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- Volume 46, Issue 5, 1998
Geophysical Prospecting - Volume 46, Issue 5, 1998
Volume 46, Issue 5, 1998
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Wavelet power spectrum analysis of heterogeneities from sonic velocity logs[Link]
By Xiao‐Ping LiThe continuous wavelet transform (CWT) is used to evaluate local variations in the power‐law exponents of sonic log data. The resulting wavelet spectrum can be compared with the corresponding global estimates obtained by conventional Fourier transform methods. In Fourier analysis, the fundamental tool used to characterize a fluctuating velocity distribution is the power spectrum. It represents the energy contained in each wavenumber and thus provides information regarding the importance of each scale of heterogeneity. However, important spatial information regarding the location of events becomes implicit in the phase angle of the Fourier transform. In this paper, it is shown how the square of the amplitude of the wavelet transform is related to the Fourier spectrum and how spatial information can be expressed in an explicit manner. Using the conservation of energy, it is shown that the average wavelet power spectrum over the total depth range is equal to the global power spectrum. A Gaussian wavelet is chosen to realize the wavelet transform. Two synthetic sonic logs with exponential and von Karman correlation functions are used to demonstrate the potential of the suggested analysis. Furthermore, the wavelet transform is applied to the KTB (Continental Deep Drilling Program) sonic log data. The wide range of applications of the CWT shows that this transform is a natural tool for characterizing the structural properties of underground heterogeneities. It offers the possibility of separating the multiscale components of heterogeneities.
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Measurement of electrical properties of contaminated soil1
Authors S. Darayan, C. Liu, L.C. Shen and D. ShattuckWe present the measured dielectric constant and conductivity of soil samples contaminated by diesel oil. Measurements of the electrical properties of contaminated soil were carried out using a guarded‐electrode sample holder and a parallel‐plate sample holder in the frequency range 2–250 MHz. Two different soil samples were measured. Both the dielectric constant and the conductivity of the contaminated soils and uncontaminated soils are compared. The measurement results show that the change in the dielectric constant of soils before and after diesel oil contamination is small but significant. These results provide a basis for using ground‐penetrating radar or other high‐frequency electromagnetic sensors in the detection of soil contamination.
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Analysis of a guided wave along a conducting structure in a borehole[Link]
Authors S. Ebihara, M. Sato and H. NiitsumaA guided wave along a borehole is often observed in borehole radar measurements. These guided waves deform the antenna pattern and can cause artefacts in radar measurements. A water‐filled borehole or a conducting logging cable can function as a waveguide for electromagnetic waves under some conditions. We describe the theoretical characteristics of such a guided wave in a borehole and compare them with our experiments. The measured signal discussed was obtained with a directional borehole radar. This radar uses a cylindrical conformal array antenna as receiver and is a model of a conducting structure in a borehole. The induced field around the borehole was compared with the theory. The most fundamental symmetrical and asymmetrical modes were TM01 and HE11, and they were identified in the measured signals using time–frequency distribution analysis and by observation of the azimuthal field distribution of the magnetic field.
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Wavelet analysis for the regional‐residual and local separation of potential field anomalies[Link]
Authors Maurizio Fedi and Tatiana QuartaA method based on the discrete wavelet transform was applied to the regional‐residual separation of potential fields and to the filtering of local anomalies. A specific space‐scale wavelet analysis, called multiresolution analysis, allowed decomposition of the signal with respect to a vast range of scales. Different analysing wavelets were applied to anomalies in both synthetic and real cases, but the more appropriate basis needed to be chosen by requiring the maximum compactness for the multiresolution analysis. Moreover, since such analysis was found not to be shift‐invariant, the same criterion was applied to choosing the best signal shift. Application of the technique to both synthetic and real cases produced an optimal space‐scale representation of the fields and a consistent regional‐residual separation. Furthermore, the space localization allowed a variety of filtered signals to be obtained, each one with a specific scale and local area content. Fourier and wavelet analyses were both applied to the filtering out of the intense Etna anomaly from the aeromagnetic field of Sicily. The wavelet method was more powerful, suppressing only the Etna volcano anomaly and leaving the rest of the map practically unchanged.
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Analysis and application of a non‐conventional underwater geoelectrical method in Lake Geneva, Switzerland[Link]
Authors François Baumgartner and Niels B. ChristensenThe electrical method presented is used for determining the resistivity of lake‐bottom sediments and is based on the d.c. electrical sounding principles. The electrode array, called the fishing rod (FR), is of pole‐pole type and is orientated vertically on a line perpendicular to the surface of the water. The technique is used for mapping resistivity anomalies located deep underwater. This paper presents an analysis of the resolution capabilities of the FR method and the results of a case study carried out in Lake Geneva, where measurements were interpreted using a one‐dimensional (1D) multilayer earth model. The analysis of the uncertainty in the model parameters of a 1D multilayer earth model is carried out using the covariance matrix of the linearized inversion problem. The results of the analyses show that when the thickness and resistivity of the water layer is known, the resistivity of the sediment layer is well determined under most circumstances. The thickness of the sediment layer is well determined when resistivity contrasts are not too low. In Lake Geneva the FR method has been used to study an old depression with a resistive channel. This application shows the efficiency of the method compared with conventional electrical methods, where water depth becomes a limiting factor. The use of an automated iterative inversion scheme in this particular case is advantageous, as a joint interpretation of the three different data sets measured with the FR method can be carried out. Finally, the result of the inversion is compared with the trial‐and‐error interpretations of a previous study.
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3D geoelectric tomography and archaeological applications1
Authors Paolo Mauriello, Dario Monna and Domenico PatellaFollowing a previous paper in which the principles of a 3D ground‐surface tomographic processing of self‐potential data were established, we extend the method to active source geoelectric surveying. The main purpose of the new tomographic approach is to obtain a physical image reconstruction of the induced electric charges distributed over buried resistivity discontinuities. The information is produced in a probabilistic sense, as the mathematical formulation underlying the method treats only the intrinsic physical nature of the generated electric field underground and the method of its ground‐surface detection, independently of the geometry of the unknown structures. In practice, a 3D tomography is realized by cross‐correlating a set of distributed electric‐field ground‐surface data with a scanning function, representing a unit positive point charge located anywhere in the lower half‐space. The resolution of the method is tested on the synthetic response of a 3D structural simulation of an archaeological target, consisting of an infinitely resistive prismatic body immersed in a half‐space, including surface inhomogeneities and layering. Finally, the field response of a 3D structure consisting of a hypogeal dromos‐chamber tomb inside the Sabine Necropolis at Colle del Forno, close to Rome, is presented and discussed.
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Volumes & issues
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Volume 72 (2023 - 2024)
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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)