This study investigates the relationships between agricultural spot markets and external uncertainties through multifractal detrending moving-average cross-correlation analysis(MF-X-DMA).The dataset contains the Grain...This study investigates the relationships between agricultural spot markets and external uncertainties through multifractal detrending moving-average cross-correlation analysis(MF-X-DMA).The dataset contains the Grains&Oilseeds Index(GOI)and its five subindices for wheat,maize,soyabeans,rice,and barley.Moreover,we use three uncertainty proxies,namely,economic policy uncertainty(EPU),geopolitical risk(GPR),and Volatility Index(VIX).We observe multifractal cross-correlations between agricultural markets and uncertainties.Furthermore,statistical tests reveal that maize has intrinsic joint multifractality with all the uncertainty proxies,highly sensitive to external shocks.Additionally,intrinsic multifractality among GOI-GPR,wheat-GPR,and soyabeans-VIX is illustrated.However,other series have apparent multifractal crosscorrelations with high probabilities.Moreover,our analysis suggests that among the three types of external uncertainties,GPR has the strongest association with grain prices,excluding maize and soyabeans.展开更多
Layering detection is an important step in petroleum engineering.Time series of post-stack seismic data and wire-line log data belong to subsurface layering.They exhibit multifractal properties with complex patterns b...Layering detection is an important step in petroleum engineering.Time series of post-stack seismic data and wire-line log data belong to subsurface layering.They exhibit multifractal properties with complex patterns because of the heterogeneity and different genetic properties in the earth layers.In a multifractal configuration,any piece of a series has a distinct Hurst exponent that reflects its nature and can be used for zone detection.Time series are post-stack seismic traces and wire-line log data near the well-bores.Self-similar Autoregressive Exogenous(SAE)model is a modified method which can place self-similar post-stack seismic and wire-line log segments across layers with the same lithology.The results satisfy the capability of layering identification from seismic data by SAE model.展开更多
In the present study an attempt is made to examine multifractality in multiparticle production in relativistic nuclear collisions;multifractality is investigated in 14.5 A GeV/c 28Si-nucleus collisions. For this, Gq-m...In the present study an attempt is made to examine multifractality in multiparticle production in relativistic nuclear collisions;multifractality is investigated in 14.5 A GeV/c 28Si-nucleus collisions. For this, Gq-moments are calculated and variations of ?are looked into. Values of mass exponents, tq, and generalised dimensions, Dq, are obtained. Analysis of multifractal moments reveals that multiplicity fluctuations are of dynamical nature.展开更多
The vertical heterogeneity of the pore structure in deep coal seams with varying ash yields is a key control for coalbed methane storage and producibility;however,its specific impact on gas adsorption is not clearly d...The vertical heterogeneity of the pore structure in deep coal seams with varying ash yields is a key control for coalbed methane storage and producibility;however,its specific impact on gas adsorption is not clearly defined.The focus of this study is the No.8 coal seam of the Carboniferous Benxi Formation in the Central-Eastern Ordos Basin.By integrating microscopic identification,proximate analysis,gas adsorption(CO_(2),N_(2),and CH_(4)),and the multifractal theory,we quantitatively characterized the nanopore structure(micropores<2 nm and mesopores 2 nm-100 nm)of coal reservoirs with varying ash yields.The results indicate that(1)ash yield is the primary factor that controls the vertical evolution of pore structures in coal seams.In low-ash yield coal seams,the extent of thermal evolution and ash yield jointly constrain the heterogeneity of pore size distribution.In mediumto high-ash yield coal seams,the heterogeneity of pore structure and pore size distribution are predominantly constrained by ash yield.(2)As the ash yield vertically increases,the mesoporous pore volume and specific surface area initially decrease and subsequently increase,while the contribution of micropores to both pore volume and specific surface area continuously diminishes.Consequently,the total pore volume and specific surface area of the coal samples exhibit a two-stage reduction close to an ash yield threshold of approximately 20%.(3)Further,the Langmuir volume for CH_(4)adsorption sharply declines below the 20%threshold,followed by a gradual decrease;in contrast,the Langmuir pressure initially decreases and subsequently increases.Hence,the vertical increase in ash yield constrains the development of pore systems and diminishes pore connectivity,thereby reducing methane adsorption capacity and adversely affecting coalbed methane productivity.(4)Low-ash yield coal reservoirs are characterized by a rapid gas breakthrough and high productivity,whereas medium-ash yield coal reservoirs generally require prolonged depressurization to achieve peak gas production.These findings reveal that in medium-high rank coal,ash yield―and not thermal evolution―is the main factor that controls vertical pore evolution and methane adsorption efficiency.The quantitative ash yield threshold(20%)established in this study provides a practical criterion for evaluating reservoir quality and predicting vertical variations in gas storage potential in the Ordos Basin.展开更多
Presently,financial portfolio managers lack a solid basis for building a reliable risk management strategy for green debt instrument investments due to the lack of compelling growth and resilience data.Therefore,this ...Presently,financial portfolio managers lack a solid basis for building a reliable risk management strategy for green debt instrument investments due to the lack of compelling growth and resilience data.Therefore,this study assesses the role of green bonds in financial markets by assessing and correlating their complex scaling behaviors across multiple periods with those of key benchmark assets(e.g.,conventional bonds,high-yield bonds,Euro-Dollar exchange,Dow Jones Industrial Index,Bitcoin,and Gold).Specifically,we explore linear and nonlinear correlation patterns using crosscorrelation tests and the dynamic conditional correlation model,focusing on bond interactions under various degrees of freedom.Our analysis reveals that although most assets exhibit nonlinear correlations,Bitcoin uniquely aligns linearly with U.S.bonds under certain conditions.Green bonds,however,display nonlinear correlations with Bitcoin and stand out for their distinct upward financial persistence.We find also that green bonds are primary drivers in the financial domain,highlighted by their pronounced interactions and the consistent cross-correlation with the Euro-Dollar exchange rate.Moreover,green bonds have the lowest multifractality,showing persistent upward trends and antipersistent downward trends,rendering them quite resilient during periods of high volatility.These results imply that green bonds may be advantageous to portfolio risk management strategies,especially during crises when diversification and hedging tactics are needed.展开更多
