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- Volume 62, Issue 6, 2014
Geophysical Prospecting - Volume 62, Issue 6, 2014
Volume 62, Issue 6, 2014
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Low‐frequency normal wave propagation in a periodically layered medium with weak contrast in elastic properties
Authors Y. Roganov and A. StovasABSTRACTWe derive the phase velocity dispersion and the scattering for wave vertically propagating in a periodically weak‐contrast horizontally layered medium with arbitrary number of layers in a period. Phase velocity dispersion is defined as the frequency dependence of vertical travel time, and scattering is defined as a reflection coefficient at the interface between the multilayered system and the corresponding Backus medium. Low‐frequency approximation is used to define a dynamic effective medium with frequency‐dependent phase velocity. The results are compared with those obtained earlier for a gradient medium. We show that the low‐frequency weak‐contrast approximation is valid for models with realistic contrasts in elastic properties.
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An overview of laboratory apparatuses to measure seismic attenuation in reservoir rocks
More LessABSTRACTIntrinsic wave attenuation at seismic frequencies is strongly dependent on rock permeability, fluid properties, and saturation. However, in order to use attenuation as an attribute to extract information on rock/fluid properties from seismic data, experimental studies on attenuation are necessary for a better understanding of physical mechanisms that are dominant at those frequencies. An appropriate laboratory methodology to measure attenuation at seismic frequencies is the forced oscillation method, but technical challenges kept this technique from being widely used. There is a need for the standardization of devices employing this method, and a comparison of existing setups is a step towards it. Here we summarize the apparatuses based on the forced oscillation method that were built in the last 30 years and were used to measure frequency‐dependent attenuation in fluid‐saturated and/or dry reservoir rocks under small strains (10−8–10−5). We list and discuss important technical aspects to be taken into account when working with these devices or in the course of designing a new one. We also present a summary of the attenuation measurements in reservoir rock samples performed with these apparatuses so far.
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Quantitative gas saturation estimation by frequency‐dependent amplitude‐versus‐offset analysis
Authors Xiaoyang Wu, Mark Chapman, Xiang‐Yang Li and Patrick BostonABSTRACTSeismic amplitudes contain important information that can be related to fluid saturation. The amplitude‐versus‐offset analysis of seismic data based on Gassmann's theory and the approximation of the Zoeppritz equations has played a central role in reservoir characterization. However, this standard technique faces a long‐standing problem: its inability to distinguish between partial gas and “fizz‐water” with little gas saturation. In this paper, we studied seismic dispersion and attenuation in partially saturated poroelastic media by using frequency‐dependent rock physics model, through which the frequency‐dependent amplitude‐versus‐offset response is calculated as a function of porosity and water saturation. We propose a cross‐plotting of two attributes derived from the frequency‐dependent amplitude‐versus‐offset response to differentiate partial gas saturation and “fizz‐water” saturation. One of the attributes is a measure of “low frequency”, or Gassmann, of reflectivity, whereas the other is a measure of the “frequency dependence” of reflectivity. This is in contrast to standard amplitude‐versus‐offset attributes, where there is typically no such separation. A pragmatic frequency‐dependent amplitude‐versus‐offset inversion for rock and fluid properties is also established based on Bayesian theorem. A synthetic study is performed to explore the potential of the method to estimate gas saturation and porosity variations. An advantage of our work is that the method is in principle predictive, opening the way to further testing and calibration with field data. We believe that such work should guide and augment more theoretical studies of frequency‐dependent amplitude‐versus‐offset analysis.
