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- Volume 71, Issue 3, 2023
Geophysical Prospecting - Volume 71, Issue 3, 2023
Volume 71, Issue 3, 2023
- ISSUE INFORMATION
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- ORIGINAL ARTICLES
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Umbilic points of slowness surface in elastic orthorhombic media
Authors Shibo Xu, Alexey Stovas and Xingguo HuangAbstractFor 3D seismic data processing, azimuth plays an important role, especially in complex subsurface regions. In such regions, elliptical or anelliptical orthorhombic models are commonly used to describe wave propagation. In these models, the behaviour of the slowness surface needs more detailed analysis. Umbilic points defined by the equal principal curvatures exist in a complex 3D model. In the vicinity of the umbilic points, the traveltime surface has the shifted hyperbola form that needs to be considered in processing operations like velocity analysis. Fractured media characterized by the orthorhombic model are more likely to have umbilic points, and it is important to address their positions. If exists, umbilic points can provide additional constraints in inverting for model parameters. Through a defined condition, we examine the position of the umbilic point and derive their explicit formulas. We analyse umbilic points for elliptical and anelliptical orthorhombic models in the numerical example. For the elliptical orthorhombic model, the formulas for the umbilic point position on different symmetry planes are derived and corresponding conditions are also identified. Further, we numerically examine umbilic point positions for anelliptical orthorhombic models and observe that the umbilic points are located out of two vertical symmetry planes. Moreover, caused by interference from two neighbouring umbilic points, a more significant deviation in traveltime is found in the anelliptical orthorhombic model.
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Fast least‐squares reverse time migration based on stable pseudo‐acoustic wave equations for tilted transverse isotropic media
Authors Oscar Mojica, Reynam C. Pestana and Alan SouzaAbstractConventional tools for seismic imaging normally ignore the anisotropy of the media to produce images of the subsurface, and such omission reduces the quality of the images. Therefore, it is necessary to develop methods which account for subsurface anisotropic properties in order to produce more accurate images. In this paper, we present a least‐squares reverse time migration based on the coupled pseudo‐acoustic equations for tilted transverse isotropic media. Thus, from the stable pseudo‐acoustic wave equation for such media, we derive the linearized modelling (Born modelling) and adjoint migration operators to implement a least‐squares reverse time migration. Then, to save time and effort on development, while ensuring optimal performance of the inversion, we based our implementation on the domain‐specific language Devito, which, in turn, allowed us to easily verify the correctness of the developed operators. Synthetic examples demonstrate the validity of our approach in dealing with tilted transverse isotropic media.
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The effect of free‐surface reflections on depth images for acquisition with buried sources and receivers: Investigation through the point spread function#
Authors Bingkai Han and Xiao‐Bi XieAbstractIn reverse time migration, if sources or receivers are buried at certain depths, the interference between the primary wave and the free‐surface reflection causes losing spectral contents in seismic data. If they are not properly compensated, errors will be carried to the target during the reverse time migration and cause a distorted image by so‐called ghost image. By invoking the point spread function, we investigate how distorted seismic data are mapped to the subsurface. Quantitative relations between the free‐surface parameters (i.e. source/receiver depth, free‐surface incident angle and near‐surface velocity) and wavenumber‐domain illumination can be created, which map missing frequency contents in seismic data to missing wavenumber contents in the point spread function. After transformed back to the space domain, we can investigate its effect on the image distortion. Numerical calculations expand the above approach to handle complex overburden structures and more realistic acquisition geometries. The proposed method provides us with a useful tool to investigate deghosting related problems, for example optimizing parameters of acquisition geometry, evaluating capabilities of existing acquisition systems and data processing technologies in suppressing the free‐surface reflection effect in the depth image, or developing new deghosting approaches.
