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- Volume 66, Issue 6, 2018
Geophysical Prospecting - Volume 66, Issue 6, 2018
Volume 66, Issue 6, 2018
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Accelerating the T‐matrix approach to seismic full‐waveform inversion by domain decomposition
Authors Morten Jakobsen and Ru‐Shan WuABSTRACTA seismic variant of the distorted Born iterative inversion method, which is commonly used in electromagnetic and acoustic (medical) imaging, has been recently developed on the basis of the T‐matrix approach of multiple scattering theory. The distorted Born iterative method is consistent with the Gauss–Newton method, but its implementation is different, and there are potentially significant computational advantages of using the T‐matrix approach in this context. It has been shown that the computational cost associated with the updating of the background medium Green functions after each iteration can be reduced via the use of various linearisation or quasi‐linearisation techniques. However, these techniques for reducing the computational cost may not work well in the presence of strong contrasts. To deal with this, we have now developed a domain decomposition method, which allows one to decompose the seismic velocity model into an arbitrary number of heterogeneous domains that can be treated separately and in parallel. The new domain decomposition method is based on the concept of a scattering‐path matrix, which is well known in solid‐state physics. If the seismic model consists of different domains that are well separated (e.g., different reservoirs within a sedimentary basin), then the scattering‐path matrix formulation can be used to derive approximations that are sufficiently accurate but far more speedy and much less memory demanding because they ignore the interaction between different domains. However, we show here that one can also use the scattering‐path matrix formulation to calculate the overall T‐matrix for a large model exactly without any approximations at a computational cost that is significantly smaller than the cost associated with an exact formal matrix inversion solution. This is because we have derived exact analytical results for the special case of two interacting domains and combined them with Strassen's formulas for fast recursive matrix inversion. To illustrate the fact that we have accelerated the T‐matrix approach to full‐waveform inversion by domain decomposition, we perform a series of numerical experiments based on synthetic data associated with a complex salt model and a simpler two‐dimensional model that can be naturally decomposed into separate upper and lower domains. If the domain decomposition method is combined with an additional layer of multi‐scale regularisation (based on spatial smoothing of the sensitivity matrix and the data residual vector along the receiver line) beyond standard sequential frequency inversion, then one apparently can also obtain stable inversion results in the absence of ultra‐low frequencies and reduced computation times.
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Differential evolution with subpopulations for high‐dimensional seismic inversion
Authors Zhibin Pan, Hao Liang, Zhaoqi Gao and Jinghuai GaoABSTRACTSeismic inversion has drawn the attention of researchers due to its capability of building an accurate earth model. Such a model will need to be discretised finely, and the dimensions of the inversion problem will be very high. In this paper, we propose an efficient differential evolution algorithm and apply it to high‐dimensional seismic inversion. Our method takes into account the differences among individuals, which are disregarded in conventional differential evolution methods, resulting to a better balance between exploration and exploitation. We divide the entire population into three subpopulations and propose a novel mutation strategy with two phases. Furthermore, we optimise the crossover operator by applying the components having the best objective function values into the crossover operator. We embed this strategy into a cooperative coevolutionary differential evolution and propose a new differential evolution algorithm referred to as a differential evolution with subpopulations. Then, we apply our scheme to both synthetic and field data; the results of high‐dimensional seismic inversion have shown that the proposed differential evolution with subpopulations achieves faster convergence and a higher‐quality solution for seismic inversion.
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Slowness domain offset and traveltime approximations in layered vertical transversely isotropic media
Authors Zvi Koren and Igor RavveABSTRACTConsidering horizontally layered transversely isotropic media with vertical symmetry axis and all types of pure‐mode and converted waves we present a new wide‐angle series approximation for the kinematical characteristics of reflected waves: horizontal offset, intercept time, and total reflection traveltime as functions of horizontal slowness. The method is based on combining (gluing) both zero‐offset and (large) finite‐offset series coefficients. The horizontal slowness is bounded by the critical value, characterised by nearly horizontal propagation within the layer with the highest horizontal velocity. The suggested approximation uses five parameters to approximate the offset, six parameters to approximate the intercept time or the traveltime, and seven parameters to approximate any two or all three kinematical characteristics. Overall, the method is very accurate for pure‐mode compressional waves and shear waves polarised in the horizontal plane and for converted waves. The application of the method to pure‐mode shear waves polarised in the vertical plane is limited due to cusps and triplications. To demonstrate the high accuracy of the method, we consider a synthetic, multi‐layer model, and we plot the normalised errors with respect to numerical ray tracing.
