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- Volume 49, Issue 3, 2001
Geophysical Prospecting - Volume 49, Issue 3, 2001
Volume 49, Issue 3, 2001
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Depth migration of shot records in heterogeneous, transversely isotropic media using optimum explicit operators
Authors Jianfeng Zhang, D.J. Verschuur and C.P.A. WapenaarA space–frequency domain 2D depth‐migration scheme is generalized for imaging in the presence of anisotropy. The anisotropy model used is that of a transversely isotropic (TI) medium with a symmetry axis that can be either vertical or tilted. In the proposed scheme the anisotropy is described in terms of Thomsen parameters; however, the scheme can accommodate a wide range of anisotropy rather than only weak anisotropy. Short spatial convolution operators are used to extrapolate the wavefields recursively in the space–frequency domain for both qP‐ and qSV‐waves. The weighted least‐squares method for designing isotropic optimum operators is extended to asymmetric optimum explicit extrapolation operators in the presence of TI media with a tilted symmetry axis. Additionally, an efficient weighted quadratic‐programming design method is developed. The short spatial length of the derived operators makes it possible for the proposed scheme to handle lateral inhomogeneities. The performance of the operators, designed by combining the weighted least‐squares and weighted quadratic‐programming methods, is demonstrated by migration impulse responses of qP and qSV propagation modes for the weak and strong TI models with both vertical and tilted symmetry axes. Finally, a table‐driven shot‐record depth‐migration scheme is proposed, which is illustrated for finite‐difference modelled shot records in TI media.
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Finding the strike direction of fractures using GPR
Authors Soon Jee Seol, Jung‐Ho Kim, Yoonho Song and Seung‐Hwan ChungGPR reflection energy varies with antenna orientation relative to the strike and dip of the reflector. This directional dependence of GPR responses was investigated through numerical experiments and was used to estimate the azimuth of fractures and joints. Three antenna configurations were considered in this study: perpendicular‐broadside (YY mode), parallel‐broadside (XX mode) and cross‐polarization (YX mode). The reflection energy in the cross‐polarization mode shows a shape characteristic similar to the strike, regardless of the dip angle. Those in the other two modes show quite different amplitudes from the strike, depending on the dip angle. We have developed a strike‐direction‐finding scheme using data obtained from the three different modes for the same survey line. The azimuth angle of each reflector was displayed in colour on the GPR profile. This scheme was applied to a field survey at a granite quarry in southern Korea. The GPR profiles showed different images of the reflectors depending on the antenna configuration. The estimated azimuths of reflectors obtained using our scheme matched fairly well with those of known fractures and joints.
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The feasibility of electromagnetic gradiometer measurements
Authors Daniel Sattel and James MacnaeThe quantities measured in transient electromagnetic (TEM) surveys are usually either magnetic field components or their time derivatives. Alternatively it might be advantageous to measure the spatial derivatives of these quantities. Such gradiometer measurements are expected to have lower noise levels due to the negative interference of ambient noise recorded by the two receiver coils. Error propagation models are used to compare quantitatively the noise sensitivities of conventional and gradiometer TEM data. To achieve this, eigenvalue decomposition is applied on synthetic data to derive the parameter uncertainties of layered‐earth models. The results indicate that near‐surface gradient measurements give a superior definition of the shallow conductivity structure, provided noise levels are 20–40 times smaller than those recorded by conventional EM instruments. For a fixed‐wing towed‐bird gradiometer system to be feasible, a noise reduction factor of at least 50–100 is required. One field test showed that noise reduction factors in excess of 60 are achievable with gradiometer measurements. However, other collected data indicate that the effectiveness of noise reduction can be hampered by the spatial variability of noise such as that encountered in built‐up areas. Synthetic data calculated for a vertical plate model confirm the limited depth of detection of vertical gradient data but also indicate some spatial derivatives which offer better lateral resolution than conventional EM data. This high sensitivity to the near‐surface conductivity structure suggests the application of EM gradiometers in areas such as environmental and archaeological mapping.
