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80th EAGE Conference & Exhibition 2018 Workshop Programme
- Conference date: 10 Jun 2018 - 15 Jul 2018
- Location: Copenhagen , Denmark
- ISBN: 978-94-6282-257-3
- Published: 10 June 2018
99 results
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An accurate Eulerian travel-time computation: implication for slope tomography
Authors J.V. Virieux, S. Sambolian, P. Le Bouteiller, S. Operto, A. Ribodetti and B. TavakoliComputation of travel-times and its spatial derivatives is at the heart of many seismic imaging techniques. We shall discuss shortly the Lagrangian, semi-lagrangian and Eulerian approaches which have been investigated in the past. Eulerian approaches enjoy recent advances when considering anisotropic media with complex topographies while having the attractive regular sampling needed for slope tomography and migration workflow. While this Eulerian approach is quite efficient for firstarrival travel-time/slope tomography and has replaced ray tracing approach, it has not yet replaced standard ray tracing tools (in spite of its irregular sampling of the medium) in migration where multiple arrivals are important. An efficient and accurate discontinuous Galerkin method for solving the non-linear Eikonal partial differential equation providing travel-times might be an attractive proposition both for tomography and migration. Thanks to this Eulerian approach, data- and domainspace definitions involve only subsurface parameters such as velocity parameters and imaging point positions for slope tomography while the forward modeling has a computational complexity depending only on the acquisition design and not on the picking density. Still bottle-necks exist when considering multiple arrivals and their identification will help to find solutions in the future.
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Diffraction wavefront tomography - efficient automated velocity inversion for multi-fold and single-channel data
Authors A.B. Bauer, B.S. Schwarz and D.G. GajewskiSeismic multi-channel acquisition offers the benefits of high data redundancy and improved illumination. However, large-offset recordings are generally expensive to acquire. For the case of passive seismic data, no offsets are available. Diffractions provide superior illumination compared to reflections, but typically have low amplitudes. However, diffractions possess unique properties, which bear the potential to improve the lateral resolution of inversion results. We present wavefront tomography as an efficient and stable tool for velocity inversion of both single-channel and multichannel as well as passive seismic data. For the case of single-channel data, we suggest an approach that reveals the diffracted background in the data through automated adaptive subtraction of the dominant reflected wavefield. Based on local stacking and coherence evaluation, the recorded diffracted events are treated as passive source wavefields characterized in terms of local properties of wavefronts emerging at the registration surface. The subsequently obtained inversion results are in good agreement with fault zones known from the local geology. In an industrial multi-channel field data example, we carried out a joint inversion of reflections and diffractions and present a laterally well-resolved velocity model, which we validate with reverse-time depth-migrated (RTM) results.
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Multi-scale traveltime inversion: a robust method for velocity estimation in difficult geological context
Authors C. Barnes and M. ChararaA robust method for velocity estimation is presented. We regularize the traveltime inversion using a multi-scale approach, gradient conditioning or joint inversion using additional seismic datasets.
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Integrating Reflection-FWI in depth imaging velocity model building workflows
Authors C.R. Rivera, E. Bergounioux, D. Otriz-Rubio and F. AudebertReflection full waveform inversion (RFWI) is the next step for wave equation based model building techniques. In this work we will present ways to integrate our implementation of Reflection full waveform inversion in depth imaging workflows with examples. Our RFWI implementation is based on multi-parameter inversion where impedance and velocity are inverted in a sequential manner, thus allowing for focusing and repositioning of misplaced reflectors.
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Traveltime based reflection full waveform inversion
More LessIn this paper, we present a new method called traveltime based reflection full waveform inversion (TT-RFWI) that corrects the kinematic errors between the synthetic and real data. With the new objective function and gradient, the proposed method aims to avoid convergence to local minima with inaccurate initial model and in the meanwhile takes benefits of reflection data. The goal is to provide a deeper reliable low-wavenumber update with reflected energy while missing a good starting background model.
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Understanding resolution and sharpness in ray based tomography
Authors D.E. Nichols and Y. YouRay based tomography is still the workhorse for velocity model building. Recent advances have shown that we can build much higher resolution models than was previously understood. We will show that some of this uplift comes from better quality data, some comes from better constraints on the model, and some comes from improvements in the inversion process.
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Shaping the velocity model beyond the diving wave penetration
More LessFull-waveform inversion (FWI) usually utilizes diving and refracted waves to update the low-wavenumber/background components of the model; however, the update is often depth limited due to the limited offset range acquired. To extend conventional FWI beyond the limits of the transmitted energy, we must use reflection data. There are several ways of using the reflections to update the background model. Field data examples demonstrate that, even in a complex subsalt Gulf of Mexico setting, the background velocity model can be updated from shallow to deep water using conventional FWI followed by reflection-based FWI.
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Ray versus full wave velocity model building: status and challenges
By G. LambaréWhile full wave based velocity model building approaches have earned their stripes during the last decade, ray based approaches remain the working horse in industry. I review here first the successes and the limitations of both families of approaches. If it appears that ray based approaches suffer of limitations in complex media, others of their characteristics like the picking (often seen as a weakness) or the computation of Fréchet derivatives may also appear in practice as decisive advantages. I believe that these are points on which we should challenge and even inspire full wave approaches. By the end rather than opposing ray based and full wave approaches I review the various trends in terms of the combination of the tools and concepts which appear from my point of view as the most promising.
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Machine Learning and Wave Equation Inversion of Skeletonized Data
More LessWe compare the full waveform inversion (FWI), skeletonized wave equation inversion (SWI), and supervised Machine Learning (ML) algorithms with one another. For velocity inversion the advantage of SWI over FWI is it is more robust and has less of a tendency in getting stuck at local minima. This is because SWI only needs to explain the kinematic information in the seismograms, which is less demanding than FWI’s difficult task of explaining all of the wiggles in every arrival. The disadvantage of SWI is that it provides a tomogram with theoretically less resolution than the ideal FWI tomogram. In this case, the SWI tomogram can be used as an excellent starting model for FWI. SWI is similar to supervised Machine Learning in that both use skeletonized representations of the original data. Simpler input data lead to simpler misfit functions characterized by quicker convergence to useful solutions. I show how a hybrid ML+SWI method and the implicit function theorem can be used to extract almost any skeletal feature in the data and invert it using the wave equation. This assumes that the skeletal data are sensitive to variations in the model parameter of interest.
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Examples of asymptotic analysis for understanding and building seismic wave-equation imaging tools
Authors H.J. Chauris, T. Zhou, E. Cocher and Y. LiMigration velocity analysis aims at determining an optimal velocity macro-model to focus energy in the subsurface. The replacement of the adjoint operator by the inverse operator in the extended subsurface offset domain offers a more robust velocity analysis approach. In order to better understand the non-linear relationship between the data and the velocity macro-model, we review here the behaviour of different wave-equation based operators through an asymptotic analysis. It is a very useful tool for interpreting and even building some imaging algorithms. In particular, we establish a mapping between the data and the subsurface image domains. This mapping offers new possibilities to better understand how velocity analysis behaves.
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The evolution of tomography and FWI: an example of high resolution velocity estimation using refraction and reflection FWI
Authors I.F. Jones, J. Singh, P. Cox, M. Warner, C. Hawke, D. Harger and S. GreenwoodThe primary objective of this project was to improve the understanding of the internal structure of the Viscata and Fortuna reservoirs, and this objective was met via clearer internal imaging of these reservoir intervals and the overlying gas-charged sediments. The underlying geophysical challenge was the presence of extensive, but small-scale low-velocity gas pockets, which gave rise to significant and cumulative image distortion at target level. This distortion had not been resolved in a vintage 2013 broadband preSDM project, as the velocity model was not sufficiently well resolved. But in the initial commercial phase of this project, high-resolution non-parametric tomography using improved broadband deghosted data enabled us to achieve the stated objectives. The follow-on work, considered here, deals with the use of full waveform inversion, to see if we could further delineate small-scale velocity anomalies, associated with the highly compartmentalized reservoir units.
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Nonlinear slope tomography: a versatile data- and challenge-driven velocity model building technique
Authors T. Allemand, P. Guillaume, F. Gamar, G. Lambaré, O. Leblanc, J. Messud and J.P. MontelMost recent depth seismic imaging studies involve both full-wave and ray-based methods as the resolution of complex ill-posed problems often require a wide range of tools. Also ray based methods suffer from well-known drawbacks, they will provide accurate results in most of the cases. Moreover, relying on nonlinear slope tomography, a challenge-driven approach can be designed for each problem by incorporating prior or external information as needed. Here we propose to show such examples of the challenge-driven approach.
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Borrowing insight from travel-time reflection tomography to solve the depth reflectivity-velocity coupling issue of RFWI.
Authors R. Baina and R. ValensiThe reflectivity-velocity coupling is one of the major reason of the slow convergence of the conventional Reflection Full Waveform Inversion (RFWI) approach. In this communication, we start by reviewing the travel-time reflection tomography (RT) and the different ways of accounting for the depth-velocity coupling. Then, we draw the connection between the inverse problem of the RFWI approach and the inverse problem of RT. From this analogy, we see that the conventional RFWI does not fully account for the reflectivity-velocity coupling effects. To overcome this issue, we propose to reformulate the conventional RFWI problem into a Reflectivity-Velocity Consistent Waveform Inversion (RVCWI) method. Finally, with a numerical example, we compare the performances of the conventional RFWI and the RVCWI approaches. This numerical experiment confirms us the very slow convergence rate of the conventional RFWI approach and the much faster convergence rate obtained with the RVCWI approach .
