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1.
    
Time-lapse seismic data are generally used to monitor the changes in dynamic reservoir properties such as fluid saturation and pore or effective pressure. Changes in saturation and pressure due to hydrocarbon production usually cause changes in the seismic velocities and as a consequence changes in seismic amplitudes and travel times. This work proposes a new rock physics model to describe the relation between saturation-pressure changes and seismic changes and a probabilistic workflow to quantify the changes in saturation and pressure from time-lapse seismic changes. In the first part of this work, we propose a new quadratic approximation of the rock physics model. The novelty of the proposed formulation is that the coefficients of the model parameters (i.e. the saturation-pressure changes) are functions of the porosity, initial saturation and initial pressure. The improvements in the results of the forward model are shown through some illustrative examples. In the second part of the work, we present a Bayesian inversion approach for saturation-pressure 4D inversion in which we adopt the new formulation of the rock physics approximation. The inversion results are validated using synthetic pseudo-logs and a 3D reservoir model for CO2 sequestration.  相似文献   

2.
    
Updating of reservoir models by history matching of 4D seismic data along with production data gives us a better understanding of changes to the reservoir, reduces risk in forecasting and leads to better management decisions. This process of seismic history matching requires an accurate representation of predicted and observed data so that they can be compared quantitatively when using automated inversion. Observed seismic data is often obtained as a relative measure of the reservoir state or its change, however. The data, usually attribute maps, need to be calibrated to be compared to predictions. In this paper we describe an alternative approach where we normalize the data by scaling to the model data in regions where predictions are good. To remove measurements of high uncertainty and make normalization more effective, we use a measure of repeatability of the monitor surveys to filter the observed time‐lapse data. We apply this approach to the Nelson field. We normalize the 4D signature based on deriving a least squares regression equation between the observed and synthetic data which consist of attributes representing measured acoustic impedances and predictions from the model. Two regression equations are derived as part of the analysis. For one, the whole 4D signature map of the reservoir is used while in the second, 4D seismic data is used from the vicinity of wells with a good production match. The repeatability of time‐lapse seismic data is assessed using the normalized root mean square of measurements outside of the reservoir. Where normalized root mean square is high, observations and predictions are ignored. Net: gross and permeability are modified to improve the match. The best results are obtained by using the normalized root mean square filtered maps of the 4D signature which better constrain normalization. The misfit of the first six years of history data is reduced by 55 per cent while the forecast of the following three years is reduced by 29 per cent. The well based normalization uses fewer data when repeatability is used as a filter and the result is poorer. The value of seismic data is demonstrated from production matching only where the history and forecast misfit reductions are 45% and 20% respectively while the seismic misfit increases by 5%. In the best case using seismic data, it dropped by 6%. We conclude that normalization with repeatability based filtering is a useful approach in the absence of full calibration and improves the reliability of seismic data.  相似文献   

3.
Gas‐Oil Gravity Drainage is to be enhanced by steam injection in a highly fractured, low permeability carbonate field in Oman. Following a successful pilot, field‐wide steam injection is being implemented, first of this type in the world. A dedicated monitoring program has been designed to track changes in the reservoir. Various observations are to be acquired, including, surface deformation, temperature measurements, microseismic, well logs, pressure and saturation measurements to monitor the reservoir. Because significant changes in the reservoir density are expected, time‐lapse gravimetry is also being considered. In this paper we investigate the feasibility of gravimetric monitoring of the thermally enhanced gravity drainage process at the carbonate field in Oman. For this purpose, forward gravity modelling is performed. Based on field groundwater measurements, the estimates of the hydrological signal are considered and it is investigated under what conditions the groundwater influences can be minimized. Using regularized inversion of synthetic gravity data, we analyse the achievable accuracy of heat‐front position estimates. In case of large groundwater variations at the field, the gravity observations can be significantly affected and, consequently, the accuracy of heat‐front monitoring can be deteriorated. We show that, by applying gravity corrections based on local observations of groundwater, the hydrological influences can to a large extent be reduced and the accuracy of estimates can be improved. We conclude that gravimetric monitoring of the heat‐front evolution has a great potential.  相似文献   

