used to reconstruct an acceptable velocity model of the subsurface. A comparison of derived velocity structures is made between that produced by the Herglotz‐Wiechert technique and that of the Dix method.
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HIGH‐FREQUENCY SHALLOW SEISMIC REFLECTION MAPPING IN TIN MINING*
More LessAbstractField results of shallow seismic reflections obtained with a propane‐oxygen detonator (POD) are presented. The survey site was in a tin‐mining area of the Kinta Valley in Malaysia. The shallow and irregular limestone bedrock is overlain by alluvial “tailing” and virgin sediments. Sizes of such mining areas can range from about 320 ± 320 m2 to 900 ± 900 m2. The survey was intended to delineate the topography of the bedrock, which is of vital importance in tin ore exploration and exploitation. The equipment included single‐ and 12‐channel signal enhancement seismographs, the POD, a hammer and thumper. The inexpensive and portable POD generates directional waves of reproducible form, variable energy of high frequency, and only a few surface waves at short offsets. Reflections at around 200 Hz were obtained from the shallow bedrock at about 25 m as well as from very shallow lithological interfaces. The interpretation of seismograms is supported by drill‐hole lithological sections and synthetic seismograms. The data illustrate the successful use of shallow reflections for mapping irregular bedrock. Reflection seismics can provide better horizontal and vertical details than the refraction method. Further improvements based on the data‐processing flexibility of new signal enhancement seismographs and synthetic seismograms are suggested.
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OFFSET CONTINUATION IN THEORY AND PRACTICE*
Authors G. BOLONDI, E. LOINGER and F. ROCCAAbstractOffset continuation is a technique that was recently proposed for the dip moveout correction. This correction can be carried out in the time‐wavenumber domain using a proper partial differential equation that links sections with different offset.
It has been shown that a single spike in a common‐offset section—corresponds to a semi‐elliptically shaped reflector with foci located at the source and receiver in the section migrated after dip moveout correction.
The sections that result after offset continuation, stack, and migration are thus a superposition not only of semicircles, but also of semi‐ellipses with different lengths of axes. This effect smears the migration alias‐noise which, without offset continuation, would appear as migration circles not close enough together to interfere destructively.
Offset continuation can improve the quality of seismic sections in several ways:
—the velocity analyses are more readable, less dispersed and dip independent; diffraction tails arrive with the same normal moveout velocity as the apex and thus diffraction‐noise can be “stacked out”;
—noise produced by aliasing in the migrated section is reduced.
In this paper we give a practical and conceptual interpretation of the offset continuation method, with a generalization to three‐dimensional volumes of data. A critical examination of several synthetic and field data examples shows the actual possibilities and advantages of offset continuation.
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AN OPERATOR APPROACH TO FORWARD MODELING, DATA PROCESSING AND MIGRATION*
More LessAbstractThe response of a seismic model to excitation by a source can be represented in terms of the action of reflection and transmission operators for portions of the structure. This approach provides a flexible framework for both modeling and processing problems.
The operator development provides a physical description of the wave propagation process and, via the expansion of reverberation operators, gives a mechanism for assessing the accuracy of approximate developments. The representation suggests new ways of developing modeling algorithms by balancing the computational effort expended on minor and major features of the model.
For processing problems, the operator representation shows the relation of processing stages to the seismic wave field and thereby indicates effective sequences of operations. For migration it is possible to specify an ideal pre‐stack migration procedure in terms of the inverse of the propagation operators and to examine the problems which need to be overcome by practical algorithms.
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STATIC CORRECTIONS FOR SHEAR WAVE SECTIONS*
Authors B. WIEST and H. A. K. EDELMANNAbstractThe computation of static corrections requires information about subsurface velocities. This information can be obtained by different methods: surface wave analysis, short refraction lines, downhole times, uphole times and first arrivals from seismograms.
For pure shear waves generated by SH sources the analysis of first arrivals from seismograms combined, if necessary, with short refraction lines has proved to be most accurate and economic.
A comparison of first‐arrival plots from P‐ and S‐wave surveys of the same line measured in areas of unconsolidated sediments in northern Germany illustrates the characteristic differences between the two velocity models. P‐waves show a marked velocity increase at the water table from about 600 to 1800 m/s. S‐wave velocities of the same strata increase gradually from about 100 to 400 m/s. As a consequence, S‐wave models are vertically and laterally more complex and, in general, show no significant velocity increase at a defined boundary as P‐wave models do. Therefore, other suitable correction levels with specific velocities must be chosen.