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Directional‐oriented wavefield imaging: a new wave‐based subsurface illumination imaging condition for reverse time migration
Authors Young Seo Kim, Constantine Tsingas and Woodon JeongABSTRACTThe key objective of an imaging algorithm is to produce accurate and high‐resolution images of the subsurface geology. However, significant wavefield distortions occur due to wave propagation through complex structures and irregular acquisition geometries causing uneven wavefield illumination at the target. Therefore, conventional imaging conditions are unable to correctly compensate for variable illumination effects. We propose a generalised wave‐based imaging condition, which incorporates a weighting function based on energy illumination at each subsurface reflection and azimuth angles. Our proposed imaging kernel, named as the directional‐oriented wavefield imaging, compensates for illumination effects produced by possible surface obstructions during acquisition, sparse geometries employed in the field, and complex velocity models. An integral part of the directional‐oriented wavefield imaging condition is a methodology for applying down‐going/up‐going wavefield decomposition to both source and receiver extrapolated wavefields. This type of wavefield decomposition eliminates low‐frequency artefacts and scattering noise caused by the two‐way wave equation and can facilitate the robust estimation for energy fluxes of wavefields required for the seismic illumination analysis. Then, based on the estimation of the respective wavefield propagation vectors and associated directions, we evaluate the illumination energy for each subsurface location as a function of image depth point and subsurface azimuth and reflection angles. Thus, the final directional‐oriented wavefield imaging kernel is a cross‐correlation of the decomposed source and receiver wavefields weighted by the illuminated energy estimated at each depth location. The application of the directional‐oriented wavefield imaging condition can be employed during the generation of both depth‐stacked images and azimuth–reflection angle‐domain common image gathers. Numerical examples using synthetic and real data demonstrate that the new imaging condition can properly image complex wave paths and produce high‐fidelity depth sections.
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High‐resolution multi‐component distributed acoustic sensing
Authors Ivan Lim Chen Ning and Paul SavaABSTRACTDistributed acoustic sensing uses an optical fibre together with an interrogator unit to perform strain measurements. The usage of distributed acoustic sensing in geophysics is attractive due to its dense spatial sampling and low operation cost if the optical fibre is freely accessible. In the borehole environment, optical fibres for distributed acoustic sensing are often readily available as a part of other sensing tools, such as for temperature and pressure. Although the distributed acoustic sensing system promises great potential for reservoir monitoring and surface seismic acquisition, the single axial strain measurement of distributed acoustic sensing along the fibre is inadequate to fully characterise the different wave modes, thus making reservoir characterisation challenging. We propose an acquisition system using five equally spaced helical optical fibres and a straight optical fibre to obtain six different strain projections. This system allows us to reconstruct all components of the 3D strain tensor at any location along the fibre. Analysing the condition number associated with the geometry of the optical fibre, we can systematically search for the optimum design parameters for our configuration. Numerical examples demonstrate the effectiveness of our proposed method to successful reconstruction of the full strain tensor from elastic wavefields of arbitrary complexity.
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S‐wave kinematics in acoustic transversely isotropic media with a vertical symmetry axis
Authors Song Jin and Alexey StovasABSTRACTAcoustic transversely isotropic models are widely used in seismic exploration for P‐wave processing and analysis. In isotropic acoustic media only P‐wave can propagate, while in an acoustic transversely isotropic medium both P and S waves propagate. In this paper, we focus on kinematic properties of S‐wave in acoustic transversely isotropic media. We define new parameters better suited for S‐wave kinematics analysis. We also establish the travel time and relative geometrical spreading equations and analyse their properties. To illustrate the behaviour of the S‐wave in multi‐layered acoustic transversely isotropic media, we define the Dix‐type equations that are different from the ones widely used for the P‐wave propagation.
