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  • 1
    Electronic Resource
    Electronic Resource
    A NEW DERIVATION OF THE WAVEFRONT CURVATURE TRANSFORMATION AT AN INTERFACE BETWEEN TWO INHOMOGENEOUS MEDIA (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 30 (1982), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: The principles for ray-tracing and wavefront curvature calculations in a three-dimensional medium are reviewed. A new derivation of the transformation of the wavefront curvature matrix at an interface between two inhomogeneous media is given. The derivation is based on a Taylor series expansion of the ray refraction equation at the interface between two inhomogeneous media, and only elementary geometric arguments are used. The wave-front curvature transformation at the interface is obtained by neglecting all terms in the direction of the surface normal.With proper definition of the variables, the derivation is also valid for a reflected wave-front. A simplified transformation rule is derived for a reflected wave of the same type as the incident wave.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2478.1982.tb01327.x
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  • 2
    Electronic Resource
    Electronic Resource
    COMPLETE INVERSION OF ZERO-OFFSET SEISMIC DATA (1986)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 34 (1986), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: The one-dimensional seismic inverse problem consists of recovering the acoustic impedance (or reflectivity function) as a function of traveltime from the reflection response of a horizontally layered medium excited by a plane-wave impulsive source. Most seismic sources behave like point sources, and the data must be corrected for geometrical spreading before the inversion procedure is applied. This correction is usually not exact because the geometrical spreading is different for primary and multiple reflections.An improved algorithm is proposed which takes the geometrical spreading from a point source into account. The zero-offset reflection response from a stack of homogeneous layers of variable thickness is used to compute the thickness, velocity and density of each layer. This is possible because the geometrical spreading contains additional information about the velocities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2478.1986.tb00524.x
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  • 3
    Electronic Resource
    Electronic Resource
    ATTENUATION OF COHERENT NOISE IN MARINE SEISMIC EXPLORATION USING VERY LONG ARRAYS (1978)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 26 (1978), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: The use of arrays to separate primary reflections from unwanted coherent seismic events is common practice in land seismic surveys. Very long source and receiver arrays have been used recently to reduce the effects of waterbottom multiples on marine seismic data.The source array consists of five uniformly spaced identical subarrays, each with five different airguns, where the distance between the subarrays may vary from 20 m56 m. The volume of each subarray is 10.3 1 (630 cu.in.) which gives a total volume of the array of 51.5 1 (3150 cu.in.) operated at a pressure of 14 MPa (2000 psi). In order to have a flexible receiver system it was decided to implement the extended receiver array in data processing by computing a weighted sum of two to five traces. The hydrophone cable consists of fifty-four channels with a group length of 50 m.Data shot with the superlong airgun array are processed by a combination of standard techniques and special procedures. In particular, the quality of the stack section is improved by using a weighted stack. The stack weights are computed by a program which takes into account the primary-to-multiple ratio.Comparisons with conventional data show significant improvements in data quality obtained by using the superlong airgun array. Examples show that the waterbottom multiples have been strongly attenuated and the deep seismic events have been enhanced.The combined array response function for dipping events is given in an appendix.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2478.1978.tb01631.x
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  • 4
    Electronic Resource
    Electronic Resource
    MAXIMUM-LIKELIHOOD ESTIMATION OF SEISMIC IMPULSE RESPONSES (1985)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 33 (1985), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: A seismic trace is assumed to consist of a known signal pulse convolved with a reflection coefficient series plus a moving average noise process (colored noise). Multiple reflections and reverberations are assumed to be removed from the trace by conventional means. The method of maximum likelihood (ML) is used to estimate the reflection coefficients and the unknown noise parameters. If the reflection coefficients are known from well logs, the seismic pulse and the noise parameters can be estimated.The maximum likelihood estimation problem is reduced to a nonlinear least-squares problem. When the further assumption is made that the noise is white, the method of maximum likelihood is equivalent to the method of least squares (LS). In that case the sampling rate should be chosen approximately equal to the Nyquist rate of the trace. Statistical and numerical properties of the ML- and the LS-estimates are discussed briefly. Synthetic data examples demonstrate that the ML-method gives better resolution and improved numerical stability compared to the LS-method.A real data example shows the ML- and LS-method applied to stacked seismic data. The results are compared with reflection coefficients obtained from well log data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2478.1985.tb00432.x
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  • 5
    Electronic Resource
    Electronic Resource
    INTERACTION BETWEEN AIRGUNS (1984)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 32 (1984), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: In the design of linear airgun arrays the interaction between the airguns is usually neglected. We review the different formulae which have been proposed for the minimum separation between airguns at which the interaction is negligible. These formulae can all be approximated by a linear function of a single variable.We have analyzed a large number of measurements in order to establish the amount of interaction between two airguns of various volumes at different pressures and depths. The resulting far-field signature has been measured and compared with the sum of the signatures from the two airguns measured in the same experimental situation. The changes in primary pulse amplitude, bubble period and primary/bubble peak-to-peak amplitude ratio were computed from the measurement data as a function of airgun separation, chamber volume, chamber pressure and airgun depth. The influence of a waveshape kit was investigated, and the effects of interaction and the effects of using a waveshape kit were compared.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2478.1984.tb01713.x
