Influence of subsurface injection on time‐lapse seismic: laboratory studies at seismic and ultrasonic frequencies

Seismic monitoring of reservoir and overburden performance during subsurface CO₂ storage plays a key role in ensuring efficiency and safety. Proper interpretation of monitoring data requires knowledge about the rock physical phenomena occurring in the subsurface formations. This work focuses on rock stiffness and elastic velocity changes of a shale overburden formation caused by both reservoir inflation induced stress changes and leakage of CO₂ into the overburden. In laboratory experiments, Pierre shale I core plugs were loaded along the stress path representative for the in situ stress changes experienced by caprock during reservoir inflation. Tests were carried out in a triaxial compaction cell combining three measurement techniques and permitting for determination of (i) ultrasonic velocities, (ii) quasistatic rock deformations, and (iii) dynamic elastic stiffness at seismic frequencies within a single test, which allowed to quantify effects of seismic dispersion. In addition, fluid substitution effects connected with possible CO₂ leakage into the caprock formation were modelled by the modified anisotropic Gassmann model. Results of this work indicate that (i) stress sensitivity of Pierre shale I is frequency dependent; (ii) reservoir inflation leads to the increase of the overburden Young's modulus and Poisson's ratio; (iii) in situ stress changes mostly affect the P‐wave velocities; (iv) small leakage of the CO₂ into the overburden may lead to the velocity changes, which are comparable with one associated with geomechanical influence; (v) non‐elastic effects increase stress sensitivity of an acoustic waves; (iv) and both geomechanical and fluid substitution effects would create significant time shifts, which should be detectable by time‐lapse seismic.     

Post‐stack stratigraphic inversion workflow applied to carbon dioxide storage: application to the saline aquifer of Sleipner field‡

In the Norwegian North Sea, the Sleipner field produces gas with a high CO₂ content. For environmental reasons, since 1996, more than 11 Mt of this carbon dioxide (CO₂) have been injected in the Utsira Sand saline aquifer located above the hydrocarbon reservoir. A series of seven 3D seismic surveys were recorded to monitor the CO₂ plume evolution. With this case study, time‐lapse seismics have been shown to be successful in mapping the spread of CO₂ over the past decade and to ensure the integrity of the overburden. Stratigraphic inversion of seismic data is currently used in the petroleum industry for quantitative reservoir characterization and enhanced oil recovery. Now it may also be used to evaluate the expansion of a CO₂ plume in an underground reservoir. The aim of this study is to estimate the P‐wave impedances via a Bayesian model‐based stratigraphic inversion. We have focused our study on the 1994 vintage before CO₂ injection and the 2006 vintage carried out after a CO₂ injection of 8.4 Mt. In spite of some difficulties due to the lack of time‐lapse well log data on the interest area, the full application of our inversion workflow allowed us to obtain, for the first time to our knowledge, 3D impedance cubes including the Utsira Sand. These results can be used to better characterize the spreading of CO₂ in a reservoir. With the post‐stack inversion workflow applied to CO₂ storage, we point out the importance of the a priori model and the issue to obtain coherent results between sequential inversions of different seismic vintages. The stacking velocity workflow that yields the migration model and the a priori model, specific to each vintage, can induce a slight inconsistency in the results.     

黄河阶地特征与地震动参数的相关性研究

在分析已有资料的基础上划分了兰州盆地与建设工程分布密切相关的T₀、T₁、T₂、T₃和T₄级黄河阶地,建立201个土层地震反应模型。通过一维等效线性化计算和反应谱分析,得出兰州盆地沉积阶地50年超越概率10%地表地震动参数,分析阶地高度和v_S≤500 m/s覆盖层厚度特征与地震动参数峰值加速度Am和加速度反应谱特征周期T_g的相关性。表明兰州盆地T₀~T₂阶地覆盖层厚度与50年超越概率10%A_m呈正相关,T₃及以上阶地覆盖层厚度对A_m增大有明显的减小作用。T_g值随T₀~T₃阶地覆盖层厚度的增加而变大,当覆盖层厚度进一步变大,T_g值不再同步增大,阶地覆盖层厚度对T_g的影响是有限的,阶地海拔高度与地表50年超越概率10%地震动参数没有关系。     