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High‐definition frequency decomposition
Authors Adam John Eckersley, James Lowell and Peter SzafianABSTRACTSpectral decomposition is a widely used technique in analysis and interpretation of seismic data. According to the uncertainty principle, there exists a lower bound for the joint time–frequency resolution of seismic signals. The highest temporal resolution is achieved by a matching pursuit approach which uses waveforms from a dictionary of functions (atoms). This method, in its pure mathematical form can result in atoms whose shape and phase have no relation to the seismic trace. The high‐definition frequency decomposition algorithm presented in this paper interleaves iterations of atom matching and optimization. It divides the seismic trace into independent sections delineated by envelope troughs, and simultaneously matches atoms to all peaks. Co‐optimization of overlapping atoms ensures that the effects of interference between them are minimized. Finally, a second atom matching and optimization phase is performed in order to minimize the difference between the original and the reconstructed trace. The fully reconstructed traces can be used as inputs for a frequency‐based reconstruction and red–green–blue colour blending. Comparison with the results of the original matching pursuit frequency decomposition illustrates that high‐definition frequency decomposition based colour blends provide a very high temporal resolution, even in the low‐energy parts of the seismic data, enabling a precise analysis of geometrical variations of geological features.
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Application of amplitude spectrum and genetic inversion to determine shaly facies distribution: a case study: Murzuq Basin, Libya
Authors Yousf Abushalah and Laura SerpaABSTRACTLate Ordovician glacial deposits of the Mamuniyat Formation are the main oil reservoir in the Murzuq Basin in Libya. Autopicking the strong reflection at the base of the Silurian shales can be used to map the top of the Mamuniyat reservoir in the area where it is in direct contact with the Silurian shales. However, in areas where the Bir Tlacsin Formation, a mud‐prone unit, is between the Silurian shales and the Mamuniyat reservoir, the top of the Mamuniyat is difficult to pick because the units juxtaposed across the boundary are too similar to produce a strong reflection. Defining the Bir Tlacsin facies is important because it impacts hydrocarbon accumulation and migration. To predict the distribution of the shaly facies of Bir Tlacsin and enhance mapping of the top Mamuniyat reservoir, we utilized a continuous wavelet transform to identify the distinctive thickness of the Hot Shale and Bir Tlacsin units. We also used genetic inversion to distinguish the bulk density of the Bir Tlacsin facies. A 64 Hz frequency gave good time resolution to the amplitude spectrum and was used to predict the facies distribution of the Bir Tlacsin. In contrast, the 24 Hz frequency showed good frequency resolution of the amplitude spectrum and was used to estimate the temporal thickness of the non‐reservoir unit of Bir Tlacsin and Hot Shale. That estimate was then used to modify the autopick horizon for the base of the Silurian reflector to approximate the top of the Mamuniyat reservoir. Because of the large density contrast between the shaly facies of the Bir Tlacsin and the underlying and overlying units, inverted density also provides a way to predict the distribution of the Bir Tlacsin through estimated temporal thickness and to enhance mapping of the top Mamuniyat reservoir through mapping the base of the inverted density of the Bir Tlacsin. A comparison between mapping of the top reservoir using spectral decomposition and inverted density with respect to autopick shows that both methods improved the top of the Mamuniyat reservoir mapping. Prediction of the presence of Bir Tlacsin and improved accuracy of the top of the Mamuniyat reservoir mapping reduce the risk of drilling the shaly facies of Bir Tlacsin and provide a better estimate of the reservoir reserve.