4.
During the time taken for seismic data to be acquired, reservoir pressure may fluctuate as a consequence of field production and operational procedures and fluid fronts may move significantly. These variations prevent accurate quantitative measurement of the reservoir change using 4D seismic data. Modelling studies on the Norne field simulation model using acquisition data from ocean-bottom seismometer and towed streamer systems indicate that the pre-stack intra-survey reservoir fluctuations are important and cannot be neglected. Similarly, the time-lapse seismic image in the post-stack domain does not represent a difference between two states of the reservoir at a unique base and monitor time, but is a mixed version of reality that depends on the sequence and timing of seismic shooting. The outcome is a lack of accuracy in the measurement of reservoir changes using the resulting processed and stacked 4D seismic data. Even for perfect spatial repeatability between surveys, a spatially variant noise floor is still anticipated to remain. For our particular North Sea acquisition data, we find that towed streamer data are more affected than the ocean-bottom seismometer data. We think that this may be typical for towed streamers due to their restricted aperture compared to ocean-bottom seismometer acquisitions, even for a favourable time sequence of shooting and spatial repeatability. Importantly, the pressure signals on the near and far offset stacks commonly used in quantitative 4D seismic inversion are found to be inconsistent due to the acquisition timestamp. Saturation changes at the boundaries of fluid fronts appear to show a similar inconsistency across sub-stacks. We recommend that 4D data are shot in a consistent manner to optimize aerial time coverage, and that additionally, the timestamp of the acquisition should be used to optimize pre-stack quantitative reservoir analysis.  相似文献   

5.
    
Unlike light oils, heavy oils do not have a well‐established scheme for modelling elastic moduli from dynamic reservoir properties. One of the main challenges in the fluid substitution of heavy oils is their viscoelastic nature, which is controlled by temperature, pressure, and fluid composition. Here, we develop a framework for fluid substitution modelling that is reliable yet practical for a wide range of cold and thermal recovery scenarios in producing heavy oils and that takes into account the reservoir fluid composition, grounded on the effective‐medium theories for estimating elastic moduli of an oil–rock system. We investigate the effect of fluid composition variations on oil–rock elastic moduli with temperature changes. The fluid compositional behaviour is determined by flash calculations. Elastic moduli are then determined using the double‐porosity coherent potential approximation method and the calculated viscosity based on the fluid composition. An increase in temperature imposes two opposing mechanisms on the viscosity behaviour of a heavy‐oil sample: gas liberation, which tends to increase the viscosity, and melting, which decreases the viscosity. We demonstrate that melting dominates gas liberation, and as a result, the viscosity and, consequently, the shear modulus of the heavy oils always decrease with increasing temperature. Furthermore, it turns out that one can disregard the effects of gas in the solution when modelling the elastic moduli of heavy oils. Here, we compare oil–rock elastic moduli when the rock is saturated with fluids that have different viscosity levels. The objective is to characterize a unique relation between the temperature, the frequency, and the elastic moduli of an oil–rock system. We have proposed an approach that takes advantage of this relation to find the temperature and, consequently, the viscosity in different regions of the reservoir.  相似文献   

6.
    
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.  相似文献   

7.
    
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.  相似文献   

8.
    
The possibility of a time‐domain electromagnetic sounding method using excitation and measurement of vertical electric fields to search for and identify deeply buried reservoirs of hydrocarbons offshore is investigated. The method operates on source–receiver offsets, which are several times less than the depth of the reservoir. Geoelectric information is obtained from the transient responses recorded in the pauses between the pulses of electric current in the absence of the source field. The basics of the method, as well as its sensitivity, resolution, and the highest accessible depth of soundings for various geological conditions in a wide range of sea depths, are analyzed. For the analysis, 1D and 3D geoelectric models of hydrocarbon reservoirs are used. It is shown that under existing technologies of excitation and measurement of vertical electric fields, the highest accessible depth of soundings can be up to 4 km. Technology for the inversion and interpretation of transient responses is demonstrated on experimental data.  相似文献   

9.
    
Seismic time‐lapse surveys are susceptible to repeatability errors due to varying environmental conditions. To mitigate this problem, we propose the use of interferometric least‐squares migration to estimate the migration images for the baseline and monitor surveys. Here, a known reflector is used as the reference reflector for interferometric least‐squares migration, and the data are approximately redatumed to this reference reflector before imaging. This virtual redatuming mitigates the repeatability errors in the time‐lapse migration image. Results with synthetic and field data show that interferometric least‐squares migration can sometimes reduce or eliminate artifacts caused by non‐repeatability in time‐lapse surveys and provide a high‐resolution estimate of the time‐lapse change in the reservoir.  相似文献   

10.
    