Repeatability analysis of land time‐lapse seismic data: CO2CRC Otway pilot project case study

Time‐lapse seismics is the methodology of choice for remotely monitoring changes in oil/gas reservoir depletion, reservoir stimulation or CO₂ sequestration, due to good sensitivity and resolving power at depths up to several kilometres. This method is now routinely applied offshore, however, the use of time‐lapse methodology onshore is relatively rare. The main reason for this is the relatively high cost of commercial seismic acquisition on land. A widespread belief of a relatively poor repeatability of land seismic data prevents rapid growth in the number of land time‐lapse surveys. Considering that CO₂ sequestration on land is becoming a necessity, there is a great need to evaluate the feasibility of time‐lapse seismics for monitoring. Therefore, an understanding of the factors influencing repeatability of land seismics and evaluating limitations of the method is crucially important for its application in many CO₂ sequestration projects. We analyse several repeated 2D and 3D surveys acquired within the Otway CO₂ sequestration pilot project (operated by the Cooperative Research Centre for Greenhouse Technologies, CO2CRC) in Australia, in order to determine the principal limitations of land time‐lapse seismic repeatability and investigate the influence of the main factors affecting it. Our findings are that the intrinsic signal‐to‐noise ratio (S/N, signal to coherent and background noise levels) and the normalized‐root‐mean‐square (NRMS) difference are controlled by the source strength and source type. However, the post‐stack S/N ratio and corresponding NRMS residuals are controlled mainly by the data fold. For very high‐fold data, the source strength and source type are less critical.     

Application of diffracted wave analysis to time‐lapse seismic data for CO2 leakage detection

Time‐lapse seismic analysis is utilized in CO₂ geosequestration to verify the CO₂ containment within a reservoir. A major risk associated with geosequestration is a possible leakage of CO₂ from the storage formation into overlaying formations. To mitigate this risk, the deployment of carbon capture and storage projects requires fast and reliable detection of relatively small volumes of CO₂ outside the storage formation. To do this, it is necessary to predict typical seepage scenarios and improve subsurface seepage detection methods. In this work we present a technique for CO₂ monitoring based on the detection of diffracted waves in time‐lapse seismic data. In the case of CO₂ seepage, the migrating plume might form small secondary accumulations that would produce diffracted, rather than reflected waves. From time‐lapse data analysis, we are able to separate the diffracted waves from the predominant reflections in order to image the small CO₂ plumes. To explore possibilities to detect relatively small amounts of CO₂, we performed synthetic time‐lapse seismic modelling based on the Cooperative Research Centre for Greenhouse Gas Technologies (CO2CRC) Otway project data. The detection method is based on defining the CO₂ location by measuring the coherency of the signal along diffraction offset‐traveltime curves. The technique is applied to a time‐lapse stacked section using a stacking velocity to construct offset‐traveltime curves. Given the amount of noise found in the surface seismic data, the predicted minimum detectable amount of CO₂ is 1000–2000 tonnes. This method was also applied to real data obtained from a time‐lapse seismic physical model. The use of diffractions rather than reflections for monitoring small amounts of CO₂ can enhance the capability of subsurface monitoring in CO₂ geosequestration projects.     

An insightful parametrization for the flatlander's interpretation of time‐lapsed seismic data

An approximation is developed that allows mapped 4D seismic amplitudes and time‐shifts to be related directly to the weighted linear sum of pore pressure and saturation changes. The weights in this relation are identified as key groups of parameters from a petroelastic model and include the reservoir porosity. This dependence on groups of parameters explains the inherent non‐uniqueness of this problem experienced by previous researchers. The proposed relation is of use in 4D seismic data feasibility studies and inversion and interpretation of the 4D seismic response in terms of pore pressure and water saturation changes. A further result is drawn from analysis of data from the North Sea and West Africa, which reveals that the relative interplay between the effects of pore pressure and saturation changes on the seismic data can be simplified to the control of a single, spatially variant parameter C_S/C_P. Combining these results with those from published literature, we find that C_S/C_P = 8 appears to be a generality across a range of clastic reservoirs with a similar mean porosity. Using this C_S/C_P value, an in situ seismic‐scale constraint for the rock stress sensitivity component of the petroelastic model is constructed considering this component carries the largest uncertainty.     

