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- Volume 65, Issue 5, 2017
Geophysical Prospecting - Volume 65, Issue 5, 2017
Volume 65, Issue 5, 2017
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Finite‐offset common reflection surface stack using global optimisation for parameter estimation: a land data example
Authors German Garabito, João Carlos Ribeiro Cruz and Walter SöllnerABSTRACTIn recent years, several research works dealing with velocity model independent seismic imaging have been published. These methods are capable of simulating arbitrary offset seismic sections by stacking a set of measured prestack seismic data along paraxial travel‐time surfaces. Hyperbolic common‐reflection‐surface travel‐time approximation is one of the most robust descriptions, which simulates not only zero‐offset but also finite‐offset sections with high accuracy from noisy multi‐coverage seismic data. In order to reconstruct seismic reflection events in common‐offset sections, the common‐reflection‐surface travel‐time approximation depends on five kinematic attributes (or parameters) for each selected point of the common‐offset seismic section. The main challenge of this method is to provide a computationally efficient data‐driven strategy for accurately determining the best set of parameters. Here, we introduce an approach for simultaneously estimating the five parameters from prestack seismic data by a very fast simulated annealing optimisation algorithm. For each sample point of the common‐offset section to be simulated, we determine only one set of common reflection surface attributes corresponding to the global maximum or the event with highest coherency. We applied our method of simultaneous global optimisation on synthetic and real data examples and showed the potential of the proposed strategy to enhance the reflection events in noisy data, even with very low signal‐to‐noise ratio. Finally, we demonstrate the regularisation capability of our method in a land seismic data example with missing traces for near, middle, and far offsets. In order to better appreciate the field data results, we present the time‐migrated sections with and without application of the proposed regularisation strategy.
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First‐arrival traveltime tomography with modified total‐variation regularization
Authors Wenbin Jiang and Jie ZhangABSTRACTFirst‐arrival traveltime tomography is a robust tool for near‐surface velocity estimation. A common approach to stabilizing the ill‐posed inverse problem is to apply Tikhonov regularization to the inversion. However, the Tikhonov regularization method recovers smooth local structures while blurring the sharp features in the model solution. We present a first‐arrival traveltime tomography method with modified total‐variation regularization to preserve sharp velocity contrasts and improve the accuracy of velocity inversion. To solve the minimization problem of the new traveltime tomography method, we decouple the original optimization problem into the two following subproblems: a standard traveltime tomography problem with the traditional Tikhonov regularization and a L2 total‐variation problem. We apply the conjugate gradient method and split‐Bregman iterative method to solve these two subproblems, respectively. Our synthetic examples show that the new method produces higher resolution models than the conventional traveltime tomography with Tikhonov regularization, and creates less artefacts than the total variation regularization method for the models with sharp interfaces. For the field data, pre‐stack time migration sections show that the modified total‐variation traveltime tomography produces a near‐surface velocity model, which makes statics corrections more accurate.
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Inferences of ocean currents from seismic streamer position data
More LessABSTRACTThis paper describes the first attempt to infer ocean currents from the shapes of seismic streamers using real data. It demonstrates that it is feasible to infer the ocean currents, using a total least‐squares solution at each shotpoint, when there is no lateral steering. There are some artefacts in the inferred currents when there is lateral steering; this is believed to be caused by errors in estimating the streamer velocity. This paper describes the residual equations that form the cost function and discusses how to choose weights in the cost function based on physical criteria. Correctly choosing weights is something of an art and requires further research to make automatic and robust.
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A study of the geophysical response of distributed fibre optic acoustic sensors through laboratory‐scale experiments
Authors Bence Papp, Daniela Donno, James E. Martin and Arthur H. HartogABSTRACTIn the past few years, distributed acoustic sensing has gained great interest in geophysics. This acquisition technology offers immense improvement in terms of efficiency when compared with current geophysical acquisition methods. However, the fundamentals of the measurement are still not fully understood because direct comparisons of fibre data with conventional geophysical sensors are difficult during field tests. We present downscaled laboratory experiments that enabled us to characterise the relationship between the signals recorded by conventional seismic point receivers and by distributed fibre optic sensors. Interrogation of the distributed optical fibre sensor was performed with a Michelson interferometer because this system is suited to compact test configurations, and it requires only a very simple data processing workflow for extracting the signal outputs. We show acoustic data that were recorded simultaneously by both the fibre optical interferometer and conventional three‐component accelerometers, thus enabling the comparison of sensor performance. We present results focused on the directionality of fibre measurements, on the amplitude variation with angle of incidence, and on the transfer function that allows accelerometer signals to be transformed into optical fibre signals. We conclude that the optical fibre response matches with the array of the displacement differences of the inline accelerometers deployed along the fibre length. Moreover, we also analysed the influence of various types of coupling and fibre cable coating on the signal responses, emphasising the importance of these parameters for field seismic acquisitions when using the distributed fibre optic technology.