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Reference ellipsoids for anisotropic media
Authors N. Ettrich, D. Gajewski and B. KashtanPerturbation methods are common tools for describing wave propagation in weakly anisotropic media. The anisotropic medium is replaced by an average isotropic medium where wave propagation can be treated analytically and the correction for the effect of anisotropy is computed by perturbation techniques. This works well for anisotropies of up to 10%. Some materials (e.g. shales), however, can exhibit a much stronger anisotropy. In this case a background is required which still can be treated analytically but is applicable to stronger P‐wave anisotropy. We present an averaging technique to compute a best‐fitting ellipsoidal medium to an arbitrary anisotropic medium. Ellipsoidal media are sufficiently simple for analytical expressions to be available for many applications and allow consideration of strong P‐wave anisotropy. The averaging of the arbitrary anisotropic medium can be carried out globally (i.e. for the whole sphere) or sectorially (e.g. for seismic waves propagating predominantly in the vertical direction). We derive linear relationships for the coefficients of the ellipsoid which depend on the elastic coefficients of the anisotropic medium. We also provide specifications for best‐fitting elliptical and best‐fitting isotropic media. Numerical examples for different rocks demonstrate the improved approximation of the anisotropic model obtained using the formulae derived, compared with the conventionally used average isotropic medium.
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Klauder wavelet removal before vibroseis deconvolution
Authors Enders A. Robinson and Muhammad SaggafThe spiking deconvolution of a field seismic trace requires that the seismic wavelet on the trace be minimum phase. On a dynamite trace, the component wavelets due to the effects of recording instruments, coupling, attenuation, ghosts, reverberations and other types of multiple reflection are minimum phase. The seismic wavelet is the convolution of the component wavelets. As a result, the seismic wavelet on a dynamite trace is minimum phase and thus can be removed by spiking deconvolution. However, on a correlated vibroseis trace, the seismic wavelet is the convolution of the zero‐phase Klauder wavelet with the component minimum‐phase wavelets. Thus the seismic wavelet occurring on a correlated vibroseis trace does not meet the minimum‐phase requirement necessary for spiking deconvolution, and the final result of deconvolution is less than optimal. Over the years, this problem has been investigated and various methods of correction have been introduced. In essence, the existing methods of vibroseis deconvolution make use of a correction that converts (on the correlated trace) the Klauder wavelet into its minimum‐phase counterpart. The seismic wavelet, which is the convolution of the minimum‐phase counterpart with the component minimum‐phase wavelets, is then removed by spiking deconvolution. This means that spiking deconvolution removes both the constructed minimum‐phase Klauder counterpart and the component minimum‐phase wavelets. Here, a new method is proposed: instead of being converted to minimum phase, the Klauder wavelet is removed directly. The spiking deconvolution can then proceed unimpeded as in the case of a dynamite record. These results also hold for gap predictive deconvolution because gap deconvolution is a special case of spiking deconvolution in which the deconvolved trace is smoothed by the front part of the minimum‐phase wavelet that was removed.
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Identification and classification of multiple reflections with self‐organizing maps
Authors Robert Essenreiter, Martin Karrenbach and Sven TreitelArtificial neural networks can be used effectively to identify and classify multiple events in a seismic data set. We use a specialized neural network, a self‐organizing map (SOM), that tries to establish rules for the characterization of the physical problem. Selected seismic data attributes from CMP gathers are used as input patterns, such that the SOM arranges the data to form clusters in an abstract space. We show with synthetic and real data how the SOM can identify and classify primaries and multiples, and how it can classify the various types of multiple corresponding to a certain generating mechanism in the subsurface.