Seismic time‐lapse effects of solution salt mining – a feasibility study

This article addresses the question whether time‐lapse seismic reflection techniques can be used to follow and quantify the effects of solution salt mining. Specifically, the production of magnesium salts as mined in the north of the Netherlands is considered. The use of seismic time‐lapse techniques to follow such a production has not previously been investigated. For hydrocarbon production and CO₂ storage, time‐lapse seismics are used to look at reservoir changes mainly caused by pressure and saturation changes in large reservoirs, while for solution mining salt is produced from caverns with a limited lateral extent, with much smaller production volumes and a fluid (brine) replacing a solid (magnesium salt). In our approach we start from the present situation of the mine and then study three different production scenarios, representing salt production both in vertical and lateral directions of the mine. The present situation and future scenarios have been transformed into subsurface models that were input to an elastic finite‐difference scheme to create synthetic seismic data. These data have been analysed and processed up to migrated seismic images, such that time‐lapse analyses of intermediate and final results could be done. From the analyses, it is found that both vertical and lateral production is visible well above the detection threshold in difference data, both at pre‐imaging and post‐imaging stages. In quantitative terms, an additional production of the mine of 6 m causes time‐shifts in the order of 2 ms (pre‐imaging) and 4 ms (post‐imaging) and amplitude changes of above 20% in the imaged sections. A laterally oriented production causes even larger amplitude changes at the edge of the cavern due to replacement of solid magnesium salt with brine introducing a large seismic contrast. Overall, our pre‐imaging and post‐imaging time‐lapse analysis indicates that the effects of solution salt mining can be observed and quantified on seismic data. The effects seem large enough to be observable in real seismic data containing noise.     

Residual drift demands in moment‐resisting steel frames subjected to narrow‐band earthquake ground motions

This paper presents the main results of the evaluation of residual inter‐story drift demands in typical moment‐resisting steel buildings designed accordingly to the Mexican design practice when subjected to narrow‐band earthquake ground motions. Analytical 2D‐framed models representative of the study‐case buildings were subjected to a set of 30 narrow‐band earthquake ground motions recorded on stations placed in soft‐soil sites of Mexico City, where most significant structural damage was found in buildings as a consequence of the 1985 Michoacan earthquake, and scaled to reach several levels of intensity to perform incremental dynamic analyses. Thus, results were statistically processed to obtain hazard curves of peak (maximum) and residual drift demands for each frame model. It is shown that the study‐case frames might exhibit maximum residual inter‐story drift demands in excess of 0.5%, which is perceptible for building's occupants and could cause human discomfort, for a mean annual rate of exceedance associated to peak inter‐story drift demands of about 3%, which is the limiting drift to avoid collapse prescribed in the 2004 Mexico City Seismic Design Provisions. The influence of a member's post‐yield stiffness ratio and material overstrength in the evaluation of maximum residual inter‐story drift demands is also discussed. Finally, this study introduces response transformation factors, T_p, that allow establishing residual drift limits compatible with the same mean annual rate of exceedance of peak inter‐story drift limits for future seismic design/evaluation criteria that take into account both drift demands for assessing a building's seismic performance. Copyright © 2013 John Wiley & Sons, Ltd.     