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A matrix‐free variant of the distorted Born iterative method for seismic full‐waveform inversion
Authors Kui Xiang, Morten Jakobsen, Kjersti Solberg Eikrem and Geir NævdalAbstractThe distorted Born iterative method reduces a nonlinear inverse scattering problem to a sequence of (ill‐posed) linear inverse scattering problems that can be solved using a regularized least‐squares formulation. This method was originally applied to two‐dimensional electromagnetic problems but has been implemented to solve acoustic and electromagnetic problems in three dimensions. It has also been applied to seismic problems but only for moderately large two‐dimensional models. Previous applications of the distorted Born iterative method to seismic inverse scattering were based on a matrix representation of the relevant integral operators. The matrix‐based implementation is simple and transparent but not very suitable for large‐scale computations since the memory requirement and computational cost scales like N2 and N3, where N is the number of grid blocks. In this paper, we introduce a matrix‐free variant of the distorted Born iterative method, which is much more suitable for large‐scale problems, since the memory requirements and computational cost have been reduced to N and Nlog(N), respectively. Our matrix‐free implementation utilizes a fast‐Fourier‐transform‐accelerated iterative method to solve the linear system that results after discretization. In the computation of Fréchet derivatives, we avoid the direct computation of Green's functions for heterogeneous media, by solving an equivalent direct scattering problem. The adjoint of the Fréchet derivative operator is also computed in an efficient matrix‐free manner, by exploiting the physical interpretation and reciprocity of the Green's function. We illustrate the potential of the matrix‐free variant of the distorted Born iterative method using synthetic waveform data for large two‐ and three‐dimensional models. The main conclusion is that the distorted Born iterative method has been transformed into a more practical tool for seismic as well as electromagnetic and acoustic nonlinear inverse scattering.
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Assessment of the impact of noise magnitude and bandwidth variations on a probabilistic inversion of reflection seismic data
AbstractAccounting for an accurate noise model is essential when dealing with real data, which are noisy due to the effect of environmental noise, failures and limitations in data acquisition and processing. Quantifying the noise model is a challenge for practitioners in formulating an inverse problem, and usually, a simple Gaussian noise model is assumed as a white noise model. Here we propose a pragmatic approach to use an estimated seismic wavelet to capture the correlated noise model (coloured noise) for the processed reflection seismic data. We assess the proposed method through a direct inversion of post‐stack seismic data associated with a carbonate reservoir of an oil field in southwest Iran to porosity, using a probabilistic sampling‐based inversion algorithm. In the probabilistic formulation of the inverse problem, we assume eight different noise models with varying bandwidth and magnitude and investigate the corresponding posterior statistics. The results indicate that if the correlated nature of the noise samples is ignored in the noise covariance matrix, some unrealistic features are generated in porosity realizations. In addition, if the noise magnitude is underestimated, the inversion algorithm overfits the data and generates a biased model with low uncertainty. Furthermore, by considering an imperfect bandwidth for the noise model, the error is propagated to the posterior realizations. Assuming the correlated noise in a probabilistic inversion resolves these issues significantly. Therefore, for inverting real seismic data where the estimation of the magnitude and correlations of the noise is not straightforward, the wavelet, which is estimated from the real seismic data, provides a good proxy for describing the correlation of the noise samples or equivalently the bandwidth of the noise model. In addition, it might be better to overestimate the noise magnitude than to underestimate it. This is true especially for an uncorrelated noise model and to a lesser degree also for the correlated noise model.
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The effect of clay and contacts between sand grains on the elastic properties of sandstones
More LessAbstractHigh‐porosity sandstones are important for hydrocarbon production, underground CO2 storage, extraction of geothermal energy and freshwater aquifers. Porosity of sandstones may be estimated using elastic wave velocities, but these depend also on fluid saturation, clay content, pore shape and contacts between sand grains. An understanding of how elastic properties of sandstones depend on these factors is important for characterizing their storage potential and for geomechanical issues, such as sanding, borehole stability, reservoir compaction and fracturing. Ultrasonic velocity measurements in clay‐bearing sandstones indicate that much of the clay in shaly sandstones is non‐load‐bearing. This enables a simple approach for modelling the elastic properties of shaly sandstones that includes the effect of pore concavity and agrees with ultrasonic P‐ and S‐velocities measured in the laboratory. Despite this agreement, some clay may reside within the contacts and may act to inhibit the development of quartz cement, thus reducing porosity loss and helping to preserve storage volume. This appears to be the case for the Lower Mt. Simon Sandstone, a target formation for underground storage of CO2 in the Illinois Basin, for which the bulk moduli agree with the predicted bulk moduli, but the shear moduli are lower than predicted. This appears to result from an increase in a shear compliance of the grain contacts that may enable sliding along the grain contacts and increase the tendency to shear failure.
