Three‐dimensional modelling of controlled‐source electromagnetic surveys using an edge finite‐element method with a direct solver

A 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.     

Insight into the marine controlled‐source electromagnetic signal propagation

In marine controlled‐source electromagnetic (CSEM) surveys the subsurface is explored by emitting low‐frequency signals from an electric dipole source close to the sea‐bed. The main goal is often to detect and describe possible thin resistive layers beneath the sea‐bed. To gain insight into how CSEM signals propagate, it is informative to study a stratified model. The electromagnetic field is then given in terms of integrals over TE‐ and TM‐polarized plane‐wave constituents. An asymptotic evaluation of the field integrals for large propagation distances results in explicit spatial expressions for the field components and the derived expressions can be used to analyse how the CSEM signals propagate. There are two major signal pathways in a standard CSEM model. One of these pathways is via the thin resistive layer and the resulting response is accounted for by a pole in the reflection response for the TM mode. The signal is propagating nearly vertically down to the resistor from the source, then guided while attenuated along the reservoir, before propagating nearly vertically up to the receiver. The response is slightly altered by the sea‐bed interface and further modified in shallow water due to multiple reflections between the sea‐surface and sea‐bed at both the source and receiver sides. The other major signal pathway is via the resistive air half‐space, the so‐called airwave. The airwave is generated by the TE mode and interacts with the subsurface via vertically propagating signals reflected between the sea‐surface and subsurface at both the source and receiver sides.     

Three‐dimensional inversion of towed streamer electromagnetic data

A towed streamer electromagnetic system capable of simultaneous seismic and electromagnetic data acquisition has recently been developed and tested in the North Sea. We introduce a 3D inversion methodology for towed streamer electromagnetic data that includes a moving sensitivity domain. Our implementation is based on the 3D integral equation method for computing responses and Fréchet derivatives and uses the re‐weighted regularized conjugate gradient method for minimizing the objective functional with focusing regularization. We present two model studies relevant to hydrocarbon exploration in the North Sea. First, we demonstrate the ability of a towed electromagnetic system to detect and characterize the Harding field, a medium‐sized North Sea hydrocarbon target. We compare our 3D inversion of towed streamer electromagnetic data with 3D inversion of conventional marine controlled‐source electromagnetic data and observe few differences between the recovered models. Second, we demonstrate the ability of a towed streamer electromagnetic system to detect and characterize the Peon discovery, which is representative of an infrastructure‐led shallow gas play in the North Sea. We also present an actual case study for the 3D inversion of towed streamer electromagnetic data from the Troll field in the North Sea and demonstrate our ability to image all the Troll West Oil and Gas Provinces and the Troll East Gas Province. We conclude that 3D inversion of data from the current generation of towed streamer electromagnetic systems can adequately recover hydrocarbon‐bearing formations to depths of approximately 2 km. We note that by obviating the need for ocean‐bottom receivers, the towed streamer electromagnetic system enables electromagnetic data to be acquired over very large areas in frontier and mature basins for higher acquisition rates and relatively lower cost than conventional marine controlled‐source electromagnetic methods.     

Inversion of inline and broadside marine controlled‐source electromagnetic data with constraints derived from seismic data

We present a structural smoothing regularization scheme in the context of inversion of marine controlled‐source electromagnetic data. The regularizing hypothesis is that the electrical parameters have a structure similar to that of the elastic parameters observed from seismic data. The regularization is split into three steps. First, we ensure that our inversion grid conforms with the geometry derived from seismic. Second, we use a seismic stratigraphic attribute to define a spatially varying regularization strength. Third, we use an indexing strategy on the inversion grid to define smoothing along the seismic geometry. Enforcing such regularization in the inversion will encourage an inversion result that is more intuitive for the interpreter to deal with. However, the interpreter should also be aware of the bias introduced by using seismic data for regularization. We illustrate the method using one synthetic example and one field data example. The results show how the regularization works and that it clearly enforces the structure derived from seismic data. From the field data example we find that the inversion result improves when the structural smoothing regularization is employed. Including the broadside data improves the inversion results even more, due to a better balancing between the sensitivities for the horizontal and vertical resistivities.     