Seismic behavior of steel buildings with out‐of‐plumb

A structure that has a permanent offset from a true vertical line is commonly referred to as being ‘out‐of‐plumb’. Out‐of‐plumb may result from construction tolerances or post‐earthquake permanent deformations in steel buildings. This paper quantifies the displacements of buildings with out‐of‐plumb in subsequent seismic events by means of inelastic dynamic time history analysis. Structures considered have different structural heights, force design reduction factors (R), and target inter‐story drifts. It is shown that buildings with greater out of plumb and force design reduction factor have larger normalized peak inter‐story drift ratio and ratio of residual‐to‐peak drift. Also, the ratio of residual‐to‐peak drift was not strongly dependent on structural height or design drift. A design procedure and example provided, based on the results obtained, show how peak and residual inter‐story drift ratio can be estimated. Copyright © 2015 John Wiley & Sons, Ltd.     

Influence of background heterogeneity on traveltime shifts for compacting reservoirs

Compaction induced by pore‐pressure decrease inside a reservoir can be monitored by measuring traveltime shifts of reflection events on time‐lapse seismic data. Recently we introduced a perturbation‐based formalism to describe traveltime shifts caused by the 3D stress‐induced velocity field around a compacting reservoir. Application of this method to homogeneous background models showed that the offset variation of traveltime shifts is controlled primarily by the anisotropic velocity perturbations and can provide valuable information about the shear and deviatoric stresses. Here, we model and analyse traveltime shifts for compacting reservoirs whose elastic properties are different from those of the surrounding medium. For such models, the excess stress is influenced primarily by the contrast in the rigidity modulus μ across the reservoir boundaries. Synthetic examples demonstrate that a significant (25% or more) contrast in μ enhances the isotropic velocity perturbations outside the reservoir. Nevertheless, the influence of background heterogeneity is mostly confined to the reservoir and its immediate vicinity and the anisotropic velocity changes are still largely responsible for the offset dependence of traveltime shifts. If the reservoir is stiffer than the host rock, the background heterogeneity reduces anisotropic velocity perturbations inside the reservoir but increases them in the overburden. As a result, in this case, the magnitude of the offset variation of traveltime shifts is generally higher for reflections from interfaces above the reservoir. We also study compaction‐induced stress/strain and traveltime shifts for a stiff reservoir embedded in a softer layered model based on velocity profiles from the Valhall Field in the North Sea. Despite producing discontinuities in strain across medium interfaces, horizontal layering does not substantially alter the overall behaviour of traveltime shifts. The most pronounced offset variation of traveltime shifts is observed for overburden events recorded at common midpoints close to the reservoir edges. On the whole, prestack analysis of traveltime shifts should help better constrain compaction‐induced velocity perturbations in the presence of realistic background heterogeneity.     

Overburden complexity and repeatability of seismic data: Impacts of positioning errors at the Oseberg field, North Sea

Repeatability of seismic data plays a crucial role in time‐lapse seismic analysis. There are several factors that can decrease the repeatability, such as positioning errors, varying tide, source variations, velocity changes in the water layer (marine data) and undesired effects of various processing steps. In this work, the complexity of overburden structure, as an inherent parameter that can affect the repeatability, is studied. A multi‐azimuth three‐dimensional vertical‐seismic‐profiling data set with 10 000 shots is used to study the relationship between overburden structure and repeatability of seismic data. In most repeatability studies, two data sets are compared, but here a single data set has been used because a significant proportion of the 10 000 shots are so close to each other that a repeatability versus positioning error is possible. We find that the repeatability decreases by a factor of approximately 2 under an overburden lens. Furthermore, we find that the X‐ and Y‐components have approximately the same sensitivity to positioning errors as the Z‐component (for the same events) in this three‐dimensional vertical‐seismic‐profiling experiment. This indicates that in an area with complex overburden, positioning errors between monitor and base seismic surveys are significantly more critical than outside such an area. This study is based on a three‐dimensional three‐component vertical‐seismic‐profiling data set from a North Sea reservoir and care should be taken when extrapolating these observations into a general four‐dimensional framework.     