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Migration Velocity Analysis with a second-order Gauss-Newton scheme: a 2D real data example
Authors R. Soubaras and B. GratacosWe present the application of a Migration Velocity Analysis with a second-order Gauss-Newton update scheme (Soubaras and Gratacos (2017)) on a real 2D dataset. This second order scheme includes a deconvolution of the gradient by the Hessian, which removes the “gradient artefacts” on the velocity gradient and produces an extended reflectivity which is a least-squares migration rather than a migration. Starting with a crude initial velocity model (linear gradient from the water bottom) and leaving the velocity unconstrained, we obtained a detailed velocity model which is consistent with the geology, as well as flattened gathers.
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Local probabilistic inversion of seismic AVO data
Authors H.J. Hansen and A.F. JakobsenThe drive towards extracting ever increasing amounts of information from seismic data has in the recent years increased the focus on the treatment and analysis of the associated uncertainties and lead to the utilization of additional information directly in the quantitative analysis of seismic data. In this context, a probabilistic framework for this quantitative analysis has a number of benefits, among these a rigorous treatment of the seismic data uncertainties, and a flexible setup for adding complementary information directly into the quantitative analysis. The following presents an approximate probabilistic method for inversion of seismic AVO data and real data examples illustrate its applicability.
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Grain-grain contacts evaluation in carbonate reservoirs
Authors J.A. Soares, R.L.C. Coura, N.M. Oliveira, L.C. Medeiros, J.J. Silva, L. Landau and A.P. Martins NetaThis work investigate the reasons for the high dispersion seen between elastic velocities and porosity of carbonate rock samples from Brazil. It is based on conventional lab petrophysical measurements, digital x-ray micro tomography image analysis and well logs usage. This gives a multiscale data integration, since micrometers from x-ray images, to metric scale from well logs. A new approach to predict elastic velocities of carbonate rocks from macro and micro porosity, as well as a quality index for grain-grain contacts was proposed. Multivariate regression functions determined for carbonates from Sergipe-Alagoas Basin, were applied to well logs of Santos Basin, which showed that the predominance of micro pores is associated to a higher values of the quality index of grain-grain contacts and to a lower values of elastic velocities. However, it is recommended to generate regression functions for rocks from the own Santos Basin, applying the proposed integrated method of laboratorial, microCT and well log investigation.
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Interpretation Benefits from a Flexible Multi-Physics Joint Inversion Approach
Authors P.L. Smilde, C. Mueller, M.H. Kringer and S. PetersenThe properties of a multi-physics joint inversion application are discussed, that takes into account the information from several geophysical methods, from well and laboratory data and from geological concepts to return a much more reliable interpretation of the model space. It facilitates to merge all these sources of information and the knowledge and capabilities of usually several expert groups in a well-balanced way. A practical approach is described, that helps to solve usual problems for such setups, like the optimal selection of common or compatible parametrizations, the flexible definition of well-delimiting, but non-conflicting boundary conditions, and satisfactory relative weighting of the diverse contributions. Furthermore, it is possible to incorporate forward modelling computations at each of the partners’ sites into the joint inversion framework. To this purpose a most suitable integration method of several suggested ones can be implemented. A practical realization based on these concepts has already proven its feasibility and is available to be extended with additional methods.
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Nonlinear 3D FE-Stability analysis of suction pile
Authors R. Schlegel, R. Lampert, S. Eckardt, K. Rognlien and F. HalvorsenSuction piles are used to anchor off-shore constructions (e.g., oil platforms) in the sea ground. For the implementation, an under-pressure is created inside the device. The task is to make sure that the suction pile does not fail due to buckling of the friction skirt. The consideration of possible imperfections in the friction skirt as well as the interaction of the suction pile with the surrounding sea ground is particularly important for this verification. State of the art to calculate the maximum possible suction presser before collapse was to use radial springs with non-linear stiffness to characterize the surrounding soil’s supporting effect. This new approach, using 3D Finite Element Simulation with highly non-linear material behavior representing the soil results in significantly increased working loads and economically improved design or installation options. To further validate the suction pressure capacity obtained with the new methodology, a verification with a series of simulation using different spring stiffnesses was carried out. Based on this, it is concluded that the results obtained by the new methodology are not only economically more valuable but rather also more physically correct.
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Lidar and UAV for Rock Mass Geomechanical Characterisation - Support to fracture studies of outcrop analogues
By A. TamburiniFracture studies of outcrop analogues represent a powerful tool in reservoir characterization. Outcrop analogues provide a valuable support in defining conceptual models to extrapolate borehole data outside the well control, trying to take into account reservoir heterogeneity
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The Use of Remote Sensing Products for Enhancing the Environment Protection and of Offshore Operations Safety
By M. FragosoOffshore operations at sea are often risky because very complex activities are performed in harsh environmental conditions. This combination of factors increases the potential for incidents that might cause harm to people, environment and assets. To be prepared for such problems, the knowledge of present and future states of the ocean is key. To reach this goal, a combination of technologies comprising in situ data collection, models and visualization tools is required to make sense of all the pieces of information and provide valuable guidance for decision makers. In this sense, satellite communications and remote sensing plays an essential and transverse role. Either for sending real-time environmental data collected in situ (e.g. drifters, floats, moored buoys), connecting equipment to their base stations (AUVs, ASVs) or for collecting ocean data through sensors onboard satellites (Sea Surface Temperature, Ocean Color, Sea Surface Height, wind and pollution detection)
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Remote sensing from space for oil prospecting
By F. RoccaRemote sensing from space implies the use of sensors of gravity or of electromagnetic radiations. I will first recall gravity surveys, as that carried out with the satellite GOCE by the European Space Agency but also, on the oceans, the results obtained by using high resolution altimetry. Then, lower frequency microwave radar imaging methodologies will be presented like ESA Biomass, and of the Argentinean and Italian Space Agencies, SAOCOM, in the bands P and L respectively (435 and 1275MHz). The penetration in the vegetation and the upper layers of the terrain (when dry) will allow the study of the Digital Terrain Model under vegetation and even the layout of the water table in desert areas. The use of microwave imaging radars at higher frequencies (band C, 5 GHz with satellites like Sentinel 1 A/B always of ESA, and band X, 10 GHz, with the satellites of the Italian Space Agency (CosmoSkyMed first and second generation), Terrasar X and Tandem X of the German DLR, and finally the Spanish Paz, allow to evaluate ground morphology and soil rugosity, to detect oil spills on sea, and finally to measure accurately millimeter ground motions.
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Remote Sensing Cloud Tools in the Geological Workflow
Authors L. Turon, J. Dupuy, D. Dhont and E. BlancartWith the increase of the amount and variety of satellite sensors and free data, the access, processing and management of satellite images becomes a real issue. These barriers are being overcome with the increase in storage space and the emergence of deported storage systems (servers, clouds, etc.). Online satellite image processing platforms now enable the processing and visualizations of large volumes of data over wide areas (Chi et al., 2016)
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Video from Space - a new dimension in Earth Observation
More LessA new dimension in Earth Observation is being opened: Color Video from Space. Very High Resolution satellite images recorded in a sequence of 25 frames per second for up to 100 seconds, and locked on to the target area of interest, will change the way we can observe our dynamic world. This will enable new depths of analysis and much improved situational awareness, as well as a deeper understanding what is happening ‘on location’. Such high revisit times become important for high value assets in a dynamic environment, for example Oil & Gas installations, mining infrastructure, ports or transportation hubs. Daily very high-resolution monitoring, with video capability, at multiple times of day, will create new exciting opportunities in the geo-located world and benefit customers in high value / high risk environments.
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Asset Digitalization and Integrity Monitoring - A UAS based approach
By S. LiuOver the last 5 years Nederlandse Aardolie Maatschappij (NAM), a joint venture between Exxon Mobil and Royal Dutch Shell, has completed a campaign of surveying 250 onshore plants and 3 offshore platforms in the Netherlands using unmanned aerial systems (UAS) [1] which are also known as drones. The UAS based survey platform has proven to be not only cost efficient but also adding significant business values in the areas of asset inspection and maintenance, HSE management, engineering basis for design [2]. In this presentation we will begin with key survey equipment and procedure followed by current rules and regulations in NL imposed by Dutch authorities, then we will present two case studies of the UAS surveys, one for an offshore platform in the southern North Sea and the other on an onshore gas processing terminal in UK.
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Subtile Interseismic Strain Rate Distribution Detected from a Spatial Frequency Analysis of InSAR
Authors T. Maurin, J. Berthelon, D. Dhont, F. Koudogbo and A. UrdirozInSAR is a convenient method to uniformly map long term strain rate and was successfully used that way in fast deforming regions. However, because the radar signal might be subject to atmospheric perturbations and could equally register anthropic or hydrologic related deformations, the monitoring of slowly deforming areas remains challenging. The surface displacement may actually be described in the spatial frequency domain as a mix of these various components: the atmospheric term, the ground term and the tectonic term. Each of these terms have a specific bandwidth that can be identified and extracted from the velocity signal. This paper present an approach based on such a spatial frequency analysis that aims at extracting the specific tectonic wavelength signal in order to capture strain rate variability in slow deforming regions.
