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- Volume 61, Issue 5, 2013
Geophysical Prospecting - Volume 61, Issue 5, 2013
Volume 61, Issue 5, 2013
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Increasing illumination and sensitivity of reverse‐time migration with internal multiples
More LessABSTRACTReverse‐time migration is a two‐way time‐domain finite‐frequency technique that accurately handles the propagation of complex scattered waves and produces a band‐limited representation of the subsurface structure that is conventionally assumed to be linear in the contrasts in model parameters. Because of this underlying linear single‐scattering assumption, most implementations of this method do not satisfy the energy conservation principle and do not optimally use illumination and model sensitivity of multiply scattered waves. Migrating multiply scattered waves requires preserving the non‐linear relation between the image and perturbation of model parameters. I modify the extrapolation of source and receiver wavefields to more accurately handle multiply scattered waves. I extend the concept of the imaging condition in order to map into the subsurface structurally coherent seismic events that correspond to the interaction of both singly and multiply scattered waves. This results in an imaging process referred to here as non‐linear reverse‐time migration. It includes a strategy that analyses separated contributions of singly and multiply scattered waves to a final non‐linear image. The goal is to provide a tool suitable for seismic interpretation and potentially migration velocity analysis that benefits from increased illumination and sensitivity from multiply scattered seismic waves. It is noteworthy that this method can migrate internal multiples, a clear advantage for imaging challenging complex subsurface features, e.g., in salt and basalt environments. The results of synthetic seismic imaging experiments, including a subsalt imaging example, illustrate the technique.
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Diffraction imaging of sub‐vertical fractures and karst with full‐resolution 3D Ground‐Penetrating Radar
Authors Mark Grasmueck, Miquel Coll Quintà, Kenri Pomar and Gregor P. EberliABSTRACTVertical fractures with openings of less than one centimetre and irregular karst cause abundant diffractions in Ground‐Penetrating Radar (GPR) records. GPR data acquired with half‐wavelength trace spacing are uninterpretable as they are dominated by spatially undersampled scattered energy. To evaluate the potential of high‐density 3D GPR diffraction imaging a 200 MHz survey with less than a quarter wavelength grid spacing (0.05 m × 0.1 m) was acquired at a fractured and karstified limestone quarry near the village of Cassis in Southern France. After 3D migration processing, diffraction apices line up in sub‐vertical fracture planes and cluster in locations of karstic dissolution features. The majority of karst is developed at intersections of two or more fractures and is limited in depth by a stratigraphic boundary. Such high‐resolution 3D GPR imaging offers an unprecedented internal view of a complex fractured carbonate reservoir model analogue. As seismic and GPR wave kinematics are similar, improvements in the imaging of steep fractures and irregular voids at the resolution limit can also be expected from high‐density seismic diffraction imaging.
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Effective anisotropic velocity model from surface monitoring of microseismic events
Authors Yang Zhang, Leo Eisner, William Barker, Michael C. Mueller and Kevin L. SmithABSTRACTWe develop a methodology to obtain a consistent velocity model from calibration shots or microseismicity observed on a buried array. Using a layered 1D isotropic model derived from checkshots as an initial velocity model, we invert P‐wave arrival times to obtain effective anisotropic parameters with a vertical axis of symmetry (VTI). The nonlinear inversion uses iteration between linearized inversion for anisotropic parameters and origin times or depths, which is specific to microseismic monitoring. We apply this technique to multiple microseismic events from several treatments within a buried array. The joint inversion of selected events shows a largely reduced RMS error indicating that we can obtain robust estimates of anisotropic parameters, however we do not show improved source locations. For joint inversion of multiple microseismic events we obtained Thomsen anisotropic parameters ε of 0.15 and δ of 0.05, which are consistent with values observed in active seismic surveys. These values allow us to locate microseismic events from multiple hydraulic fracture treatments separated across thousands of metres with a single velocity model. As a result, we invert the effective anisotropy for the buried array region and are able to provide a more consistent microseismicity mapping for past and future hydraulic fracture stimulations.
