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- Volume 60, Issue 5, 2012
Geophysical Prospecting - Volume 60, Issue 5, 2012
Volume 60, Issue 5, 2012
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Low‐frequency wave propagation in periodically layered media
Authors Yuriy Roganov and Alexey StovasABSTRACTIn this paper, we consider wave propagation in a layered medium. Using the Baker‐Campbell‐Hausdorff series, we expand the logarithm of a propagator matrix in series of frequency. The series coefficients allow us to extend the effective Backus medium for low frequencies.
The proposed technique is applied to vertical propagation in a periodically layered and binary medium as well as for a gradient medium. The velocity dispersion equations are derived for these media. We also consider the layered medium with monoclinic anisotropy. We illustrate the accuracy of the proposed method on synthetic and well‐log data.
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Virtual signals combination – phase analysis for 2D and 3D data representation (acoustic medium)
Authors Flavio Poletto, Cinzia Bellezza, Kees Wapenaar and Aronne CragliettoABSTRACTWe formulate the Kirchhoff‐Helmholtz representation theory for the combination of seismic interferometry signals synthesized by cross‐correlation and by cross‐convolution in acoustic media. The approach estimates the phase of the virtual reflections from the boundary encompassing a volume of interest and subtracts these virtual reflections from the total seismic‐interferometry wavefield. The reliability of the combination result, relevant for seismic exploration, depends on the stationary‐phase and local completeness in partial coverage regions. The analysis shows the differences in the phase of the corresponding seismic interferometry (by cross‐correlation) and virtual reflector (by cross‐convolution) signals obtained by 2D and 3D formulations, with synthetic examples performed to remove water layer multiples in ocean bottom seismic (OBS) acoustic data.
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Elastic properties of seafloor sediments from the modelling of amplitudes of multiple water waves recorded on the seafloor off Bear Island, North Atlantic
Authors Marek Grad, Rolf Mjelde, Wojciech Czuba, Aleksander Guterch and the IPY Project GroupABSTRACTWide‐angle seismic data acquired by use of air‐guns and ocean bottom seismometers (OBS) contain strong direct water arrivals and multiples, generally considered as noise and thus not included in the modelling. However, a recent study showed that standard ray‐tracing modelling of the water multiples recorded off the Bear Island, North Atlantic, provided a reliable estimate of the velocity distribution in the water layer. Here, we demonstrate that including the amplitudes in the modelling provide valuable information about the VP contrast at the seafloor, as well as the VP/VS ratio and attenuation (QP) of the uppermost sediments. The VP contrast at the seafloor is estimated at about 250 m/s, within a precision of approximately ±30 m/s. The VP/VS ratio in the uppermost sedimentary layer is modelled in the range 2.25–2.50 and the QP factor is estimated at 1000 for the water, 30–50 for the uppermost layer and 40–50 for the second sedimentary layer. The values obtained for the sediments suggest a lithology dominated by silty clays, with porosity below average.
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Blocky regularization schemes for Full‐Waveform Inversion★
More LessABSTRACTWith ill‐posed inverse problems such as Full‐Waveform Inversion, regularization schemes are needed to constrain the solution. Whereas many regularization schemes end up smoothing the model, an undesirable effect with FWI where high‐resolution maps are sought, blocky regularization does not: it identifies and preserves strong velocity contrasts leading to step‐like functions. These models might be needed for imaging with wave‐equation based techniques such as Reverse Time Migration or for reservoir characterization. Enforcing blockiness in the model space amounts to enforcing a sparse representation of discontinuities in the model. Sparseness can be obtained using the ℓ1 norm or Cauchy function which are related to long‐tailed probability density functions. Detecting these discontinuities with vertical and horizontal gradient operators helps constraining the model in both directions. Blocky regularization can also help recovering higher wavenumbers that the data used for inversion would allow, thus helping controlling the cost of FWI. While the Cauchy function yields blockier models, both ℓ1 and Cauchy attenuate illumination and inversion artifacts.