Analysis of time‐lapse travel‐time and amplitude changes to assess reservoir compartmentalization

Fluid depletion within a compacting reservoir can lead to significant stress and strain changes and potentially severe geomechanical issues, both inside and outside the reservoir. We extend previous research of time‐lapse seismic interpretation by incorporating synthetic near‐offset and full‐offset common‐midpoint reflection data using anisotropic ray tracing to investigate uncertainties in time‐lapse seismic observations. The time‐lapse seismic simulations use dynamic elasticity models built from hydro‐geomechanical simulation output and a stress‐dependent rock physics model. The reservoir model is a conceptual two‐fault graben reservoir, where we allow the fault fluid‐flow transmissibility to vary from high to low to simulate non‐compartmentalized and compartmentalized reservoirs, respectively. The results indicate time‐lapse seismic amplitude changes and travel‐time shifts can be used to qualitatively identify reservoir compartmentalization. Due to the high repeatability and good quality of the time‐lapse synthetic dataset, the estimated travel‐time shifts and amplitude changes for near‐offset data match the true model subsurface changes with minimal errors. A 1D velocity–strain relation was used to estimate the vertical velocity change for the reservoir bottom interface by applying zero‐offset time shifts from both the near‐offset and full‐offset measurements. For near‐offset data, the estimated P‐wave velocity changes were within 10% of the true value. However, for full‐offset data, time‐lapse attributes are quantitatively reliable using standard time‐lapse seismic methods when an updated velocity model is used rather than the baseline model.     

基于典型地质特征分析的大同盆地VS30预测研究

土体剪切波速是进行土层地震反应分析的动力学参数，对场地地震动参数确定具有重要意义。基于地质地貌分析，将大同盆地划分为5类典型地质单元。对盆地1429个钻孔剪切波速资料进行分析，探讨V_S30与V_S20的相关性，研究土体埋深、岩性、地质单元、标贯击数及密实度等地质特征对V_S的影响，并基于地质单元、剪切波速比、密实度系数及第四系上部覆盖层厚度相关性分析给出土体V_S30预测模型。研究结果表明，基于典型地质特征的V_S30预测模型拟合优度R2>0.90，预测精度很高，对于离散性较大、直接拟合估算较差及无剪切波速场地来说，以区分地质单元及土体类型的方式进行V_S30分解预测是良好的研究思路。首次在区分地质单元及土体类型的前提下提出剪切波速比及密实度系数，并将其与第四系上部覆盖层厚度综合应用于V_S30预测研究。研究结果可为大同盆地城市防震减灾规划、震害预测、区域性地震安全评价提供重要技术支撑。     

Determination of the seismic performance factors for post‐tensioned rocking timber wall systems

Post‐tensioned technologies for concrete seismic resistant buildings were first developed in the 1990s during the PREcast Seismic Structural Systems program. Among different solutions, the hybrid system proved to be the most resilient solution providing a combination of re‐centering and energy dissipative contributions respectively by using post‐tensioned tendons and mild steel reinforcement. The system, while providing significant strength and energy dissipation, reduces structural element damage and limits post‐earthquake residual displacements. More recently, the technology was extended to laminated veneer lumber (LVL) structural members, and extensive experimental and numerical work was carried out and allowed the development of reliable analytical and numerical models as well as design guidelines. On the basis of the experimental and numerical outcomes, this paper presents the evaluation of the seismic performance factors for post‐tensioned rocking LVL walls using the FEMA P‐695 procedure. Several archetype buildings were designed considering different parameters such as the building and story height, the type of seismic resistant system, the magnitude of gravity loads and the seismic design category. Lumped plasticity models were developed for each index archetype to simulate the behavioral aspects and collapse mechanisms. Non‐linear quasi‐static analyses were carried out to evaluate the system over‐strength factor; moreover, non‐linear time history analyses were performed using the incremental dynamic analysis concept to assess the collapse of each building. From the results of quasi‐static and dynamic analyses the response modification factor, R, system over‐strength factor, Ω₀, and deflection amplification factor, C_d, values of, respectively, 7, 3.5 and 7.5 are recommended. Copyright © 2016 John Wiley & Sons, Ltd.     