As an important component of secondary aerosols,sulfate plays a crucial role in regulating atmospheric radiative balance and influencing the secondary formation of ozone(O_(3)).In real atmosphere,atmospheric oxidants ...As an important component of secondary aerosols,sulfate plays a crucial role in regulating atmospheric radiative balance and influencing the secondary formation of ozone(O_(3)).In real atmosphere,atmospheric oxidants NO_(2)and O_(3)can promote the oxidation of SO_(2)to form sulfate(SO_(4)^(2−))through multiphase chemistry that occur at different time scales.Due to the combined impact of meteorology,pollution sources,atmospheric chemistry,etc.,time-scale dependence of SO_(2)-SO_(4)^(2−)conversion makes the impact of NO_(2)/O_(3)on it more complex.In this study,based on long-term time series(2013-2020)of air pollution variables from seven stations in Hong Kong,the Multifractal Detrended Cross-Correlation Analysis(MFDCCA)method has been employed to quantify the cross-correlations between SO_(2)and SO_(4)^(2−)in real atmosphere at different time scales,for examining the time-scale dependence of SO_(2)-SO_(4)^(2−)conversion efficiency.Furthermore,the Pearson correlation analysis has been used to study the influence of NO_(2)/O_(3)on SO_(2)-SO_(4)^(2−)conversion,and the regional and seasonal differences have been analyzed by considering factors such as meteorology,pollution sources,and regional transport.Changes in the main components of secondary aerosols are closely linked with the co-control of regional PM_(2.5)and O_(3).Therefore,the exploration of the impact of co-existing NO_(2)/O_(3)gases on the secondary formation of sulfates in real atmosphere is significant.展开更多
The carbonate-rich shale of the Permian Wujiaping Formation in Sichuan Basin exhibits significant heterogeneity in its lithology and pore structure,which directly influence its potential for shale gas extraction.This ...The carbonate-rich shale of the Permian Wujiaping Formation in Sichuan Basin exhibits significant heterogeneity in its lithology and pore structure,which directly influence its potential for shale gas extraction.This study assesses the factors that govern pore heterogeneity by analyzing the mineral composition of the shale,as well as its pore types and their multifractal characteristics.Three primary shale facies-siliceous,mixed,and calcareous-are identified based on mineralogy,and their multifractal characteristics reveal strongly heterogeneous pore structures.The brittleness of siliceous shale,rich in quartz and pyrite,is favorable for hydraulic fracturing;while calcareous shale,with higher levels of calcite,exhibits reduced brittleness.Multifractal analysis,using nitrogen adsorption isotherms,reveals complex pore structures across different shale facies,with siliceous shale showing better pore connectivity and uniformity.The types of pores in shales include organic matter pores,interparticle pores,and intraparticle pores,among which organic matter pores are the most abundant.Pore size distribution and connectivity are notably higher in siliceous shale compared to calcareous shale,which exhibit a predominance of micropores and more isolated pore structures.Pore heterogeneity of the carbonate-rich shale in the Wujiaping Formation is primarily governed by its intrinsic mineral composition,carbonate diagenesis,mechanical compaction,and its subsequent thermal maturation with the micro-migration of organic matter.This study highlights the importance of mineral composition,especially the presence of dolomite and calcite,in shaping pore heterogeneity.These findings emphasize the critical role of shale lithofacies and pore structure in optimizing shale gas extraction methods.展开更多
Biotite content critically influences rock mechanical behavior and threatens underground engineering stability.Uniaxial compression tests with acoustic emission(AE)monitoring were conducted on granite pegmatite sample...Biotite content critically influences rock mechanical behavior and threatens underground engineering stability.Uniaxial compression tests with acoustic emission(AE)monitoring were conducted on granite pegmatite samples having varying biotite content.Peak frequency distribution analysis,rise angleaverage frequency(RA-AF)analysis,multifractal theory,and a dynamic multifractal algorithm were applied to explore the relationship between damage evolution and AE characteristics.Results indicate that increased biotite content reduces uniaxial compressive strength and elastic modulus,enhances plastic deformation,and increases the proportion of shear cracks.The segmented evolution of the dynamic multifractal parameter Δα_(m) is biotite-dependent.Oscillations during the elastic phase signify localized shear crack initiation and propagation;their attenuation in the plastic phase reflects frictional closure along biotite cleavage planes,promoting elastic energy storage and delaying release.AE-based damage models and time-varying signals characterize rock damage progression.Stress concentrations around biotite minerals foster localized shear band formation,leading to concentrated shear failure at lower damage levels.Higher biotite content accelerates crack propagation,while smooth cleavage planes lower the fracture energy threshold,reducing strength and stiffness.These findings enhance understanding of biotite-influenced progressive rock damage and underpin stability monitoring and early-warning systems for underground engineering.展开更多