水平层状介质中基于DTA的三维电磁波逆散射快速模拟算法

为提高水平层状介质中三维电磁波散射和逆散射数值模拟的效率,在对角张量近似(DTA)的基础上根据不同回代方式得到了求解积分方程的DTA1和DTA2两种近似. 这两种近似可以作为计算积分方程稳定型双共轭梯度快速Fourier变换(BCGS-FFT)算法的初始猜测值和预条件因子,从而形成效率更高的混合DTA-BCGS算法. 散射实例说明了DTA2的高精度和混合DTA-BCGS算法尤其是混合DTA2-BCGS算法的高效率. 由于DTA2近似程度更高,将DTA2与变型Born迭代反演方法(DBIM)相结合形成了一种对三维异常体进行重构的快速电磁波逆散射技术. 文中的逆散射实例说明所开发的逆散射技术对重构水平层状介质中的任意三维异常体是非常有效的.     

Controlled‐source electromagnetic monitoring of reservoir oil saturation using a novel borehole‐to‐surface configuration

To advance and optimize secondary and tertiary oil recovery techniques, it is essential to know the areal propagation and distribution of the injected fluids in the subsurface. We investigate the applicability of controlled‐source electromagnetic methods to monitor fluid movements in a German oilfield (Bockstedt, onshore Northwest Germany) as injected brines (highly saline formation water) have much lower electrical resistivity than the oil within the reservoir. The main focus of this study is on controlled‐source electromagnetic simulations to test the sensitivity of various source–receiver configurations. The background model for the simulations is based on two‐dimensional inversion of magnetotelluric data gathered across the oil field and calibrated with resistivity logs. Three‐dimensional modelling results suggest that controlled‐source electromagnetic methods are sensitive to resistivity changes at reservoir depths, but the effect is difficult to resolve with surface measurements only. Resolution increases significantly if sensors or transmitters can be placed in observation wells closer to the reservoir. In particular, observation of the vertical electric field component in shallow boreholes and/or use of source configurations consisting of combinations of vertical and horizontal dipoles are promising. Preliminary results from a borehole‐to‐surface controlled‐source electromagnetic field survey carried out in spring 2014 are in good agreement with the modelling studies.     

A land controlled‐source electromagnetic experiment using a deep vertical electric dipole: experimental settings,processing, and first data interpretation

A multichannel borehole‐to‐surface controlled‐source electromagnetic experiment was carried out at the onshore CO₂ storage site of Hontomín (Spain). The electromagnetic source consisted of a vertical electric dipole located 1.5 km deep, and the electric field was measured at the surface. The subsurface response has been obtained by calculating the transfer function between the transmitted signal and the electric field at the receiver positions. The dataset has been processed using a fast processing methodology, appropriate to be applied on controlled‐source electromagnetics (CSEM) data with a large signal‐to‐noise ratio. The dataset has been analysed in terms of data quality and repeatability errors, showing data with low experimental errors and good repeatability. We evaluate if the induction of current along the casing of the injection well can reproduce the behaviour of the experimental data.     

基于电场矢量波动方程的三维可控源电磁法有限单元法数值模拟

从可控源电磁法的基本原理出发,推导了基于电场矢量波动方程的三维边值问题,利用广义变分原理,把边值问题转换为变分问题,并引入散度条件,避免了伪解的出现,使有限元计算在理论上更加完备.在准静态近似条件下,把水平电偶极子在空中和大地的远区电场闭合表达式作为有限元计算中的区域外边界条件,解决了边界条件加载的困难;把应用于地震模拟中的伪delta函数引入到可控源电磁法中的三维有限元模拟中,消除了源点的奇异性,提高了方程组的稳定性.通过对均匀大地和层状介质模型的模拟,检验了程序的正确性,并对典型的地质体模型进行了数值模拟,分析了其变化规律.     

