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Proceedings of the IEEE

Issue 3 • Date March 1986

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Displaying Results 1 - 23 of 23
  • [Front cover and table of contents]

    Page(s): c1
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  • Scanning the issue

    Page(s): 387 - 388
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  • Comparison of some inverse methods for wave propagation in layered media

    Page(s): 389 - 400
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    The one-dimensional wave equation in a layered medium is considered. The inverse problem consists of computing the acoustic impedance of the layered medium from the reflection response measured at the surface. For a discrete medium consisting of homogeneous layers of equal traveltime the Levinson algorithm is used to compute the reflection coefficients at the interfaces between the layers. For a medium with continuously varying parameters, an iterative frequency-domain method based on the Riccati equation is used. When these methods are applied to band-limited synthetic seismic data, the result is a filtered version of the acoustic impedance. When the noise level is increased, both methods diverge. For a medium consisting of homogeneous layers of unknown thickness, the reflection coefficients and the traveltimes are estimated simultaneously by using a detection scheme combined with a numerical solution of the wave equation. The performance of three different methods were compared on synthetic data. The first method is based on downward continuation of the upgoing and downgoing wavefield. The second method is based on the computation of the wavefield at the surface, and progressively removing the effect of the layers once they have been identified. The third method is based on layer removal in the frequency domain. In all these cases, the seismic pulse was assumed to be known, and the same detection scheme was used. Numerical simulations indicate that, with the detection scheme used, the method based on surface calculations gave slightly better results than the method using downward continuation. Both these methods gave improved results compared to the layer removal scheme when applied to data with medium noise level. All three detection methods proved to have superior performance compared to the classical method using the Levinson algorithm or the iterative frequency-domain method. For small noise levels, the detection methods all gave a very good reconstruction of the acoustic impedance. For medium and high noise levels, the detection methods remained stable, although a number of false reflectors were found. View full abstract»

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  • One-dimensional normal-incidence inversion: A solution procedure for band-limited and noisy data

    Page(s): 401 - 414
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    In this paper we present a one-dimensional normal-incidence inversion procedure for reflection seismic data. A lossless layered system is considered which is characterized by reflection coefficients and traveltimes. A priori knowledge for the unknown parameters, in the form of statistics, is incorporated into a nonuniform layered system, and a maximum a posteriori estimation procedure is used for the estimation of the system's unknown parameters (i.e., we assume a random reflector model) from noisy and band-limited data. Our solution to the inverse problem includes a downward continuation procedure for estimation of the states of the system. The state sequences are composed of overlapping wavelets. We show that estimation of the unknown parameters of a layer is equivalent to estimation of the amplitude and detection of the time delay of the first wavelet in the upgoing state sequence of the layer. A suboptimal maximum-likelihood deconvolution procedure is employed to perform estimation and detection. The most desirable features of the proposed algorithm are its layer-recursive structure and its ability to process noisy and band-limited data. View full abstract»

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  • Seismic inversion in terms of pre-stack migration and multiple elimination

    Page(s): 415 - 427
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    A discussion is given on multidimensional seismic inversion techniques. It is argued that seismic inversion techniques should be subdivided in two categories: 1) inversion for the macro parameters of the subsurface, 2) inversion for the detail in the subsurface, both categories requiring a significantly different approach. Ample attention is paid to the different inversion techniques in multi-experiment, multi-offset, seismic migration. They are generally referred to as "pre-stack migration." Particularly, techniques based on the one-way wave equation are compared with techniques based on the two-way wave equation. Computational diagrams of the so-called shot record migration are given. The close relationship between multi-offset seismic migration and inverse scattering algorithms is shown. A scheme for the elimination of surface-related multiples is given. It is proposed as a first step prior to the process of one-way, multi-offset seismic migration. View full abstract»

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  • Migration of seismic data by the WKBJ method