Understanding the rate-dependent shear behavior of rough joints is crucial.This study explores the ratedependent shear behavior of rough joints through direct shear tests conducted under constant normal stiffness(CNS)...Understanding the rate-dependent shear behavior of rough joints is crucial.This study explores the ratedependent shear behavior of rough joints through direct shear tests conducted under constant normal stiffness(CNS)boundary conditions,with the shear failure process monitored using acoustic emission(AE)technology.As the shear rate increases,both the peak and ultimate shear stresses of rough joints exhibit a decrease,highlighting a pronounced rate-dependent behavior.Asperity degradation under different shear rates is effectively characterized by normalized AE counts,exhibiting a three-stage Sshaped trend:Stage I(quiescent),Stage II(growth),and Stage III(stable).The simultaneous occurrence of the lowest AE b-value and the highest AE amplitude closely aligns with the moment of peak shear stress.This synchronization suggests that AE events of significant energy are predominantly clustered around the peak shear stress,which critically influences the overall progression of failure.Three failure modes of asperities were categorized,including the biting-off failure mode(BFM),the climbing-sliding failure mode(CFM),and the hybrid biting-off and climbing-sliding failure mode(HFM).Analysis of the multifractal spectra reveals that both the multifractal spectrum width(Δα)and the fractal dimension variability(Δf)diminish as the shear rate increases,suggesting that the complexity of the failure modes is inversely related to the shear rate.With increasing shear rates,the dominant failure mode evolves from BFM to CFM.The research findings facilitate a comprehensive understanding of the ratedependent shear behavior of rough joints,providing valuable guidance for rational support in underground engineering.展开更多
The multifractal characteristics of organic-rich shale developed along the margins of basins are essential for understanding reservoir heterogeneity,gas storage mechanisms,and the identification of favorable explorati...The multifractal characteristics of organic-rich shale developed along the margins of basins are essential for understanding reservoir heterogeneity,gas storage mechanisms,and the identification of favorable exploration targets.This study systematically investigates the pore structure of marine shale in the Zhaotong area of the National Shale Gas Exploration Demonstration Area in China by integrating analytical methods such as X-ray diffraction,low-pressure N_(2) adsorption,and field emission scanning electron microscopy with the Frenkel-HalseyHill fractal model.The results reveal that:(1)four distinct shale lithofacies(SL)types were identified-argillaceous/siliceous mixed SL(Type Ⅰ:M-2),carbonate/siliceous mixed SL(Type Ⅱ:M and M-1),argillaceous-rich siliceous SL(Type Ⅲ:S-3),and carbonate-rich and argillaceous/carbonate siliceous SL(Type Ⅳ:S-1 and S-2);(2)Types Ⅱ and Ⅳ generally exhibit higher fractal dimensions(D_(1),D_(2),and D_(3))than Types Ⅰ and Ⅲ,indicating the former’s more complex pore architectures,rougher pore surfaces,and greater potential for gas adsorption;(3)for Types Ⅰ and Ⅲ,fractal dimensions exhibit positive correlations with organic matter content,pore structural parameters,and gas content,suggesting their effectiveness as indicators of reservoir quality.In contrast,in Types Ⅱ and Ⅳ,the D_(2) dimension is positively correlated with gas content,implying that mesopores play a significant role in gas occurrence,even in tectonically modified settings.These results highlight the utility of fractal analysis as a robust method for evaluating reservoirs in structurally complex geological environments.展开更多
Unveiling the underlying physical mechanisms governing the fracture of brittle rocks is imperative for preventing rockbursts.The novelty of this study lies in the analysis of the dynamic response process of rock three...Unveiling the underlying physical mechanisms governing the fracture of brittle rocks is imperative for preventing rockbursts.The novelty of this study lies in the analysis of the dynamic response process of rock three-dimensional(3D)deformation under true triaxial stress,and the surge behavior of timedependent multifractal spectrum has been successfully used to warn of progressive failure inside the rock.Firstly,this study analyzed the dynamic adjustment trajectory of rock deformation,specifically lateral strain,within the framework of the Poisson effect.This analysis highlighted the intricate dependence of rock mechanical properties on the intermediate principal stress.Secondly,by defining the crack interval function(ICF),this study compared the disparities between the two crack growth stages(strengthening stage and weakening stage)under varying stress levels.It was found that the fracture activity of granite system has significant multifractal characteristics.Notably,the multifractal spectrum emerges as a valuable tool for characterizing the distinct fracture properties of rocks,encompassing both the crack scale and the associated energy.Finally,a quantitative criterion grounded in the multifractal parameters of the acoustic emission(AE)time series was formulated,and it indicates that the abrupt changes observed in the time-dependent fractal spectra can serve as precursor indicators for the progressive development of rockbursts.展开更多
Disordered ferromagnets with a domain structure that exhibit a hysteresis loop when driven by the external magnetic field are essential materials for modern technological applications.Therefore,the understanding and p...Disordered ferromagnets with a domain structure that exhibit a hysteresis loop when driven by the external magnetic field are essential materials for modern technological applications.Therefore,the understanding and potential for controlling the hysteresis phenomenon in thesematerials,especially concerning the disorder-induced critical behavior on the hysteresis loop,have attracted significant experimental,theoretical,and numerical research efforts.We review the challenges of the numerical modeling of physical phenomena behind the hysteresis loop critical behavior in disordered ferromagnetic systems related to the non-equilibriumstochastic dynamics of domain walls driven by external fields.Specifically,using the extended Random Field Ising Model,we present different simulation approaches and advanced numerical techniques that adequately describe the hysteresis loop shapes and the collective nature of the magnetization fluctuations associated with the criticality of the hysteresis loop for different sample shapes and varied parameters of disorder and rate of change of the external field,as well as the influence of thermal fluctuations and demagnetizing fields.The studied examples demonstrate how these numerical approaches reveal newphysical insights,providing quantitativemeasures of pertinent variables extracted from the systems’simulated or experimentally measured Barkhausen noise signals.The described computational techniques using inherent scale-invariance can be applied to the analysis of various complex systems,both quantum and classical,exhibiting non-equilibrium dynamical critical point or self-organized criticality.展开更多