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A central difference method with low numerical dispersion for solving the scalar wave equation
Authors Dinghui Yang, Ping Tong and Xiaoying DengABSTRACTIn this paper, we propose a nearly‐analytic central difference method, which is an improved version of the central difference method. The new method is fourth‐order accurate with respect to both space and time but uses only three grid points in spatial directions. The stability criteria and numerical dispersion for the new scheme are analysed in detail. We also apply the nearly‐analytic central difference method to 1D and 2D cases to compute synthetic seismograms. For comparison, the fourth‐order Lax‐Wendroff correction scheme and the fourth‐order staggered‐grid finite‐difference method are used to model acoustic wavefields. Numerical results indicate that the nearly‐analytic central difference method can be used to solve large‐scale problems because it effectively suppresses numerical dispersion caused by discretizing the scalar wave equation when too coarse grids are used. Meanwhile, numerical results show that the minimum sampling rate of the nearly‐analytic central difference method is about 2.5 points per minimal wavelength for eliminating numerical dispersion, resulting that the nearly‐analytic central difference method can save greatly both computational costs and storage space as contrasted to other high‐order finite‐difference methods such as the fourth‐order Lax‐Wendroff correction scheme and the fourth‐order staggered‐grid finite‐difference method.
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The issues of prestack reverse time migration and solutions with Graphic Processing Unit implementation
Authors Hongwei Liu, Bo Li, Hong Liu, Xiaolong Tong, Qin Liu, Xiwen Wang and Wenqing LiuABSTRACTPrestack reverse time migration (RTM) is a very useful tool for seismic imaging but has mainly three bottlenecks: highly intensive computation cost, low‐frequency band imaging noise and massive memory demand. Traditionally, PC‐clusters with thousands of computation nodes are used to perform RTM but it is too expensive for small companies and oilfields. In this article, we use Graphic Processing Unit (GPU) architecture, which is cheaper and faster to implement RTM and we obtain an order of magnitude higher speedup ratio to solve the problem of intensive computation cost. Aiming at the massive memory demand, we adopt the pseudo random boundary condition that sacrifices the computation cost but reduces the memory demand. For rugged topography RTM, it is difficult to deal with the rugged free boundary condition with the finite difference method. We employ a simplified boundary condition that avoids the abundant logical judgment to make the GPU implementation possible and does not induce any sacrifice on efficiency. Besides, we have also done some tests on multi‐GPU implementation for wide azimuth geometries using the latest GPU cards and drivers. Finally, we discuss the challenges of anisotropy RTM and GPU solutions. All the jobs stated above are based on GPU and the synthetic data examples will show the efficiency of the algorithm and solutions.
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Characterizing production‐induced anisotropy of fractured reservoirs having multiple fracture sets
Authors Colin M. Sayers and Lennert D. den BoerABSTRACTSince natural fractures in petroleum reservoirs play an important role in determining fluid flow during production, knowledge of the orientation and density of fractures is required to optimize production. This paper outlines the underlying theory and implementation of a fast and efficient algorithm for upscaling a Discrete Fracture Network (DFN) to predict the fluid flow, elastic and seismic properties of fractured rocks. Potential applications for this approach are numerous and include the prediction of fluid flow, elastic and seismic properties for fractured reservoirs, model‐based inversion of seismic Amplitude Versus Offset and Azimuth (AVOA) data and the optimal placement and orientation of infill wells to maximize production. Given that a single fracture network may comprise hundreds of thousands of individual fractures, the sheer size of typical DFNs has tended to limit their practical applications. This paper demonstrates that with efficient algorithms, the utility of Discrete Fracture Networks can be extended far beyond mere visualization.
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An equivalent medium model for wave simulation in fractured porous rocks
Authors Du Qi‐Zhen, Wang Xue‐Mei, Ba Jing and Zhang QiangABSTRACTSeismic wave propagation in reservoir rocks is often strongly affected by fractures and micropores. Elastic properties of fractured reservoirs are studied using a fractured porous rock model, in which fractures are considered to be embedded in a homogeneous porous background. The paper presents an equivalent media model for fractured porous rocks. Fractures are described in a stress‐strain relationship in terms of fracture‐induced anisotropy. The equations of poroelasticity are used to describe the background porous matrix and the contents of the fractures are inserted into a matrix. Based on the fractured equivalent‐medium theory and Biot's equations of poroelasticity, two sets of porosity are considered in a constitutive equation. The porous matrix permeability and fracture permeability are analysed by using the continuum media seepage theory in equations of motion. We then design a fractured porous equivalent medium and derive the modified effective constants for low‐frequency elastic constants due to the presence of fractures. The expressions of elastic constants are concise and are directly related to the properties of the main porous matrix, the inserted fractures and the pore fluid.
The phase velocity and attenuation of the fractured porous equivalent media are investigated based on this model. Numerical simulations are performed. We show that the fractures and pores strongly influence wave propagation, induce anisotropy and cause poroelastic behaviour in the wavefields. We observe that the presence of fractures gives rise to changes in phase velocity and attenuation, especially for the slow P‐wave in the direction parallel to the fracture plane.