Two‐dimensional controlled‐source electromagnetic interferometry by multidimensional deconvolution: spatial sampling aspects

We use numerically modelled data sets to investigate the sensitivity of electromagnetic interferometry by multidimensional deconvolution to spatial receiver sampling. Interferometry by multidimensional deconvolution retrieves the reflection response below the receivers after decomposition of the fields into upward and downward decaying fields and deconvolving the upward decaying field by the downward decaying field. Thereby the medium above the receiver level is replaced with a homogeneous half‐space, the sources are redatumed to the receiver level and the direct field is removed. Consequently, in a marine setting the retrieved reflection response is independent of any effect of the water layer and the air above. A drawback of interferometry by multidimensional deconvolution is a possibly unstable matrix inversion, which is necessary to retrieve the reflection response. Additionally, in order to correctly separate the upward and the downward decaying fields, the electromagnetic fields need to be sampled properly. We show that the largest possible receiver spacing depends on two parameters: the vertical distance between the source and the receivers and the length of the source. The receiver spacing should not exceed the larger of these two parameters. Besides these two parameters, the presence of inhomogeneities close to the receivers may also require a dense receiver sampling. We show that by using the synthetic aperture concept, an elongated source can be created from conventionally acquired data in order to overcome these strict sampling criteria. Finally, we show that interferometry may work under real‐world conditions with random noise and receiver orientation and positioning errors.     

Passive and active control of three‐dimensional buildings

The majority of the recent research effort on structural control considers two‐dimensional plane structures. However, not all buildings can be modelled as plane structures, thus limiting the capability of the proposed procedures only to regular and symmetrical structures. A new procedure is developed in this paper to analyse three‐dimensional buildings utilizing passive and active control devices. In the building model, the floors are assumed rigid in their own plane resulting in three degrees of freedom at each floor. Two types of active control devices utilizing an active tuned mass damper and an active bracing system are considered. The effect of passive mass dampers and active control force in the equations of motion is incorporated by using the Hamilton's principle. The passive parameters of the dampers as well as the controller gain is then optimized using a genetic based optimizer where the H₂, H_∞ and L₁ norms are taken as the objective functions. Copyright © 2000 John Wiley & Sons, Ltd.     

Controlled source electromagnetic three‐dimensional grid‐modelling based on a complex resistivity structure of the seafloor: effects of acquisition parameters and geometry of multi‐layered resistors

A comprehensive controlled source electromagnetic (CSEM) modelling study, based on complex resistivity structures in a deep marine geological setting, is conducted. The study demonstrates the effects of acquisition parameters and multi‐layered resistors on CSEM responses. Three‐dimensional (3D) finite difference time domain (FDTD) grid‐modelling is used for CSEM sensitivity analysis. Interpolation of normalized CSEM responses provides attributes representing relative sensitivity of the modelled structures. Modelling results show that fine grid, 1 × 1 km receiver spacing, provides good correlations between CSEM responses and the modelled structures, irrespective of source orientation. The resolution of CSEM attributes decreases for receiver spacing >2 × 2 km, when using only in‐line data. Broadside data in the grid geometry increase data density by 100 – approximately 200% by filling in in‐line responses and improve the resolution of CSEM attributes. Optimized source orientation (i.e., oblique to the strike of an elongated resistor) improves the structural definition of the CSEM anomalies for coarse‐grid geometries (receiver spacing ≥3 × 3 km). The study also shows that a multi‐resistor anomaly is not simply the summation but a cumulative response with mutual interference between constituent resistors. The combined response of constituent resistors is approximately 50% higher than the cumulative response of the multi‐resistor for 0.5 Hz at 4000 m offset. A gradual inverse variation of offset and frequency allows differentiation of CSEM anomalies for multi‐layered resistors. Similar frequency‐offset variations for laterally persistent high‐resistivity facies show visual continuity with varying geometric expressions. 3D grid‐modelling is an effective and adequate tool for CSEM survey design and sensitivity analysis.     

