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- Volume 44, Issue 4, 1996
Geophysical Prospecting - Volume 44, Issue 4, 1996
Volume 44, Issue 4, 1996
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Seismic inversion through Tabu Search1
Authors Rikke Vinther and Klaus MosegaardAbstractHighly non‐linear seismic trace inversion problems can be solved efficiently by an implementation of Tabu Search, a meta‐heuristic method related to artificial intelligence. The implementation under consideration is a deterministic, global search that combines the advantages ofa local search, giving a quick descent to local misfit minima, with an ability to cross misfit barriers in the model space. Once Tabu Search has found an area of low misfit, it performs an extensive exploration of its deepest points. This property makes it possible to use Tabu Search for a semiquantitative resolution and uncertainty analysis of the inverse problem.
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Reflection from a deep interface in a strongly heterogeneous layered medium1
Authors Pawel Lewicki and Robert BurridgeAbstractWe consider the problem of acoustic pulse propagation through a layered medium with a reflector at one end. The fluctuations in the medium properties are assumed to be strong, i.e. of finite amplitude, rapid in comparison to the typical wavelength and to have statistical structure. The depth of the reflector is assumed to be large in comparison to the wavelength. In this regime, simple formulae for the reflected pulse and its arrival time at the surface are obtained. The amplitude of the pulse is broadened and attenuated as a result of multiple scattering: the fine‐layered structure of the medium can be characterized by a single constant which appears in the formula for the limiting waveform and which measures the size of the fluctuations in the medium. Within the theory, the commonly observed discrepancy between the integrated sonic traveltime and the seismic traveltime can be studied and understood. The theory is a natural extension of the long‐wavelength effective medium theory of Backus. The analysis is rigorous and based on the invariant embedding technique.
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Evaluation of transport and storage properties in the soil and groundwater zone from induced polarization measurements1
Authors F.D. Börner, J.R. Schopper and A. WellerAbstractSpectral induced polarization as well as complex electrical measurements are used to estimate, on a non‐invasive basis, hydraulic permeability in aquifers. Basic laboratory measurements on a variety of shaly sands, silts and clays showed that the main feature of their conductivity spectra in the frequency range from 10‐3 to 103 Hertz is a nearly constant phase angle. Thus, a constant‐phase‐angle model of electrical conductivity is applied to interpret quantitatively surface and borehole spectral induced polarization measurements. The model allows for the calculation of two independent electrical parameters from only one frequency scan and a simple separation of electrical volume and interface effects. The proposed interpretation algorithm yields the true formation factor, the cation exchange capacity and the surface‐area‐to‐porosity ratio, which corresponds to the inverse hydraulic radius. Using a Kozeny–Carman‐like equation, the estimation of hydraulic permeability is possible.
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A numerical laboratory for simulation and visualization of seismic wavefields1
Authors F. J. Serón, J. Badal and F. J. SabadellAbstractComputational seismic modelling (CSM) plays an important role in the geophysical industry as an established aid to seismic interpreters. Numerical solution of the elastic wave equations has proved to be a very important tool for geophysicists in both forward modelling and migration. Among the techniques generally used in CSM, we consider the finite‐element method (FEM) and investigate its computational and visualization requirements. The CSMFEM program, designed for this purpose and developed on an IBM 3090 computer with vector facility, is described in detail. It constitutes a numerical laboratory for performing computer experiments. Two Newmark type algorithms for time integration are compared with other time integration schemes, and both direct and iterative methods for solving the corresponding large sparse system of linear algebraic equations are analysed. Several numerical experiments to simulate seismic energy propagation through heterogeneous media are performed. Synthetics in the form of common shot gathers, vertical seismic profiles and snapshots are suitably displayed, since with the large amounts of data obtained from CSM research, methods for visualization of the computed results must be developed. The FEM is compared with other numerical tools, such as finite‐difference and pseudo‐spectral methods.
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Event‐oriented velocity estimation based on prestack data in time or depth domain1
Authors Einar Iversen and Håvar GjøystdalAbstractA 2D reflection tomographic method is described, for the purpose of estimating an improved macrovelocity field for prestack depth migration. An event‐oriented local approach of the ‘layer‐stripping’ type has been developed, where each input event is defined by its traveltime and a traveltime derivative, taken with respect to one of four coordinates in the source/receiver and midpoint half‐offset systems.