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Scale effects on modelling the seismic signature of gas: results from an outcrop analogue
Authors Maria‐Daphne Mangriotis, Colin MacBeth and Angel BriceñoABSTRACTNumerous examples of reservoir fields from continental and marine environments involve thin‐bedded geology, yet, the inter‐relationship between thin‐bedded geology, fluid flow and seismic wave propagation is poorly understood. In this paper, we explore the 4D seismic signature due to saturation changes of gas within thin layers, and address the challenge of identifying the relevant scales and properties, which correctly define the geology, fluid flow and seismic wave propagation in the field. Based on the study of an outcrop analogue for a thin‐bedded turbidite, we model the time‐lapse seismic response to fluid saturation changes for different levels of model scale, and explore discrepancies in quantitative seismic attributes caused by upscaling. Our model reflects the geological complexity associated with thin‐bedded turbidites, and its coupling to fluid flow, which in turn affects the gas saturation distribution in space, and its time‐lapse seismic imprint. Rock matrix and fluid properties are modelled after selected fields to reproduce representative field models with realistic impedance contrasts. In addition, seismic modelling includes multiples, in order to assess their contribution in seismic propagation through thin gas layers. Our results show that multiples could contribute significantly to the measured amplitudes in the case of thin‐bedded geology. This suggests that forward/inverse modelling involving the flow simulation and seismic domains used in time‐lapse seismic interpretation should account for thin layers, when these are present in the geological setting.
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CO2 storage in the high Arctic: efficient modelling of pre‐stack depth‐migrated seismic sections for survey planning
Authors P. Lubrano Lavadera, D. Kühn, B.D.E. Dando, I. Lecomte, K. Senger and Å. DrottningABSTRACTThe sequestration of CO2 in subsurface reservoirs constitutes an immediate counter‐measure to reduce anthropogenic emissions of CO2, now recognized by international scientific panels to be the single most critical factor driving the observed global climatic warming. To ensure and verify the safe geological containment of CO2 underground, monitoring of the CO2 site is critical. In the high Arctic, environmental considerations are paramount and human impact through, for instance, active seismic surveys, has to be minimized. Efficient seismic modelling is a powerful tool to test the detectability and imaging capability prior to acquisition and thus improve the characterization of CO2 storage sites, taking both geological setting and seismic acquisition set‐up into account. The unique method presented here avoids the costly generation of large synthetic data sets by employing point spread functions to directly generate pre‐stack depth‐migrated seismic images. We test both a local‐target approach using an analytical filter assuming an average velocity and a full‐field approach accounting for the spatial variability of point spread functions. We assume a hypothetical CO2 plume emplaced in a sloping aquifer inspired by the conditions found at the University of Svalbard CO2 lab close to Longyearbyen, Svalbard, Norway, constituting an unconventional reservoir–cap rock system. Using the local‐target approach, we find that even the low‐to‐moderate values of porosity (5%–18%) measured in the reservoir should be sufficient to induce significant change in seismic response when CO2 is injected. The sensitivity of the seismic response to changes in CO2 saturation, however, is limited once a relatively low saturation threshold of 5% is exceeded. Depending on the illumination angle provided by the seismic survey, the quality of the images of five hypothetical CO2 plumes of varying volume differs depending on the steepness of their flanks. When comparing the resolution of two orthogonal 2D surveys to a 3D survey, we discover that the images of the 2D surveys contain significant artefacts, the CO2‐brine contact is misplaced and an additional reflector is introduced due to the projection of the point spread function of the unresolvable plane onto the imaging plane. All of these could easily lead to a misinterpretation of the behaviour of the injected CO2. Our workflow allows for testing the influence of geological heterogeneities in the target aquifer (igneous intrusions, faults, pervasive fracture networks) by utilizing increasingly complex and more realistic geological models as input as more information on the subsurface becomes available.
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Vertical seismic profiling using a daisy‐chained deployment of fibre‐optic cables in four wells simultaneously – Case study at the Ketzin carbon dioxide storage site
Authors Julia Götz, Stefan Lüth, Jan Henninges and Thomas ReinschABSTRACTThe geological storage of carbon dioxide is considered as one of the measures to reduce greenhouse gas emissions and to mitigate global warming. Operators of storage sites are required to demonstrate safe containment and stable behaviour of the storage complex that is achieved by geophysical and geochemical monitoring, combined with reservoir simulations. For site characterization, as well as for imaging the carbon dioxide plume in the reservoir complex and detecting potential leakage, surface and surface‐borehole time‐lapse seismic monitoring surveys are the most widespread and established tools. At the Ketzin pilot site for carbon dioxide storage, permanently installed fibre‐optic cables, initially deployed for distributed temperature sensing, were used as seismic receiver arrays, demonstrating their ability to provide high‐resolution images of the storage formation. A vertical seismic profiling experiment was acquired using 23 source point locations and the daisy‐chained deployment of a fibre‐optic cable in four wells as a receiver array. The data were used to generate a 3D vertical seismic profiling cube, complementing the large‐scale 3D surface seismic measurements by a high resolution image of the reservoir close to the injection well. Stacking long vibro‐sweeps at each source location resulted in vertical seismic profiling shot gathers characterized by a signal‐to‐noise ratio similar to gathers acquired using geophones. A detailed data analysis shows strong dependency of data quality on borehole conditions with significantly better signal‐to‐noise ratio in regions with good coupling conditions.