An empirical test on long memory between price and trading volume of China metals futures market was given with MF-DCCA method. The empirical results show that long memory feature with a certain period exists in price...An empirical test on long memory between price and trading volume of China metals futures market was given with MF-DCCA method. The empirical results show that long memory feature with a certain period exists in price-volume correlation and a fittther proof was given by analyzing the source of multifractal feature. The empirical results suggest that it is of important practical significance to bring the fractal market theory and other nonlinear theory into the analysis and explanation of the behavior in metal futures market.展开更多
Complex networks have recently attracted much attention in diverse areas of science and technology. Many networks such as the WWW and biological networks are known to display spatial heterogeneity which can be charact...Complex networks have recently attracted much attention in diverse areas of science and technology. Many networks such as the WWW and biological networks are known to display spatial heterogeneity which can be characterized by their fractal dimensions. Multifractal analysis is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. In this paper, we introduce a new box-covering algorithm for multifractal analysis of complex networks. This algorithm is used to calculate the generalized fractal dimensions Dq of some theoretical networks, namely scale-free networks, small world networks, and random networks, and one kind of real network, namely protein protein interaction networks of different species. Our numerical results indicate the existence of multifractality in scale-free networks and protein protein interaction networks, while the multifractal behavior is not clear-cut for small world networks and random networks. The possible variation of Dq due to changes in the parameters of the theoretical network models is also discussed.展开更多
The multifractality of energy and thermal dissipation of fully developed intermittent turbulence is investigated in the urban canopy layer under unstable conditions by the singularity spectrum for the fractal dimensio...The multifractality of energy and thermal dissipation of fully developed intermittent turbulence is investigated in the urban canopy layer under unstable conditions by the singularity spectrum for the fractal dimensions of sets of singularities characterizing multifractals. In order to obtain high-order moment properties of smallscale turbulent dissipation in the inertial range, an ultrasonic anemometer with a high sampling frequency of 100 Hz was used. The authors found that the turbulent signal could be singular everywhere. Moreover, the singular exponents of energy and thermal dissipation rates are most frequently encountered at around 0.2, which is significantly smaller than the singular exponents for a wind tunnel at a moderate Reynolds number. The evidence indicates a higher intermittency of turbulence in the urban canopy layer at a high Reynolds number, which is demonstrated by the data with high temporal resolution. Furthermore, the temperature field is more intermittent than the velocity field. In addition, a large amount of samples could be used for verification of the results.展开更多
We investigate the approximating capability of Markov modulated Poisson processes (MMPP) for modeling multifractal Internet traffic. The choice of MMPP is motivated by its ability to capture the variability and correl...We investigate the approximating capability of Markov modulated Poisson processes (MMPP) for modeling multifractal Internet traffic. The choice of MMPP is motivated by its ability to capture the variability and correlation in moderate time scales while being analytically tractable. Important statistics of traffic burstiness are described and a customized moment-based fitting procedure of MMPP to traffic traces is presented. Our methodology of doing this is to examine whether the MMPP can be used to predict the performance of a queue to which MMPP sample paths and measured traffic traces are fed for comparison respectively, in addition to the goodness-of-fit test of MMPP. Numerical results and simulations show that the fitted MMPP can approximate multifractal traffic quite well, i.e. accurately predict the queueing performance.展开更多
In this article,the Multi-Fractal Detrended Fluctuation Analysis(MF-DFA)method is adopted to study the temperature,i.e.,the maximum temperature(Tmax),mean temperature(Tavg)and minimum(Tmin)air temperature,multifractal...In this article,the Multi-Fractal Detrended Fluctuation Analysis(MF-DFA)method is adopted to study the temperature,i.e.,the maximum temperature(Tmax),mean temperature(Tavg)and minimum(Tmin)air temperature,multifractal characteristics and their formation mechanism,in the typical temperature zones in the coastal regions in Guangdong,Jiangsu and Liaoning Provinces.Following are some terms and concepts used in the present study.Multifractality is defined as a term that characterizes the complexity and self-similarity of objects,and fractal characteristics depict the distribution of probability over the whole set caused by different local conditions or different levels in the process of evolution.Fractality strength denotes the fluctuation range of the data set,and long-range correlation(LRC)measures the stability of the climate system and the trend of climate change in the future.In this research,it is found that the internal stability and feedback mechanism of climate systems in different regions show regional differences.Furthermore,the research also proves that the Tavg,Tmaxand Tminof the above three provinces are highly multifractal.The temperature series multifractality of each province decreases in the order of temperature series multifractality of Liaoning>temperature series multifractality of Guangdong>temperature series multifractality of Jiangsu,and the corresponding long-range correlations follow the same order.It reveals that the most stable temperature series is that of Liaoning,followed by the temperature series of Guangdong,and the most unstable one is that of Jiangsu.Liaoning has the most stable climate system,and it will thus be less responsive to the future climate warming.The stability of the climate system in Jiangsu is the weakest,and its temperature fluctuation will continue to increase in the future,which will probably result in the meteorological disasters of high temperature and heat wave there.Guangdong possesses the strongest degree of multifractal strength,which indicates that its internal temperature series fluctuation is the largest among the three regions.The Tmaxmultifractal strength