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Pore fluid viscosity effects on P‐ and S‐wave anisotropy in synthetic silica‐cemented sandstone with aligned fractures
Authors Philip Tillotson, Mark Chapman, Jeremy Sothcott, Angus Ian Best and Xiang‐Yang LiABSTRACTUltrasonic (500 kHz) P‐ and S‐wave velocity and attenuation anisotropy were measured in the laboratory on synthetic, octagonal‐shaped, silica‐cemented sandstone samples with aligned penny‐shaped voids as a function of pore fluid viscosity. One control (blank) sample was manufactured without fractures, another sample with a known fracture density (measured from X‐ray CT images). Velocity and attenuation were measured in four directions relative to the bedding fabric (introduced during packing of successive layers of sand grains during sample construction) and the coincident penny‐shaped voids (fractures). Both samples were measured when saturated with air, water (viscosity 1 cP) and glycerin (100 cP) to reveal poro‐visco‐elastic effects on velocity and attenuation, and their anisotropy. The blank sample was used to estimate the background anisotropy of the host rock in the fractured sample; the bedding fabric was found to show transverse isotropy with shear wave splitting (SWS) of 1.45 ± 1.18% (i.e. for S‐wave propagation along the bedding planes). In the fractured rock, maximum velocity and minimum attenuation of P‐waves was seen at 90° to the fracture normal. After correction for the background anisotropy, the fractured sample velocity anisotropy was expressed in terms of Thomsen's weak anisotropy parameters ε, γ & δ. A theory of frequency‐dependent seismic anisotropy in porous, fractured, media was able to predict the observed effect of viscosity and bulk modulus on ε and δ in water‐ and glycerin‐saturated samples, and the higher ε and δ values in air‐saturated samples. Theoretical predictions of fluid independent γ are also in agreement with the laboratory observations. We also observed the predicted polarisation cross‐over in shear‐wave splitting for wave propagation at 45° to the fracture normal as fluid viscosity and bulk modulus increases.
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An experimental study of solid matrix weakening in water‐saturated Savonnières limestone
Authors Maxim Lebedev, Moyra E.J. Wilson and Vassily MikhaltsevitchABSTRACTPetrophysical properties of carbonate reservoirs are less predictable than that of siliciclastic reservoirs. One of the main reasons for this is the physical and chemical interactions of carbonate rocks with pore fluids. Such interactions can significantly change the elastic properties of the rock matrix and grains, making the applicability of Gassmann's fluid substitution procedure debatable. This study is an attempt to understand the mechanisms of fluid‐rock interactions and the influence of these interactions on elastic parameters of carbonates. We performed precise indentation tests on Savonnières limestone at a microscale level under dry, distilled water, and n‐Decane saturated conditions. Our experiments display softening of the rock matrix after water saturation. We have found that mainly the ooid cortices, peloid nuclei and prismatic intergranular cement are affected by water flooding. We also observed a shear modulus reduction in Savonnières limestone in an experiment performed at ultrasonic frequencies. One of the most important results obtained in our experimental study is that the Gassmann fluid substitution theory might not always be applicable to predict the elastic moduli of fluid‐saturated limestones.
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Measurements of the elastic and anelastic properties of sandstone flooded with supercritical CO2
Authors Vassily Mikhaltsevitch, Maxim Lebedev and Boris GurevichABSTRACTThe aim of this study was to investigate the effects of supercritical CO2 (scCO2) injection on the elastic and anelastic properties of sandstone at seismic and ultrasonic frequencies. We present the results of the low‐frequency and ultrasonic experiments conducted on water‐saturated sandstone (Donnybrook, Western Australia) flooded with scCO2. The sandstone was cut in the direction perpendicular to a formation bedding plane and tested in a Hoek triaxial pressure cell. During the experiments with scCO2, the low‐frequency and ultrasonic systems and the pump dispensing scCO2 were held at a temperature of 42°C. The elastic parameters obtained for the sandstone with scCO2 at seismic (0.1 Hz–100 Hz) and ultrasonic (∼0.5 MHz) frequencies are very close to those for the dry rock. The extensional attenuation was also measured at seismic frequencies for the dry, water‐saturated, and scCO2‐injected sandstones. The applicability of Gassmann's fluid substitution theory to obtained results was also tested during the experiments.