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Compressional‐wave Q estimation from full‐waveform sonic data
Authors A. Dasios, T.R. Astin and C. McCannThere is significant evidence that the anelastic loss of seismic energy is linked to petrophysical properties such as porosity, permeability and clay content. Thus, reliable estimation of anelastic attenuation from seismic data can lead to improved methods for the prediction of petrophysical properties. This paper is concerned with methods for the estimation of attenuation at sonic frequencies (5–30 KHz) from in situ data. Two independent methods have been developed and tested for estimating compressional‐wave attenuation from full‐waveform sonic data. A well‐established technique, the logarithm spectral ratio (LSR) method, is compared with a new technique, the instantaneous frequency (IF) method. The LSR method uses the whole spectrum of the seismic pulse whilst the IF method uses a carefully estimated value of instantaneous frequency which is representative of the centre frequency of the pulse. In the former case, attenuation estimation is based on the relative variation of amplitudes at different frequencies, whilst in the latter case it is based on the shift of the centre frequency of the pulse to lower values during anelastic wave propagation. The IF method does not assume frequency independence of Q which is a necessary assumption for the LSR method, and it provides a stable frequency log, the peak instantaneous frequency (PIF) log, which may be used as an indicator for attenuation under certain limitations. The development and implementation of the two methods is aimed at minimizing the effect of secondary arrivals, such as leaky modes, and involved a series of parameter tests. Testing of the two methods using full‐waveform sonic data of variable quality, obtained from a gas‐bearing sandstone reservoir, showed that the IF method is in general more stable and suitable for full‐waveform sonic data compared with the LSR method. This was evident especially in data sets with high background noise levels and wave‐interference effects. For good quality data, the two methods gave results that showed good agreement, whilst comparison with other log types further increased confidence in the results obtained. A significant decrease (approximately 5 KHz) in the PIF values was observed in the transition from an evaporite/shale sequence to the gas‐bearing sandstone. Average Q values of 54 and 51 were obtained using good quality data from a test region within the gas‐saturated sandstone reservoir, using the LSR and IF methods, respectively.
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Adaptation of prestack migration to multi‐offset ground‐penetrating radar (GPR) data
Authors Donatienne Leparoux, Dominique Gibert and Philippe CôteIn adapting the prestack migration technique used in seismic imaging to the inversion of ground‐penetrating radar (GPR) from time‐ to depth‐sections, we show that the theoretical integral formulation of the inversion can be applied to electromagnetic problems, albeit with three assumptions. The first two assumptions concern the electromagnetic characteristics of the medium, primarily that the medium must be perfectly resistive and non‐dispersive, and the third concerns the antennae radiation pattern, which is taken to be 2D. The application of this adaptation of the inversion method is confirmed by migrating actual GPR measurements acquired on the test site of the Laboratoire Central des Ponts et Chaussées. The results show good agreement with the geometry of the structures in the medium and confirm that the possible departure from the assumption of a purely resistive medium has no visible effect on the information concerning the geometry of scattering and reflecting structures. The field experiments also show that prestack migration processing is sufficiently robust with regard to the assumption of a non‐dispersive medium. The assumption of a 2D antennae radiation pattern, however, produces artefacts that could be significant for laterally heterogeneous media. Nevertheless, where the medium is not highly laterally heterogeneous, the migration gives a clear image of the scattering potential due to the geometry of structural contrasts in the medium; the scatterers are well focused from diffraction hyperbolae and well localized. Spatial geometry has limited dimensional accuracy and positions are located with a maximum error equal to the minimum wavelength of the signal bandpass. Objects smaller than one wavelength can nevertheless be detected and well focused if their dielectric contrasts are sufficiently high, as in the case of iron or water in gneiss gravels. Furthermore, the suitability of multi‐offset protocols to estimate the electromagnetic propagating velocity and to decrease the non‐coherent noise level of measurements is confirmed. Our velocity estimation is based on the semblance calculation of multi‐offset migrated images, and we confirmed the relevance of this quantification method using numerical data. The signal‐to‐noise ratio is improved by summing multi‐offset results after the addition of random noise on measurements. Thus the adaptation of prestack migration to multi‐offset radar measurements significantly improves the resolution of the scattering potential of the medium. Limitations associated with the methods used here suggest that 3D algorithms should be applied to strongly laterally heterogeneous media and further studies concerning the waveform inversion are necessary to obtain information about the electric nature of the medium.
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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 19 (1971)
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Volume 17 (1969)
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Volume 16 (1968)
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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)