    Page(s): 428 - 439
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    Migration is a term used in reflection seismology to describe the process of moving the recorded reflection events to their correct spatial positions by backward projection or depropagation. Although seismic records have been migrated since the very first reflection survey in 1921 in Oklahoma, it was the paper by Loewenthal, Lu, Robertson, and Sherwood [1] in 1976 that introduced the exploding-reflector model and numerical wave-equation methods that developed into the time migration techniques in use by the petroleum exploration industry today. Despite the fact that Hubral [2] introduced the more advanced topic of depth migration in 1977, the time migration methods have been the subject of so many research papers that an integrated treatment is warranted. The time migration methods can be described as various ways of implementing the classical WKBJ approximation (i.e., geometrical acoustics), well known in theoretical seismology and other areas of applied physics. The exploding reflectors hypothesis depends on an inherent (but, in fact, incidental) assumption that the amplitude of the seismic pulse is invariant as it is transmitted through the earth layers. Loewenthal et al. based this assumption on the requirement that the medium be weakly inhomogeneous as well as on the paper by Foster [3] in 1975, who had concluded that transmission effects in the continuous one-dimensional seismic model are unsubstantial, and at the surface (where the reflection seismograms are recorded) transmission effects are not present at all. Although Foster regarded this as a general result, the work of Gray [4] in 1984 shows that it is indeed a consequence of the WKBJ approximation, and so is valid only in those situations where the WKBJ approximation is applicable. The phase term which makes up the essential element of time migration (as well as various other types of migration methods) is the WKBJ phase correction factor, so time migration methods such as the conventional versions of Kirchhoff migration, finite-difference migration, and frequency-wavenumber (f-k) migration are not general wave-equation methods but are simply aspects of the WKBJ approximation. In fact, it can be said that most of conventional seismic processing in general is none other than WKBJ (i.e., geometrica- l acoustics). View full abstract»

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  • Imaging and inversion of zero-offset seismic data

    Page(s): 440 - 456
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    We present some of the basic problems of seismic inverse theory and some of the basic principles used in solving them. The one-dimensional (1-D) acoustic inverse problem is treated as an introduction to the more important and difficult three-dimensional (3-D) imaging and inverse problems. We argue that certain aspects of seismic data (e.g., CMP stacking and band- and aperture-limiting) are sufficient to prevent a useful generalization to 3-D of some very sophisticated 1-D solution techniques. This leaves such simple and relatively crude methods as Born inversion as useful candidates for generalization from one to three dimensions. A close investigation of 1-D Born inversion yields fairly general principles for overcoming its inadequacies, which are limited accuracy in mapping size and location of reflection events. These principles are based on ray theory, and lead directly to analogous improvements in higher dimensional seismic inversion techniques. These improvements, combined with others which are based on the fact that seismic data reside in the high-frequency regime as far as mapping isolated reflectors is concerned, yield an integral solution of the higher dimensional acoustic inverse problem which has been shown to be useful in practice. View full abstract»

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  • Pre-stack reverse-time migration for elastic waves with application to synthetic offset vertical seismic profiles

    Page(s): 457 - 465
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    A pre-stack migration algorithm for elastic waves in two-dimensional variable-velocity media is developed, implemented, and tested. The algorithm operates in the time-space domain and is based on reverse-time finite-difference extrapolation of elastic waves. The algorithm is explained and demonstrated in the context of imaging of elastic vertical seismic profile data, but is applicable to any source-recorder geometry. Synthetic test examples include a point diffractor, laterally homogeneous layers, and the flank of a salt dome. View full abstract»

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  • Multidimensional born inversion with a wide-band plane-wave source

    Page(s): 466 - 475
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    The inverse scattering problem for an acoustic medium is considered within the homogeneous background Born approximation. A constant-density acoustic medium is probed by a wide-band plane-wave source. The scattered field is observed along a receiver array located outside the medium. Two methods for partial reconstruction of the medium velocities are presented. In the first method (the slant-stack method), the projections of the velocity potential at a range of angles are obtained from the plane-wave components of the scattered field. The range of available projection angles is determined by the receiver array aperture and the incidence direction of the probing plane wave. The medium velocities are, then, partially reconstructed from available projections via well-known methods of straight-line tomography. In the second method (the imaging-filtering method), the observed traces are filtered, back-propagated into the medium, and imaged at the source traveltimes, in the same way as in migration. The resulting image is, then, filtered by a linear space-invariant filter to obtain a partial reconstruction of the medium velocities. Both reconstruction methods are illustrated by some synthetic examples for several receiver geometries. View full abstract»

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  • An application of Marquardt's procedure to the seismic inverse problem

    Page(s): 476 - 486
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    The seismic inverse problem is to infer characteristics of the subsurface from measurements of the wave field at the surface. The Marquardt procedure offers one approach to this problem. In applying this procedure, a linear relationship is developed between the wave field and some parameter which describes a physical property of the subsurface. Then a selection criterion is designed to choose the subsurface parameter which provides the best match for the observed seismic data. View full abstract»

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  • Inversion of band-limited reflection seismograms: Theory and practice