of Jiangsu is stronger than that of Liaoning,while the Tavgand Tminmultifractal strength of Jiangsu is weaker than that of Liaoning,showing that Jiangsu has a larger internal Tmaxfluctuation than Liaoning does,while it has a smaller fluctuation of Tavgand Tminthan Liaoning does.Guangdong and Liaoning both show the strongest Tminmultifractal strength,followed by Tavgmultifractal strength,and the weakest Tmax multifractal strength.However,Jiangsu has the strongest Tmax,followed by Tavg,and the weakest Tmin.The research findings show that these phenomena are closely related to solar radiation,monsoon strength,topography and some other factors.In addition,the multifractality of the temperature time series results from the negative power-law distribution and long-range correlation,in which the long-range correlation influence of temperature series itself plays the dominant role.With the backdrop of global climate change,this research can provide a theoretical basis for the prediction of the spatial-temporal air temperature variation in the eastern coastal areas of China and help us understand its characteristics and causes,and thus the present study will be significant for the environmental protection of coastal areas.展开更多
A multifractal analysis to study the multiparticle dynamics in 60A and 200A GeV, 16O-AgBr collisions has been performed in the pseudorapidity phase space. Multifractal moments, Gq, as the function of pseudorapidity bi...A multifractal analysis to study the multiparticle dynamics in 60A and 200A GeV, 16O-AgBr collisions has been performed in the pseudorapidity phase space. Multifractal moments, Gq, as the function of pseudorapidity bin size for different order of the moments, q, have been calculated. The power-law behaviour has been observed in the considered data sets. The variations of multifractal dimension, Dq, and the multifractal spectral function, f(aq), with order of the moments, q, have been studied thoroughly. Dq is found to decrease with increasing order of moments, q, indicating thereby a self-similar behaviour in the multiparticle production for the considered collisions. We have also found a concave downward curve of multifractal spectral function with maximum at q = 0.展开更多
A systematic analysis of the data on 14.5A GeV/c 28Si-nucleus collisions is carried out to investigate the behaviours of Renyi dimensions, Dq and Multifractal Spectral Function, f(αq). The Renyi dimensions, Dq are ob...A systematic analysis of the data on 14.5A GeV/c 28Si-nucleus collisions is carried out to investigate the behaviours of Renyi dimensions, Dq and Multifractal Spectral Function, f(αq). The Renyi dimensions, Dq are observed to decrease with increasing order of the moments, q. However, the Multifractal Spectra are concave downwards with their maxima occurring around αq =1.21±0.01. A continuous curve representing Multifractal Spectral Function, f(αq), characterizes manifestation of fluctuations in the rapidity space.展开更多
Pore structure characteristics are important to oil and gas exploration in complex low-permeability reservoirs. Using multifractal theory and nuclear magnetic resonance （NMR）, we studied the pore structure of low-pe...Pore structure characteristics are important to oil and gas exploration in complex low-permeability reservoirs. Using multifractal theory and nuclear magnetic resonance （NMR）, we studied the pore structure of low-permeability sandstone rocks from the 4th Member （Es4） of the Shahejie Formation in the south slope of the Dongying Sag. We used the existing pore structure data from petrophysics, core slices, and mercury injection tests to classify the pore structure into three categories and five subcategories. Then, the T2 spectra of samples with different pore structures were interpolated, and the one- and three-dimensional fractal dimensions and the multifractal spectrum were obtained. Parameters a （intensity of singularity） andf（a） （density of distribution） were extracted from the multifractal spectra. The differences in the three fractal dimensions suggest that the pore structure types correlate with a andf（a）. The results calculated based on the multifractal spectrum is consistent with that of the core slices and mercury injection. Finally, the proposed method was applied to an actual logging profile to evaluate the pore structure of low-permeability sandstone reservoirs.展开更多
基金supported by the National Social Science Fund Major Projects(22&ZD160).
文摘This study investigates the relationships between agricultural spot markets and external uncertainties through multifractal detrending moving-average cross-correlation analysis(MF-X-DMA).The dataset contains the Grains&Oilseeds Index(GOI)and its five subindices for wheat,maize,soyabeans,rice,and barley.Moreover,we use three uncertainty proxies,namely,economic policy uncertainty(EPU),geopolitical risk(GPR),and Volatility Index(VIX).We observe multifractal cross-correlations between agricultural markets and uncertainties.Furthermore,statistical tests reveal that maize has intrinsic joint multifractality with all the uncertainty proxies,highly sensitive to external shocks.Additionally,intrinsic multifractality among GOI-GPR,wheat-GPR,and soyabeans-VIX is illustrated.However,other series have apparent multifractal crosscorrelations with high probabilities.Moreover,our analysis suggests that among the three types of external uncertainties,GPR has the strongest association with grain prices,excluding maize and soyabeans.
文摘Layering detection is an important step in petroleum engineering.Time series of post-stack seismic data and wire-line log data belong to subsurface layering.They exhibit multifractal properties with complex patterns because of the heterogeneity and different genetic properties in the earth layers.In a multifractal configuration,any piece of a series has a distinct Hurst exponent that reflects its nature and can be used for zone detection.Time series are post-stack seismic traces and wire-line log data near the well-bores.Self-similar Autoregressive Exogenous(SAE)model is a modified method which can place self-similar post-stack seismic and wire-line log segments across layers with the same lithology.The results satisfy the capability of layering identification from seismic data by SAE model.
文摘In the present study an attempt is made to examine multifractality in multiparticle production in relativistic nuclear collisions;multifractality is investigated in 14.5 A GeV/c 28Si-nucleus collisions. For this, Gq-moments are calculated and variations of ?are looked into. Values of mass exponents, tq, and generalised dimensions, Dq, are obtained. Analysis of multifractal moments reveals that multiplicity fluctuations are of dynamical nature.