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Preserved travel‐time smoothing in orthorhombic media
Authors Shibo Xu and Alexey StovasABSTRACTCertain degree of smoothness of velocity models is required for most ray‐based migration and tomography. Applying conventional smoothing in model parameters results in offset‐dependent travel‐time errors for reflected events, which can be large even for small contrasts in model parameters between the layers. This causes the shift in both the depth and residual moveout of the migrated images. To overcome this problem in transversely isotropic medium with a vertical symmetry axis, the preserved travel‐time smoothing method was proposed earlier. We extend this method for orthorhombic media with and without azimuthal variation between the layers. We illustrate this method for a single interface between two orthorhombic layers and show that the smoothing‐driven errors in travel time are very small for practical application.
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Perturbation‐based moveout approximations in anisotropic media
Authors Shibo Xu, Alexey Stovas and Qi HaoABSTRACTThe moveout approximations play an important role in seismic data processing. The standard hyperbolic moveout approximation is based on an elliptical background model with two velocities: vertical and normal moveout. We propose a new set of moveout approximations based on a perturbation series in terms of anellipticity parameters using the alternative elliptical background model defined by vertical and horizontal velocities. We start with a transversely isotropic medium with a vertical symmetry axis. Then, we extend this approach to a homogeneous orthorhombic medium. To define the perturbation coefficients for a new background, we solve the eikonal equation with horizontal velocities in transversely isotropic medium with a vertical symmetry axis and orthorhombic media. To stabilise the perturbation series and improve the accuracy, the Shanks transform is applied for all the cases. We select different parameterisations for both velocities and anellipticity parameters for an orthorhombic model. From the comparison in traveltime error, the new moveout approximations result in better accuracy comparing with the standard perturbation‐based methods and other approximations.
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Elastic wave‐vector decomposition in heterogeneous anisotropic media
Authors Yanadet Sripanich, Sergey Fomel, Junzhe Sun and Jiubing ChengABSTRACTThe goal of wave‐mode separation and wave‐vector decomposition is to separate a full elastic wavefield into three wavefields with each corresponding to a different wave mode. This allows elastic reverse‐time migration to handle each wave mode independently. Several of the previously proposed methods to accomplish this task require the knowledge of the polarisation vectors of all three wave modes in a given anisotropic medium. We propose a wave‐vector decomposition method where the wavefield is decomposed in the wavenumber domain via the analytical decomposition operator with improved computational efficiency using low‐rank approximations. The method is applicable for general heterogeneous anisotropic media. To apply the proposed method in low‐symmetry anisotropic media such as orthorhombic, monoclinic, and triclinic, we define the two S modes by sorting them based on their phase velocities (S1 and S2), which are defined everywhere except at the singularities. The singularities can be located using an analytical condition derived from the exact phase‐velocity expressions for S waves. This condition defines a weight function, which can be applied to attenuate the planar artefacts caused by the local discontinuity of polarisation vectors at the singularities. The amplitude information lost because of weighting can be recovered using the technique of local signal–noise orthogonalisation. Numerical examples show that the proposed approach provides an effective decomposition method for all wave modes in heterogeneous, strongly anisotropic media.
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Directional interpolation of multicomponent data
More LessABSTRACTA method for interpolation of multicomponent streamer data based on using the local directionality structure is presented. The derivative components are used to estimate a vector field that locally describes the direction with the least variability. Given this vector field, the interpolation can be phrased in terms of the solution of a partial differential equation that describes how energy is transported between regions of missing data. The approach can be efficiently implemented using readily available routines for computer graphics. The method is robust to noise in the measurements and particularly towards high levels of low‐frequent noise that is present in the derivative components of the multicomponent streamer data.