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Probabilistic inversion into lithology and fluid classes in the North Sea – Comparison of one- and two-step approach
Authors E. Aker, H. Kjønsberg, P. Røe and Ø. KrøsnesLithology and fluid prediction from seismic data is traditionally done in two steps; first an inversion of the seismic data to elastic parameters, and subsequently a prediction of lithology and fluid based on a rock physics model linking the elastic parameters to individual lithology and fluid combinations. Recently, a number of inversion algorithms have been developed that, based on Bayesian statistical methodology, estimate the probability of lithology and fluid directly from seismic data. In this paper we compare the performance of two state-of-the-art Bayesian inversion algorithms on a real data set from the Volund field in the North Sea. The first algorithm follows the traditional two-step approach and cannot take into account the stratigraphic ordering of lithology and fluid. The second algorithm, referred to as one-step, evaluates possible lithology and fluid combinations within a vertical window around each inversion point enabling correct stratigraphic ordering. We find that the one-step inversion resolves more details and honours the data more strongly than the two-step approach. The latter is more prone to return the prior model if information in the seismic data is not sufficiently strong. Both models detect hydrocarbon filled sand injectites that are typical for the field.
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Solving for facies in seismic inversion as essential for realistic reservoir models
More LessTraditional seismic inversion approaches solve in two steps, first for the elastic properties of the subsurface using seismic data, followed by facies classification. We perform the inversion of facies and elastic properties simultaneous. The stochastic (or geostatistical) inversion is done on a stratigraphic structural grid in a Bayesian framework using the MCMC Markov Chain Monte Carlo algorithm. Combining all seismic, well and geological constraints simultaneously is required to reduce uncertainty and ensure a consistent and unbiased integration of all data.
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Facies-based Reservoir Characterisation through the Asset lifecycle
More LessSeismic lacks low frequencies, so for absolute seismic inversion a so-called Low Frequency Models (LFM) is required. Starting from an empty LFM, we would like to post Sand values where there is Sand, Shale values where there is Shale, etc. Typically we don’t know precisely where the various facies are located in the subsurface; after all, understanding the facies distribution is one of the main aims of seismic inversion. So populating the LFM as outlined in the previous paragraph is not normally possible. The LFM’s constructed to date are therefore compromised (e.g. well log interpolation leads to averaging, resulting in impedance values unrepresentative of the facies present). Importantly, during the inversion the seismic cannot ‘fix’ a compromised LFM as – we come full circle here – seismic lacks low frequencies! We introduce a facies-based approach that overcomes this issue. For each facies expected (e.g. Shale, Water-Sand, Oil-Sand), a LFM is constructed, and all are input to the inversion (i.e. the low frequency information is over-specified). The inversion can then decide which LFM is used where, based on the facies estimate, which is one of the quantities inverted for. So the LFM ultimately used in the inversion is an output, not an input.
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Fluid Prediction from Time-lapse Seismic AVO Data
Authors O.B. Forberg, Ø. Kjøsnes and H. OmreReliable reservoir characterization of both the porosity/permeability and the fluid distribution is important for reservoir management. Geoscientific experience, seismic data with good coverage and logs along a small number of well traces provide the basis for this characterization. The time-static porosity/permeability distribution is challenging to assess, while the time-dynamic fluid distribution is even more challenging to monitor. Reliable characterization of the dynamic fluid filling is crucial for reservoir engineering management including the design of efficient infill well drilling programs. Our study is focused on prediction of the fluid dynamics based on time-lapse seismic AVO data. We apply spatial Bayesian inversion methodology, necessitating a prior model on the reservoir characteristics. This is challenging because the saturation is bimodal. We present a solution using a selection Gaussian prior model and a Gauss-linear relationship between the reservoir characteristics and the seismic responses. The methodology is tested on seismic data generated from well observations from Kneler in the Alvheim oil and gas field. The results are encouraging, preserving the bimodality of the saturation even in the presence of considerable error.
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Investigating the relationship between prior information and seismic resolution in a Bayesian setting.
By P.E. HarrisModern, one-step inversions build litho-class boundaries into the inversion process by coupling the elastic property inversion with the lithology identification process. This sharpens the result and may permit the identification of very thin units that are not necessarily recognised in a traditional inversion. A further benefit of modern techniques is that the locations of horizons can be updated within the inversion process, again exploiting the interaction between elastic properties and lithology identification in the one-step process. These remarks suggest that it is the interplay between elastic properties and spatial/temporal (geological) information that improves results of modern inversion over the traditional. In effect, resolution is improved by combining separation of litho-classes in elastic properties with separation in a spatio-temporal sense. To a large degree, the geological information is captured in the prior model. In exploration settings, where little is known, the classification process becomes essentially just a partitioning of the elastic property space, and the resolution is similar to that recoverable from a traditional elastic property inversion. However, as more prior information becomes available, it becomes possible to resolve litho-classes that may overlap in elastic properties due to their spatial distribution.
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Probabilistic Seismic Inversion of Facies and Petrophysical Properties Using Gaussian Mixture and Markov Chain prior Models
Authors T. Fjeldstad and P. AvsethPrediction of petrophysical properties and elastic attributes has become an important part of the exploration phase in the oil and gas industry to predict the presence of hydrocarbons subsurface. We focus on prediction of lithology/fluid classes, petrophysical properties and elastic attributes given geophysical observations. State of the art techniques are often based on minimization of the error, with respect to a given loss function, between a synthetic forward model and the observed data, either by probabilistic assessment or numerical optimization. We operate in a Bayesian framework where the objective is to assess the posterior probability density/mass function of the variables of interest subsurface.
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4D seismic coda waves
By D.E. LumleyTime-lapse seismic imaging of the earth's interior, and quantitative estimation of time-varying changes in rock and fluid properties, has produced many spectacular results over the past 30 years; however, we are still making many approximations, and extracting only a small percentage of the information available in the full time-lapse seismic wavefields. I will present advanced concepts in full wavefield imaging and inversion (including 4D RTM and 4D FWI) to enhance 4D seismic reservoir monitoring.
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Target-oriented elastic full-waveform inversion through acoustic extended migration redatuming
Authors E. Biondi, B. Biondi and G. BarnierElastic full-waveform inversion (FWI) has the potential of simultaneously invert all the scales of the elastic subsurface model while accounting for the elastic effects present in the recorded data. However, its application on production field datasets is limited by its high computational cost. In fact, the computational time of the elastic Green’s functions involved during any data inversion is much higher compared to the cost of the acoustic ones.
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Using one-way propagators to build a full wavefield inversion process
Authors E.J. Verschuur, M. Davydenko and A. GargNowadays, there is a strong emphasis on explaining the full seismic wavefield for obtaining detailed subsurface information, which is indeed the way forward to improve the final resolution of images and – after that – reservoir properties. Within the full waveform inversion (FWI) community there is a strong bias towards one type of modelling, which is the finite-difference based solutions of the wave equation. However, one issue associated with FWI is that it does not yet provide a full strategy towards a broadband elastic reservoir inversion process. Traditionally, FWI is used for estimating the velocity model that is used as input for standard migration-inversion approaches, thereby losing the advantages of the full waveform approach, such as including the effect of multiples. As an alternative, the Joint Migration Inversion process, with an operator-based modelling engine, provides an open framework that can include many physical features (such as anisotropy, elastic angle-dependent reflectivity), without having to re-implement a certain wave equation. By using one-way propagators in combination with reflectivity operators, a full two-way response can be built. It provides consistent full wavefield outputs that can lead to accurate elastic parameters in the reservoir, while fully removing the overburden imprint.
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Review of different expressions for the extended Born approximate inverse operator
Authors H.J. Chauris and E. CocherSeveral authors have published different expressions for the pseudo-inverse operator in the case of the subsurface extended Born modelling. We review here the principles to establish such inverse operators and show the close relationships between them. With one of the strategy, we then illustrate how triplicated wave fields can be properly handled and how the inverse operator can be incorporated as a preconditioner for least-squares migration in the extended domain.
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Multiple-parameters inversion: enhancing wave-matter interaction
Authors J. Virieux, R. Brossier, L. Métivier, P. Trinh, W. Zhou and P. YangSeismic waves honor wave propagation equation which is described by local model parameters. Full waveform inversion (FWI) attempts to distinguish automatically between reflection and transmission regimes through the implicit analysis of the different phases with variable signals expressed into seismic traces. Therefore, this approach, sensitive to phase and amplitude information, should require adequat description of different model parameters such as velocities, anisotropy coefficients and attenuation quality factors embedded into the spatial heterogeneous description of the model. Based on a single scattering approximation, FWI relies on the amplitude modulation in order to distinguish between model parameters at a point of the medium without considering important effects coming from spatial variations: only illumination (and curvature to lesser extent) is considered. Overcoming this limitation could be achieved by approximate scale separation specifying the wave-matter interaction often expressed through velocity/impedance parameterization or by preconditioning the model update through prior information. These additional strategies complement nicely the highresolution performance of FWI without too drastic restriction in the model building. It does not overcome the intrinsic influence of large-amplitude phases compared to small-amplitude phases which is a characteristic feature of least-squares methods. Alternative strategies could be foreseen essentially based on stricter scale separation.
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Least-squares imaging with multiples
Authors R. Soubaras and B. GratacosWe present an imaging tool derived from an Inversion Velocity Analysis (IVA) framework. Using a second-order Gauss-Newton update (Soubaras and Gratacos (2017)), we jointly invert for the source wavelet and for an extended reflectivity, by minimizing the data misfit between the measured raw shot records and the modeled shots. The second order update results in a reflectivity which is a least-squares migration. The modeling is based on one-way wave-equation propagation and includes the source wavelet, source and receiver ghost and multiples up to a given order. The presence of the multiples makes the wavelet estimation stable as the wavelet-reflectivity ambiguity is solved by fitting the first order modeled multiple to the data. As an unconstrained extended reflectivity is used, amplitude versus angle (AVA) effects are estimated. The input can be raw shots as source wavelet estimation and deconvolution, source and receiver deghosting and multiple attenuation are automatically performed by the joint inversion. An example on a real 2D real dataset is shown.