基金sponsored by the National Natural Science Foundation of China(Grant No.42202205)Natural Science Foundation of Shandong Province,China(Grant No.ZR2021QD072).-。
文摘The vertical heterogeneity of the pore structure in deep coal seams with varying ash yields is a key control for coalbed methane storage and producibility;however,its specific impact on gas adsorption is not clearly defined.The focus of this study is the No.8 coal seam of the Carboniferous Benxi Formation in the Central-Eastern Ordos Basin.By integrating microscopic identification,proximate analysis,gas adsorption(CO_(2),N_(2),and CH_(4)),and the multifractal theory,we quantitatively characterized the nanopore structure(micropores<2 nm and mesopores 2 nm-100 nm)of coal reservoirs with varying ash yields.The results indicate that(1)ash yield is the primary factor that controls the vertical evolution of pore structures in coal seams.In low-ash yield coal seams,the extent of thermal evolution and ash yield jointly constrain the heterogeneity of pore size distribution.In mediumto high-ash yield coal seams,the heterogeneity of pore structure and pore size distribution are predominantly constrained by ash yield.(2)As the ash yield vertically increases,the mesoporous pore volume and specific surface area initially decrease and subsequently increase,while the contribution of micropores to both pore volume and specific surface area continuously diminishes.Consequently,the total pore volume and specific surface area of the coal samples exhibit a two-stage reduction close to an ash yield threshold of approximately 20%.(3)Further,the Langmuir volume for CH_(4)adsorption sharply declines below the 20%threshold,followed by a gradual decrease;in contrast,the Langmuir pressure initially decreases and subsequently increases.Hence,the vertical increase in ash yield constrains the development of pore systems and diminishes pore connectivity,thereby reducing methane adsorption capacity and adversely affecting coalbed methane productivity.(4)Low-ash yield coal reservoirs are characterized by a rapid gas breakthrough and high productivity,whereas medium-ash yield coal reservoirs generally require prolonged depressurization to achieve peak gas production.These findings reveal that in medium-high rank coal,ash yield―and not thermal evolution―is the main factor that controls vertical pore evolution and methane adsorption efficiency.The quantitative ash yield threshold(20%)established in this study provides a practical criterion for evaluating reservoir quality and predicting vertical variations in gas storage potential in the Ordos Basin.
基金Benjamin M.Tabak(Grant no.305485/2022-9)gratefully acknowledges financial support from the CNPq foundation and CAPES Foundation。
文摘Presently,financial portfolio managers lack a solid basis for building a reliable risk management strategy for green debt instrument investments due to the lack of compelling growth and resilience data.Therefore,this study assesses the role of green bonds in financial markets by assessing and correlating their complex scaling behaviors across multiple periods with those of key benchmark assets(e.g.,conventional bonds,high-yield bonds,Euro-Dollar exchange,Dow Jones Industrial Index,Bitcoin,and Gold).Specifically,we explore linear and nonlinear correlation patterns using crosscorrelation tests and the dynamic conditional correlation model,focusing on bond interactions under various degrees of freedom.Our analysis reveals that although most assets exhibit nonlinear correlations,Bitcoin uniquely aligns linearly with U.S.bonds under certain conditions.Green bonds,however,display nonlinear correlations with Bitcoin and stand out for their distinct upward financial persistence.We find also that green bonds are primary drivers in the financial domain,highlighted by their pronounced interactions and the consistent cross-correlation with the Euro-Dollar exchange rate.Moreover,green bonds have the lowest multifractality,showing persistent upward trends and antipersistent downward trends,rendering them quite resilient during periods of high volatility.These results imply that green bonds may be advantageous to portfolio risk management strategies,especially during crises when diversification and hedging tactics are needed.
基金supported by the National Natural Science Foundation of China(No.52160024)the Natural Science Foundation of Hunan Province,China(No.2022JJ30475)+2 种基金the Innovation Team Funds of China West Normal University(No.KCXTD2023-4)the Natural Science Foundation of Sichuan,China(No.24NSFSC0537)the Fundamental Research Funds of China West Normal University(Nos.22kE015 and 22kE016).
文摘As an important component of secondary aerosols,sulfate plays a crucial role in regulating atmospheric radiative balance and influencing the secondary formation of ozone(O_(3)).In real atmosphere,atmospheric oxidants NO_(2)and O_(3)can promote the oxidation of SO_(2)to form sulfate(SO_(4)^(2−))through multiphase chemistry that occur at different time scales.Due to the combined impact of meteorology,pollution sources,atmospheric chemistry,etc.,time-scale dependence of SO_(2)-SO_(4)^(2−)conversion makes the impact of NO_(2)/O_(3)on it more complex.In this study,based on long-term time series(2013-2020)of air pollution variables from seven stations in Hong Kong,the Multifractal Detrended Cross-Correlation Analysis(MFDCCA)method has been employed to quantify the cross-correlations between SO_(2)and SO_(4)^(2−)in real atmosphere at different time scales,for examining the time-scale dependence of SO_(2)-SO_(4)^(2−)conversion efficiency.Furthermore,the Pearson correlation analysis has been used to study the influence of NO_(2)/O_(3)on SO_(2)-SO_(4)^(2−)conversion,and the regional and seasonal differences have been analyzed by considering factors such as meteorology,pollution sources,and regional transport.Changes in the main components of secondary aerosols are closely linked with the co-control of regional PM_(2.5)and O_(3).Therefore,the exploration of the impact of co-existing NO_(2)/O_(3)gases on the secondary formation of sulfates in real atmosphere is significant.
基金supported by research projects P23057 and JKK4624004 of Jianghan Oilfield Company,SINOPEC.