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Effects of fracture intersections on seismic dispersion: theoretical predictions versus numerical simulations
Authors Junxin Guo, J. Germán Rubino, Stanislav Glubokovskikh and Boris GurevichABSTRACTThe detection and characterisation of domains of intersecting fractures are important goals in several disciplines of current interest, including exploration and production of unconventional reservoirs, nuclear waste storage, CO2 sequestration, and groundwater hydrology, among others. The objective of this study is to propose a theoretical framework for quantifying the effects of fracture intersections on the frequency‐dependent elastic properties of fluid‐saturated porous and fractured rocks. Three characteristic frequency regimes for fluid pressure communication are identified. In the low‐frequency limit, fractures are in full pressure communication with the embedding porous matrix and with other fractures. Conversely, in the high‐frequency limit, fractures are hydraulically isolated from the matrix and from other fractures. At intermediate frequencies, fractures are hydraulically isolated from the matrix porosity but can be in hydraulic communication with each other, depending on whether fracture sets are intersecting. For each frequency regime, the effective stiffness coefficients are derived using the linear‐slip theory and anisotropic Gassmann equations. Explicit mathematical expressions for the two characteristic frequencies that separate the three frequency regimes are also determined. Theoretical predictions are then applied to two synthetic 2D samples, each containing two orthogonal fracture sets: one with and another without intersections. The resulting stiffness coefficients, Thomsen‐style anisotropy parameters, and the transition frequencies show good agreement with corresponding numerical simulations. The theoretical results are applicable not only to 2D but also to 3D fracture systems and are amenable to being employed in inversion schemes designed to characterise fracture systems.
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Multistep inversion workflow for 3D long‐offset damped elastic waves in the Fourier domain
Authors Petr V. Petrov and Gregory A. NewmanABSTRACTWe present a new workflow for imaging damped three‐dimensional elastic wavefields in the Fourier domain. The workflow employs a multiscale imaging approach, in which offset lengths are laddered, where frequency content and damping of the data are changed cyclically. Thus, the inversion process is launched using short‐offset and low‐frequency data to recover the long spatial wavelength of the image at a shallow depth. Increasing frequency and offset length leads to the recovery of the fine‐scale features of the model at greater depths. For the fixed offset, we employ (in the imaging process) a few discrete frequencies with a set of Laplace damping parameters. The forward problem is solved with a finite‐difference frequency‐domain method based on a massively parallel iterative solver. The inversion code is based upon the solution of a least squares optimisation problem and is solved using a nonlinear gradient method. It is fully parallelised for distributed memory computational platforms. Our full‐waveform inversion workflow is applied to the 3D Marmousi‐2 and SEG/EAGE Salt models with long‐offset data. The maximum inverted frequencies are 6 Hz for the Marmousi model and 2 Hz for the SEG/EAGE Salt model. The detailed structures are imaged successfully up to the depth approximately equal to one‐third of the maximum offset length at a resolution consistent with the inverted frequencies.
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Characterisation and multifaceted anisotropy assessment of Corvio sandstone for geological CO2 storage studies
ABSTRACTWe present a comprehensive characterisation of the physical, mineralogical, geomechanical, geophysical, and hydrodynamic properties of Corvio sandstone. This information, together with a detailed assessment of anisotropy, is needed to establish Corvio sandstone as a useful laboratory rock‐testing standard for well‐constrained studies of thermo–hydro–mechanical–chemical coupled phenomena associated with CO2 storage practices and for geological reservoir studies in general. More than 200 core plugs of Corvio sandstone (38.1 and 50 mm diameters, 2:1 length‐to‐diameter ratio) were used in this characterisation study, with a rock porosity of 21.7 ± 1.2%, dry density 2036 ± 32 kg m−3, and unconfined compressive and tensile strengths of 41 ± 3.28 and 2.3 ± 0.14 MPa, respectively. Geomechanical tests show that the rock behaves elastically between ∼10 and ∼18 MPa under unconfined conditions with associated Young's modulus and Poisson's ratio of 11.8 ± 2.8 GPa and 0.34 ± 0.01 GPa, respectively. Permeability abruptly decreases with confining pressure up to ∼10 MPa and then stabilises at ∼1 mD. Ultrasonic P‐ and S‐wave velocities vary from about 2.8–3.8 km s−1 and 1.5–2.4 km s−1, respectively, over confining and differential pressures between 0.1 and 35 MPa, allowing derivation of associated dynamic elastic moduli. Anisotropy was investigated using oriented core plugs for electrical resistivity, elastic wave velocity and attenuation, permeability, and tracer injection tests. Corvio sandstone shows weak transverse isotropy (symmetry axis normal to bedding) of <10% for velocity and <20% for attenuation.
