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- Volume 48, Issue 2, 2000
Geophysical Prospecting - Volume 48, Issue 2, 2000
Volume 48, Issue 2, 2000
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Sensitivity of reflection seismic data to oil‐column height in high‐porosity sandstones
Authors Sarah Ryan‐Grigor and Colin M. SayersTuning is the effect of interference between the reflections from the top and bottom of a thin layer on the amplitude of the composite reflection. For a homogeneous sandstone reservoir containing an oil column overlying brine, interference between the reflection from the top reservoir and the oil/water contact is a function of the height of the oil column. If the properties of the sandstone do not vary across the oil/water contact, the SS, PS and SP reflection coefficients from the oil/water contact are small in comparison to the PP reflection coefficient. This allows analytic expressions for the effective PP and PS reflection coefficients from the reservoir to be derived that include all P‐wave multiples within the oil column. For a given source/receiver offset, the component of the wavevector inside the oil column normal to the interface is larger for the PPPP reflection than for the PPPS reflection, due to the asymmetry in the raypath for the PPPS reflection. The PPPS reflection is therefore useful for determining oil‐column heights larger than that discriminated by the PPPP reflection, especially when used at wider offsets.
A convenient classification of the AVO response of hydrocarbon‐bearing sandstone reservoirs overlain by shale is the scheme of Rutherford and Williams. Class 1 sands have higher acoustic impedance for normal incidence than the overlying shale, Class 2 sands have nearly the same acoustic impedance as the shale and Class 3 sands have lower acoustic impedance. Synthetic shot gathers calculated for these three classes as a function of oil‐column height show that a combination of the PPPP and the PPPS amplitudes can be plotted as a tuning trajectory, which can be used to determine the oil‐column height. This method is most sensitive for reservoirs that belong to AVO classes 1 and 2, and therefore may be useful in AVO analysis of Class 1 and 2 reservoirs where the traditional AVO indicators (developed for Class 3 reservoirs) do not work very well. These results demonstrate the usefulness of shear waves recorded in the marine environment at wide offsets.
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Time‐varying time‐shift correction by quasi‐elastic deformation of seismic traces [Link]
More LessResidual static correction is based on a model of time shifts (delays) that depend solely on source and receiver locations at the surface. This assumption is valid if all raypaths are vertical in the near‐surface layering. We consider a more general model of the time‐varying time shifts that remain after hyperbolic NMO correction (of non‐hyperbolic trajectories) and static correction. We assume that the wavelet distortion caused by the time‐varying shifts is smooth. We have developed an algorithm for its correction (phase correction), based on minimization of the target functional with a penalty term similar to the quasi‐elastic energy of the time‐axis deformation. The use of a mechanical analogy for optimization is well known (e.g. simulated annealing). We propose here a stable numerical method that deals with a pair of seismic traces. It may be applied to phase correction of CMP (or CDP) gathers and stacked sections. Synthetic and field examples confirm that our method appreciably increases the signal‐to‐noise ratio, and improves the coherence and resolution.
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An electromagnetic modelling tool for the detection of hydrocarbons in the subsoil
More LessElectromagnetic geophysical methods, such as ground‐penetrating radar (GPR), have proved to be optimal tools for detecting and mapping near‐surface contaminants. GPR has the capability of mapping the location of hydrocarbon pools on the basis of contrasts in the effective permittivity and conductivity of the subsoil. At radar frequencies (50 MHz to 1 GHz), hydrocarbons have a relative permittivity ranging from 2 to 30, compared with a permittivity for water of 80. Moreover, their conductivity ranges from zero to 10 mS/m, against values of 200 mS/m and more for salt water. These differences indicate that water/hydrocarbon interfaces in a porous medium are electromagnetically ‘visible’. In order to quantify the hydrocarbon saturation we developed a model for the electromagnetic properties of a subsoil composed of sand and clay/silt, and partially saturated with air, water and hydrocarbon. A self‐similar theory is used for the sandy component and a transversely isotropic constitutive equation for the shaly component, which is assumed to possess a laminated structure. The model is first verified with experimental data and then used to obtain the properties of soils partially saturated with methanol and aviation gasoline. Finally, a GPR forward‐modelling method computes the radargrams of a typical hydrocarbon spill, illustrating the sensitivity of the technique to the type of pore‐fluid. The model and the simulation algorithm provide an interpretation methodology to distinguish different pore‐fluids and to quantify their degree of saturation.
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Dip moveout of converted waves and parameter estimation in transversely isotropic media [Link]
Authors Ilya Tsvankin and Vladimir GrechkaFor transverse isotropy with a vertical symmetry axis (VTI media), P‐wave reflection data alone are insufficient for building velocity models in depth. Here, we show that all parameters of VTI media responsible for propagation of P‐ and SV‐waves (the P‐wave and S‐wave vertical velocities VP0 and VS0 and the anisotropic parameters ε and δ) can be obtained by combining P‐wave traveltimes with the moveout of PS‐waves converted at a horizontal and dipping interface. Using converted modes, rather than pure S‐waves, avoids the need for expensive shear‐wave excitation on land and makes the method suitable for offshore exploration.
The inversion algorithm is based on a new analytic description of the dip moveout of PS‐waves developed for symmetry planes of anisotropic media (and for any vertical plane in models with weak azimuthal anisotropy). The common‐midpoint (CMP) traveltime–offset relationship, derived in a parametric form and represented through the components of the slowness vector of the P‐ and S‐waves, makes it possible to compute the moveout curve of the PS‐wave without two‐point ray tracing. This formalism also leads to closed‐form solutions for moveout attributes, such as the coordinates (xmin, tmin) of the traveltime minimum, the normal‐moveout (NMO) velocity defined at x = xmin and the slope of the moveout curve (apparent slowness) at zero offset.