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Least-squares reverse-time migration with dynamic time warping
More LessLeast-squares reverse-time migration (LSRTM) has been shown to improve image quality over conventional RTM by enhancing the resolution, balancing illumination, and suppressing migration artefacts. However, it is also known to be sensitive to velocity errors. In the presence of velocity errors, predicted data show different moveouts from the observed data, which will hinge LSRTM convergence and yield sub-optimal results. To mitigate velocity errors, we propose to apply dynamic time warping (DTW) to the observed data and shift them towards the predicted data to improve data matching and subsequently images. In this paper, we show 2 synthetic examples and 1 real data example to demonstrate the advantages of dynamic time warping. Our observations show that dynamic time warping helps with event focusing, corrects phase distortion, improves event amplitudes, and thus improves event continuity.
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Q-least-squares reverse time migration with viscoacoustic deblurring filters
By C.Y.Q. ChenAttenuation compensation least-square reverse time migration (Q-LSRTM) linearly inverts for the subsurface reflectivity model from lossy data. It can compensate for the amplitude loss and phase distortion due to the strong subsurface attenuation compared to the conventional migration methods. However, the inverted images from Q-LSRTM with a certain number of iterations are often observed to have lower resolution when compared with the benchmark acoustic LSRTM from acoustic data. This because the adjoint Q propagators used for backpropagating the residual are also attenuative. To increase the resolution and accelerate the convergence of Q-LSRTM, we used viscoacoustic deblurring filters as a preconditioner for Q-LSRTM. Numerical tests on synthetic and field data demonstrate that the Q-LSRTM combined with viscoacoustic deblurring filters can produce images with higher resolution and more balanced amplitudes when there is strong atteunation in the background medium. The proposed preconditioning method is also shown to significantly increase the convergence rate of Q-LSRTM.
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FWI velocity models for quantitative interpretation of a deep water GOM dataset
Authors Y. Cobo, C. Calderon-Macias and S. ChiFull waveform inversion (FWI) has become the method of choice for deriving shallow velocity models that potentially improve interpretation of images in complex geologically settings. Recently, a combination of diving waves and reflections is being used resulting in an increase of depth range for updating the model. In this work, we evaluate the potential for utilizing velocities from FWI as a background model for quantitative interpretation. Our results show that using a velocity model as a low frequency model (LFM) with a higher vertical and lateral resolution obtained from the FWI process results in a higher quality post-stack inversion compared to the traditional approach that uses sparse well velocities extrapolated within a structural framework as a LFM.
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Q tomography with ray and waves
More LessSeismic wave propagation can be simulated using ray-based methods or wave-equation-based methods. Ray methods are based on high frequency approximation. Those methods work well in a geological setting with smooth velocity variation in the subsurface. However, ray-based methods can fail in imaging the complex media e.g., below or near salt, where wave-equation-based methods are known to be more robust for imaging. In this study, we examine the advantages of the wave-equation-based method over the ray -based method in the case of Q tomography in a complex setting. We employ a synthetic model that has salt bodies with rugose salt boundaries. Two attenuation anomalies are included: one is above the top of salt; the other one is close to the steep salt flank. We measure the attenuation effects from the spectral loss of the seismic events at near offsets (0 m - 600 m) and at mid offsets (600 m -1,200 m). We then do a least-squares inversion of the same measurements to update our Q model using ray- and wave-equation- based tomography. Through the numerical tests, we would like to study how the complex overburden impacts Q inversion differently in ray- and wave-equation based tomography.
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Recent advances in Q model building and Q-compensating migration for imaging in the presence of complex gas clouds using P waves
Authors N.I.L. Xie, N.I.L. Wang, N.I.L. Xiao and N.I.L. LatterThe presence of absorption (Q) anomalies in the overburden, typically associated with gas accumulations, can obscure seismic imaging and reduce our ability to see and interpret events inside the resulting “shadow zone”. In this paper we present our recent developments for addressing these challenges. We review progress made in the area of Q-compensating prestack depth migration (Q-PSDM) in order to deal with the co-existing multi-pathing and absorption effects for imaging through complex gas clouds using P-waves. In addition, to mitigate the problem associated with over-boosting of noise and migration artefacts introduced by Q-PSDM, more advanced imaging methods, such as least-squares Q-migration, have been developed to maximize the benefit of Q-PSDM. We then highlight a recently developed visco-acoustic full-waveform inversion (Q-FWI) model building technique for joint estimation of Q and velocity models. This has been applied to a production example from the Norwegian North Sea, where we see that the Q-FWI detects attenuating bodies of varying strength and scale throughout the survey and provides a clear uplift in the subsequent imaging process.
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Reservoir Monitoring Through DAS Measurements
By J. ChavarriaDistributed Acoustic Sensing (DAS) has increasingly been conducted for various seismic applications in a variety of geologic and operational settings. Advances on DAS hardware are now enabling operators to acquire repeatable seismic data on demand. These reduced cost acquisitions take advantage of existing Fiber Optic (FO) installations in the borehole. Advances in FO are further enabling the acquisition of data in traditional surface seismic applications. Examples of time lapse reservoir monitoring using DAS are presented here. It is shown that DAS measurements can be used to track various physical processes including water floods, steam injection, fracturing of rocks and CO2 injection
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Continuous DAS VSP monitoring using surface orbital vibrators: field trials for optimal configuration at the CO2CRC Otway Project
Authors J. Correa, B.M. Freifeld, R. Pevzner, T. Wood, K. Tertyshnikov and A. BonaReservoir monitoring usually involves a combination of seismic surveys acquired using a large array of seismic receivers and mobile sources to image the subsurface changes. Such surveys rely on accurate positioning of both source points and receivers. Permanent reservoir monitoring seeks to overcome the limitations of the conventional approach, such as poor repitability and high survey costs, by fixing either the seismic receivers, sources or both. At the CO2CRC Otway Research Facility, we are exploring the use of distributed acoustic sensing (DAS) combined with permanent surface orbital vibrators (SOVs) to acquire high quality time-lapse seismic data at relatively low cost, while significantly reducing the land access issues. To study the feasibility of using such monitoring method, we present the analysis of a series of Vertical Seismic Profile (VSP) acquisitions acquired with a cemented fibre-optic cable. We test different SOV sweep designs, and evaluate DAS ability to record the acoustic signal. The results show that the DAS/SOV configuration was able to deliver high quality VSP datasets, sufficient to image the target interval.
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Results from a Clair DAS VSP Pilot and Lessons Learned for DAS Surveillance on Clair Ridge
Authors L.M. Saxton, M. Ball, S. Soulas, G. Zhan and M. WebsterWe show results from a DAS 3D VSP field trial acquired over the Clair field offshore West of Shetland in 2017. The primary objectives of the field trial were to i) prove that DAS technology can be used to generate a high-quality static 3D VSP image at Clair in the image area predicted by modelling, ii) assess the impact of production related noise on the final 3D image and iii) determine the acquisition requirements (source density and source volume) for future DAS VSP programme on Clair Ridge. Analysis of the impact of production flow noise are shown along with assessments of the impact of source density, source volume and dual fibre recording on final image quality and signal to noise ratios. The results from this study are being used to determine acquisition requirements for future DAS VSP programmes on Clair Ridge and to assess the feasibility of using DAS for localized on demand, cost effective 4D surveillance around the development wells.
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Vertical Seismic Profiling Combining Three-Component Geophones with Single-Axis DAS Sensors
Authors J.B.U. Haldorsen, L. Jahren, M. Milenkovic and T. HiltonCombining VSP measurements made by geophones with DAS data, it is important to realize the differences between a DAS sensor and a three-component geophone, and also between a DAS sensor and a single-axis geophone. We explore these differences in order to create optimum VSP images.
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Looking beyond seismic sensors: engineering considerations for topside and subsea PRM interfaces
Authors L.A. Woodhouse, H. Frøyshov and M. Thompsonies of the technologies involved. The debate can be further matured by recognising that PRM needs to meet all the requirements in an overall system architecture – both subsea and topside. Attempts should be made to understand and learn from those who regularly work with similar infrastructure, such as subsea production control systems and subsea cables. Critical interface engineering considerations are presented for typical fibre optic (FO) PRM systems implemented upon floating production storage and offloading (FPSO) platforms. Early integration into a project's concept phase can improve the business case and ensure future PRM implementation is feasible.
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Seismic and Microseismic Detection Using a Wide Dynamic-Range Distributed an Engineered Fiber Optic Acoustic Sensor
More LessDistributed Acoustic Sensing (DAS) has been demonstrated as a new tool for detecting seismic signals and sensing ground motion for geophysical applications. The technology has rapidly moved from being a novel idea to demonstrating game changing capabilities. The small diameter rugged fiber optic sensing cable is providing new viable commercial opportunities for wellbore and land seismic and microseismic measurements. The DAS technology also seeks to disrupt conventional geophysical surveying methods and enable the realisation of new applications where the fibre optic cable can be readily deployed as a dense wide-aperture phase-array sensor in novel configurations. Silixa has recently developed a new sensing system (Carina) that combines the properties of an engineered fiber with bright scatter centers (Constellation fibre) with a low-noise and wide dynamic-range opto-electronic interrogator to achieve significant improvements in signal-to-noise performance. The step-change in the performance have a significant economic and environmental impacts for on-demand reservoir monitoring specially in offshore and subsea applications.