    Page(s): 487 - 497
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    This paper examines the problem of recovering the acoustic impedance from band-limited normal incidence reflection seismograms. Recognizing the inherent nonuniqueness in the inversion, we proceed by constructing an impedance model which satisfies the processed seismogram, has a minimum of structural variation, honors any point impedance constraints that are provided, and incorporates information from stacking velocities. The constrained inversion is carried out in a single operation using linear programming methods. The constructed impedance is consistent with available geological and geophysical information and therefore constitutes a well-constrained estimate of the true earth impedance. A basic assumption in our inversion is that each seismic trace is a band-limited representation of the true reflectivity function. When seismic data do not conform with this assumption, pre-inversion processing of the data is required; this involves a series of data checks and possible corrections. A complete processing sequence incorporating all steps of the practical inversion is presented and illustrated with field data examples. View full abstract»

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  • Pre-stack inversion of a 1-D medium

    Page(s): 498 - 508
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    Assuming a one-dimensional (1-D) acoustic medium and a known density, we want to determine the velocity distribution from pre-stack surface seismic data. Basically, we have to identify a distributed parameter in the two-dimensional (2-D) wave equation. This inverse problem is set as an optimization problem. This allows us to expect that the information redundancy available in the data will provide an optimal signal-to-noise enhancement. Since the forward modeling we use gives a complete solution of the wave equation, all the events explained by acoustic wave propagation, such as guided waves or high-order multiples, will be used to infer information about the velocity distribution. From the above arguments we may expect an accurate result with high resolution, even with noise-corrupted data. Although the developed methodology is not optimal at all, the numerical experiments confirm this expectation and illustrate the power of the proposed inversion method. View full abstract»

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  • On the state equations of nonlinear networks and the uniqueness of their solutions

    Page(s): 513 - 514
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    Concerning the equilibrium points and the uniqueness of solutions, some wrong results have appeared recently about the state description of nonlinear networks; in contrast to those results in [1], it is shown through the same example that every critical (or singular) point where the state derivative vanishes is not an equilibrium point, and the state description in terms of the capacitor voltage leads to a unique solution consistent with the physical constraints of the network. View full abstract»

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  • Some important properties of synchronous oscillators

    Page(s): 516 - 518
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    A Synchronous Oscillator (SO) tracks, filters, divides, and amplifies the input carrier in a single process. Narrow-resolution bandwidth, high input-signal sensitivity, and fast acquisition are the most important properties of the SO, while the resolution bandwidth remains as its most unique functional behavior. View full abstract»

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  • Adaptive invariant novelty filters

    Page(s): 518 - 519
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    The multiple-channel novelty filters of associative memory are derived from the retina neuron network point-spread function. Scale and rotation invariance is achieved by the input data flowing through the nonuniform polar exponential sampling to a uniform output space. Image domain bandpassing techniques are then used to extract the low-band and high-band frequency contents of the equivalent novelty filters. View full abstract»

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  • A Hilbert transform product theorem

    Page(s): 520 - 521
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    The usual product theorem for Hilbert transforms states that under certain conditions x(t)y(t), the Hilbert transform of a product of two signals x(t) and y(t), is equal to x(t)y^(t), a result having repeated use in simplifying calculations involving modulated waveforms. Several sufficient conditions for the theorem to hold are well-known and appear in the literature. Here, using a time-domain approach, we derive a necessary and sufficient condition for the validity of the theorem and show as an example two signals which have the desired property but which do not satisfy any of the earlier sufficient conditions. View full abstract»

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  • Covariance and power spectrum of a sinusoidal carrier, angel modulated by a uniformly distributed random process

    Page(s): 522 - 523
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    The covariance and power spectrum of a sinusoidal carrier, angle modulated by a zero mean random signal having a rectangular probability density is studied. Numerical calculations have been carried out when the modulating noisy signal has been shaped by an RC filter. View full abstract»

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  • Spectral estimation by repetitive L1-norm minimization

    Page(s): 523 - 524
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    The use of the simplex for spectral estimation of noisy harmonic processes is very effective when the number of sinusoids is known and is taken into account. In the present letter a method is proposed for determining this number by properly extending the method of simplex estimation. View full abstract»

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  • Developments in expert systems

    Page(s): 525 - 526
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  • Design of testable logic circuits

    Page(s): 525
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  • Book alert

    Page(s): 526 - 527
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  • [Back cover]

    Page(s): c4
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