Multi‐dimensional analyses of the SEAM controlled source electromagnetic data—the story of a blind test of interpretation workflows

Using a subset of the SEG Advanced Modeling Program Phase I controlled‐source electromagnetic data, we apply our standard controlled‐source electromagnetic interpretation workflows to delineate a simulated hydrocarbon reservoir. Experience learned from characterizing such a complicated model offers us an opportunity to refine our workflows to achieve better interpretation quality. The exercise proceeded in a blind test style, where the interpreting geophysicists did not know the true resistivity model until the end of the project. Rather, the interpreters were provided a traditional controlled‐source electromagnetic data package, including electric field measurements, interpreted seismic horizons, and well log data. Based on petrophysical analysis, a background resistivity model was established first. Then, the interpreters started with feasibility studies to establish the recoverability of the prospect and carefully stepped through 1D, 2.5D, and 3D inversions with seismic and well log data integrated at each stage. A high‐resistivity zone is identified with 1D analysis and further characterized with 2.5D inversions. Its lateral distribution is confirmed with a 3D anisotropic inversion. The importance of integrating all available geophysical and petrophysical data to derive more accurate interpretation is demonstrated.     

A numerical comparison of time and frequency‐domain marine electromagnetic methods for hydrocarbon exploration in shallow water

In shallow water the frequency domain controlled source electromagnetic method is subject to airwave saturation that strongly limits the sensitivity to resistive hydrocarbon targets at depth. It has been suggested that time‐domain CSEM may offer an improved sensitivity and resolution of these deep targets in the presence of the airwave. In order to examine and test these claims, this work presents a side‐by‐side investigation of both methods with a main focus on practical considerations, and how these effect the resolution of a hydrocarbon reservoir. Synthetic noisy data for both time‐domain and frequency domain methods are simulated using a realistic frequency dependent noise model and frequency dependent scaling for representative source waveforms. The synthetic data studied here include the frequency domain response from a compact broadband waveform, the time‐domain step‐response from a low‐frequency square wave and the time‐domain impulse response obtained from pseudo‐random binary sequences. These data are used in a systematic resolution study of each method as a function of water‐depth, relative noise and stacking length. The results indicate that the broadband frequency domain data have the best resolution for a given stacking time, whereas the time‐domain data require prohibitively longer stacking times to achieve similar resolution.     

Three‐dimensional controlled‐source electromagnetic modelling with a well casing as a grounded source: a hybrid method of moments and finite element scheme

Steel well casings in or near a hydrocarbon reservoir can be used as source electrodes in time‐lapse monitoring using grounded line electromagnetic methods. A requisite component of carrying out such monitoring is the capability to numerically model the electromagnetic response of a set of source electrodes of finite length. We present a modelling algorithm using the finite‐element method for calculating the electromagnetic response of a three‐dimensional conductivity model excited using a vertical steel‐cased borehole as a source. The method is based on a combination of the method of moments and the Coulomb‐gauged primary–secondary potential formulation. Using the method of moments, we obtain the primary field in a half‐space due to an energized vertical steel casing by dividing the casing into a set of segments, each assumed to carry a piecewise constant alternating current density. The primary field is then substituted into the primary–secondary potential finite‐element formulation of the three‐dimensional problem to obtain the secondary field. To validate the algorithm, we compare our numerical results with: (i) the analytical solution for an infinite length casing in a whole space, excited by a line source, and (ii) a three‐layered Earth model without a casing. The agreement between the numerical and analytical solutions demonstrates the effectiveness of our algorithm. As an illustration, we also present the time‐lapse electromagnetic response of a synthetic model representing a gas reservoir undergoing water flooding.     

Two‐dimensional and three‐dimensional computational models in hydrodynamic and morphodynamic reconstructions of a river bend: sensitivity and functionality

