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- Volume 49, Issue 2, 2001
Geophysical Prospecting - Volume 49, Issue 2, 2001
Volume 49, Issue 2, 2001
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Implementing the fast marching eikonal solver: spherical versus Cartesian coordinates
Authors Tariq Alkhalifah and Sergey FomelSpherical coordinates are a natural orthogonal system for describing wavefronts emanating from a point source. A regular grid distribution in the Cartesian‐coordinate system tends to undersample the wavefront description near the source (at the highest wavefront curvature) and oversample it away from the source. Spherical coordinates, in general, provide a more balanced grid distribution for characterizing point‐source wavefronts. Our numerical implementation confirms that the recently introduced fast marching algorithm is both a highly efficient and an unconditionally stable eikonal solver. However, its first‐order approximation of traveltime derivatives can induce relatively large traveltime errors for waves propagating in a diagonal direction with respect to the coordinate system. Examples, including the IFP Marmousi and the SEG/EAGE 3D salt‐dome models, show that a spherical‐coordinate implementation of the method results in far fewer errors in traveltime calculation than the conventional Cartesian‐coordinate implementation, and with practically no loss in computational advantages.
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The 3D shear experiment over the Natih field in Oman: the effect of fracture‐filling fluids on shear propagation
Authors C.M. Van Der Kolk, W.S. Guest and J.H.H.M. PottersThis is the final paper in a series on the 3D multicomponent seismic experiment in Oman. In this experiment a 3D data set was acquired using three‐component geophones and with three source orientations. The data set will subsequently be referred to as the Natih 9C3D data set. We present, for the first time, evidence demonstrating that shear waves are sensitive to fluid type in fractured media. Two observations are examined from the Natih 9C3D data where regions of gas are characterized by slow shear‐wave velocities. One is that the shear‐wave splitting map of the Natih reservoir exhibits much larger splitting values over the gas cap on the reservoir. This increase in splitting results from a decrease in the slow shear‐wave velocity which senses both the fractures and the fracture‐filling fluid. Using a new effective‐medium model, it was possible to generate a splitting map for the reservoir that is corrected for this fluid effect. Secondly, an anomaly was encountered on the shear‐wave data directly above the reservoir. The thick Fiqa shale overburden exhibits a low shear‐wave velocity anomaly that is accompanied by higher shear reflectivity and lower frequency content. No such effects are evident in the conventional P‐wave data. This feature is interpreted as a gas chimney above the reservoir, a conclusion supported by both effective‐medium modelling and the geology.
With this new effective‐medium model, we show that introduction of gas into vertically fractured rock appears to decrease the velocity of shear waves (S2), polarized perpendicular to the fracture orientation, whilst leaving the vertical compressional‐wave velocity largely unaffected. This conclusion has direct implications for seismic methods in exploration, appraisal and development of fractured reservoirs and suggests that here we should be utilizing S‐wave data, as well as the conventional P‐wave data, as a direct hydrocarbon indicator.
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AVO investigations of shallow marine sediments
Authors M. Riedel and F. TheilenAmplitude‐variation‐with‐offset (AVO) analysis is based on the Zoeppritz equations, which enable the computation of reflection and transmission coefficients as a function of offset or angle of incidence. High‐frequency (up to 700 Hz) AVO studies, presented here, have been used to determine the physical properties of sediments in a shallow marine environment (20 m water depth). The properties that can be constrained are P‐ and S‐wave velocities, bulk density and acoustic attenuation. The use of higher frequencies requires special analysis including careful geometry and source and receiver directivity corrections. In the past, marine sediments have been modelled as elastic materials. However, viscoelastic models which include absorption are more realistic. At angles of incidence greater than 40°, AVO functions derived from viscoelastic models differ from those with purely elastic properties in the absence of a critical angle of incidence. The influence of S‐wave velocity on the reflection coefficient is small (especially for low S‐wave velocities encountered at the sea‐floor). Thus, it is difficult to extract the S‐wave parameter from AVO trends. On the other hand, P‐wave velocity and density show a considerably stronger effect. Attenuation (described by the quality factor Q) influences the reflection coefficient but could not be determined uniquely from the AVO functions. In order to measure the reflection coefficient in a seismogram, the amplitudes of the direct wave and the sea‐floor reflection in a common‐midpoint (CMP) gather are determined and corrected for spherical divergence as well as source and streamer directivity. At CMP locations showing the different AVO characteristics of a mud and a boulder clay, the sediment physical properties are determined by using a sequential‐quadratic‐programming (SQP) inversion technique. The inverted sediment physical properties for the mud are: P‐wave velocity α=1450±25 m/s, S‐wave velocity β=90±35 m/s, density ρ=1220±45 kg/m3, quality factor for P‐wave QP=15±200, quality factor for S‐wave QS=10±30. The inverted sediment physical properties for the boulder clay are: α=1620±45 m/s,β=360±200 m/s,ρ=1380±85 kg/m3,QP=790±660,QS=25±10.
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A Hamiltonian approach to asymptotic seismic reflection and diffraction modelling
Authors A. Hanyga, A.B. Druzhinin, A.D. Dzhafarov and L. FrøylandA model‐independent Hamiltonian formulation of paraxial and diffracted ray‐tracing equations is presented. It is applied to asymptotic Green's function computations. The medium can have an arbitrary number of interfaces, possibly intersecting at diffracting edges and vertices. Continuously varying model parameters and anisotropy are allowed. The algorithm for elastic waves, involving accuracy control and amplitude computation, is implemented in a platform‐independent object‐orientated C++ package. Numerical tests and modelling examples are presented.