A workflow for simultaneous joint PP‐PS prestack inversion of data from the Schiehallion field on the United Kingdom Continental Shelf is presented and discussed. The main challenge, describing reasonable PS to PP data registration before any prestack or joint PP‐PS inversion, was overcome thanks to a two‐stage process addressing the signal envelope, then working directly on the seismic data to estimate appropriate time‐variant time‐shift volumes. We evaluated the benefits of including PS along with PP prestack seismic data in a joint inversion process to improve the estimated elastic property quality and also to enable estimation of density compared with other prestack and post‐stack inversion approaches. While the estimated acoustic impedance exhibited a similar quality independent of the inversion used (PP post‐stack, PP prestack or joint PP‐PS prestack inversion) the shear impedance estimation was noticeably improved by the joint PP‐PS prestack inversion when compared to the PP prestack inversion. Finally, the density estimated from joint PP and PS prestack data demonstrated an overall good quality, even where not well‐controlled. The main outcome of this study was that despite several data‐related limitations, inverting jointly correctly processed PP and PS data sets brought extra value for reservoir delineation as opposed to PP‐only or post‐stack inversion.  相似文献   

11.
    
At the CO2CRC Otway geosequestration site, the abundance of borehole seismic and logging data provides a unique opportunity to compare techniques of Q (measure of attenuation) estimation and validate their reliability. Specifically, we test conventional time-domain amplitude decay and spectral-domain centroid frequency shift methods versus the 1D waveform inversion constrained by well logs on a set of zero-offset vertical seismic profiles. The amplitude decay and centroid frequency shift methods of Q estimation assume that a seismic pulse propagates in a homogeneous medium and ignore the interference of the propagating wave with short-period multiples. The waveform inversion explicitly models multiple scattering and interference on a stack of thin layers using high-resolution data from sonic and density logs. This allows for stable Q estimation in small depth windows (in this study, 150 m), and separation of the frequency-dependent layer-induced scattering from intrinsic absorption. Besides, the inversion takes into account band-limited nature of seismic data, and thus, it is less dependent on the operating frequency bandwidth than on the other methods. However, all considered methods of Q estimation are unreliable in the intervals where subsurface significantly deviates from 1D geometry. At the Otway site, the attenuation estimates are distorted by sub-vertical faults close to the boreholes. Analysis of repeated vertical seismic profiles reveals that 15 kt injection of the CO2-rich fluid into a thin saline aquifer at 1.5 km depth does not induce detectable absorption of P-waves at generated frequencies 5–150 Hz, most likely because the CO2 plume in the monitoring well is thin, <15 m. At the Otway research site, strong attenuation Q ≈ 30–50 is observed only in shaly formations (Skull Creek Mudstone, Belfast Mudstone). Layer-induced scattering attenuation is negligible except for a few intervals, namely 500–650 m from the surface, and near the injection interval, at around 1400–1550 m, where Qscat ≈ 50–65.  相似文献   

12.
    
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.  相似文献   

13.
    
The frequent time‐lapse observations from the life of field seismic system across the Valhall field provide a wealth of information. The responses from the production and injection wells can be observed through time‐shift and amplitude changes. These observations can be compared to modelled synthetic seismic responses from a reservoir simulation model of the Valhall Field. The observed differences between the observations and the modelling are used to update and improve the history match of the reservoir model. The uncertainty of the resulting model is reduced and a more confident prediction of future reservoir performance is provided. A workflow is presented to convert the reservoir model to a synthetic seismic response and compare the results to the observed time‐lapse responses for any time range and area of interest. Correlation based match quality factors are calculated to quantify the visual differences. This match quality factor allows us to quantitatively compare alternative reservoir models to help identify the parameters that best match the seismic observations. Three different case studies are shown where this workflow has helped to reduce the uncertainty range associated with specific reservoir parameters. By updating various reservoir model parameters we have been able to improve the match to the observations and thereby improve the overall reservoir model predictability. The examples show positive results in a range of different reservoir modelling issues, which indicates the flexibility of this workflow and the ability to have an impact in most reservoir modelling challenges.  相似文献   

14.
    