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Seismic attenuation and velocity dispersion in fractured rocks: The role played by fracture contact areas
Authors J. Germán Rubino, Tobias M. Müller, Marco Milani and Klaus HolligerABSTRACTThe presence of fractures in fluid‐saturated porous rocks is usually associated with strong seismic P‐wave attenuation and velocity dispersion. This energy dissipation can be caused by oscillatory wave‐induced fluid pressure diffusion between the fractures and the host rock, an intrinsic attenuation mechanism generally referred to as wave‐induced fluid flow. Geological observations suggest that fracture surfaces are highly irregular at the millimetre and sub‐millimetre scale, which finds its expression in geometrical and mechanical complexities of the contact area between the fracture faces. It is well known that contact areas strongly affect the overall mechanical fracture properties. However, existing models for seismic attenuation and velocity dispersion in fractured rocks neglect this complexity. In this work, we explore the effects of fracture contact areas on seismic P‐wave attenuation and velocity dispersion using oscillatory relaxation simulations based on quasi‐static poroelastic equations. We verify that the geometrical and mechanical details of fracture contact areas have a strong impact on seismic signatures. In addition, our numerical approach allows us to quantify the vertical solid displacement jump across fractures, the key quantity in the linear slip theory. We find that the displacement jump is strongly affected by the geometrical details of the fracture contact area and, due to the oscillatory fluid pressure diffusion process, is complex‐valued and frequency‐dependent. By using laboratory measurements of stress‐induced changes in the fracture contact area, we relate seismic attenuation and dispersion to the effective stress. The corresponding results do indeed indicate that seismic attenuation and phase velocity may constitute useful attributes to constrain the effective stress. Alternatively, knowledge of the effective stress may help to identify the regions in which wave induced fluid flow is expected to be the dominant attenuation mechanism.
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Anisotropic effective conductivity in fractured rocks by explicit effective medium methods
Authors Pål Næverlid Sævik, Morten Jakobsen, Martha Lien and Inga BerreABSTRACTIn this work, we assess the use of explicit methods for estimating the effective conductivity of anisotropic fractured media. Explicit methods are faster and simpler to use than implicit methods but may have a more limited range of validity. Five explicit methods are considered: the Maxwell approximation, the T‐matrix method, the symmetric and asymmetric weakly self‐consistent methods, and the weakly differential method, where the two latter methods are novelly constructed in this paper. For each method, we develop simplified expressions applicable to flat spheroidal “penny‐shaped” inclusions. The simplified expressions are accurate to the first order in the ratio of fracture thickness to fracture diameter. Our analysis shows that the conductivity predictions of the methods fall within known upper and lower bounds, except for the T‐matrix method at high fracture densities and the symmetric weakly self‐consistent method when applied to very thin fractures. Comparisons with numerical results show that all the methods give reliable estimates for small fracture densities. For high fracture densities, the weakly differential method is the most accurate if the fracture geometry is non‐percolating or the fracture/matrix conductivity contrast is small. For percolating conductive fracture networks, we have developed a scaling relation that can be applied to the weakly self‐consistent methods to give conductivity estimates that are close to the results from numerical simulations.
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Anomalous electrical resistivity anisotropy in clean reservoir sandstones
Authors Laurence J. North and Angus I. BestABSTRACTWe report novel laboratory measurements of the full electrical resistivity tensor in reservoir analogue quartzose sandstones with clay contents less than 1.5%. We show that clean, homogeneous, visually uniform sandstone samples typically display between 15% and 25% resistivity anisotropy with minimum resistivity normal to the bedding plane. Thin‐section petrography, analysis of fabric anisotropy, and comparison to finite‐element simulations of grain pack compaction show that the observed anisotropy symmetries and magnitudes can be explained by syn‐depositional and post‐depositional compaction processes. Our findings suggest that: electrical resistivity anisotropy is likely to be present in most clastic rocks as a consequence of ballistic deposition and compaction; compaction may be deduced from measurements of electrical anisotropy; and the anisotropy observed at larger scales in well logging and controlled‐source electromagnetic data, with maximum resistivity normal to bedding, is most likely the result of meso‐scale (10−1 m–101 m) periodic layering of electrically dissimilar lithologies.
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Burial stress and elastic strain of carbonate rocks
More LessABSTRACTBurial stress on a sediment or sedimentary rock is relevant for predicting compaction or failure caused by changes in, e.g., pore pressure in the subsurface. For this purpose, the stress is conventionally expressed in terms of its effect: “the effective stress” defined as the consequent elastic strain multiplied by the rock frame modulus. We cannot measure the strain directly in the subsurface, but from the data on bulk density and P‐wave velocity, we can estimate the rock frame modulus and Biot's coefficient and then calculate the “effective vertical stress” as the total vertical stress minus the product of pore pressure and Biot's coefficient. We can now calculate the elastic strain by dividing “effective stress” with the rock frame modulus. By this procedure, the degree of elastic deformation at a given time and depth can be directly expressed. This facilitates the discussion of the deformation mechanisms. The principle is illustrated by comparing carbonate sediments and sedimentary rocks from the North Sea Basin and three oceanic settings: a relatively shallow water setting dominated by coarse carbonate packstones and grainstones and two deep water settings dominated by fine‐grained carbonate mudstones and wackestones.