Time‐lapse seismic modelling of CO2 fluid substitution in the Devonian Redwater Reef,Alberta, Canada

Common shot ray tracing and finite difference seismic modelling experiments were undertaken to evaluate variations in the seismic response of the Devonian Redwater reef in the Alberta Basin, Canada after replacement of native pore waters in the upper rim of the reef with CO₂. This part of the reef is being evaluated for a CO₂ storage project. The input geological model was based on well data and the interpretation of depth‐converted, reprocessed 2D seismic data in the area. Pre‐stack depth migration of the ray traced and finite difference synthetic data demonstrate similar seismic attributes for the Mannville, Nisku, Ireton, Cooking Lake, and Beaverhill Lake formations and clear terminations of the Upper Leduc and Middle Leduc events at the reef margin. Higher amplitudes at the base of Upper‐Leduc member are evident near the reef margin due to the higher porosity of the foreslope facies in the reef rim compared to the tidal flat lagoonal facies within the central region of the reef. Time‐lapse seismic analysis exhibits an amplitude difference of about 14% for Leduc reflections before and after CO₂ saturation and a travel‐time delay through the reservoir of 1.6 ms. Both the ray tracing and finite difference approaches yielded similar results but, for this particular model, the latter provided more precise imaging of the reef margin. From the numerical study we conclude that time‐lapse surface seismic surveys should be effective in monitoring the location of the CO₂ plume in the Upper Leduc Formation of the Redwater reef, although the differences in the results between the two modelling approaches are of similar order to the effects of the CO₂ fluid replacement itself.     

On the treatment of uncertainty in seismic vulnerability and portfolio risk assessment

In a related study developed by the authors, building fragility is represented by intensity‐specific distributions of damage exceedance probability of various damage states. The contribution of the latter has been demonstrated in the context of loss estimation of building portfolios, where it is shown that the proposed concept of conditional fragility functions provides the link between seismic intensity and the uncertainty in damage exceedance probabilities. In the present study, this methodology is extended to the definition of building vulnerability, whereby vulnerability functions are characterized by hazard‐consistent distributions of damage ratio per level of primary seismic intensity parameter—Sa(T₁). The latter is further included in a loss assessment framework, in which the impact of variability and spatial correlation of damage ratio in the probabilistic evaluation of seismic loss is accounted for, using test‐bed portfolios of 2, 5, and 8‐story precode reinforced concrete buildings located in the district of Lisbon, Portugal. This methodology is evaluated in comparison with current state‐of‐the‐art methods of vulnerability and loss calculation, highlighting the discrepancies that can arise in loss estimates when the variability and spatial distributions of damage ratio, influenced by ground motion properties other than the considered primary intensity measure, are not taken into account.     

Vp‐Vs relationship and amplitude variation with offset modelling of glauconitic greensand‡

The relationship between V_p and V_s may be used to predict V_s where only V_p is known. V_p/V_s is also used to identify pore fluids from seismic data and amplitude variation with offset analysis. Theoretical, physical, as well as statistical empirical V_p‐V_s relationships have been proposed for reservoir characterization when shear‐wave data are not available. In published work, the focus is primarily on the V_p‐V_s relationship of quartzitic sandstone. In order to broaden the picture we present V_p‐V_s relationships of greensand composed of quartz and glauconite by using data from the Paleocene greensand Nini oil field in the North Sea. A V_p‐V_s relationship derived from modelling is compared with empirical V_p‐V_s regressions from laboratory data as well as from log data. The accuracy of V_s prediction is quantified in terms of root‐mean‐square error. We find that the V_p‐V_s relationship derived from modelling works well for greensand shear‐wave velocity prediction. We model the seismic response of glauconitic greensand by using laboratory data from the Nini field. Our studies here reveal that brine‐saturated glauconitic greensand can have a similar seismic response to that from oil‐saturated quartzitic sandstone and that oil‐saturated strongly cemented greensand can have a similar amplitude variation with offset response to that from brine‐saturated weakly cemented greensand.     