Resistivity monitoring surveys are used to detect temporal changes in the subsurface using repeated measurements over the same site. The positions of the electrodes are typically measured at the start of the survey program and possibly at occasional later times. In areas with unstable ground, such as landslide‐prone slopes, the positions of the electrodes can be displaced by ground movements. If this occurs at times when the positions of the electrodes are not directly measured, they have to be estimated. This can be done by interpolation or, as in recent developments, from the resistivity data using new inverse methods. The smoothness‐constrained least squares optimisation method can be modified to include the electrode positions as additional unknown parameters. The Jacobian matrices with the sensitivity of the apparent resistivity measurements to changes in the electrode positions are then required by the optimisation method. In this paper, a fast adjoint‐equation method is used to calculate the Jacobian matrices required by the least squares method to reduce the calculation time. In areas with large near‐surface resistivity contrasts, the inversion routine sometimes cannot accurately distinguish between electrode displacements and subsurface resistivity variations. To overcome this problem, the model for the initial time‐lapse dataset (with accurately known electrode positions) is used as the starting model for the inversion of the later‐time dataset. This greatly improves the accuracy of the estimated electrode positions compared to the use of a homogeneous half‐space starting model. In areas where the movement of the electrodes is expected to occur in a fixed direction, the method of transformations can be used to include this information as an additional constraint in the optimisation routine.  相似文献   

15.
The Zafra de Záncara anticline (also known as the El Hito anticline), located in the Loranca Cenozoic Basin (part of the Tagus Basin, Central Spain), had been studied by several oil companies during the late 1960s and early 1970s. In 2009, within the ‘Plan for selection and characterization of suitable structures of CO2 geological storage’, this anticline was selected as a potential CO2 storage site. A preliminary three-dimensional geological model, based on five geological cross sections that were constrained with the interpretation of the available seismic profiles (that are rather old and do not have very good quality), was created. With the aim of improving the geological knowledge of the Zafra de Záncara anticline and helping to investigate the suitability of a nearby anticline, namely La Rambla, as another structural closure that might make it a possible CO2 storage site, a local gravity survey (1 station every km2) was carried out in the area, seven new geological cross sections, based on these existing seismic profiles and field geology, were build, and a new three-dimensional geological model that included both anticlines, improved through three-dimensional stochastic gravity inversion, was constructed. The densities needed for the geological formations of the model come from the analysis of rock samples, logging data from El Hito-1 drillhole and petrophysical information from Instituto Geológico y Minero de España database. The inversion has improved the knowledge about the geometry of the anticlines’ traps and seals as well as the geometry of the basement relief and the structural relationship between basement and cover.  相似文献   

16.
    
The hydrodynamic characterization of the epikarst, the shallow part of the unsaturated zone in karstic systems, has always been challenging for geophysical methods. This work investigates the feasibility of coupling time‐lapse refraction seismic data with petrophysical and hydrologic models for the quantitative determination of water storage and residence time at shallow depth in carbonate rocks. The Biot–Gassmann fluid substitution model describing the seismic velocity variations with water saturation at low frequencies needs to be modified for this lithology. I propose to include a saturation‐dependent rock‐frame weakening to take into account water–rock interactions. A Bayesian inversion workflow is presented to estimate the water content from seismic velocities measured at variable saturations. The procedure is tested first with already published laboratory measurements on core samples, and the results show that it is possible to estimate the water content and its uncertainty. The validated procedure is then applied to a time‐lapse seismic study to locate and quantify seasonal water storage at shallow depth along a seismic profile. The residence time of the water in the shallow layers is estimated by coupling the time‐lapse seismic measurements with rainfall chronicles, simple flow equations, and the petrophysical model. The daily water input computed from the chronicles is used to constraint the inversion of seismic velocities for the daily saturation state and the hydrodynamic parameters of the flow model. The workflow is applied to a real monitoring case, and the results show that the average residence time of the water in the epikarst is generally around three months, but it is only 18 days near an infiltration pathway. During the winter season, the residence times are three times shorter in response to the increase in the effective rainfall.  相似文献   

17.
    
Time-lapse seismic data is useful for identifying fluid movement and pressure and saturation changes in a petroleum reservoir and for monitoring of CO2 injection. The focus of this paper is estimation of time-lapse changes with uncertainty quantification using full-waveform inversion. The purpose of also estimating the uncertainty in the inverted parameters is to be able to use the inverted seismic data quantitatively for updating reservoir models with ensemble-based methods. We perform Bayesian inversion of seismic waveform data in the frequency domain by combining an iterated extended Kalman filter with an explicit representation of the sensitivity matrix in terms of Green functions (acoustic approximation). Using this method, we test different strategies for inversion of the time-lapse seismic data with uncertainty. We compare the results from a sequential strategy (making a prior from the monitor survey using the inverted baseline survey) with a double difference strategy (inverting the difference between the monitor and baseline data). We apply the methods to a subset of the Marmousi2 P-velocity model. Both strategies performed well and relatively good estimates of the monitor velocities and the time-lapse differences were obtained. For the estimated time-lapse differences, the double difference strategy gave the lowest errors.  相似文献   

18.
    