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Theoretical study on multi‐level source design
Authors Honglei Shen, Thomas Elboth, Gang Tian, Jakub Warszawski and Didrik LiljaABSTRACTThis paper studies aspects that influence the de‐ghosting performance of marine multi‐level sources based on a modified Johnson model. The normalized squared error between actual signature and its corresponding ghost‐free signature is introduced to evaluate the multi‐level source design. The results show that optimum depth combinations and volume combinations exist in the design. However, there is also some flexibility in the volume combination which makes it possible to optimize with respect to residual bubble oscillation. By considering both operational aspects and performance, we propose that three or four levels in a multi‐level source are reasonable. Compared to a horizontal source, a multi‐level source can be designed to reduce the notch effect, strengthen the down‐going energy and improve the energy transmission directivity. Studies of the influence of depth and firing time deviations indicate that a multi‐level source is more stable than a normal horizontal source in an operational environment.
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Full waveform inversion and the truncated Newton method: quantitative imaging of complex subsurface structures
Authors L. Métivier, F. Bretaudeau, R. Brossier, S. Operto and J. VirieuxABSTRACTFull waveform inversion is a powerful tool for quantitative seismic imaging from wide‐azimuth seismic data. The method is based on the minimization of the misfit between observed and simulated data. This amounts to the solution of a large‐scale nonlinear minimization problem. The inverse Hessian operator plays a crucial role in this reconstruction process. Accounting accurately for the effect of this operator within the minimization scheme should correct for illumination deficits, restore the amplitude of the subsurface parameters, and help to remove artefacts generated by energetic multiple reflections. Conventional minimization methods (nonlinear conjugate gradient, quasi‐Newton methods) only roughly approximate the effect of this operator. In this study, we are interested in the truncated Newton minimization method. These methods are based on the computation of the model update through a matrix‐free conjugate gradient solution of the Newton linear system. We present a feasible implementation of this method for the full waveform inversion problem, based on a second‐order adjoint state formulation for the computation of Hessian‐vector products. We compare this method with conventional methods within the context of 2D acoustic frequency full waveform inversion for the reconstruction of P‐wave velocity models. Two test cases are investigated. The first is the synthetic BP 2004 model, representative of the Gulf of Mexico geology with high velocity contrasts associated with the presence of salt structures. The second is a 2D real data‐set from the Valhall oil field in North sea. Although, from a computational cost point of view, the truncated Newton method appears to be more expensive than conventional optimization algorithms, the results emphasize its increased robustness. A better reconstruction of the P‐wave velocity model is provided when energetic multiple reflections make it difficult to interpret the seismic data. A better trade‐off between regularization and resolution is obtained when noise contamination of the data requires one to regularize the solution of the inverse problem.
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Internal multiple attenuation by Kirchhoff extrapolation
Authors Vincenzo Lipari, Carlo Fortini, Emmanuel Spadavecchia and Nicola BienatiABSTRACTSurface‐related multiple elimination is the leading methodology for surface multiple removal. This data‐driven approach can be extended to interbed multiple prediction at the expense of a huge increase of the computational burden. This cost makes model‐driven methods still attractive, especially for the three dimensional case. In this paper we present a methodology that extends Kirchhoff wavefield extrapolation to interbed multiple prediction. In Kirchhoff wavefield extrapolation for surface multiple prediction a single round trip to an interpreted reflector is added to the recorded data. Here we show that interbed multiples generated between two interpreted reflectors can be predicted by applying the Kirchhoff wavefield extrapolation operator twice. In the first extrapolation step Kirchhoff wavefield extrapolation propagates the data backward in time to simulate a round trip to the shallower reflector. In the second extrapolation step Kirchhoff wavefield extrapolation propagates the data forward in time to simulate a round trip to the deeper reflector. In the Kirchhoff extrapolation kernel we use asymptotic Green's functions. The prediction of multiples via Kirchhoff wavefield extrapolation is possibly sped up by computing the required traveltimes via a shifted hyperbola approximation. The effectiveness of the method is demonstrated by results on both synthetic and field data sets.