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Efficient Bayesian inversion of borehole geophysical measurements with a gradient‐based Markov chain Monte Carlo method
Authors Tianqi Deng, Joaquín Ambía and Carlos Torres‐VerdínAbstractWell logs are geophysical measurements of rock properties acquired continuously along a borehole. Because of the physics underlying their operation, borehole logging instruments perform local spatial averages of rock properties in the vicinity of the borehole, yielding well logs that are often affected by tool design, layer boundaries, borehole environmental conditions and mud‐filtrate invasion. Such environmental effects are ubiquitous and can lead to errors in petrophysical–property estimations from well logs if not accounted for in the interpretation. Separate well‐log inversion mitigates environmental effects by matching well logs with their numerical simulations. The latter simulations rely on specific assumptions about the relative geometry of the borehole and the rocks penetrated by the well. For vertical wells penetrating horizontal layers, it is common to assume piecewise‐constant layer properties that we collectively refer to as the earth model; some of these properties have a direct relationship to well logs (e.g. resistivity, gamma ray, density and acoustic slowness). Well‐log inversion is traditionally approached with deterministic methods such as the Levenberg–Marquardt algorithm to minimize the differences between well logs and their numerical simulations, often without accounting for the relationship between measurement noise and model uncertainty. Bayesian inversion, on the other hand, yields the posterior probability distribution of estimated properties and intrinsically quantifies their uncertainty. However, Bayesian Well‐log inversion usually involves the implementation of Markov chain Monte Carlo sampling, which requires a prohibitive number of forward simulations and is therefore not suitable for rapid petrophysical and/or elastic and mechanical evaluations of rocks. We introduce an efficient Bayesian Well‐log inversion method using a gradient‐based Markov chain Monte Carlo method. Gradient‐based Markov chain Monte Carlo is a group of relatively new Markov chain Monte Carlo algorithms that combine gradient updates with Hessian‐based sampling. gradient‐based Markov chain Monte Carlo draws samples efficiently from the posterior probability distribution using the gradient information to guide samples towards high‐probability regions and the Hessian to approximate the posterior probability distribution locally. We verify the gradient‐based Markov chain Monte Carlo inversion method with the inversion of synthetic well logs, including gamma ray, resistivity, density, neutron porosity, photoelectric factor and compressional/shear‐wave slowness. Results show that gradient‐based Markov chain Monte Carlo decreases the computational cost by more than 90% compared to conventional Markov chain Monte Carlo sampling. Next, gradient‐based Markov chain Monte Carlo inversion is applied to a field example from the Central North Sea, where conventional interpretation methods yield shale concentration, sandstone porosity and water saturation with errors up to 19.2%, 14.9% and 48.8%, respectively. Gradient‐based Markov chain Monte Carlo inversion products satisfactorily reproduce the available measurements with only a modest increase in computational cost compared to deterministic inversion approaches.
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A comprehensive study of some features from characteristics of enhanced ground‐penetrating radar wave images through convenient data processing within carbonate rock, west of Assiut, Egypt
Authors Mohamed Osman Ebraheem and Hamza Ahmed IbrahimAbstractThe Eocene limestone plateau, west of Assiut, is characterized by different sedimentary structural features such as fractures, karst, cavities and marble. All conventional methods failed to detect these features due to their inhomogeneities. In this study, a ground‐penetrating radar survey was applied to an area including an old quarry of marble lying at the eastern part of the limestone plateau. The field survey was carried out using a 200‐MHz antenna following the profiling and areal mapping techniques. The acquired ground‐penetrating radar wave images were processed and interpreted using the available software program to enhance the different reflection characteristics from the subsurface anomalous materials. A series of the three‐dimensional model cross section with variable depths were constructed to identify and characterize different georadar facies changes vertically and laterally. The obtained results were adjusted and compared with the excavated features of the quarry; therefore, ground‐penetrating radar anomalies and reflections were calibrated. In the present study, the ground‐penetrating radar survey succeeded in differentiating between dense limestone rocks, onyx marble and microstructural features resulting from recent tectonism. Moreover, the investigation of ground‐penetrating radar reflection waves is useful in differentiating between low‐ and high‐quality limestone and onyx marble. This study identifies the various features of the limestone plateau lying below the ground surface, west of Assiut, that are to be taken into account by planners when establishing new urban centres on the plateau in the future.
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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)