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Approximating constant‐Q seismic propagation in the time domain
Authors Tieyuan Zhu, José M. Carcione and Jerry M. HarrisABSTRACTIn this study, we investigate the accuracy of approximating constant‐Q wave propagation by series of Zener or standard linear solid (SLS) mechanisms. Modelling in viscoacoustic and viscoelastic media is implemented in the time domain using the finite‐difference (FD) method. The accuracy of numerical solutions is evaluated by comparison with the analytical solution in homogeneous media. We found that the FD solutions using three SLS relaxation mechanisms as well as a single SLS mechanism, with properly chosen relaxation times, are quite accurate for both weak and strong attenuation. Although the RMS errors of FD simulations using a single relaxation mechanism increase with increasing offset, especially for strong attenuation (Q = 20), the results are still acceptable for practical applications. The synthetic data of the Marmousi‐II model further illustrate that the single SLS mechanism, to model constant Q, is efficient and sufficiently accurate. Moreover, it benefits from less computational costs in computer time and memory.
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Visco‐acoustic prestack reverse‐time migration based on the time‐space domain adaptive high‐order finite‐difference method
Authors Hongyong Yan and Yang LiuABSTRACTIt is important to include the viscous effect in seismic numerical modelling and seismic migration due to the ubiquitous viscosity in an actual subsurface medium. Prestack reverse‐time migration (RTM) is currently one of the most accurate methods for seismic imaging. One of the key steps of RTM is wavefield forward and backward extrapolation and how to solve the wave equation fast and accurately is the essence of this process. In this paper, we apply the time‐space domain dispersion‐relation‐based finite‐difference (FD) method for visco‐acoustic wave numerical modelling. Dispersion analysis and numerical modelling results demonstrate that the time‐space domain FD method has great accuracy and can effectively suppress numerical dispersion. Also, we use the time‐space domain FD method to solve the visco‐acoustic wave equation in wavefield extrapolation of RTM and apply the source‐normalized cross‐correlation imaging condition in migration. Improved imaging has been obtained in both synthetic and real data tests. The migration result of the visco‐acoustic wave RTM is clearer and more accurate than that of acoustic wave RTM. In addition, in the process of wavefield forward and backward extrapolation, we adopt adaptive variable‐length spatial operators to compute spatial derivatives to significantly decrease computing costs without reducing the accuracy of the numerical solution.
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Flexural waves in drill‐string tubulars with variable loads
Authors Flavio Poletto, José M. Carcione and Giorgia PinnaABSTRACTWe revisit the equations governing the bending motions in thin rods and analyse the filtration of flexural waves in vertical drill strings pre‐stressed by gravity. The aim is to study transverse drill‐string vibrations at seismic frequencies for acoustic communication purposes and provide an algorithm for processing reflected and transmitted bending motions generated by downhole lateral vibrations. We obtain the dispersion equation, including attenuation due to a gravity pre‐stress gradient and frequency‐dependent reflection and transmission coefficients at the interface between subsequent tube intervals. We then develop a propagation‐matrix algorithm to simulate flexural waves in a drill string consisting in an assembly of multiple tube sections of different dimensions. The deflection vibrations are obtained at any arbitrary recording point in the drill string. The modelling is cross‐checked with a full‐wave grid algorithm. The analysis shows that the waves produced by a concentrated force are partitioned in standing and propagating modes, which are calculated by using the flexural impedance of the drill string. Moreover, the reflection coefficients weakly depend on the pre‐stress conditions and pre‐stress has important effects for far‐field signal transmission with variable weight on bit (WOB). We discuss the approximations and limits of the method with respect to realistic drilling conditions.
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Application of randomized sampling schemes to curvelet‐based sparsity‐promoting seismic data recovery
Authors Reza Shahidi, Gang Tang, Jianwei Ma and Felix J. HerrmannABSTRACTReconstruction of seismic data is routinely used to improve the quality and resolution of seismic data from incomplete acquired seismic recordings. Curvelet‐based Recovery by Sparsity‐promoting Inversion, adapted from the recently‐developed theory of compressive sensing, is one such kind of reconstruction, especially good for recovery of undersampled seismic data. Like traditional Fourier‐based methods, it performs best when used in conjunction with randomized subsampling, which converts aliases from the usual regular periodic subsampling into easy‐to‐eliminate noise. By virtue of its ability to control gap size, along with the random and irregular nature of its sampling pattern, jittered (sub)sampling is one proven method that has been used successfully for the determination of geophone positions along a seismic line. In this paper, we extend jittered sampling to two‐dimensional acquisition design, a more difficult problem, with both underlying Cartesian and hexagonal grids. We also study what we term separable and non‐separable two‐dimensional jittered samplings. We find hexagonal jittered sampling performs better than Cartesian jittered sampling, while fully non‐separable jittered sampling performs better than separable jittered sampling. Two other 2D randomized sampling methods, Poisson Disk sampling and Farthest Point sampling, both known to possess blue‐noise spectra, are also shown to perform well.
