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- Volume 59, Issue 2, 2011
Geophysical Prospecting - Volume 59, Issue 2, 2011
Volume 59, Issue 2, 2011
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True amplitude imaging by inverse generalized Radon transform based on Gaussian beam decomposition of the acoustic Green's function
Authors M.I. Protasov and V.A. TcheverdaABSTRACTTrue amplitude migration is one of the most important procedures of seismic data processing. As a rule it is based on the decomposition of the velocity model of the medium into a known macrovelocity component and its sharp local perturbations to be determined. Under this decomposition the wavefield can be considered as the superposition of an incident and reflected/scattered waves. The single scattering approximation introduces the linear integral operator that connects the sharp local perturbations of the macrovelocity model with the multishot/multioffset data formed from reflected/scattered waves. We develop the pseudoinverse of this operator using the Gaussian beam based decomposition of acoustic Green's functions. The computation of this pseudoinverse operator is done pointwise by shooting Gaussian beams from the target area towards the acquisition system.
The numerical implementation of the pseudoinverse operator was applied to the synthetic data Sigsbee2A. The results obtained demonstrate the high quality of the true amplitude images computed both in the smooth part of the model and under the salt body.
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Global surface wave inversion with model constraints‡
More LessABSTRACTPractical applications of surface wave inversion demand reliable inverted shear‐wave profiles and a rigorous assessment of the uncertainty associated to the inverted parameters. As a matter of fact, the surface wave inverse problem is severely affected by solution non‐uniqueness: the degree of non‐uniqueness is closely related to the complexity of the observed dispersion pattern and to the experimental inaccuracies in dispersion measurements. Moreover, inversion pitfalls may be connected to specific problems such as inadequate model parametrization and incorrect identification of the surface wave modes. Consequently, it is essential to tune the inversion problem to the specific dataset under examination to avoid unnecessary computations and possible misinterpretations.
In the heuristic inversion algorithm presented in this paper, different types of model constraints can be easily introduced to bias constructively the solution towards realistic estimates of the 1D shear‐wave profile. This approach merges the advantages of global inversion, like the extended exploration of the parameter space and a theoretically rigorous assessment of the uncertainties on the inverted parameters, with the practical approach of Lagrange multipliers, which is often used in deterministic inversion, which helps inversion to converge towards models with desired properties (e.g., ‘smooth’ or ‘minimum norm' models). In addition, two different forward kernels can be alternatively selected for direct‐problem computations: either the conventional modal inversion or, instead, the direct minimization of the secular function, which allows the interpreter to avoid mode identification. A rigorous uncertainty assessment of the model parameters is performed by posterior covariance analysis on the accepted solutions and the modal superposition associated to the inverted models is investigated by full‐waveform modelling. This way, the interpreter has several tools to address the more probable sources of inversion pitfalls within the framework of a rigorous and well‐tested global inversion algorithm. The effectiveness and the versatility of this approach, as well as the impact of the interpreter's choices on the final solution and on its posterior uncertainty, are illustrated using both synthetic and real data. In the latter case, the inverted shear velocity profiles are blind compared with borehole data.
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Seismic anisotropy in a hydrocarbon field estimated from microseismic data
Authors O.H. Al‐Harrasi, A. Al‐Anboori, A. Wüstefeld and J.‐M. KendallABSTRACTThe study of seismic anisotropy in exploration seismology is gaining interest as it provides valuable information about reservoir properties and stress directions. In this study we estimate anisotropy in a petroleum field in Oman using observations of shear‐wave splitting from microseismic data. The data set was recorded by arrays of borehole geophones deployed in five wells. We analyse nearly 3400 microearthquakes, yielding around 8500 shear‐wave splitting measurements. Stringent quality control reduces the number of reliable measurements to 325. Shear‐wave splitting modelling in a range of rock models is then used to guide the interpretation.
The difference between the fast and slow shear‐wave velocities along the raypath in the field ranges between 0–10% and it is controlled both by lithology and proximity to the NE‐SW trending graben fault system that cuts the field formations. The anisotropy is interpreted in terms of aligned fractures or cracks superimposed on an intrinsic vertical transversely isotropic (VTI) rock fabric. The highest magnitudes of anisotropy are within the highly fractured uppermost unit of the Natih carbonate reservoir. Anisotropy decreases with depth, with the lowest magnitudes found in the deep part of the Natih carbonate formation. Moderate amounts of anisotropy are found in the shale cap rock. Anisotropy also varies laterally with the highest anisotropy occurring either side of the south‐eastern graben fault. The predominant fracture strikes, inferred from the fast shear‐wave polarizations, are consistent with the trends of the main faults (NE‐SW and NW‐SE). The majority of observations indicate subvertical fracture dip (>70°). Cumulatively, these observations show how studies of shear‐wave splitting using microseismic data can be used to characterize fractures, important information for the exploitation of many reservoirs.