文摘The carbonate-rich shale of the Permian Wujiaping Formation in Sichuan Basin exhibits significant heterogeneity in its lithology and pore structure,which directly influence its potential for shale gas extraction.This study assesses the factors that govern pore heterogeneity by analyzing the mineral composition of the shale,as well as its pore types and their multifractal characteristics.Three primary shale facies-siliceous,mixed,and calcareous-are identified based on mineralogy,and their multifractal characteristics reveal strongly heterogeneous pore structures.The brittleness of siliceous shale,rich in quartz and pyrite,is favorable for hydraulic fracturing;while calcareous shale,with higher levels of calcite,exhibits reduced brittleness.Multifractal analysis,using nitrogen adsorption isotherms,reveals complex pore structures across different shale facies,with siliceous shale showing better pore connectivity and uniformity.The types of pores in shales include organic matter pores,interparticle pores,and intraparticle pores,among which organic matter pores are the most abundant.Pore size distribution and connectivity are notably higher in siliceous shale compared to calcareous shale,which exhibit a predominance of micropores and more isolated pore structures.Pore heterogeneity of the carbonate-rich shale in the Wujiaping Formation is primarily governed by its intrinsic mineral composition,carbonate diagenesis,mechanical compaction,and its subsequent thermal maturation with the micro-migration of organic matter.This study highlights the importance of mineral composition,especially the presence of dolomite and calcite,in shaping pore heterogeneity.These findings emphasize the critical role of shale lithofacies and pore structure in optimizing shale gas extraction methods.
基金provided by the National Key R&D Program of China(No.2024YFC3012605)the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection Independent Research Project(Nos.SKLGP2022Z001,SKLGP2023Z029 and SKLGP2022K027)。
文摘Biotite content critically influences rock mechanical behavior and threatens underground engineering stability.Uniaxial compression tests with acoustic emission(AE)monitoring were conducted on granite pegmatite samples having varying biotite content.Peak frequency distribution analysis,rise angleaverage frequency(RA-AF)analysis,multifractal theory,and a dynamic multifractal algorithm were applied to explore the relationship between damage evolution and AE characteristics.Results indicate that increased biotite content reduces uniaxial compressive strength and elastic modulus,enhances plastic deformation,and increases the proportion of shear cracks.The segmented evolution of the dynamic multifractal parameter Δα_(m) is biotite-dependent.Oscillations during the elastic phase signify localized shear crack initiation and propagation;their attenuation in the plastic phase reflects frictional closure along biotite cleavage planes,promoting elastic energy storage and delaying release.AE-based damage models and time-varying signals characterize rock damage progression.Stress concentrations around biotite minerals foster localized shear band formation,leading to concentrated shear failure at lower damage levels.Higher biotite content accelerates crack propagation,while smooth cleavage planes lower the fracture energy threshold,reducing strength and stiffness.These findings enhance understanding of biotite-influenced progressive rock damage and underpin stability monitoring and early-warning systems for underground engineering.
基金supported by the Nagasaki University Global Human Resource Development Scholarship and the Support for Pioneering Research Initiated by the Next Generation.
文摘Understanding the rate-dependent shear behavior of rough joints is crucial.This study explores the ratedependent shear behavior of rough joints through direct shear tests conducted under constant normal stiffness(CNS)boundary conditions,with the shear failure process monitored using acoustic emission(AE)technology.As the shear rate increases,both the peak and ultimate shear stresses of rough joints exhibit a decrease,highlighting a pronounced rate-dependent behavior.Asperity degradation under different shear rates is effectively characterized by normalized AE counts,exhibiting a three-stage Sshaped trend:Stage I(quiescent),Stage II(growth),and Stage III(stable).The simultaneous occurrence of the lowest AE b-value and the highest AE amplitude closely aligns with the moment of peak shear stress.This synchronization suggests that AE events of significant energy are predominantly clustered around the peak shear stress,which critically influences the overall progression of failure.Three failure modes of asperities were categorized,including the biting-off failure mode(BFM),the climbing-sliding failure mode(CFM),and the hybrid biting-off and climbing-sliding failure mode(HFM).Analysis of the multifractal spectra reveals that both the multifractal spectrum width(Δα)and the fractal dimension variability(Δf)diminish as the shear rate increases,suggesting that the complexity of the failure modes is inversely related to the shear rate.With increasing shear rates,the dominant failure mode evolves from BFM to CFM.The research findings facilitate a comprehensive understanding of the ratedependent shear behavior of rough joints,providing valuable guidance for rational support in underground engineering.
基金supported by the National Natural Science Foundation of China(Grant No.42272163)the Fund of State Key Laboratory of Deep Oil and Gas,China University of Petroleum(East China)(Grant No.SKLDOG2024-ZYTS-01).
文摘The multifractal characteristics of organic-rich shale developed along the margins of basins are essential for understanding reservoir heterogeneity,gas storage mechanisms,and the identification of favorable exploration targets.This study systematically investigates the pore structure of marine shale in the Zhaotong area of the National Shale Gas Exploration Demonstration Area in China by integrating analytical methods such as X-ray diffraction,low-pressure N_(2) adsorption,and field emission scanning electron microscopy with the Frenkel-HalseyHill fractal model.The results reveal that:(1)four distinct shale lithofacies(SL)types were identified-argillaceous/siliceous mixed SL(Type Ⅰ:M-2),carbonate/siliceous mixed SL(Type Ⅱ:M and M-1),argillaceous-rich siliceous SL(Type Ⅲ:S-3),and carbonate-rich and argillaceous/carbonate siliceous SL(Type Ⅳ:S-1 and S-2);(2)Types Ⅱ and Ⅳ generally exhibit higher fractal dimensions(D_(1),D_(2),and D_(3))than Types Ⅰ and Ⅲ,indicating the former’s more complex pore architectures,rougher pore surfaces,and greater potential for gas adsorption;(3)for Types Ⅰ and Ⅲ,fractal dimensions exhibit positive correlations with organic matter content,pore structural parameters,and gas content,suggesting their effectiveness as indicators of reservoir quality.In contrast,in Types Ⅱ and Ⅳ,the D_(2) dimension is positively correlated with gas content,implying that mesopores play a significant role in gas occurrence,even in tectonically modified settings.These results highlight the utility of fractal analysis as a robust method for evaluating reservoirs in structurally complex geological environments.