The first post‐injection seismic monitor survey at the Ketzin pilot CO2 storage site: results from time‐lapse analysis

The injection of CO₂ at the Ketzin pilot CO₂ storage site started in June 2008 and ended in August 2013. During the 62 months of injection, a total amount of about 67 kt of CO₂ was injected into a saline aquifer. A third repeat three‐dimensional seismic survey, serving as the first post‐injection survey, was acquired in 2015, aiming to investigate the recent movement of the injected CO₂. Consistent with the previous two time‐lapse surveys, a predominantly west–northwest migration of the gaseous CO₂ plume in the up‐dip direction within the reservoir is inferred in this first post‐injection survey. No systematic anomalies are detected through the reservoir overburden. The extent of the CO₂ plume west of the injection site is almost identical to that found in the 2012 second repeat survey (after injection of 61 kt); however, there is a significant decrease in its size east of the injection site. Assessment of the CO₂ plume distribution suggests that the decrease in the size of the anomaly may be due to multiple factors, such as limited vertical resolution, CO₂ dissolution, and CO₂ migration into thin layers, in addition to the effects of ambient noise. Four‐dimensional seismic modelling based on dynamic flow simulations indicates that a dynamic balance between the newly injected CO₂ after the second repeat survey and the CO₂ migrating into thin layers and being dissolved was reached by the time of the first post‐injection survey. In view of the significant uncertainties in CO₂ mass estimation, both patchy and non‐patchy saturation models for the Ketzin site were taken into consideration.     

An estimation method for effective stress changes in a reservoir from 4D seismics data

Advances in seismics acquisition and processing and the widespread use of 4D seismics have made available reliable production‐induced subsurface deformation data in the form of overburden time‐shifts. Inversion of these data is now beginning to be used as an aid to the monitoring of a reservoir's effective stress. Past solutions to this inversion problem have relied upon analytic calculations for an unrealistically simplified subsurface, which can lead to uncertainties. To enhance the accuracy of this approach, a method based on transfer functions is proposed in which the function itself is calibrated using numerically generated overburden strain deformation calculated for a small select group of reference sources. This technique proves to be a good compromise between the faster but more accurate history match of the overburden strain using a geomechanical simulator and the slower, less accurate analytic method. Synthetic tests using a coupled geomechanical and fluid flow simulator for the South Arne field confirm the efficacy of the method. Application to measured time‐shifts from observed 4D seismics indicates compartmentalization in the Tor reservoir, more heterogeneity than is currently considered in the simulation model and moderate connectivity with the overlying Ekofisk formation.     

Seismic performance and new design procedure for chevron‐braced frames

The paper is concerned with the seismic design of steel‐braced frames in which the braces are configured in a chevron pattern. According to EuroCode 8 (EC8), the behaviour factor q, which allows for the trade‐off between the strength and ductility, is set at 2.5 for chevron‐braced frames, while 6.5 is assigned for most ductile steel moment‐resisting frames. Strength deterioration in post‐buckling regime varies with the brace's slenderness, but EC8 adopts a unique q value irrespective of the brace slenderness. The study focuses on reevaluation of the q value adequate for the seismic design of chevron‐braced frames. The present EC8 method for the calculation of brace strength supplies significantly different elastic stiffnesses and actual strengths for different values of brace slenderness. A new method to estimate the strength of a chevron brace pair is proposed, in which the yield strength (for the brace in tension) and the post‐buckling strength (for the brace in compression) are considered. The new method ensures an identical elastic stiffness and a similar strength regardless of the brace slenderness. The advantage of the proposed method over the conventional EC8 method is demonstrated for the capacity of the proposed method to control the maximum inter‐storey drift. The q values adequate for the chevron‐braced frames are examined in reference to the maximum inter‐storey drifts sustained by most ductile moment‐resisting frames. When the proposed method is employed for strength calculation, the q value of 3.5 is found to be reasonable. It is notable that the proposed method does not require larger cross‐sections for the braces compared to the cross‐sections required for the present EC8 method. Copyright © 2005 John Wiley & Sons, Ltd.