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Stacking angle‐domain common‐image gathers for normalization of illumination
Authors Guochang Liu, Sergey Fomel and Xiaohong ChenABSTRACTUnequal illumination of the subsurface highly impacts the quality of seismic imaging. Different image points receive different folds of reflection‐angle illumination, which can be caused by irregular acquisition or by wave propagation in complex media. Illumination problems can deteriorate amplitudes in migrated images. To address this problem, we present a method of stacking angle‐domain common‐image gathers, in which we use local similarity with soft thresholding to determine the folds of local illumination. Normalization by local similarity regularizes local illumination of reflection angles for each image point of the subsurface model. This approach compensates for irregular illumination by selective stacking in the image space, regardless of the cause of acquisition or propagation irregularities. Additional migration is not required because the methodology is implemented in the reflection angle domain after migration. We use two synthetic examples to demonstrate that our method can normalize migration amplitudes and effectively suppress migration artefacts.
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Preserved‐amplitude angle domain migration by shot‐receiver wavefield continuation
Authors Frédéric Joncour, Gilles Lambaré and Julie Svay‐LucasABSTRACTWe present preserved‐amplitude downward continuation migration formulas in the aperture angle domain. Our approach is based on shot‐receiver wavefield continuation. Since source and receiver points are close to the image point, a local homogeneous reference velocity can be approximated after redatuming. We analyse this approach in the framework of linearized inversion of Kirchhoff and Born approximations. From our analysis, preserved‐amplitude Kirchhoff and Born inverse formulas can be derived for the 2D case. They involve slant stacks of filtered subsurface offset domain common image gathers followed by the application of the appropriate weighting factors. For the numerical implementation of these formulas, we develop an algorithm based on the true amplitude version of the one‐way paraxial approximation. Finally, we demonstrate the relevance of our approach with a set of applications on synthetic datasets and compare our results with those obtained on the Marmousi model by multi‐arrival ray‐based preserved‐amplitude migration. While results are similar, we observe that our results are less affected by artefacts.
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The free surface assumption for marine data‐driven demultiple methods*
Authors Martijn Frijlink, Roald van Borselen and Walter SöllnerABSTRACTIn the past, integral formulations for marine data‐driven demultiple methods have been derived from reciprocity theorems. Two fundamental assumptions in these derivations were that the sea‐surface is flat and has a known reflection coefficient, often taken to be minus one. In this paper, we show that for dual sensor data these assumptions can be relaxed. The sea‐surface has to obey the same conditions as any other reflecting boundary in the subsurface: it must be constant in time but shape and reflection strength can vary in space. For both surface‐related multiple elimination, and multiple attenuation by multi‐dimensional deconvolution, we derive integral equations that depend only on the measured pressure and particle velocity fields. Finally, we show there is an intimate connection between the integral equations for the methods.
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Harmonic by harmonic removal technique for improving vibroseis data quality
More LessABSTRACTIn this paper, an improved method is presented to reduce vibrator harmonic distortion, one harmonic at a time and the method is illustrated with both simulated and field data. This method improves on the previous method that treated all the harmonics at once. The significant contribution in this procedure is a considerable reduction for the harmonics without any alteration for the weakest signals possibly present in positive and negative times. The core of the proposed technique depends on an accurate simulation for all the harmonics one by one existing in the positive and negative times of the data after cross‐correlation with the fundamental sweep and then subtracting the simulated harmonics from the original data using an optimization procedure. The steps and mathematical equations of the procedure are explained in detail in the body of the article in the section titled ‘harmonic by harmonic attenuation procedure’. Accordingly, a well‐developed procedure for enhancing the vibroseis data quality in both down‐ and up‐sweep data is illustrated. The procedure was tested on both synthetic and field data sets.
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Estimation of changes in water column velocities and thicknesses from time lapse seismic data
Authors Bård Osdal and Martin LandrøABSTRACTSea‐bed diffractions are frequently observed for several of the fields in the Norwegian Sea and the Barents Sea. This is a challenge in time lapse seismic analysis, since diffracted multiples are difficult to remove by processing and therefore is a major source of poor time lapse data quality. In this work we test if the diffractions can be used for enhanced 4D interpretation. By analysing the time‐shift of the sea‐bed diffraction hyperbola between the base and monitor it is tested if changes in water velocity and tides can be estimated.
Two models using time lapse diffraction analysis are tested: the first one simply adds time‐shifts for the two branches of the diffraction hyperbola and this average time‐shift is then used to estimate the water velocity change. The other method uses an inversion method based on the diffraction equation for a point diffractor to estimate the velocity change. In‐line common‐midpoint shifts are estimated by subtracting the time‐shifts of both hyperbola branches followed by direct inversion. The diffraction based time‐shifts are compared to time‐shifts estimated by standard cross‐correlation of the sea‐bed reflection. The averaging method gives slightly higher uncertainties, while the inversion using an exact traveltime equation gives similar uncertainties compared to the sea‐bed reflection method.