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Grey wolf optimizer: a new strategy to invert geophysical data sets
Authors Aayush Agarwal, Akash Chandra, Shalivahan Shalivahan and Roshan K SinghABSTRACTThere is no meta‐heuristic approach best suited for solving all optimization problems making this field of study highly active. This results in enhancing current approaches and proposing new meta‐heuristic algorithms. Out of all meta‐heuristic algorithms, swarm intelligence is preferred as it can preserve information about the search space over the course of iterations and usually has fewer tuning parameters. Grey Wolves, considered as apex predators, motivated us to simulate Grey Wolves in the optimization of geophysical data sets. The grey wolf optimizer is a swarm‐based meta‐heuristic algorithm, inspired by mimicking the social leadership hierarchy and hunting behaviour of Grey Wolves. The leadership hierarchy is simulated by alpha, beta, delta and omega types of wolves. The three main phases of hunting, that is searching, encircling and attacking prey, is implemented to perform the optimization. To evaluate the efficacy of the grey wolf optimizer, we performed inversion on the total gradient of magnetic, gravity and self‐potential anomalies. The results have been compared with the particle swarm optimization technique. Global minimum for all the examples from grey wolf optimizer was obtained with seven wolves in a pack and 2000 iterations. Inversion was initially performed on thin dykes for noise‐free and noise‐corrupted (up to 20% random noise) synthetic data sets. The inversion on a single thin dyke was performed with a different search space. The results demonstrate that, compared with particle swarm optimization, the grey wolf optimizer is less sensitive to search space variations. Inversion of noise‐corrupted data shows that grey wolf optimizer has a better capability in handling noisy data as compared to particle swarm optimization. Practical applicability of the grey wolf optimizer has been demonstrated by adopting four profiles (i.e. surface magnetic, airborne magnetic, gravity and self‐potential) from the published literature. The grey wolf optimizer results show better data fit than the particle swarm optimizer results and match well with borehole data.
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Estimating external magnetic field differences at high geomagnetic latitudes from a single station
Authors Ciarán D. Beggan, Laurence Billingham and Ellen ClarkeABSTRACTProviding an accurate estimate of the magnetic field on the Earth's surface at a location distant from an observatory has useful scientific and commercial applications, such as in repeat station data reduction, space weather nowcasting or aeromagnetic surveying. While the correlation of measurements between nearby magnetic observatories at low and mid‐latitudes is good, at high geomagnetic latitudes () the external field differences between observatories increase rapidly with distance, even during relatively low magnetic activity. Thus, it is of interest to describe how the differences (or errors) in external magnetic field extrapolation from a single observatory grow with distance from its location. These differences are modulated by local time, seasonal and solar cycle variations, as well as geomagnetic activity, giving a complex temporal and spatial relationship. A straightforward way to describe the differences are via confidence intervals for the extrapolated values with respect to distance. To compute the confidence intervals associated with extrapolation of the external field at varying distances from an observatory, we used 695 station‐years of overlapping minute‐mean data from 37 observatories and variometers at high latitudes from which we removed the main and crustal fields to isolate unmodelled signals. From this data set, the pairwise differences were analysed to quantify the variation during a range of time epochs and separation distances. We estimate the 68.3%, 95.4% and 99.7% confidence levels (equivalent to the 1σ, 2σ and 3σ Gaussian error bounds) from these differences for all components. We find that there is always a small non‐zero bias that we ascribe to instrumentation and local crustal field induction effects. The computed confidence intervals are typically twice as large in the north–south direction compared to the east‐west direction and smaller during the solstice months compared to the equinoxes.
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