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Effect of the Angular Response of a Fiber-optic Cable on DAS VSP Recordings in Lateral Wells
Authors M.E. Willis, X. Wu, A. Padhi, A. Ellmauthaler and M. LeBlancThe angular response of a fiber-optic cable to incident seismic energy when used with distributed acoustic sensing is well known, but it is difficult to understand its effect on survey design without additional visualization and quantification. We present a simulation demonstrating the effect of the angular amplitude response for lateral wells on both P and S waves. We find that the vertical portion of a moderately deep well has an excellent response to reflection events and a good response for direct waves, which is dependent on the source offset. The horizontal portion of the well has a much weaker response for P waves and an encouraging response for S waves. For a shallow SAGD-type geometry, the diversity of incident angles yields an excellent amplitude response for both the direct and reflected energy for channels that are not directly under the source. This study makes the case for a pre-survey modeling of the effect of the fiber-optic cable amplitude response in order to assist the choice of acquisition parameters
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Optimising DAS VSP data acquisition parameters: theory and experiments at Curtin training well facility
Authors R. Pevzner, A. Bona, J. Correa, K. Tertyshnikov, G. Palmer and O. ValishinDistributed acoustic sensing (DAS) technology has demonstrated significant progress over the last few years. From being a promising and novel technology where practical applications were limited by the lack of sensitivity, it has advanced to the stage where it can clearly outperform conventional downhole geophones. With a growing number of projects relying on fibre optics as a primary seismic sensing technique, it is important to understand how the specific DAS data acquisition parameters are linked to the quality of the seismic data and the ability to record different components of the wavefield. In this presentation, we will summarise the findings from a series of experiments conducted on the Curtin/NGL training well facility. The focus of this presentation is the relationship of key DAS data acquisition parameters with the quality of the acquired seismic records.
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Comparative study of DAS and geophone VSP data
More LessDistribute Acoustic Sensing (DAS) is kind of sensing system using optical fiber as sensing element and transmitting signal medium. Optical fiber acquisition has become an important development trend of borehole seismic technology due to its advantages such as full well coverage, high sampling rate, high efficiency, high temperature and pressure resistance and economic. In this paper, a dual-well Walkaway DAS VSP data was acquired at Liaohe oilfield in East China. We analyzed the advantages and disadvantages of DAS VSP data with that acquired with geophone. We believe that in the area of East China, with the simple surface conditions, the casing settled cable acquisition can get high sampling and quality VSP data, it shows potential application of DAS VSP technology in oil and gas exploration and development.
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Improving Static Modelo Robustness of Pre-Salt Reservoir
Authors C.E.B.S. Abreu, C.E.L. Pereira, P.H.S. Sales, M.P.A. Júnior and R.S.M. CorrêaSuccessful implementation of the Pre-Salt DP&P projects in Brazilian ultra-deep waters, where huge capital investments are a major issue, depends much on the robustness and confidence of the available static and dynamic reservoir models. The first discovery of these large oil and gas reserves found along the southeastern coast of Brazil was made in 2006, and represented a new chapter in the global oil history. Since then, Petrobras has been facing major technological challenges in a broad suite of areas and disciplines, from Reservoirs to Logistics, including Subsea and Well technology, Completion and Stimulation, and many others areas, with massive investments in R&D and working in collaboration with partners, suppliers, universities, and research centers to make it technologically and economically feasible to produce oil and gas in the Pre-Salt.
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The Winner Strategy of Petrophysical Driven Seismic Reservoir Characterisation
Authors C.T. Tarchiani, R.L. Tagliamonte, G. Carrasquero and M. CatanzaroFor a successful integration of seismic within a reservoir model, the reservoir geophysical program must be tailored to support geologic work and has to be focused on solving engineering and geological objectives. Seismic prediction capability is evaluated by means of well data analysis and modelling within a shared workflow for formation evaluation and geophysical activities. In this workflow we start from reservoir and petrophysical needs, consolidating the rule of a petrophysical characterisation optimised to Rock Physics Modelling and to seismic property estimation.
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Integrated 4D Quantitative Interpretation for Assisted Reservoir Model Updating
By H.J. HansenTime-lapse (4D) seismic has repeatedly demonstrated its value in impacting the reservoir model by directly measuring the state of the reservoir. The objective of its use in reservoir modeling is typically to relate the 4D seismic response with a given noise level to changes in reservoir properties, such as effective stress, saturations and reservoir geometry. The current work outlines the use of quantitative interpretation in a 4D context where information from different physical domains are integrated. Examples with real data illustrate the impact on reservoir model updating.
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Geostatistical seismic inversion: a review and the road ahead
Authors L.A. Azevedo, R. Nunes, A. Soares and V. DemyanovGeostatistical seismic inversion techniques are conventional tools for seismic reservoir characterization and able to integrate well and seismic reflection data while inferring highly variable petro-elastic models from both post- and pre-stack seismic reflection data. In this framework the model parameter space is perturbed by stochastic sequential simulation and co-simulation. While it allows assessing the spatial uncertainty for each property, the use of stochastic sequential simulation and co-simulation as the perturbation engine of the model parameter space assumes: a given spatial continuity pattern for each property of interest, as revealed by a variogram model; that the distribution of each property is known as interpreted from the existing well log-data; and that there are no uncertainties during seismic interpretation used for the regionalization of inversion area based on main seismic reflections and statistical properties. Here we show a brief overview of geostatistical seismic inversion methodologies able to invert seismic reflection data directly for subsurface elastic and rock properties discussing its advantages and disadvantages. Then, we point the road ahead and how these approached can be coupled with adaptive stochastic sampling to quantify uncertainty in geological parameters which are frequently assumed to be true.
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Pragmatic use of a massive Permanent Reservoir Monitoring seismic library for reservoir model update and well planning: examples from the Valhall field.
Authors N.H. Haller, F.I. If and P.R. PatonThe Valhall chalk field has been a pioneer for seismic technologies for almost 2 decades. This giant field, on production since 1982, has subsequently seen its subsurface revealed by 2D seismic, 3D seismic in 1992, then 4D seismic with ultimately the installation of a permanent array . If there is no doubt that seismic data have contributed to our current understanding of the field, challenge still remains in transfering the details of seismic interpretation into a reservoir model in order to support effective reservoir management. This paper will illustrate the pragmatic approach used by the well planning team under the constraints of short timing and abundance of seismic information
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Efficient integration of 4D seismic data in history matching with ensemble methods.
Authors T.A. Alsos, M. Heide and B.T. SamuelsenThe development of the Fast Model Update workflow for integrated reservoir modelling, including use of ensemble methods for history matching has opened for new opportunities for integration of 4D seismic observations into the model. All the individual modelling steps from depth conversion and structural modelling to gridding, property modelling and flow simulations is set up in one automated workflow. Forward modelling of 4D seismic data can be added to the end of the workflow. Many realisations of the model are run in parallel, and the misfit between the observations and the simulated response is used to update the input parameters. Adding 4D seismic observations in the misfit calculation is feasible, for different types of 4D attributes. Case examples show that this can lead to improvement in history match, alternative solutions, and new learning about the reservoir that can be important for the model prediction.
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Potential Pitfalls Related to the Use of Seismic Constraint during Geological Model Infilling
By T. CadoretThis presentation describes the main steps of a typical workflow dedicated to geological model infilling using a seismic constraint. Then, some potential pitfalls encountered in a case study will be discussed.
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4D Seismic - Some examples of repeated seismic and Permanent Reservoir Monitoring
By T. ColeouSeismic monitoring or 4D has started onshore on a few cases more than 30 years ago but has really developed over the last two decades, first in offshore fields where seismic image is generally of good quality, then onshore with more difficulties to achieve similar repeatability. In this presentation, several case studies of offshore and onshore 4D seismic form CGG’s experience are presented. The techniques used for monitoring, permanent or not, are adapted to the degree of complexity of the objectives and provide valuable support to reservoir engineers for tracking production related changes in the reservoir in order to economically optimize oil recovery. Although the economic objectives are often the same, production schemes and reservoir characteristics are different from case to case.
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Including Internal Multiples in Imaging Marine Data with Anisotropy - A joint migration inversion application.
Authors A Alshuhail and E. VerschuurMultiples can be defined as reflected events that have bounced more than once in the subsurface. Conventionally, multiples are considered as noise and are rarely taken into account in the imaging process. By ignoring multiples, they can appear as spurious events in the seismic image. They can also mask weaker primaries that arrive at a similar time. It is for this reason many technique shave been developed in order to distinguish multiples and attenuate them (Verschuur et al., 1992; Coates and Weglein, 1996). Recently, there has been a drive to utilize multiples rather than eliminating them (Zhang and Schuster, 2013; Berkhout, 2014b; Zuberi and Alkhalifah, 2014; Berkhout and Verschuur, 2016). Utilizing them can broaden the subsurface illumination and attenuate the effect of shadow zones (Davydenko and Verschuur, 2017), and therefore, they can provide a more balanced illumination of the subsurface (Kumar etal.,2014;Luetal.,2015). An other benefit that comes out of using multiples is that it enables imaging structures from below as shown by Davydenko and Verschuur (2013, 2017). A significant issue that arises when imaging with multiples is that anaccurate velocity model is needed. Multiples are generally more sensitive velocity model errors because they travel a greater distance in the subsurface compared to primaries.