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Seismic refraction, isotropic anisotropic seismic tomography on an ancient monument (Antonino and Faustina temple ad 141)
Authors Ettore Cardarelli and Rita De NardisThis paper describes the results of using geophysical techniques to investigate three columns of the Pronaos of the Antonino and Faustina temple (ad 141) in Rome, Italy; the columns are of cipollino marble which shows alternate sequences of mica and calcite beds. We applied seismic refraction using traditional interpretation, and seismic transmission tomography. The comparison between the results of the refraction study and the 2D and 3D isotropic tomographic analyses suggested anisotropic characteristics for the marble, and this prompted us to perform a further tomographic experiment, taking into account these characteristics of the material. Assuming an elliptical model, the main directions of anisotropy were detected. Two velocity fields corresponding to the main directions of the anisotropy were measured and anomalies such as cracks and fractures were noted. The conjugate‐gradient algorithm was used to invert the data. The results of the isotropic and anisotropic models were compared. The correlation between the methods highlighted the characteristics of the marble, i.e. anisotropy, depth of the weathering, fractures and small cracks. The results show that the material of the columns is in reasonable condition, with the exception of a surface area 6 cm to 15 cm deep that we estimate has been weathered for 2000 years, and that has been particularly affected by pollution in the last century.
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Pulled array continuous electrical sounding with an additional inductive source: an experimental design study
Authors Niels B. Christensen and Kurt SørensenElectrical and electromagnetic profiling methods are used extensively in environmental geophysical investigations for many different purposes. The pulled array continuous electrical sounding (PACES) method, where a tail of electrodes is towed behind a small vehicle while continuously and simultaneously measuring several electrode configurations, has been used extensively for mapping the vulnerability of aquifers in Denmark. Measurements are taken every 1 m, and 10–15 km of profile can be achieved in one day.
This paper presents a theoretical study of the resolution capabilities of PACES measurements as they are now performed, and an experimental design study for including an inductive source in the measuring equipment. The joint interpretation of the galvanic data set of ordinary PACES measurements with inductive data from a horizontal magnetic dipole source will enhance the resolution capabilities of the data set significantly. The study is carried out as an analysis of the uncertainty of the model parameters of one‐dimensional three‐layer models using the estimation error variances of the inversion problem.
The results indicate that the addition of only two frequency data from a magnetic dipole source will substantially improve the resolution of the subsurface resistivity structure. The improvement is model dependent, but reduction in the relative error of model parameters by an order of magnitude is observed.
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Robust inversion of vertical electrical sounding data using a multiple reweighted least‐squares method
Authors Milton J. Porsani, Sri Niwas and Niraldo R. FerreiraThe root cause of the instability problem of the least‐squares (LS) solution of the resistivity inverse problem is the ill‐conditioning of the sensitivity matrix. To circumvent this problem a new LS approach has been investigated in this paper. At each iteration, the sensitivity matrix is weighted in multiple ways generating a set of systems of linear equations. By solving each system, several candidate models are obtained. As a consequence, the space of models is explored in a more extensive and effective way resulting in a more robust and stable LS approach to solving the resistivity inverse problem. This new approach is called the multiple reweighted LS method (MRLS). The problems encountered when using the L1‐ or L2‐norm are discussed and the advantages of working with the MRLS method are highlighted. A five‐layer earth model which generates an ill‐conditioned matrix due to equivalence is used to generate a synthetic data set for the Schlumberger configuration. The data are randomly corrupted by noise and then inverted by using L2, L1 and the MRLS algorithm. The stabilized solutions, even though blurred, could only be obtained by using a heavy ridge regression parameter in L2‐ and L1‐norms. On the other hand, the MRLS solution is stable without regression factors and is superior and clearer. For a better appraisal the same initial model was used in all cases. The MRLS algorithm is also demonstrated for a field data set: a stable solution is obtained.
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Constraints in 3D gravity inversion
Authors Olivier Boulanger and Michel ChouteauA three‐dimensional (3D) inversion program is developed to interpret gravity data using a selection of constraints. This selection includes minimum distance, flatness, smoothness and compactness constraints, which can be combined using a Lagrangian formulation. A multigrid technique is also implemented to resolve separately large and short gravity wavelengths. The subsurface in the survey area is divided into rectangular prismatic blocks and the problem is solved by calculating the model parameters, i.e. the densities of each block. Weights are given to each block depending on depth, a priori information on density and the density range allowed for the region under investigation. The present computer code is tested on modelled data for a dipping dike and multiple bodies. Results combining different constraints and a weight depending on depth are shown for the dipping dike. The advantages and behaviour of each method are compared in the 3D reconstruction. Recovery of geometry (depth, size) and density distribution of the original model is dependent on the set of constraints used. From experimentation, the best combination of constraints for multiple bodies seems to be flatness and a minimum volume for the multiple bodies. The inversion method is tested on real gravity data from the Rouyn‐Noranda (Quebec) mining camp. The 3D inversion model for the first 10 km is in agreement with the known major lithological contacts at the surface; it enables the determination of the geometry of plutons and intrusive rocks at depth.
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Using refracted shear waves for velocity estimation
Authors L. Pautet, W.A. Kuperman and L. DormanThe most difficult part of multicomponent processing is the estimation of the shear‐wave velocity map for migration. We used refracted shear waves and a simple iterative method called wavefield continuation (WFC) to evaluate the shallow shear‐wave velocity profile on a real data example. The WFC was developed in 1981 by Clayton and McMechan to determine compressional‐wave velocity profiles from refracted compressional waves. The application to refracted shear waves is straightforward. The real data example shows that shear structure can be easily determined independently of the compressional structure.
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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)