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  • 6
    Electronic Resource
    Electronic Resource
    ADAPTIVE LONG-PERIOD MULTIPLE ATTENUATION (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 27 (1979), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: A least squares estimation procedure is used to estimate the pulse-shape, amplitude function, and arrival time of multiple reflected signals. The estimates of the multiple reflections are subtracted from the data which are subsequently processed by standard methods. The estimation algorithm is applied continuously along the seismic line for each shot point or common datum point. In some cases it is advantageous to apply a pulse-shaping filter prior to using the estimation algorithm.The effectiveness of the technique is demonstrated by studying common shot point gathers, velocity analyses, and stacked sections derived from field data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2478.1979.tb00992.x
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  • 7
    Electronic Resource
    Electronic Resource
    SEISMIC SIGNAL DETECTION AND PARAMETER ESTIMATION (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 27 (1979), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: In the mathematical theory of seismic signal detection and parameter estimation given, the seismic measurements are assumed to consist of a sum of signals corrupted by additive Gaussian white noise uncorrelated to the signals. Each signal is assumed to consist of a signal pulse multiplied by a space-dependent amplitude function and with a space-dependent arrival time. The signal pulse, amplitude, and arrival time are estimated by the method of maximum likelihood.For this signal-and-noise model, the maximum likelihood method is equivalent to the method of least squares which will be shown to correspond to using the signal energy as coherency measure. The semblance coefficient is equal to the signal energy divided by the measurement energy. For this signal model we get a more general form of the semblance coefficient which reduces to the usual expression in the case of a constant signal amplitude function.The signal pulse, amplitude, and arrival time can be estimated by a simple iterative algorithm. The effectiveness of the algorithm on seismic field data is demonstrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2478.1979.tb00955.x
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  • 8
    Electronic Resource
    Electronic Resource
    COMPUTATION OF ZERO-OFFSET VERTICAL SEISMIC PROFILES INCLUDING GEOMETRICAL SPREADING AND ABSORPTION (1985)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 33 (1985), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Synthetic vertical seismic profiles (VSP) provide a useful tool in the interpretation of VSP data, allowing the interpreter to analyze the propagation of seismic waves in the different layers. A zero-offset VSP modeling program can also be used as part of an inversion program for estimating the parameters in a layered model of the subsurface.Proposed methods for computing synthetic VSP are mostly based on plane waves in a horizontally layered elastic or anelastic medium. In order to compare these synthetic VSP with real data a common method is to scale the data with the spherical spreading factor of the primary reflections. This will in most cases lead to artificial enhancement of multiple reflections.We apply the ray series method to the equations of motion for a linear viscoelastic medium after having done a Fourier transformation with respect to the time variable. This results in a complex eikonal equation which, in general, appears to be difficult to solve. For vertically traveling waves in a horizontally layered viscoelastic medium the solution is easily found to be the integral along the ray of the inverse of the complex propagation velocity. The spherical spreading due to a point source is also complex, and it is equal to the integral along the ray of the complex propagation velocity.Synthetic data examples illustrate the differences between spherical, cylindrical, and plane waves in elastic and viscoelastic layered media.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2478.1985.tb00422.x
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  • 9
    Electronic Resource
    Electronic Resource
    THE SPECTRAL FUNCTION OF A VERTICALLY INHOMOGENEOUS MEDIUM (1988)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 36 (1988), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Elastic, acoustic and electromagnetic waves in media consisting of vertically inhomogeneous layers are considered in a common formulation. The spectral function of a vertically inhomogeneous medium is the downward energy flux due to an impulsive source at the top of the first layer. A propagation-invariant form is used to derive several identities for the reflection and transmission matrices. When the top layer is bounded by a free surface, one of the expressions reduces to a formula derived by Kunetz for the one-dimensional wave equation.A source radiating upwards and downwards gives a discontinuity in the propagation-invariant form which is equal to the source energy. A new formula is derived for when the source is located just beneath the top interface of the layers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2478.1988.tb02147.x
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  • 10
    Electronic Resource
    Electronic Resource
    COMPUTATION OF SIGNATURES OF LINEAR AIRGUN ARRAYS (1987)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 35 (1987), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Far-field signatures from an airgun array are usually obtained by carrying out extensive field measurements. In order to decrease the need for such measurements, we have developed a method for computing signatures from linear airgun arrays where the distances between the airguns are such that the non-linear interaction among the airguns is negligible.The signature from a single airgun of a given type is computed from the following airgun parameters: airgun chamber volume, chamber pressure, airgun depth and position of the waveshape plate within the chamber. For calibration purposes, a recorded signature for one set of airgun parameters has to be provided for each type of airgun. The signatures are computed by using empirical relations between signature properties and the airgun parameters, and by treating the primary and bubble pulses separately.The far-field signature from a linear airgun array can now be computed by summation of the delayed signatures from the airguns in the array. Practical results are shown for an array with different PAR (Bolt) 1500 C airguns.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2478.1987.tb00818.x
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