Recent work has shown that the results of reflection tomography may be improved by performing event picking in a prestack depth domain. We adopt this approach and allow events to be picked either before or after prestack depth migration. Hence, if events have been picked in a depth domain, such as the common‐shot depth domain or the common‐offset depth domain, then a depth‐time transformation is required before velocity estimation. The event transformation may, for example, be done by conventional kinematic ray tracingr and with respect to the original depth‐migration velocity field. By this means, we expect the input events for velocity updating to become less sensitive to migration velocity errors.
For the purpose of velocity estimation, events are subdivided into two categories; reference horizon events and individual events. The reference horizon events correspond to a fixed offset in order to provide basic information about reflector geometry, whereas individual events, corresponding to any offset, are supposed to provide the additional information needed for velocity estimation. An iterative updating approach is used, based on calculation of derivatives of event reflection points with respect to velocity. The event reflection points are obtained by ray‐theoretical depth conversion, and reflection‐point derivatives are calculated accurately and efficiently from information pertaining to single rays. A number of reference horizon events and a single individual event constitute the minimum information required to update the velocity locally, and the iterations proceed until the individual event reflection point is consistent with those of the reference horizon events. Normally, three to four iterations are sufficient to attain convergence. As a by‐product of the process, we obtain so‐called uncertainty amplification factors, which relate a picking error to the corresponding error in the estimated velocity or depth horizon position.
The vector formulation of the updating relationship makes it applicable to smooth horizons having arbitrary dips and by applying velocity updating in combination with a flexible model‐builder, very general macro‐model structures can be obtained. As a first step in the evaluation of the new method, error‐free traveltime events were generated by applying forward ray tracing within given macrovelocity models. When using such ‘perfect’ observations, the velocity estimation algorithm gave consistent reconstructions of macro‐models containing interfaces with differential dip and curvature, a low‐velocity layer and a layer with a laterally varying velocity function.
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A physical model for shear‐wave velocity prediction1
Authors Shiyu Xu and Roy E. WhiteAbstractThe clay‐sand mixture model of Xu and White is shown to simulate observed relationships between S‐wave velocity (or transit time), porosity and clay content. In general, neither S‐wave velocity nor S‐wave transit time is a linear function of porosity and clay content. For practical purposes, clay content is approximated by shale volume in well‐log applications. In principle, the model can predict S‐wave velocity from lithology and any pair of P‐wave velocity, porosity and shale volume. Although the predictions should be the same if all measurements are error free, comparison of predictions with laboratory and logging measurements show that predictions using P‐wave velocity are the most reliable. The robust relationship between S‐ and P‐wave velocities is due to the fact that both are similarly affected by porosity, clay content and lithology. Moreover, errors in the measured P‐wave velocity are normally smaller than those in porosity and shale volume, both of which are subject to errors introduced by imperfect models and imperfect parameters when estimated from logs.
Because the model evaluates the bulk and shear moduli of the dry rock frame by a combination of Kuster and Toksöz’ theory and differential effective medium theory, using pore aspect ratios to characterize the compliances of the sand and clay components, the relationship between P‐ and S‐wave velocities is explicit and consistent. Consequently the model sidesteps problems and assumptions that arise from the lack of knowledge of these moduli when applying Gassmann's theory to this relationship, making it a very flexible tool for investigating how the vP‐vs relationship is affected by lithology, porosity, clay content and water saturation. Numerical results from the model are confirmed by laboratory and logging data and demonstrate, for example, how the presence of gas has a more pronounced effect on P‐wave velocity in shaly sands than in less compliant cleaner sandstones.
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Seismic migration and absorbing boundaries with a one‐way wave system for heterogeneous media1
Authors Nanxun Dai, Antonios Vafidis and Ernest R. KanasewichAbstractA first‐order one‐way wave system has been created based on characteristic analysis of the acoustic wave system and optimization of the dispersion relation. We demonstrate that this system is equivalent to a third‐order scalar partial‐differential equation which, for a homogeneous medium, reduces to a form similar to the 45° paraxial wave equation. This system describes accurately waves propagating in a 2D heterogeneous medium at angles up to 75°.
The one‐way wave system representing downgoing waves is used for a modified reverse time migration method. As a wavefield extrapolator in migration, the downgoing wave system propagates the reflection events backwards to their reflectors without scattering at the discontinuities in the velocity model. Hence, images with amplitudes proportional to reflectivity can be obtained from this migration technique. We present examples of the application of the new migration method to synthetic seismic data where P‐P reflections P‐SV converted waves are present.
Absorbing boundaries, useful in the generation of synthetic seismograms, have been constructed by using the one‐way wave system. These boundaries absorb effectively waves impinging over a wide range of angles of incidence.
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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)