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Monitoring and volumetric estimation of injected CO2 using 4D seismic, petrophysical data, core measurements and well logging: a case study at Ketzin, Germany
ABSTRACTMore than 50 000 tons of CO2 have been injected at Ketzin into the Stuttgart Formation, a saline aquifer, at approximately 620 m depth, as of summer 2011. We present here results from the 1st repeat 3D seismic survey that was performed at the site in autumn 2009, after about 22 000 tons of CO2 had been injected. We show here that rather complex time‐lapse signatures of this CO2 can be clearly observed within a radius of about 300 m from the injection well. The highly irregular amplitude response within this radius is attributed to the heterogeneity of the injection reservoir. Time delays to a reflection below the injection level are also observed. Petrophysical measurements on core samples and geophysical logging of CO2 saturation levels allow an estimate of the total amount of CO2 visible in the seismic data to be made. These estimates are somewhat lower than the actual amount of CO2 injected at the time of the survey and they are dependent upon the choice of a number of parameters. In spite of some uncertainty, the close agreement between the amount injected and the amount observed is encouraging for quantitative monitoring of a CO2 storage site using seismic methods.
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Two‐dimensional controlled‐source electromagnetic interferometry by multidimensional deconvolution: spatial sampling aspects
Authors Jürg Hunziker, Evert Slob, Yuanzhong Fan, Roel Snieder and Kees WapenaarABSTRACTWe use numerically modelled data sets to investigate the sensitivity of electromagnetic interferometry by multidimensional deconvolution to spatial receiver sampling. Interferometry by multidimensional deconvolution retrieves the reflection response below the receivers after decomposition of the fields into upward and downward decaying fields and deconvolving the upward decaying field by the downward decaying field. Thereby the medium above the receiver level is replaced with a homogeneous half‐space, the sources are redatumed to the receiver level and the direct field is removed. Consequently, in a marine setting the retrieved reflection response is independent of any effect of the water layer and the air above. A drawback of interferometry by multidimensional deconvolution is a possibly unstable matrix inversion, which is necessary to retrieve the reflection response. Additionally, in order to correctly separate the upward and the downward decaying fields, the electromagnetic fields need to be sampled properly. We show that the largest possible receiver spacing depends on two parameters: the vertical distance between the source and the receivers and the length of the source. The receiver spacing should not exceed the larger of these two parameters. Besides these two parameters, the presence of inhomogeneities close to the receivers may also require a dense receiver sampling. We show that by using the synthetic aperture concept, an elongated source can be created from conventionally acquired data in order to overcome these strict sampling criteria. Finally, we show that interferometry may work under real‐world conditions with random noise and receiver orientation and positioning errors.
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A gradient‐ratio method for the semi‐automatic interpretation of gravity map data sets
More LessABSTRACTThe application of semi‐automatic interpretation techniques to potential field data can be of significant assistance to a geophysicist. This paper generalizes the magnetic vertical contact model tilt‐depth method to gravity data using a vertical cylinder and buried sphere models. The method computes the ratio of the vertical to the total horizontal derivative of data and then identifies circular contours within it. Given the radius of the contour and the contour value itself, the depth to the source can be determined. The method is applied both to synthetic and gravity data from South Africa. The Matlab source code can be obtained from the author upon request.
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High‐accuracy practical spline‐based 3D and 2D integral transformations in potential‐field geophysics
Authors Bingzhu Wang, Stephen S. Gao, Kelly H. Liu and Edward S. KrebesABSTRACTPotential, potential field and potential‐field gradient data are supplemental to each other for resolving sources of interest in both exploration and solid Earth studies. We propose flexible high‐accuracy practical techniques to perform 3D and 2D integral transformations from potential field components to potential and from potential‐field gradient components to potential field components in the space domain using cubic B‐splines. The spline techniques are applicable to either uniform or non‐uniform rectangular grids for the 3D case, and applicable to either regular or irregular grids for the 2D case. The spline‐based indefinite integrations can be computed at any point in the computational domain. In our synthetic 3D gravity and magnetic transformation examples, we show that the spline techniques are substantially more accurate than the Fourier transform techniques, and demonstrate that harmonicity is confirmed substantially better for the spline method than the Fourier transform method and that spline‐based integration and differentiation are invertible. The cost of the increase in accuracy is an increase in computing time. Our real data examples of 3D transformations show that the spline‐based results agree substantially better or better with the observed data than do the Fourier‐based results. The spline techniques would therefore be very useful for data quality control through comparisons of the computed and observed components. If certain desired components of the potential field or gradient data are not measured, they can be obtained using the spline‐based transformations as alternatives to the Fourier transform techniques.
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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 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)