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Towards quantitative evaluation of gas injection using time‐lapse seismic data
Authors Reza Falahat, Asghar Shams and Colin MacBethABSTRACTOf particular concern in the monitoring of gas injection for the purposes of storage, disposal or improved oil recovery is the exact spatial distribution of the gas volumes in the subsurface. In principle this requirement is addressed by the use of 4D seismic data, although it is recognized that the seismic response still largely provides a qualitative estimate of moved subsurface fluids. Exact quantitative evaluation of fluid distributions and associated saturations remains a challenge to be solved. Here, an attempt has been made to produce mapped quantitative estimates of the gas volume injected into a clastic reservoir. Despite good results using three accurately repeated seismic surveys, time‐delay and amplitude attributes reveal fine‐scale differences though large‐scale agreement in the estimated fluid movement. These differences indicate disparities in the nature of the two attributes themselves, which can be explained by several possible causes. Of most impact are the effects of processing and migration, wave interference effects and noise from non‐repeatability of the seismic surveys. This subject highlights the need for a more careful consideration in 4D acquisition, amplitude processing and use of true amplitude preserving attributes in quantitative interpretation.
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Two triaxial induction tools: sensitivity to radial invasion profile‡
More LessABSTRACTI study the responses of two different triaxial induction tools to invaded dipping anisotropic formations. I show that the triaxial measurements have generally higher sensitivity to the radial invasion profile, compared to the conventional induction measurements. This enables accurate interpretation of both the anisotropic formation properties and the invasion parameters. Multi‐spacing and single‐spacing multi‐frequency triaxial induction tools can both be used for this purpose. Failure to take the invasion properties into account may lead to misinterpretation of the vertical formation resistivity. Symmetrization of the apparent conductivity matrix opens ways for a visual interpretation of triaxial induction logs for the formation and the invasion zone properties. This technique enables simpler and faster inversion algorithms. I study how the effect of a conductive annulus forming around the invasion zone couples with effects of the dipping anisotropy and the dipping boundaries and show when these effects are additive. Thus, a visual detection of log parts affected by a conductive annulus becomes possible.
The key tool for interpretation in complex 3D scenarios is efficient modelling software. I use a 3D finite‐difference modelling approach to simulate responses of induction logging tools of the new generation. Its high efficiency enables simultaneous multi‐spacing and multi‐frequency computing of the tool responses to arbitrary 3D anisotropic formations that made the study possible.
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Sensitivity and inversion of marine electromagnetic data in a vertically anisotropic stratified earth
Authors Christophe Ramananjaona, Lucy MacGregor and David AndréisABSTRACTThe controlled‐source electromagnetic (CSEM) and magnetotelluric method (MT) are two techniques that can be jointly used to explore the resistivity structure of the earth. Such methods have, in recent years, been applied in marine environments to the exploration and appraisal of hydrocarbons. In many situations the electric properties of the earth are anisotropic, with differences between resistivity in the vertical direction typically much higher than those in the horizontal direction. In cases such as this, the two modes of the time‐harmonic electromagnetic field are altered in different ways, implying that the sensitivity to the earth resistivity may vary significantly from one particular resistivity component (scalar, horizontal or vertical) to another, depending on the measurement configuration (range, azimuth, frequency or water depth). In this paper, we examine the sensitivity of the electromagnetic field to a vertically anisotropic earth for a typical set of configurations, compare inversion results of synthetic data characterizing a vertically anisotropic earth obtained using the isotropic and anisotropic assumptions and show that correctly accounting for anisotropy can prevent artefacts in inversion results.
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Electromagnetic fields generated by finite‐length wire sources: comparison with point dipole solutions
Authors Rita Streich and Michael BeckenABSTRACTIn present‐day land and marine controlled‐source electromagnetic (CSEM) surveys, electromagnetic fields are commonly generated using wires that are hundreds of metres long. Nevertheless, simulations of CSEM data often approximate these sources as point dipoles. Although this is justified for sufficiently large source‐receiver distances, many real surveys include frequencies and distances at which the dipole approximation is inaccurate. For 1D layered media, electromagnetic (EM) fields for point dipole sources can be computed using well‐known quasi‐analytical solutions and fields for sources of finite length can be synthesized by superposing point dipole fields. However, the calculation of numerous point dipole fields is computationally expensive, requiring a large number of numerical integral evaluations. We combine a more efficient representation of finite‐length sources in terms of components related to the wire and its end points with very general expressions for EM fields in 1D layered media. We thus obtain a formulation that requires fewer numerical integrations than the superposition of dipole fields, permits source and receiver placement at any depth within the layer stack and can also easily be integrated into 3D modelling algorithms. Complex source geometries, such as wires bent due to surface obstructions, can be simulated by segmenting the wire and computing the responses for each segment separately. We first describe our finite‐length wire expressions and then present 1D and 3D examples of EM fields due to finite‐length sources for typical land and marine survey geometries and discuss differences to point dipole fields.
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Volume 72 (2023 - 2024)
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Volume 59 (2011)
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Volume 18 (1970 - 2006)
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