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Shallow water attenuation of multiples by inversion(SWAMI)
Authors A. Kumar, G. Hampson and T. ThompsonIn marine geophysics it is difficult to acquire very short offsets due to a number of operational constraints. This is a widely recognised problem in shallow water because SRME needs the near offset primary reflections to predict the free surface multiples. However, given the data with multiples measured at the available offsets, we can derive a multichannel prediction filter which is an excellent approximation of the sea-bed reflector and any other reflectors included in the design. The filter is designed by minimizing the energy in the output of a prediction error process, in a somewhat analogous manner to predictive deconvolution. By use of the focal transform, it is constrained to be composed of a sparse set of hyperbolic functions based upon the wave equation. Given this filter, we may proceed to predict the multiples and remove them as part of an adaptive subtraction scheme.
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Utilizing Surface Multiples in sparse deepwater OBN surveys
Authors A.M. Mahdad, P. Docherty and K. CraftInnovative seismic technologies enable us to achieve higher quality seismic images and reservoir models while reducing the cost of seismic acquisition and processing. A great example of these innovative methods is blended acquisition, in which multiple sources are firing within a shorter time window that result in significantly shorter acquisition time. The utilization of surface multiples, which can be considered as a natural form of blending is not yet very well established by the industry. However, recently much more attention has been drawn to the possibility of utilizing surface multiples in seismic imaging, rather than removing them. Surface multiples can be considered as secondary sources that illuminate the subsurface many times at different angles. Therefore, they have a significant potential to overcome the shortcomings of seismic acquisition by filling the illumination gaps resulting from imperfect acquisition, especially in sparse acquisition geometries. In this work we discuss the possibilities of improving the quality of seismic images in sparse node acquisition by utilizing surface multiples. We investigate two separate acquisition scenarios, namely, sparse node coverage and sparse node sampling. The impact of including surface multiples will be analyzed for these scenarios.
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Using surface multiples to image across large acquisition gaps
Authors A. Nath and E.J. VerschuurWhile surface-related multiples have long been considered as noise in seismic data, recently the consensus is changing to accept multiples as a tool for better illumination of the subsurface. In this paper we explore the different strategies of exploiting the surface-related multiples specifically in case of large acquisition gaps. Since surfacerelated multiples travel different propagation paths compared to the primaries, they illuminate a wider area making them vital in such cases of limited illumination. Existing imaging methods include surface-related multiples by reinjecting the total measured data as a downgoing wavefield. This however, makes the method dependent on a dense receiver configuration and, therefore, sensitive to missing data. Addressing a way around this problem, we will illustrate a `non-linear' inversion approach in which all multiples are modeled from the original source field. Such modeling makes the method less dependent on the receiver geometry, therefore, helping us in case of limited illumination. We also demonstrate a `hybrid' method on both synthetic and field data to overcome the effects of incomplete data by utilising the benefits of both `linear' and `non-linear' method. The results indicate substantial mitigation of effects on the image previously caused due to incomplete data and better images compared to the `linear' inversion methods.
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Internal multiple modelling and subtraction to reduce the risk in quantitative interpretation: An overview of the challenge, initial assessment, and way forward.
Authors A.C. Ramirez, E. Sadhikov and L.T.W. SigernesWhat is the business value that internal multiple technology can bring at the seismic quantitative interpretation stage? This is the question that we ought to start answering, as we move the internal multiple prediction and attenuation technology from a mostly academic pursuit to a standard part of seismic processing. For years, internal multiples have been neglected in seismic processing. This means that a large majority of the data used for interpretation and analysis are contaminated with these events. This contamination is not always easy to identify. For example, it can appear too weak compared to nearby primaries, interfere with them, or have enough strength and coherency –increasing the risk of interpreting them as real horizons. Furthermore, interference can create false dimming or brightening of events, obstructing quantitative analysis. We believe that there is untapped business value in utilizing and further developing internal multiple technology.
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Data enhancement through improved attenuation of internal multiples in the stack domain
Authors E.S. Sadhikov, A.C. Ramirez, L.T.W. Sigernes and S.K. FossThe internal multiple prediction method based on Inverse Scattering Series is an efficient tool to predict internal multiple energy present in the data. It is entirely data driven, without the need for, e.g., interpreted horizons or a velocity model. When applied as a quality assurance and control tool it provides the interpreter with valuable information on areas where there is a high chance of internal multiple contamination and interference with primary energy. Predicting a model of the internal multiples present in the data, can allow an interpreter to have a better control of the reservoir geometry and to reduce uncertainties in structural interpretation. Additional application of adaptive subtraction can further improve data for analysis and quantitative interpretation, and can lead to improved reservoir characterization. In this work, we focus on the data driven prediction of internal multiples in time migrated data, after stack, and present our initial work on interpreter-guided adaptive subtraction.
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Seismic interpretation when short-period internal multiples are present
Authors J. Hilterman, F.I. Nicholson, M. Pareja and C. QiLong-period internal multiple suppression is difficult when severe short-period multiples are present in flat geologic environments. The propagating signal is bell-shaped followed by a higher-frequency noise coda. Standard deconvolution processes are suspect. Starting with these geologic conditions, an interpretation process is proposed that allows validation of long-period multiple suppression at well locations. Primary-only and multiple-only synthetics with time-varying propagating wavelets are created for validating the multiple technique. Since short-period multiples are not suppressed, well ties are facilitated by morphing multiple synthetics to primary-only synthetics. These principles are part of an interpretation workflow applied to various worldwide basins that contain both short- and long-period multiples.
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Attenuation of near-surface multiples on land seismic data: challenges, practical aspects and open issues
Authors F.X. de Melo, C. Kostov, A. El-Emam and H. BayriWe discuss attenuation of near-surface multiples on land seismic data using examples from a pilot test survey in Northern Kuwait. While the current combination of prediction and adaptive subtraction provides essential preparation of the data for subsequent processing steps, the review of current approximations and limitations points to directions for future developments linking characterization of the near surface (possibly using multiples as signal) and the attenuation of near-surface generated multiples.
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Long-range seismic sound measurements and modeling – what does it take to get it right?
Authors B. Martin, L. Horwich, C. Morris, M.N. Matthews and K. BrokerIncreased interest in seismic survey’s possible disturbance of marine life and masking of biologically-relevant sounds means that the accuracy of acoustic propagation models at ranges well beyond auditory injury distances is important. The models are used to predict the effects of noise before a survey occurs as well as to model the noise exposure of tagged animals from actual surveys. The definition of long range depends on the animals of concern – it could be 5 km for porpoise, or 100 km for baleen whales. This abstract summarizes two projects where precise measurements of seismic airgun sounds were made over a wide range of distances from the source. We present typical data collected over ranges of .1-150 km, the frequency content as a function of range, and how the modeled levels compared to the measurements. For data collected in Baffin Bay, the model accuracy is highly dependent on the accuracy of the bathymetric data. For measurements at the edge of the Gran Banks, high resolution date-specific sound speed profiles are required to accurately model received sound levels.
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Rapid Autonomous Marine 4D (RAM4D) – an unmanned, time-lapse offshore seismic acquisition system
Authors D.A. Chalenski, P.J. Hatchell, J.L. Lopez and K. BrokerShell has been developing a novel geophysical source vessel system, called Rapid Autonomous Marine 4D (RAM4D), to enable frequent and cost-effective 4D surveillance at offshore fields. RAM4D is envisioned as a low-cost, low-footprint unmanned and autonomous vessel deploying a small source (typical <500 in3) shooting into permanent or semipermanent receiver technologies such as Ocean Bottom Cables (OBC) or Distributed Acoustic Sensing Vertical Seismic Profiles (DAS VSP). These receiver technologies are good candidates for surveillance with RAM4D to reduce acquisition costs (OPEX) and due to their high quality 4D data. Shell has completed two field trials during 2017 in a Louisiana lake, and plans an offshore trial to explore the robustness of the system in typical field conditions. RAM4D has been developed openly with the expectation that technology uptake will occur quickest and most efficiently if our work is communicated externally and developed non-exclusively.
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Environmental impact of a set of marine compressed air source configurations – a comparative study
Authors J.F. Wisløff, M. Bastard and E. AsgedomThe interest in the environmental impact of marine seismic sources has steadily increased over recent years as the risk of potentially harming or disturbing marine life has been brought into stronger focus. Designing a seismic source setup that simultaneously fulfill geophysical requirements and minimize the environmental footprint is often required up front of a seismic survey, but is difficult to assess. While the geophysical requirements of a survey are depending on geology and survey objectives, the output of a given source configuration does not. We have assessed, through modelling of the seismic source and analytical homogeneous propagation modelling, the decrease in environmental impact of the most frequently considered mitigation measures as a non-survey dependent comparative study. We show that many of the most frequently used mitigation measures have limited effect while other measures, especially changing the source setup to consist of triggering individual source elements separated in time, will result in a relatively stronger decrease of the potential environmental impact. This quantitative assessment gives a platform for understanding and evaluating different mitigation measures to lower the environmental impact of the seismic source.
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The IOGP E&P Sound & Marine Life Joint Industry Programme – an international research programme to fill key data gaps
Authors K. Bröker, K. Speirs, D. Hedgeland, G. Wolinsky, B. Gisiner, G. Adams and M. JenkersonIn response to increasing societal and regulatory concerns over the effect of sound on marine life, the E&P industry has been playing a pro-active role to manage this issue, through the establishment of the SML JIP. The SML JIP, under the auspices of the International Association of Oil and Gas Producers, is a partnership of 12 oil and gas companies and the International Association of Geophysical Contractors (IAGC). It is currently the largest non-governmental funder of research on this topic, having committed US $55 million to date. In order to advance understanding of the interaction between sound from oil and gas operations and marine life, the objectives of the SML JIP are 1) Support planning of E&P projects and risk assessments, 2) Provide the basis for appropriate operational measures that are protective of marine life, and 3) Inform policy and regulatory development. This program has resulted in the publication of more than 45 reports and over 100 peer-reviewed papers by independent scientists. All these research projects supported the data needs for thorough Environmental Impact Assessments (EIAs) and associated impact mitigation. An example of a SML JIP funded study is presented as well.