The parameter‐estimation algorithm operates with reflection moveout of P‐ and PS‐waves from a horizontal and dipping reflector. The NMO velocities of P‐ and PS‐waves from horizontal events and the ratio of the corresponding zero‐offset traveltimes yield three equations for the four unknown medium parameters. The remaining parameter is found from an overdetermined system of equations that includes the P‐wave NMO velocity and moveout attributes of the PS‐wave for a dipping event. Numerical analysis shows that the PS‐wave dip‐moveout signature plays a crucial role in obtaining accurate estimates of the anisotropic parameters. The joint inversion of P and PS data provides the necessary information not only for P‐wave depth imaging in VTI media, but also for the processing of PS‐waves, including re‐sorting of PS traces into common‐reflection‐point gathers and transformation to zero offset (TZO).
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Assessment of the reliability of 2D inversion of apparent resistivity data[Link]
Authors Abel I. Olayinka and Ugur YaramanciThe reliability of inversion of apparent resistivity pseudosection data to determine accurately the true resistivity distribution over 2D structures has been investigated, using a common inversion scheme based on a smoothness‐constrained non‐linear least‐squares optimization, for the Wenner array. This involved calculation of synthetic apparent resistivity pseudosection data, which were then inverted and the model estimated from the inversion was compared with the original 2D model. The models examined include (i) horizontal layering, (ii) a vertical fault, (iii) a low‐resistivity fill within a high‐resistivity basement, and (iv) an upfaulted basement block beneath a conductive overburden. Over vertical structures, the resistivity models obtained from inversion are usually much sharper than the measured data. However, the inverted resistivities can be smaller than the lowest, or greater than the highest, true model resistivity. The substantial reduction generally recorded in the data misfit during the least‐squares inversion of 2D apparent resistivity data is not always accompanied by any noticeable reduction in the model misfit. Conversely, the model misfit may, for all practical purposes, remain invariant for successive iterations. It can also increase with the iteration number, especially where the resistivity contrast at the bedrock interface exceeds a factor of about 10; in such instances, the optimum model estimated from inversion is attained at a very low iteration number. The largest model misfit is encountered in the zone adjacent to a contact where there is a large change in the resistivity contrast. It is concluded that smooth inversion can provide only an approximate guide to the true geometry and true formation resistivity.
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Magnetic field transforms with low sensitivity to the direction of source magnetization and high centricity [Link]
Authors Petar Stavrev and Daniela GerovskaMagnetic data interpretation faces difficulties due to the various shapes of magnetic anomalies and the positions of their extrema with respect to the causative bodies for different directions of the source magnetization. The well‐known transforms — reduction to the pole, pseudogravity field, and analytic signal (total gradient) — help in reducing the problem. Another way to achieve the required effect is the transformation of magnetic data, ΔT or Z, into values of the anomalous magnetic intensity T. In this respect, we have found some transforms based on differential operators such as the gradient of T and its modulus R = |∇T|, the Laplacian L = ∇2T, the product T ∇2T and its square root Q, and the Laplacian ∇2(T2) and its square root E, to be useful. They are slightly sensitive to the magnetization orientation and their extrema occur above the sources.
For a 2D anomaly of a homogeneous causative body, the proposed transforms do not depend on the inclination of magnetization. In the 3D case, such independence does not exist even for the elementary field of a point dipole. The influence of the magnetization direction is estimated by an integral coefficient of sensitivity. This coefficient takes values of up to 2.0 for ΔT or Z anomalies, while their transforms T, R, E, Q and L have values of less than 0.28, 0.29, 0.24, 0.16 and 0.07, respectively, i.e. on average, 10 times less. The estimation of the centricity is carried out using the relative deviation of the principal extremum of the anomaly or its transforms from the epicentre of the model body at a depth equal to 100 units. For a ΔT anomaly this deviation is up to 67%; for the L transform it is less than 8%; for Q, E, R and T it is less than 10%, 15%, 20% and 25%, respectively.
The proposed transforms take only non‐negative values. With respect to their shape, the peripheral magnetic extrema are removed, the anomalous configuration is simplified and the resolution of complicated interference patterns is improved. Their calculation does not require additional data for the direction of magnetization, which is an essential advantage over the reduction‐to‐the‐pole and pseudogravity‐field transforms. A joint analysis of the measured field and its transforms T, E and L offers possibilities for more confident separation of the anomalous effects and direct correlation to their sources. The model tests performed and the 3D field applications to real magnetic data confirm the useful properties of the transforms suggested here.
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2D finite‐difference viscoelastic wave modelling including surface topography [Link]
Authors Stig O. Hestholm and Bent RuudWe have pursued two‐dimensional (2D) finite‐difference (FD) modelling of seismic scattering from free‐surface topography. Exact free‐surface boundary conditions for the particle velocities have been derived for arbitrary 2D topographies. The boundary conditions are combined with a velocity–stress formulation of the full viscoelastic wave equations. A curved grid represents the physical medium and its upper boundary represents the free‐surface topography. The wave equations are numerically discretized by an eighth‐order FD method on a staggered grid in space, and a leap‐frog technique and the Crank–Nicholson method in time.
In order to demonstrate the capabilities of the surface topography modelling technique, we simulate incident point sources with a sinusoidal topography in seismic media of increasing complexities. We present results using parameters typical of exploration surveys with topography and heterogeneous media. Topography on homogeneous media is shown to generate significant scattering. We show additional effects of layering in the medium, with and without randomization, using a von Kármán realization of apparent anisotropy. Synthetic snapshots and seismograms indicate that prominent surface topography can cause back‐scattering, wave conversions and complex wave patterns which are usually discussed in terms of inter‐crust heterogeneities.
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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)