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Direct inversion for a fluid factor and its application in heterogeneous reservoirs
Authors Zhaoyun Zong, Xingyao Yin and Guochen WuABSTRACTPrestack seismic inversion plays an important role in estimating elastic parameters that are sensitive to reservoirs and fluid underground. In this paper, a simultaneous inversion method named FMR‐AVA (Fluid Factor, Mu (Shear modulus), Rho (Density)‐Amplitude Variation with Angle) is proposed based on partial angle stack seismic gathers. This method can be used for direct inversion for the fluid factor, shear modulus and density of heterogeneous reservoirs. Firstly, an FMR approximation equation of a reflection coefficient is derived based on poroelasticity with P‐ and S‐wave moduli. Secondly, a stable simultaneous AVA inversion approach is presented in a Bayesian scheme. This approach has little dependence on initial models. Furthermore, it can be applied in heterogeneous reservoirs whose initial models for inversion are not easy to establish. Finally, a model test shows the superiority of this FMR‐AVA inversion method in stability and independence of initial models. We obtain a reasonable fluid factor, shear modulus and density even with smooth initial models and moderate Gaussian noise. A real data case example shows that the inverted fluid factor, shear modulus and density fit nicely with well log interpretation results, which verifies the effectiveness of the proposed method.
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Reservoir parameter classification of a Miocene formation using a fractal approach to well logging, porosimetry and nuclear magnetic resonance
Authors Jadwiga A. Jarzyna, Maria J. Bala, Zofia M. Mortimer and Edyta PuskarczykABSTRACTA methodology for rock classification is presented that considers lithology and reservoir parameters on the basis of a combined fractal analysis of well logs and mercury porosimetry results with nuclear magnetic resonance outcomes. A sandy‐shaly thinly‐bedded Miocene gas bearing formation in the Carpathian Foredeep is investigated. Fractal correlation dimensions D2 calculated for standard logs are used to distinguish sandstone as the most homogeneous lithological group with the highest porosity. The fractal analysis also confirmed observations of gas accumulations in sandstone, shaly sandstone and sandy claystone as rocks of high porosity. The results of two laboratory methods are combined to improve reservoir properties assessment and evaluate movable media in pore space; this technique was based on the similarity of mercury porosimetry results plotted as cumulative intrusion volume versus pressure or pore diameter and also the curves of cumulative porosity and transverse relaxation time distributions using nuclear magnetic resonance. Close values of porosity from logs, recorded in situ and in laboratory measurements, provide the link between fractal analysis and porosimetry and nuclear magnetic resonance measurements.
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Estimation of pore‐pressure change in a compacting reservoir from time‐lapse seismic data
Authors Margarita Corzo, Colin MacBeth and Olav BarkvedABSTRACTAn approach is developed to estimate pore‐pressure changes in a compacting chalk reservoir directly from time‐lapse seismic attributes. It is applied to data from the south‐east flank of the Valhall field. The time‐lapse seismic signal of the reservoir in this area is complex, despite the fact that saturation changes do not have an influence. This complexity reflects a combination of pressure depletion, compaction and stress re‐distribution throughout the reservoir and into the surrounding rocks. A simple relation is found to link the time‐lapse amplitude and time‐shift attributes to variations in the key controlling parameter of initial porosity. This relation is sufficient for an accurate estimation of pore‐pressure change in the inter‐well space. Although the time‐lapse seismic estimates mostly agree with reservoir simulation, unexplained mismatches are apparent at a small number of locations with lower porosities (less than 38%). The areas of difference between the observations and predictions suggest possibilities for simulation model updating or a better understanding of the physics of the reservoir.