A comparison of “tgd‐corrections” (correction time between geophone position and datum level) for P‐ and S‐waves in areas of unconsolidated sediments shows that their ratio is different from the P‐/S‐velocity ratio for the respective correction level because of the greater depth of the S‐wave refractor. Therefore, P‐ and S‐waves are influenced by different near‐surface anomalies, and time corrections calculated for both wave types are largely independent.
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SEISMIC REFRACTION METHOD TO STUDY THE FOUNDATION ROCK OF A DAM*
By N. P. DUTTAAbstractDynamic elastic moduli like E, μ, K and μ of the foundation rock of a dam have been determined by finding Vp‐ and Vs‐velocities by seismic refraction with a hammer as source. Some parameters such as “fracture frequency” and “rock quality designation” (RQD) of the foundation rock have been derived using “average regression curves” and Vp‐velocities. By comparing K/μ with Vp/Vs, a few locations showing weathered conditions have been demarcated. This compares well with RQD values of those locations.
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ESTIMATES OF TERRESTRIAL THERMAL GRADIENTS AND HEAT FLOW VARIATIONS WITH DEPTH IN THE HINTON‐EDSON AREA OF THE ALBERTA BASIN DERIVED FROM PETROLEUM BOTTOM‐HOLE TEMPERATURE DATA*
Authors C. KUSHIGBOR, H. L. LAM, J. A. MAJOROWICZ and M. RAHMANAbstractThere is a significant increase in terrestrial heat flow with depth in the Hinton‐Edson area of the deep part of the western Canadian sedimentary basin in Alberta. This is especially true near the Rocky Mountain foothills which is an area of high relief, high hydraulic head and regional water recharge. Gravity‐imposed downward movement of meteoric water through the thick sedimentary strata with velocities as low as 10–10 m/s to 0.5 × 10–9 m/s may cause an increase of heat flow with depth. Such disturbance of heat flow with depth on a regional scale in the sedimentary strata means that it is not possible to determine the background conductive steady‐state heat flow associated with crustal or upper mantle heat sources in such an area from measurement of conductive heat flow in the part of the sedimentary column where water movement occurs. This is because the convective portion cannot be determined, particularly when measurements are made in only part of the regional hydrodynamic system of the basin.
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A NUMERICAL DIRECT INTERPRETATION METHOD OF RESISTIVITY SOUNDINGS USING THE PEKERIS MODEL*
More LessAbstractA numerical method is presented for direct interpretation of resistivity sounding measurements. The early part of the resistivity transform curve derived from field observations by standard methods is approximated by a two‐layer curve. The resistivity of the first layer is determined from the arithmetic mean of the successive computations which are carried on each of three successive discrete values of the resistivity transform curve. Using this mean value of the resistivity, the thickness of the first layer is computed from the sample values in pairs of the resistivity transform curve. After these determinations, the top layer is removed by Pekeris's reduction equation. The parameters of the second layer are obtained from the discrete values of the reduced transform curve (which corresponds to the second part of the resistivity transform curve) by the same procedure as described for the first layer.
The same computational scheme is repeated until the parameters of all intermediate layers are obtained. The resistivity of the substratum is determined from the reduction equation.
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INDUCED POLARIZATION IN ELECTROMAGNETIC INDUCTIVE SCHEMES*
Authors J. R. WAIT and P. DEBROUXAbstractUsing homogeneous full‐space and half‐space models, we show that induced‐polarization properties of the medium influence the inductive coupling between two circuits. It is suggested that existing methods to interpret electromagnetic sounding data should be viewed with caution if the electro‐chemical dispersion is not taken into account.
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ZERO—PHASE FORWARD FILTERS FOR RESISTIVITY SOUNDING*
By L. MANSINHAAbstractForward filters to transform the apparent resistivity function over a layered half‐space into the resistivity transform have been derived for a number of sample intervals. The filters have no apparent Gibbs' oscillations and hence require no phase shift. In addition, the end points of the filter were modified to compensate for truncation. The filters were tested on simulated ascending and descending two‐layer cases. As expected, “dense” filters with sample spacing of In (10)/6 or smaller performed very well. However, even “sparse” filters with spacing of In (10)/2 and a total of nine coefficients have peak errors of less than 5% for p1:p2 ratios of 10–6 to 106. If a peak error of 5.5% is acceptable, then an even sparser filter with only seven coefficients at a spacing of 3 In (10)/5 may be used.
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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)