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Non‐convex compressed sensing with frequency mask for seismic data reconstruction and denoising
By Ali GholamiABSTRACTCompressed Sensing has recently proved itself as a successful tool to help address the challenges of acquisition and processing seismic data sets. Compressed sensing shows that the information contained in sparse signals can be recovered accurately from a small number of linear measurements using a sparsity‐promoting regularization. This paper investigates two aspects of compressed sensing in seismic exploration: (i) using a general non‐convex regularizer instead of the conventional one‐norm minimization for sparsity promotion and (ii) using a frequency mask to additionally subsample the acquired traces in the frequency‐space () domain. The proposed non‐convex regularizer has better sparse recovery performance compared with one‐norm minimization and the additional frequency mask allows us to incorporate a priori information about the events contained in the wavefields into the reconstruction. For example, (i) seismic data are band‐limited; therefore one can use only a partial set of frequency coefficients in the range of reflections band, where the signal‐to‐noise ratio is high and spatial aliasing is low, to reconstruct the original wavefield, and (ii) low‐frequency characteristics of the coherent ground rolls allow direct elimination of them during reconstruction by disregarding the corresponding frequency coefficients (usually bellow 10 Hz) via a frequency mask. The results of this paper show that some challenges of reconstruction and denoising in seismic exploration can be addressed under a unified formulation. It is illustrated numerically that the compressed sensing performance for seismic data interpolation is improved significantly when an additional coherent subsampling is performed in the domain compared with the domain case. Numerical experiments from both simulated and real field data are included to illustrate the effectiveness of the presented method.
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Full‐waveform based microseismic event detection and signal enhancement: An application of the subspace approach
Authors Fuxian Song, Norm R. Warpinski, M. Nafi Toksöz and H. Sadi KuleliABSTRACTMicroseismic monitoring has proven invaluable for optimizing hydraulic fracturing stimulations and monitoring reservoir changes. The signal to noise ratio of the recorded microseismic data varies enormously from one dataset to another, and it can often be very low, especially for surface monitoring scenarios. Moreover, the data are often contaminated by correlated noises such as borehole waves in the downhole monitoring case. These issues pose a significant challenge for microseismic event detection. In addition, for downhole monitoring, the location of microseismic events relies on the accurate polarization analysis of the often weak P‐wave to determine the event azimuth. Therefore, enhancing the microseismic signal, especially the low signal to noise ratio P‐wave data, has become an important task. In this study, a statistical approach based on the binary hypothesis test is developed to detect the weak events embedded in high noise. The method constructs a vector space, known as the signal subspace, from previously detected events to represent similar, yet significantly variable microseismic signals from specific source regions. Empirical procedures are presented for building the signal subspace from clusters of events. The distribution of the detection statistics is analysed to determine the parameters of the subspace detector including the signal subspace dimension and detection threshold. The effect of correlated noise is corrected in the statistical analysis. The subspace design and detection approach is illustrated on a dual‐array hydrofracture monitoring dataset. The comparison between the subspace approach, array correlation method, and array short‐time average/long‐time average detector is performed on the data from the far monitoring well. It is shown that, at the same expected false alarm rate, the subspace detector gives fewer false alarms than the array short‐time average/long‐time average detector and more event detections than the array correlation detector. The additionally detected events from the subspace detector are further validated using the data from the nearby monitoring well. The comparison demonstrates the potential benefit of using the subspace approach to improve the microseismic viewing distance. Following event detection, a novel method based on subspace projection is proposed to enhance weak microseismic signals. Examples on field data are presented, indicating the effectiveness of this subspace‐projection‐based signal enhancement procedure.