Machine learning methods including support-vector-machine and deep learning are applied to facies classification problems using elastic impedances acquired from a Paleocene oil discovery in the UK Central North Sea. Both of the supervised learning approaches showed similar accuracy when predicting facies after the optimization of hyperparameters derived from well data. However, the results obtained by deep learning provided better correlation with available wells and more precise decision boundaries in cross-plot space when compared to the support-vector-machine approach. Results from the support-vector-machine and deep learning classifications are compared against a simplified linear projection based classification and a Bayes-based approach. Differences between the various facies classification methods are connected by not only their methodological differences but also human interactions connected to the selection of machine learning parameters. Despite the observed differences, machine learning applications, such as deep learning, have the potential to become standardized in the industry for the interpretation of amplitude versus offset cross-plot problems, thus providing an automated facies classification approach.  相似文献   

19.
    
Rock fractures are of great practical importance to petroleum reservoir engineering because they provide pathways for fluid flow, especially in reservoirs with low matrix permeability, where they constitute the primary flow conduits. Understanding the spatial distribution of natural fracture networks is thus key to optimising production. The impact of fracture systems on fluid flow patterns can be predicted using discrete fracture network models, which allow not only the 6 independent components of the second‐rank permeability tensor to be estimated, but also the 21 independent components of the fully anisotropic fourth‐rank elastic stiffness tensor, from which the elastic and seismic properties of the fractured rock medium can be predicted. As they are stochastically generated, discrete fracture network realisations are inherently non‐unique. It is thus important to constrain their construction, so as to reduce their range of variability and, hence, the uncertainty of fractured rock properties derived from them. This paper presents the underlying theory and implementation of a method for constructing a geologically realistic discrete fracture network, constrained by seismic amplitude variation with offset and azimuth data. Several different formulations are described, depending on the type of seismic data and prior geologic information available, and the relative strengths and weaknesses of each approach are compared. Potential applications of the method are numerous, including the prediction of fluid flow, elastic and seismic properties of fractured reservoirs, model‐based inversion of seismic amplitude variation with offset and azimuth data, and the optimal placement and orientation of infill wells to maximise production.  相似文献   

20.
Full‐waveform inversion is an appealing technique for time‐lapse imaging, especially when prior model information is included into the inversion workflow. Once the baseline reconstruction is achieved, several strategies can be used to assess the physical parameter changes, such as parallel difference (two separate inversions of baseline and monitor data sets), sequential difference (inversion of the monitor data set starting from the recovered baseline model) and double‐difference (inversion of the difference data starting from the recovered baseline model) strategies. Using synthetic Marmousi data sets, we investigate which strategy should be adopted to obtain more robust and more accurate time‐lapse velocity changes in noise‐free and noisy environments. This synthetic application demonstrates that the double‐difference strategy provides the more robust time‐lapse result. In addition, we propose a target‐oriented time‐lapse imaging using regularized full‐waveform inversion including a prior model and model weighting, if the prior information exists on the location of expected variations. This scheme applies strong prior model constraints outside of the expected areas of time‐lapse changes and relatively less prior constraints in the time‐lapse target zones. In application of this process to the Marmousi model data set, the local resolution analysis performed with spike tests shows that the target‐oriented inversion prevents the occurrence of artefacts outside the target areas, which could contaminate and compromise the reconstruction of the effective time‐lapse changes, especially when using the sequential difference strategy. In a strongly noisy case, the target‐oriented prior model weighting ensures the same behaviour for both time‐lapse strategies, the double‐difference and the sequential difference strategies and leads to a more robust reconstruction of the weak time‐lapse changes. The double‐difference strategy can deliver more accurate time‐lapse variation since it can focus to invert the difference data. However, the double‐difference strategy requires a preprocessing step on data sets such as time‐lapse binning to have a similar source/receiver location between two surveys, while the sequential difference needs less this requirement. If we have prior information about the area of changes, the target‐oriented sequential difference strategy can be an alternative and can provide the same robust result as the double‐difference strategy.  相似文献   

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