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Out‐of‐plane effects in 2D borehole‐to‐surface resistivity tomography and applications in mineral exploration
Authors Gang Zhang, Gui‐Bin Zhang, Zheng‐yuan Jia and Qing‐Tian LüABSTRACTIn this paper, we discuss the effects of anomalous out‐of‐plane bodies in two‐dimensional (2D) borehole‐to‐surface electrical resistivity tomography with numerical resistivity modelling and synthetic inversion tests. The results of the two groups of synthetic resistivity model tests illustrate that anomalous bodies out of the plane of interest have an effect on two‐dimensional inversion and that the degree of influence of out‐of‐plane body on inverted images varies. The different influences are derived from two cases. One case is different resistivity models with the same electrode array, and the other case is the same resistivity model with different electrode arrays. Qualitative interpretation based on the inversion tests shows that we cannot find a reasonable electrode array to determine the best inverse solution and reveal the subsurface resistivity distribution for all types of geoelectrical models. Because of the three‐dimensional effect arising from neighbouring anomalous bodies, the qualitative interpretation of inverted images from the two‐dimensional inversion of electrical resistivity tomography data without prior information can be misleading. Two‐dimensional inversion with drilling data can decrease the three‐dimensional effect. We employed two‐ and three‐dimensional borehole‐to‐surface electrical resistivity tomography methods with a pole–pole array and a bipole–bipole array for mineral exploration at Abag Banner and Hexigten Banner in Inner Mongolia, China. Different inverse schemes were carried out for different cases. The subsurface resistivity distribution obtained from the two‐dimensional inversion of the field electrical resistivity tomography data with sufficient prior information, such as drilling data and other non‐electrical data, can better describe the actual geological situation. When there is not enough prior information to carry out constrained two‐dimensional inversion, the three‐dimensional electrical resistivity tomography survey is the better choice.
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Exploring seismic inversion methodologies for non‐stationary geological environments: a benchmark study between deterministic and geostatistical seismic inversion
Authors Sérgio Carmo, Leonardo Azevedo and Amílcar SoaresABSTRACTThis paper presents a comparison between subsurface impedance models derived from different deterministic and geostatistical seismic inversion methodologies applied to a challenging synthetic dataset. Geostatistical seismic inversion methodologies nowadays are common place in both industry and academia, contrasting with traditional deterministic seismic inversion methodologies that are becoming less used as part of the geo‐modelling workflow. While the first set of techniques allows the simultaneous inference of the best‐fit inverse model along with the spatial uncertainty of the subsurface elastic property of interest, the second family of inverse methodology has proven results in correctly predicting the subsurface elastic properties of interest with comparatively less computational cost. We present herein the results of a benchmark study performed over a realistic three‐dimensional non‐stationary synthetic dataset in order to assess the performance and convergence of different deterministic and geostatistical seismic inverse methodologies. We also compare and discuss the impact of the inversion parameterisation over the exploration of the model parameter space. The results show that the chosen seismic inversion methodology should always be dependent on the type and quantity of the available data, both seismic and well‐log, and the complexity of the geological environment versus the assumptions behind each inversion technique. The assessment of the model parameter space shows that the initial guess of traditional deterministic seismic inversion methodologies is of high importance since it will determine the location of the best‐fit inverse solution.
