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  • 1
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    In:  Geophys. Prospecting, Tokyo, Elsevier, vol. 22, no. 3, pp. 458-475, pp. L16603
    Publication Date: 1974
    Keywords: Stacking ; Velocity analysis ; Applied geophysics ; Seismics (controlled source seismology) ; Layers
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  • 2
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 40 (1992), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: There is a general lack of awareness among ‘lay’ professionals (geophysicists included) regarding the limitations in the use of least-squares. Using a simple numerical model under simulated conditions of observational errors, the performance of least-squares and other goodness-of-fit criteria under various error conditions are investigated. The results are presented in a simplified manner that can be readily understood by the lay earth scientist. It is shown that the use of least-squares is, strictly, only valid either when the errors pertain to a normal probability distribution or under certain fortuitous conditions. The correct power to use (e.g. square, cube, square root, etc.) depends on the form of error distribution. In many fairly typical practical situations, least-squares is one of the worst criteria to use. In such cases, data treatment, ‘robust statistics’ or similar processes provide an alternative approach.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 22 (1974), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: A correct derivation of rms, average and interval velocities from one another and from common depth point stacking velocities requires a clear understanding of the relationships between these velocities. We relate the average velocity to the rms velocity through a “heterogeneity factor” which is a quantity that gives a measure of the degree of velocity heterogeneity in the ground. The interval velocity is a quantity which varies according to the method of its derivation. The difference between rms and stacking velocities depends on the heterogeneity factor and on the length of the spread. Unless allowed for, this difference can reverse the advantages of long spreads and cause large errors in interval velocity determinations. It may be removed through a number of techniques. The accuracy of stacking velocities in the presence of random “noise” is independent of the heterogeneity factor. Relevant expressions can be broken down into simple formulae which give the accuracy quickly and with good precision.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 21 (1973), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: A rigorous proof is presented to show that over a horizontally layered ground the rms velocity cannot exceed the stacking velocity. The proof helps to illustrate the difference between stacking and rms velocities in a quantitative manner. The series of Taner and Koehler (1969) is used for the purpose. Convergence of this series is tested. Including more terms will not necessarily improve the convergence. Although the series is rapidly convergent when the spread length/depth ratio is small, strong oscillations are observed when this ratio is high.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 21 (1973), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 22 (1974), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Science Ltd
    Geophysical prospecting 49 (2001), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Uplift and the accompanying reduction in overburden result in anomalously high velocity in the uplifted rock unit relative to its current depth. The present work utilizes the non-uniqueness of the parameters of instantaneous velocity versus depth functions as an effective tool for uplift studies. The linear function with its two parameters, V0 and k, is a very simple function and is used as the illustrative vehicle. In the parameter space, i.e. in a plot where one axis represents V0 and the other axis represents k, non-uniqueness can be represented by contours of equal goodness-of-fit values between the observed data and the fitted function. The contour delimiting a region of equivalent solutions in the parameter space is called a ‘solution trough’. Uplift corresponds to a rotation of the solution trough in the parameter space. It is shown that, in terms of relative depth changes, there are five possible configurations (five cases) of uplift in a given area (the mobile location) relative to another area (the reference location). The cases depend on whether the uplifted location had attained a (pre-uplift) maximum depth of burial that was greater than, similar to, or smaller than the maximum depth of burial at the reference location. Interpretation of the relationships between the solution troughs corresponding to the different locations makes it possible to establish which of the five cases applies to the uplifted location and to estimate the amount of uplift that the unit had undergone at that location. The difficulty in determining the reduction in velocity due to decompaction resulting from uplift is a main source of uncertainty in the estimate of the amount of uplift. This is a common problem with all velocity-based methods of uplift estimation. To help around this difficulty, the present work proposes a first-order approximation method for estimating the effect of decompaction on velocity in an uplifted area.
    Type of Medium: Electronic Resource
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  • 8
    ISSN: 0012-821X
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Geosciences , Physics
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Earth and Planetary Science Letters 11 (1971), S. 257-262 
    ISSN: 0012-821X
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Geosciences , Physics
    Type of Medium: Electronic Resource
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  • 10
    ISSN: 1741-2765
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A theoretical solution has been obtained for the stress distribution throughout a cylindrical specimen loaded in compression, which takes into account different degrees of friction at the end surfaces. To check the solution experimentally, a cylindrical model was constructed from epoxy sheets, with electrical-resistance strain gages embedded between the sheets and also bonded to the cylindrical surface. With the specimen under axial compression, strain measurements were recorded within the elastic range of the epoxy. Reasonable agreement with the theoretical solution was observed for the two types of end conditions. In one case the cylinder was in direct contact with the platens of the testing machine, in the other case a Teflon sheet was placed between the two surfaces.
    Type of Medium: Electronic Resource
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