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Seismic surveys and the Greenland regulation
The early tens saw a growing interest in searching for hydrocarbon deposits in offshore Greenland Waters. Deeper Arctic waters have propagation conditions and a marine mammal fauna different from better-studied temperate or shallow-water regions, and there are therefore many unknowns when it comes to negative impacts on marine mammals when conducting seismic surveys in Greenland. The Greenland Environmental Agency for Mineral Resource Activities (EAMRA) therefore established a rather strict regulation of seismic surveys to protect marine mammals during seismic surveys. The regulation is built on four pillars; 1) an annual application cycle, 2) modeling of noise emissions, 3) time-closure areas for vulnerable species and 3) a requirement of noise monitoring during seismic surveys. In 2012 four seismic surveys were planned for Baffin Bay, Greenland. The surveys were accompanied by three studies to examine the effects on the soundscape and narwhals: 1) Propagation of airgun pulses, 2) aerial surveys to examine narwhal distribution, 3) an interview study with narwhal hunters to examine potential changes to the narwhal hunt. The overall results will be presented at the workshop.
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The Marine Vibrator JIP and Ongoing Marine Vibroseis Development
Authors M.R. Jenkerson, A.J. Feltham, N. Henderson, V.E. Nechayuk, M. Girard and A.J. CozzensFor over three decades the desire to better control the output of marine seismic sources and concerns over the environmental impact of impulsive sources have driven the development of alternative source designs. Previous advances in Marine Vibrator designs for both geophysical and military use coupled with the significantly increased efficiencies in land vibrator operations as well as more effective shallow water operation, have led to a resurgence of interest in the use of marine vibrators. The Marine Vibrator Joint Industry Project (MV JIP), sponsored by ExxonMobil, Shell, and Total, was started in 2011 and has supported the development of three separate Marine Vibrator technologies. This presentation analyses the advantages of the marine vibroseis technology, discusses the status of the prototypes being developed by the MV JIP and briefly reviews prototype developments by other companies.
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Modelling Propagation of Sound Emitted by Mini-Airguns
Authors M.K. Prior and H.W. JansenA modelling approach is described in which time-domain underwater-acoustic source functions are generated using a model that predicts the motion of air-bubbles generated by mini-airguns operated at various pressures. These time-series are Fourier-transformed to produce frequency-domain descriptions of the source. These are combined with complex transfer functions describing the propagation of sound in shallow-water waveguide geometries so that source spectra can be converted to received spectra by a simple multiplication process for specified source and receiver positions. Received spectra can be inverse-Fourier transformed to produce time-series of received signals. Calculations are performed to yield three acoustic variables: one pressure and two particle velocities (in the radial and vertical directions). Time-series are shown for a test environment in which total acoustic fields are made up of contributions from waterborne and bottom-interacting paths.
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Methodology for assessment of cumulative effects of impulsive sounds
Authors N.A. Kinneging, R.P.A. Dekeling and A.M. Von Benda BeckmannIn this paper an overview of the European policy on underwater noise is given in relation to seismic surveys. The recent developments in these policies and the methodologies to monitor and assess the effects of underwater noise will be presented.
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Economical viability utilizing environmentally friendlier acquisition strategies
By P. HanssenMany believe that environmentally friendlier seismic acquisition means worse data quality and increased cost, but the opposite can be shown. Existing geophysical methods in combination with new and upcoming technologies makes it possible to save survey costs, have less environmental impact, and record better data. The main cost-driver is vessel time and reducing it using passive methods or other geophysical methods to reduce the target area is the highest priority. Then one can focus on structures with highest priority by applying active seismic with novel methods and new technologies. Reducing the Sound Pressure Level, avoiding unnecessary frequencies and reducing saillines with Marine Vibrators will be the standard acquisition requirements in the future.
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Towards a Marine Seismic Point Source
By P.E. DhelieMultiples can be defined as reflected events that have bounced more than once in the subsurface. Conventionally, multiples are considered as noise and are rarely taken into account in the imaging process. By ignoring multiples, they can appear as spurious events in the seismic image. They can also mask weaker primaries that arrive at a similar time. It is for this reason many technique shave been developed in order to distinguish multiples and attenuate them (Verschuur et al., 1992; Coates and Weglein, 1996). Recently, there has been a drive to utilize multiples rather than eliminating them (Zhang and Schuster, 2013; Berkhout, 2014b; Zuberi and Alkhalifah, 2014; Berkhout and Verschuur, 2016). Utilizing them can broaden the subsurface illumination and attenuate the effect of shadow zones (Davydenko and Verschuur, 2017), and therefore, they can provide a more balanced illumination of the subsurface (Kumar etal.,2014;Luetal.,2015). An other benefit that comes out of using multiples is that it enables imaging structures from below as shown by Davydenko and Verschuur (2013, 2017). A significant issue that arises when imaging with multiples is that anaccurate velocity model is needed. Multiples are generally more sensitive velocity model errors because they travel a greater distance in the subsurface compared to primaries.
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The Evidence for Environmental Effects from Seismic Survey Sound: What to Mitigate, Monitor, and Regulate, and Why?
By B. GisinerSeismic surveys are now subject to an increasing number of precautionary environmental risk mitigation measures ranging from pre-survey risk modeling to visual and acoustic monitoring for marine life, and even exclusion from some areas, shutdowns, and more. The scientific support is often inferred indirectly from other sound sources due to a lack of data on seismic sound itself. Direct injury from sound was an early concern (Finneran, 2015; NOAA 2016). But as concern about injury diminishes, attention has shifted more toward effects on behavior and health. The biological consequence of such disruptions is usually expressed in population terms, including effects on commercially exploited species. The initial regulatory response was to place observers on seismic ships and to move or shut down the source when protected marine animals were detected nearby. The logistic and financial burdens of these added obligations have become part of an increased cost of exploration. More recent regulatory responses such as closing areas to seismic surveys or seeking alternative sound source technologies offer even greater technical and financial challenges to the industry.
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Effective monitoring of nearshore seismic surveys off Sakhalin and mitigation of sound exposure for a feeding whale population
By R. RaccaThe northeastern shelf of Sakhalin Island, Russian Federation, is an important feeding ground of a critically endangered population of gray whales (Eschrichtius robustus) which convene annually in the region near the mouth of Piltun lagoon. In 2010 and again in 2015, Sakhalin Energy Investment Company conducted repeat (4D) seismic surveys to characterize changes to the subsurface from hydrocarbon production at the two platforms, required for efficient positioning of new wells; the original 3D seismic data had been acquired in 1997. Considerable effort went into the development for the 2010 seismic survey of a Monitoring and Mitigation Plan (MMP) that would recognize not just the necessity of preventing exposure of a critically endangered foraging population of gray whales to damaging or behaviourally interfering seismic pulse levels, but also the importance of collecting high quality acoustic and visual monitoring data to be used in studies of potential effects. This resulted in an effective framework for sound exposure estimation, measurement and mitigation and a highly structured shore based visual observation program capable of providing robust data on distribution and behaviour of the animals. Measured revisions and enhancements for the 2015 seismic survey MMP addressed some shortcomings of the earlier version for greater efficacy.
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Review and evaluation of low visibility real-time monitoring techniques
Authors U.K. Verfuss, D. Gillespie, J. Gordon, T.A. Marques, B. Miller, R. Plunkett and J. TheriaultAnthropogenic sound emitted into the sea has the potential to impact marine mammal by masking relevant sound, causing behavioural changes and, in extreme cases, induce auditory injury or death. It is often required to monitor an operational area of offshore projects for the presence of marine mammals in order to reduce the risk of potential impact. This kind of monitoring is traditionally conducted by trained visual observers, which scan the sea surface for marine mammals. This method, however, is restricted to daylight hours and fair weather conditions. The talk presents a review and evaluation of monitoring methods that could now, or in the near future, be used for marine mammal monitoring for mitigation purposes in periods of low visibility during which the effectiveness of visual observers is reduced.
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Exploration Success Equation
By A.V. MilkovThere are several definitions of petroleum exploration success. Geological (or technical) success is defined as finding oil & gas accumulations. Commercial (or economic) success means finding oil and gas accumulations that result in financial profits. Another, less common definition is finding oil and gas accumulations that, on a portfolio basis, have total resource volumes and create total monetary value as predicted before the drilling. However, exploration companies commonly deliver exploration results that are not consistent with pre-drill predictions. For example, Rudolph and Goulding (2017) studied drilling results from ExxonMobil conventional exploration in 1994-2015 and found that delivered volumes were 27% larger than pre-drill predictions. On the other hand, the study of Lundin’s exploration on the Norwegian Continental Shelf (NCS) in 2011-2015 revealed that the company delivered volumes that were 45% below the expectation from the portfolio of 25 wells (Milkov, 2017).
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Overconfidence and optimism in the oil industry: surfacing systematic biases and distortions in probabilistic practice
By G. KeithIn order to hold a meaningful discussion on the accuracy, or otherwise, of our probabilistic assessments, it is necessary to have a meaningful sense of what constitutes an accurate assessment. Pragmatically, this is equivalent to understanding how we can validate probabilistic statements regarding events against their outcomes.