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Compaction trend versus seismic anisotropy in shaly formations
Authors Marina Pervukhina and Patrick N.J. RasolofosaonABSTRACTShales comprise more than 60% of sedimentary rocks and form natural seals above hydrocarbon reservoirs. Their sealing capacity is also used for storage of nuclear wastes. The world's most important conventional oil and gas reservoirs have their corresponding source rocks in shale. Furthermore, shale oil and shale gas are the most rapidly expanding trends in unconventional oil and gas. Shales are notorious for their strong elastic anisotropy, i.e., so‐called vertical transverse isotropy. This vertical transverse isotropy, characterised by a vertical axis of invariance, is of practical importance as it is required for correct surface seismic data interpretation, seismic to well tie, and amplitude versus offset analysis. A rather classical paradigm makes a clear link between compaction in shales and the alignment of the clay platelets (main constituent of shales). This would imply increasing anisotropy strength with increasing compaction. Our main purpose is to check this prediction on two large databases in shaly formations (more than 800 samples from depths of 0–6 km) by extracting the major trends in the relation between seismic anisotropy and compaction. The statistical analysis of the database shows that the simultaneous increase in density and velocity, a classical compaction signature, is quite weakly correlated with the anisotropy strength. As a consequence, compaction can be excluded as a major cause of seismic anisotropy, at least in shaly formations. Also, the alignment of the clay platelets can explain most of the anisotropy measurements of both databases. Finally, a method for estimating the orientation distribution function of the clay platelets from the measurement of the anisotropy parameters is suggested.
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On the approximation of the potential fields when using right rectangular prisms
Authors Michele De Stefano and Stefano PanepintoABSTRACTDue to its simplicity, stability, and efficiency, the use of right rectangular prisms is still widespread for potential field modelling and inversion. It is well known that modelling the subsurface with Cartesian grids has important consequences in terms of accuracy of the results. In this paper, we review the main issues that geophysicists face in day‐to‐day work when trying to use right rectangular prisms for performing gravity or full tensor gravity modelling and inversions. We demonstrate the results both theoretically and through Monte Carlo simulations, also exploiting concepts from fractal geometry. We believe that the guidelines contained in this paper may suggest a good practice for the day‐to‐day work of geophysicists dealing with gravity and full tensor gravity data.
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Transient electromagnetic surveys with unimodal transverse magnetic field: ideas and results
Authors Vladimir S. Mogilatov, Arkadiy V. Zlobinskiy and Boris P. BalashovABSTRACTThe theory behind transient electromagnetic surveys can be well described in terms of transverse magnetic and transverse electric modes. Soundings using transverse magnetic and transverse electric modes require different source configurations. In this study, we consider an alternating transverse magnetic field excitation by a circular electric dipole. The circular electric dipole transmitter is a horizontal analogue of the vertical electric dipole. Offshore surveys using circular electric dipole might represent an alternative to the conventional marine controlled‐source electromagnetic method at shallow sea and/or for exploring relatively small targets. Field acquisition is carried out by recording either electric or magnetic responses. Electric responses bear information on the 1D structure of a layered earth and successfully resolve high‐resistivity targets in marine surveys. Land‐based circular electric dipole soundings are affected by induced polarisation. On the contrary, magnetic responses are absent on the surface of a 1D earth, and as a result, they are very sensitive to any and even very small 3D conductivity perturbations. In addition, they are sensitive to induced polarisation or some other polarisation effects in the subsurface. At present, circular electric dipole transmitters and magnetic receivers are successfully used in on‐land mineral and petroleum exploration.
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Research Note: The sensitivity of surface seismic P‐wave data in transversely isotropic media to reflector depth
More LessABSTRACTThe leading component of the high‐frequency asymptotic description of the wavefield, given by the travel time, is governed by the eikonal equation. In anisotropic media, traveltime measurements from seismic experiments conducted along one surface cannot constrain the long‐wavelength attribute of the medium along the orthogonal‐to‐the‐surface direction, as anisotropy introduces an independent parameter controlling wave propagation in the orthogonal direction. Since travel times measured on the Earth's surface in transversely isotropic media with a vertical symmetry axis are mainly insensitive to the absolute value of the anisotropic parameter responsible for relating these observations to depth δ, the travel time was perturbed laterally to investigate the traveltime sensitivity to lateral variations in δ. This formulation can be used to develop inversion strategies for lateral variations in δ in acoustic transversely isotropic media, as the surface‐recorded data are sensitive to it even if the model is described by the normal moveout velocity and horizontal velocity, or the anellipticity parameter η. Numerical tests demonstrate the enhanced sensitivity of our data when the model is parameterised with a lateral change in δ.
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Volume 72 (2023 - 2024)
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