This study assesses hydrodynamic and morphodynamic model sensitivity and functionality in a curved channel. The sensitivity of a depth‐averaged model to user‐defined parameters (grain size, roughness, transverse bed slope effect, transport relations and secondary flow) is tested. According to the sensitivity analysis, grain size, transverse bed slope effect and sediment transport relations are critical to simulated meander bend morphodynamics. The parametrization of grain size has the most remarkable effect: field‐based grain size parametrization is necessary in a successful morphodynamic reconstruction of a meander bend. The roughness parametrization method affects the distribution of flow velocities and therefore also morphodynamics. The combined effect of various parameters needs further research. Two‐dimensional (2D) and three‐dimensional (3D) reconstructions of a natural meander bend during a flood event are assessed against field measurements of acoustic Doppler current profiler and multi‐temporal mobile laser scanning data. The depth‐averaged velocities are simulated satisfactorily (differences from acoustic Doppler current profiler velocities 5–14%) in both 2D and 3D simulations, but the advantage of the 3D hydrodynamic model is unquestionable because of its ability to model vertical and near‐bed flows. The measured and modelled near‐bed flow, however, differed notably from each other's, the reason of which was left open for future research. It was challenging to model flow direction beyond the apex. The 3D flow features, which also affected the distribution of the bed shear stress, seem not to have much effect on the predicted morphodynamics: the 2D and 3D morphodynamic reconstructions over the point bar resembled each other closely. Although common features between the modelled and measured morphological changes were also found, some specific changes that occurred were not evident in the simulation results. Our results show that short‐term, sub‐bend scale morphodynamic processes of a natural meander bend are challenging to model, which implies that they are affected by factors that have been neglected in the simulations. The modelling of short‐term morphodynamics in natural curved channel is a challenge that requires further study. Copyright © 2014 John Wiley & Sons, Ltd.     

Field test of sub‐basalt hydrocarbon exploration with marine controlled source electromagnetic and magnetotelluric data

The recent use of marine electromagnetic technology for exploration geophysics has primarily focused on applying the controlled source electromagnetic method for hydrocarbon mapping. However, this technology also has potential for structural mapping applications, particularly when the relative higher frequency controlled source electromagnetic data are combined with the lower frequencies of naturally occurring magnetotelluric data. This paper reports on an extensive test using data from 84 marine controlled source electromagnetic and magnetotelluric stations for imaging volcanic sections and underlying sediments on a 128‐km‐long profile. The profile extends across the trough between the Faroe and Shetland Islands in the North Sea. Here, we focus on how 2.5D inversion can best recover the volcanic and sedimentary sections. A synthetic test carried out with 3D anisotropic model responses shows that vertically transverse isotropy 2.5D inversion using controlled source electromagnetic and magnetotelluric data provides the most accurate prediction of the resistivity in both volcanic and sedimentary sections. We find the 2.5D inversion works well despite moderate 3D structure in the synthetic model. Triaxial inversion using the combination of controlled source electromagnetic and magnetotelluric data provided a constant resistivity contour that most closely matched the true base of the volcanic flows. For the field survey data, triaxial inversion of controlled source electromagnetic and magnetotelluric data provides the best overall tie to well logs with vertically transverse isotropy inversion of controlled source electromagnetic and magnetotelluric data a close second. Vertical transverse isotropy inversion of controlled source electromagnetic and magnetotelluric data provided the best interpreted base of the volcanic horizon when compared with our best seismic interpretation. The structural boundaries estimated by the 20‐Ω·m contour of the vertical resistivity obtained by vertical transverse isotropy inversion of controlled source electromagnetic and magnetotelluric data gives a maximum geometric location error of 11% with a mean error of 1.2% compared with the interpreted base of the volcanic horizon. Both the model study and field data interpretation indicate that marine electromagnetic technology has the potential to discriminate between low‐resistivity prospective siliciclastic sediments and higher resistivity non‐prospective volcaniclastic sediments beneath the volcanic section.     

Seismic response of three‐dimensional r/c multi‐storey frame building under uni‐ and bi‐directional input ground motion

This paper deals with seismic analysis of plan‐asymmetric r/c frame multi‐storey buildings. Non‐linear numerical analyses are carried out by using a lumped plasticity model for beams and a multi‐spring model for columns, the latter one introduced to account for axial force–biaxial bending moment interaction. A comparison between numerical analyses and experimental test results is reported in order to calibrate the numerical model, showing that the adopted model is very suitable. In order to study the effects of the earthquake orthogonal component, the seismic response of the modelled structure under uni‐directional excitation is compared to the one under bi‐directional excitation. Such comparison shows that the maximum base shear and the top displacement are not very sensitive to the presence of the orthogonal component, which, conversely, leads to large increase in the column plastic excursions. Copyright © 2007 John Wiley & Sons, Ltd.     