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Analogue play statistics for improved pre-drill risking: North Sea case study
By K. MyersThere is evidence that the industry is systematically over-estimating the commercial chance of success (CoCS) and volume especially in high risk plays. The bias in commercial risking and pre-drill volume estimation is not a new phenomenon and persists today. Analogue play statistics can help address potential bias by providing objective calibration and sense-checking of success rates and discovery sizes.
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Addressing the causes of uncalibrated predictions & underperformance in oil & gas ventures
Authors M. Bond and P.D. CarragherPersistent biases affect the important work of estimating the range of uncertainty of oil and gas resources and reserves, the chance of success for a wildcat well, and the chance that an unconventional resource project will be successful. These biases result in chronic underperformance in the oil and gas industry as evidenced by predicted volumes that are overoptimistic; uncalibrated success rates, and poor economic results in unconventional projects.
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Direct inversion of seismic reflection data
By P.B. HardyThe prominent inversion based methods we use to estimate velocity models of the subsurface using seismic data have practical weaknesses that limit their application.
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Focusing conditions: a comparison between different Marchenko imaging strategies
Authors G.A. Meles, C. Reinicke, K. Wapenaar, J. Brackenhoff and J.W. ThorbeckeMarchenko imaging allows retrieving images from single-sided reflection measurements without artefacts due to internal multiples. A key step in Marchenko imaging is the retrieval of the so-called focusing function from the reflection measurements and a background model. The conventional focusing function obeys a point focusing condition, i.e. it focuses inside the medium of interest both in space and in time. Based on this focusing property one can retrieve up- and downgoing Green’s functions that are associated with a virtual point source or receiver inside the medium, which can be used for imaging. Recently, a new focusing function has been introduced that creates a plane wave instead of a point focus. Using the new focusing function one can retrieve medium responses associated to an up- and downgoing plane wave source or receiver inside the medium, enabling imaging based on plane wave sources. We compare Marchenko imaging using the conventional and the new focusing condition.
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Wave-Equation Dispersion Inversion of Guided P Waves in a Waveguide of Arbitrary Geometry
Authors J. Li, S. Hanafy and G. SchusterWe present the theory for wave-equation inversion of dispersion curves obtained from guided P waves. The misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves, and the inverted result is a high-resolution estimate of the near-surface P-velocity model. This procedure, denoted as the wave equation dispersion inversion of guided Pwaves (WDG), is valid for near-surface waveguides with irregular layers. It is less prone to the cycle skipping problems of full waveform inversion (FWI) and can sometimes provide velocity models with higher resolution than wave-equation traveltime tomography (WT). The synthetic and field data examples demonstrate that WDG for guided P-waves can accurately reconstruct the P-wave velocity distribution in laterally heterogeneous media.
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Understanding multiples in land seismic data
More LessThe limited success of wave equation based methods for multiple removal on land is likely due to a fundamental lack of understanding of the relevant multiple mechanism. Where are the strongest multiples generated? Are multiples mostly surface multiples, generated by reflection at the free surface? Or is it the base of the weathering layer that is the source of significant multiple energy, so that we should talk about interbed multiples instead? What is the relative contribution of interbed multiples to the total multiple energy? What is the role of elastic effects, in particular mode conversions? In this paper, we will discuss an attempt to advance our understanding of the multiple mechanism in a typical Middle East land setting. The basic approach is to combine a variety of techniques providing shallow subsurface information (shallow well logs, modal elastic inversion, elastic full waveform inversion, surface consistent deconvolution filters) to obtain a single consistent and detailed shallow model and to subsequently compare synthetic forward modeled data and actual field data to challenge various multiple mechanism scenarios.
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Making acoustic and elastic internal multiple prediction work efficiently and without artifacts
Authors K.A. Innanen, J. Sun and A.S. IversonFor prediction and removal of internal multiples, inverse scattering series methods operate in situations where an accurate velocity model and generator picks are absent or difficult to determine. The technology has produced remarkable results, however, its regular, practical, and value-added use requires algorithms which simultaneously incorporate (1) flexibility, in the sense of domain of computation; (2) non stationarity, in selection of the searchlimiting parameters associated with the method; (3) extension to elastic/multicomponent data; and (4) correct ordering of sub-events in input data preparation, even in the presence of complex wave phenomena such as multiple elastic conversions. In this paper we summarize the development of an integrated set of inverse series prediction algorithms that are designed to address these issues and push forward the practical applicability of this type of technology.
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A single-sided representation for the homogeneous Green's function, accounting for all multiples
Authors K. Wapenaar, J. Brackenhoff, J. Thorbecke, J. van der Neut and E. SlobThe homogeneous Green's function, i.e., the superposition of the causal Green's function and its time reversal, is traditionally represented by a closed boundary integral. This integral representation finds applications in holographic imaging, seismic interferometry and time-reversal acoustics. In principle these methods account for all multiples, but only when the medium is accessible from all sides. Here we discuss a single-sided representation of the homogeneous Green's function, which also accounts for all multiples, but which can be used when the medium is accessible from one side only. We indicate the application of this representation for seismic imaging, accounting for internal multiple scattering.
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Applications of the Marchenko method in the data domain
Authors J.A. Brakenhoff, M. Stating and L. ZhangThe Marchenko method has been proven on synthetic data, but there are few quality field data examples. We show that by slightly adjusting the Marchenko method the multiples in an image with a complex salt overburden can be greatly reduced. We also show that on a field dataset the homogeneous Green's function in the subsurface can be retrieved, consisting of a direct field as well as several orders of multiples.
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An overview of Marchenko-based redatuming: past, present, (and future)
By M. RavasiMarchenko-based redatuming methods aim to produce full-waveform propagators from single-sided reflection data and an estimate of the subsurface velocity model. In this talk, I will first review various alternative approaches proposed in the literature and discuss how they differ from each other and from the original formulation of Wapenaar et al (2014). Using a common notation throughout, the key novelty of each method will be highlighted as well as their strengths and limitations with respect to application to field data. Finally, I will discuss the way forward, both in terms of implementation details (e.g., 3D) and theoretical advances (e.g., active role of multiples), that are the topics of current research in the community and can be seen as key enablers for a more widespread use of the Marchenko equation in geophysical applications.
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Towards the prediction of internal multiples from thin layering by Marchenko
Authors R.F. Hegge, G.A. Meles and C.P.A. WapenaarThe presence of internal multiples in our data due to strong reflectors could inhibit or complicate the correct (quantitative) interpretation in particular when, after imaging, they cross reflectors or areas of interest. Commonly used internal multiple prediction and subtraction workflows deal with these kind of situations reasonably well. Unfortunately, situations exist whereby internal multiples are not ‘simply’ crossing events. For instance, a package of thin layers can produce a ‘cloud’ of internal multiples, which completely obscures deeper primaries as observed in a dataset acquired at or near the Arabian Peninsula. So far, all available workflows fail to handle this particular case. Note that when just the subtraction is not feasible, the separate imaging of the predicted internal multiples could still be of benefit to the interpretation process. With this case in mind, a collaboration project was initiated to evaluate Marchenko based internal multiple prediction for thin layering using a series of datasets from synthetic models in, mostly, blind tests. This abstract presents the first observations from the initial results.
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Least-Squares Full Wavefield Migration
Authors S. Lu, F. Liu and N. CheminguiConventional seismic processing uses only primary reflections for imaging, and treats high-order reflected events (multiples) as noise. Separated Wavefield IMaging (SWIM) uses the downgoing pressure wavefield to exploit the extended illumination provided by surface-multiple energy, effectively converting all receivers into virtual sources. We present a Least-Squares inversion solution for depth migration of the full reflected wavefield that includes both primary and high-order reflected energy. Standard migration of primaries and SWIM are complementary and can augment the overall imaging results when they are combined correctly. Whilst full-wavefield migration (FWM) is able to jointly image both primary and high-order reflected energy, it cannot easily balance the contribution of each component, and also involves crosstalk due to the natural blending scheme. The Least-Squares full wavefield migration (LS-FWM) described here directly computes the earth’s reflection image in an iterative manner, thereby avoiding crosstalk noise. Successful applications to both synthetic and field data examples demonstrate that LS-FWM greatly improves the imaging illumination and resolution compared to conventional migration.
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Non-Gaussian Linear Inversion of Reflection Seismic Data
Authors P.S. Christiansen, T.M. Hansen and H.J. HansenThe method of seismic inversion aims to estimate subsurface properties from seismic data, thereby providing us with a model of the earth. Often model parameters are assumed to be Gaussian distributed because it makes the inverse problem more tractable as it can be solved analytically by least-squares based algorithms (Buland and Omre, 2003).
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Integrating Gradient Information with Probabilistic Traveltime Tomography Using the Hamiltonian Monte Carlo Algorithm
Authors A. Zunino and K. MosegaardSeismic traveltime tomography is a popular methodology used to infer the velocity structure of the subsurface (Cerveny, 2001; Nolet, 2008) which has been used across all the scales from near surface imaging to global seismology. In near surface seismology inversion for traveltime is employed to construct velocity models used for further processing of seismic data and crucial to correctly assess deep structures. Formally, the relationship between velocity and traveltime can be described by the eikonal equation (Nolet, 2008), a nonlinear partial differential equation describing the arrival time for a given velocity model as a function of position. Solving numerically the eikonal equation (Vidale, 1988; Podvin and Lecomte, 1991; Rawlinson and Sambridge, 2004) for a given source, provides the traveltime at all grid nodes at once, hence saving a substantial amount of computational time compared to the traditional ray-tracing approach.
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