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Reflection and transmission of attenuated waves at the boundary between two dissimilar poroelastic solids saturated with two immiscible viscous fluids
Authors M. Kumar and M.D. SharmaABSTRACTThe phenomenon of reflection and transmission of plane harmonic waves at the plane interface between two dissimilar poroelastic solids saturated with two immiscible viscous fluids is investigated. Both porous media are considered dissipative due to the presence of viscosity in pore‐fluids. Four attenuated (three dilatational and one shear) waves propagate in such a dissipative porous medium. A finite non‐dimensional parameter is used to define the effective connections between the surface‐pores of two media at their common interface. Another finite parameter represents the gas‐share in the saturation of pores. An attenuated wave in a dissipative medium is described through the specification of directions of propagation and maximum attenuation. A general representation of an attenuated wave is defined through its inhomogeneous propagation, i.e., different directions for propagation and attenuation. Incidence of an inhomogeneous wave is considered at the interface between two dissipative porous solids. This results in four reflected and four transmitted inhomogeneous waves. Expressions are derived for the partition of incident energy among the reflected and transmitted waves. Numerical examples are studied to determine the effects of saturating pore fluid, frequency, surface‐pore connections and wave inhomogeneity on the strengths of reflected and transmitted waves. Interaction energy due to the interference of different (inhomogeneous) waves is calculated in both the dissipative porous media to verify the conservation of incident energy.
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Float‐transient electromagnetic method: in‐loop transient electromagnetic measurements on Lake Holzmaar, Germany
Authors L. Mollidor, B. Tezkan, R. Bergers and J. LöhkenABSTRACTLake sediments may serve as archives on paleoclimatic fluctuations, geomagnetic field variations and volcanic activities. Lake Holzmaar in Eifel/Germany is a maar lake and its lacustrine sediments provide paleoclimatic proxy data. Therefore, knowledge about the geometry and, especially, about the thickness of the sediments is very important for determining an optimum drilling location for paleoclimatic studies.
We have developed a floating in‐loop transient electromagnetic method field set up (Float‐transient electromagnetic method) with a transmitter and receiver size of 18 × 18 m2 and 6 × 6 m2 respectively. This special set up enables in‐loop transient electromagnetic method measurements on the surface of freshwater lakes that define the geometry and the thickness of sediments beneath such lakes thus helping to determine optimum drilling locations. Due to the modular design of the new Float‐transient electromagnetic method field set up, this system can be handled by two operators and can easily be transported.
Sixteen in‐loop soundings were carried out on the surface of Lake Holzmaar. The transient electromagnetic method data could not be interpreted by conventional 1D inversions because of the 3D distribution of subsurface conductivity caused by the lake's geometry. Three‐dimensional finite element modelling was applied to explain the observed transients and the 3D conductivity distribution beneath the lake was recovered by taking its geometry into account. The 3D interpretation revealed approximately 55 m thick sediments beneath 20 m deep water in the central part of the lake.
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Interpretation of tensor gravity data using an adaptive tilt angle method
Authors Ahmed Salem, Sheona Masterton, Simon Campbell, J. Derek Fairhead, Jade Dickinson and Colm MurphyABSTRACTFull Tensor Gravity Gradiometry (FTG) data are routinely used in exploration programmes to evaluate and explore geological complexities hosting hydrocarbon and mineral resources. FTG data are typically used to map a host structure and locate target responses of interest using a myriad of imaging techniques. Identified anomalies of interest are then examined using 2D and 3D forward and inverse modelling methods for depth estimation. However, such methods tend to be time consuming and reliant on an independent constraint for clarification. This paper presents a semi‐automatic method to interpret FTG data using an adaptive tilt angle approach. The present method uses only the three vertical tensor components of the FTG data (Tzx, Tzy and Tzz) with a scale value that is related to the nature of the source (point anomaly or linear anomaly). With this adaptation, it is possible to estimate the location and depth of simple buried gravity sources such as point masses, line masses and vertical and horizontal thin sheets, provided that these sources exist in isolation and that the FTG data have been sufficiently filtered to minimize the influence of noise. Computation times are fast, producing plausible results of single solution depth estimates that relate directly to anomalies. For thick sheets, the method can resolve the thickness of these layers assuming the depth to the top is known from drilling or other independent geophysical data. We demonstrate the practical utility of the method using examples of FTG data acquired over the Vinton Salt Dome, Louisiana, USA and basalt flows in the Faeroe‐Shetland Basin, UK. A major benefit of the method is the ability to quickly construct depth maps. Such results are used to produce best estimate initial depth to source maps that can act as initial models for any detailed quantitative modelling exercises using 2D/3D forward/inverse modelling 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 55 (2007)
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Volume 52 (2004)
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