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Gabor‐frame‐based Gaussian packet migration
Authors Yu Geng, Ru‐Shan Wu and Jinghuai GaoABSTRACTWe present a Gaussian packet migration method based on Gabor frame decomposition and asymptotic propagation of Gaussian packets. A Gaussian packet has both Gaussian‐shaped time–frequency localization and space–direction localization. Its evolution can be obtained by ray tracing and dynamic ray tracing. In this paper, we first briefly review the concept of Gaussian packets. After discussing how initial parameters affect the shape of a Gaussian packet, we then propose two Gabor‐frame‐based Gaussian packet decomposition methods that can sparsely and accurately represent seismic data. One method is the dreamlet–Gaussian packet method. Dreamlets are physical wavelets defined on an observation plane and can represent seismic data efficiently in the local time–frequency space–wavenumber domain. After decomposition, dreamlet coefficients can be easily converted to the corresponding Gaussian packet coefficients. The other method is the Gabor‐frame Gaussian beam method. In this method, a local slant stack, which is widely used in Gaussian beam migration, is combined with the Gabor frame decomposition to obtain uniform sampled horizontal slowness for each local frequency. Based on these decomposition methods, we derive a poststack depth migration method through the summation of the backpropagated Gaussian packets and the application of the imaging condition. To demonstrate the Gaussian packet evolution and migration/imaging in complex models, we show several numerical examples. We first use the evolution of a single Gaussian packet in media with different complexities to show the accuracy of Gaussian packet propagation. Then we test the point source responses in smoothed varying velocity models to show the accuracy of Gaussian packet summation. Finally, using poststack synthetic data sets of a four‐layer model and the two‐dimensional SEG/EAGE model, we demonstrate the validity and accuracy of the migration method. Compared with the more accurate but more time‐consuming one‐way wave‐equation‐based migration, such as beamlet migration, the Gaussian packet method proposed in this paper can correctly image the major structures of the complex model, especially in subsalt areas, with much higher efficiency. This shows the application potential of Gaussian packet migration in complicated areas.
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Image enhancement by multi‐parameter characterization of common image gathers
Authors Raanan Dafni and Moshe ReshefABSTRACTWe present an innovative approach for seismic image enhancement using multi‐parameter angle‐domain characterization of common image gathers. A special subsurface angle‐domain imaging system is used to generate the multi‐parameter common image gathers in a summation‐free image space. The imaged data associated with each common image gathers depth point contain direction‐dependent opening‐angle image contributions from all the available incident and scattered wave‐pairs at this point. Each direction‐dependent opening‐angle data can be differently weighted according to its coherency measure. Once the optimal migration velocity is used, it is assumed that in the actual specular direction, the coherency measure (semblance) along reflection events, from all available opening angles and opening azimuths, is larger than that along non‐specular directions. The computed direction‐dependent semblance attribute is designed to operate as an imaging filter which enhances specular migration contributions and suppresses all others in the final migration image. The ability to analyse the structural properties of the image points by the multi‐parameter common image gather allows us to better handle cases of complicated wave propagation and to improve the image quality at poorly illuminated regions or near complex structures. The proposed method and some of its practical benefits are demonstrated through detailed analysis of synthetic and real data examples.
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Three‐dimensional modelling of controlled‐source electromagnetic surveys using an edge finite‐element method with a direct solver
Authors Yonghyun Chung, Jeong‐Sul Son, Tae Jong Lee, Hee Joon Kim and Changsoo ShinABSTRACTA fully three‐dimensional finite‐element algorithm has been developed for simulating controlled‐source electromagnetic surveys. To exploit the advantages of geometric flexibility, frequency‐domain Maxwell's equations of the secondary electric field were discretised using edge‐based finite elements while the primary field was calculated analytically for a horizontally layered‐earth model. The resulting system of equations for the secondary field was solved using a parallel version of direct solvers. The accuracy of the algorithm was successfully verified by comparisons with integral‐equations and iterative solutions, and the applicability to models containing large conductivity contrasts was verified against published data. The advantages of geometry‐conforming meshes have been demonstrated by comparing different mesh systems to simulate an inclined sheet model. A comparison of the performance between direct and iterative solvers demonstrated the superior efficiency of direct solvers, particularly for multisource problems.
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Volumes & issues
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Volume 72 (2023 - 2024)
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Volume 71 (2022 - 2023)
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Volume 70 (2021 - 2022)
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Volume 69 (2021)
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Volume 68 (2020)
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Volume 67 (2019)
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Volume 66 (2018)
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Volume 65 (2017)
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Volume 64 (2015 - 2016)
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Volume 63 (2015)
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Volume 62 (2014)
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Volume 61 (2013)
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Volume 60 (2012)
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Volume 59 (2011)
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Volume 58 (2010)
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Volume 56 (2008)
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Volume 55 (2007)
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Volume 53 (2005)
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Volume 46 (1998)
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Volume 31 (1983)
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Volume 30 (1982)
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Volume 29 (1981)
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Volume 27 (1979)
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Volume 26 (1978)
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Volume 21 (1973)
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Volume 19 (1971)
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Volume 6 (1958)
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Volume 1 (1953)