Achieving a more realistic assessment of rockfall hazards by coupling three‐dimensional process models and field‐based tree‐ring data

Sound knowledge of the spatial and temporal patterns of rockfalls is fundamental for the management of this very common hazard in mountain environments. Process‐based, three‐dimensional simulation models are nowadays capable of reproducing the spatial distribution of rockfall occurrences with reasonable accuracy through the simulation of numerous individual trajectories on highly‐resolved digital terrain models. At the same time, however, simulation models typically fail to quantify the ‘real’ frequency of rockfalls (in terms of return intervals). The analysis of impact scars on trees, in contrast, yields real rockfall frequencies, but trees may not be present at the location of interest and rare trajectories may not necessarily be captured due to the limited age of forest stands. In this article, we demonstrate that the coupling of modeling with tree‐ring techniques may overcome the limitations inherent to both approaches. Based on the analysis of 64 cells (40 m × 40 m) of a rockfall slope located above a 1631‐m long road section in the Swiss Alps, we illustrate results from 488 rockfalls detected in 1260 trees. We illustrate that tree impact data cannot only be used (i) to reconstruct the real frequency of rockfalls for individual cells, but that they also serve (ii) the calibration of the rockfall model Rockyfor3D, as well as (iii) the transformation of simulated trajectories into real frequencies. Calibrated simulation results are in good agreement with real rockfall frequencies and exhibit significant differences in rockfall activity between the cells (zones) along the road section. Real frequencies, expressed as rock passages per meter road section, also enable quantification and direct comparison of the hazard potential between the zones. The contribution provides an approach for hazard zoning procedures that complements traditional methods with a quantification of rockfall frequencies in terms of return intervals through a systematic inclusion of impact records in trees. Copyright © 2014 John Wiley & Sons, Ltd.     

Illuminating and optimising a three‐dimensional model of an oil shale seam and its volume distribution using the transient electromagnetic induction method,central part of Jordan

The oil shale exploration program in Jordan is undertaking great activity in the domain of applied geophysical methods to evaluate bitumen‐bearing rock. In the study area, the bituminous marl or oil shale exhibits a rock type dominated by lithofacies layers composed of chalky limestone, marls, clayey marls, and phosphatic marls. The study aims to present enhancements for oil shale seam detection using progressive interpretation from a one‐dimensional inversion to a three‐dimensional modelling and inversion of ground‐based transient electromagnetic data at an area of stressed geological layers. The geophysical survey combined 58 transient electromagnetic sites to produce geoelectrical structures at different depth slices, and cross sections were used to characterise the horizon of the most likely sites for mining oil shale. The results show valuable information on the thickness of the oil shale seam at 3.7 Ωm, which is correlated to the geoelectrical layer between 2‐ and 4 ms transient time delays, and at depths ranging between 85 and 105 m. The 300 m penetrated depth of the transient electromagnetic soundings allows the resolution of the main geological units at narrow resistivity contrast and the distinction of the main geological structures that constrain the detection of the oil shale seam. This geoelectrical layer at different depth slices illustrates a localised oil shale setting and can be spatially correlated with an area bounded by fold and fault systems. Also, three‐dimensional modelling and inversion for synthetic and experimental data are introduced at the faulted area. The results show the limitations of oil shale imaging at a depth exceeding 130 m, which depends on the near‐surface resistivity layer, the low resistivity contrast of the main lithological units, and the degree of geological detail achieved at a suitable model's misfit value.     

Nonlinear finite element analysis of three‐dimensional free and harmonically forced vibrations of stranded conductor cables

The 3D finite deformation beam model originally developed by Simo is appropriately modified to derive a finite element formulation for the static and dynamic analysis of flexible electrical conductors. In contrast to what is currently carried out in the literature, a linear viscoelastic constitutive equation and an additional mass proportional damping mechanism are introduced to account for energy dissipation in a physically consistent way. The model is used for simulation of free and forced vibration tests performed on an actual electrical conductor. Energy balance calculations illustrate the reliability of the computations. The experiments reveal amplitude dependence of both stiffness and damping, pointing out the presence of material nonlinearity in the cable. The development of numerical models that can account for the amplitude dependence of bending stiffness and energy dissipation capacity is subject of current computational and experimental work. Copyright © 2014 John Wiley & Sons, Ltd.