基金funding support from the National Natural Science Foundation of China(Grant No.U2034207)the Natural Science Foundation of Hebei Province(Grant No.E2021210099).
文摘Unveiling the underlying physical mechanisms governing the fracture of brittle rocks is imperative for preventing rockbursts.The novelty of this study lies in the analysis of the dynamic response process of rock three-dimensional(3D)deformation under true triaxial stress,and the surge behavior of timedependent multifractal spectrum has been successfully used to warn of progressive failure inside the rock.Firstly,this study analyzed the dynamic adjustment trajectory of rock deformation,specifically lateral strain,within the framework of the Poisson effect.This analysis highlighted the intricate dependence of rock mechanical properties on the intermediate principal stress.Secondly,by defining the crack interval function(ICF),this study compared the disparities between the two crack growth stages(strengthening stage and weakening stage)under varying stress levels.It was found that the fracture activity of granite system has significant multifractal characteristics.Notably,the multifractal spectrum emerges as a valuable tool for characterizing the distinct fracture properties of rocks,encompassing both the crack scale and the associated energy.Finally,a quantitative criterion grounded in the multifractal parameters of the acoustic emission(AE)time series was formulated,and it indicates that the abrupt changes observed in the time-dependent fractal spectra can serve as precursor indicators for the progressive development of rockbursts.
基金Djordje Spasojevic and Svetislav Mijatovic acknowledge the support from the Ministry of Science,TechnologicalDevelopment and Innovation of the Republic of Serbia(Agreement No.451-03-65/2024-03/200162)S.J.ibid.(Agreement No.451-03-65/2024-03/200122)Bosiljka Tadic from the Slovenian Research Agency(program P1-0044).
文摘Disordered ferromagnets with a domain structure that exhibit a hysteresis loop when driven by the external magnetic field are essential materials for modern technological applications.Therefore,the understanding and potential for controlling the hysteresis phenomenon in thesematerials,especially concerning the disorder-induced critical behavior on the hysteresis loop,have attracted significant experimental,theoretical,and numerical research efforts.We review the challenges of the numerical modeling of physical phenomena behind the hysteresis loop critical behavior in disordered ferromagnetic systems related to the non-equilibriumstochastic dynamics of domain walls driven by external fields.Specifically,using the extended Random Field Ising Model,we present different simulation approaches and advanced numerical techniques that adequately describe the hysteresis loop shapes and the collective nature of the magnetization fluctuations associated with the criticality of the hysteresis loop for different sample shapes and varied parameters of disorder and rate of change of the external field,as well as the influence of thermal fluctuations and demagnetizing fields.The studied examples demonstrate how these numerical approaches reveal newphysical insights,providing quantitativemeasures of pertinent variables extracted from the systems’simulated or experimentally measured Barkhausen noise signals.The described computational techniques using inherent scale-invariance can be applied to the analysis of various complex systems,both quantum and classical,exhibiting non-equilibrium dynamical critical point or self-organized criticality.
基金Project(13&ZD024)supported by the Major Program of the National Social Science Fund of ChinaProject(71073177)supported by the National Natural Science Foundation of China+3 种基金Project(CX2012B107)supported by the Graduate Student Innovation Project of Hunan Province,ChinaProject(13YJAZH149)supported by the Social Science Fund of Ministry of Education of ChinaProject(2011ZK2043)supported by the Key Program of the Soft Science Research Project of Hunan Province,ChinaProject(12JJ4077)supported by Natural Science Foundation of Hunan Province of China
文摘An empirical test on long memory between price and trading volume of China metals futures market was given with MF-DCCA method. The empirical results show that long memory feature with a certain period exists in price-volume correlation and a fittther proof was given by analyzing the source of multifractal feature. The empirical results suggest that it is of important practical significance to bring the fractal market theory and other nonlinear theory into the analysis and explanation of the behavior in metal futures market.
基金Project supported by the Australian Research Council (Grant No. DP0559807)the National Natural Science Foundation of China (Grant No. 11071282)+5 种基金the Science Fund for Changjiang Scholars and Innovative Research Team in University (PCSIRT)(Grant No. IRT1179)the Program for New Century Excellent Talents in University (Grant No. NCET-08-06867)the Research Foundation of the Education Department of Hunan Province of China (Grant No. 11A122)the Natural Science Foundationof Hunan Province of China (Grant No. 10JJ7001)the Science and Technology Planning Project of Hunan Province of China(Grant No. 2011FJ2011)the Lotus Scholars Program of Hunan Province of China,the Aid Program for Science and Technology Innovative Research Team in Higher Education Institutions of Hunan Province of China,and a China Scholarship Council-Queensland University of Technology Joint Scholarship
文摘Complex networks have recently attracted much attention in diverse areas of science and technology. Many networks such as the WWW and biological networks are known to display spatial heterogeneity which can be characterized by their fractal dimensions. Multifractal analysis is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. In this paper, we introduce a new box-covering algorithm for multifractal analysis of complex networks. This algorithm is used to calculate the generalized fractal dimensions Dq of some theoretical networks, namely scale-free networks, small world networks, and random networks, and one kind of real network, namely protein protein interaction networks of different species. Our numerical results indicate the existence of multifractality in scale-free networks and protein protein interaction networks, while the multifractal behavior is not clear-cut for small world networks and random networks. The possible variation of Dq due to changes in the parameters of the theoretical network models is also discussed.
基金supported by the National Natural Science Foundation of China(Grant Nos.11472272 and 91215302)the Special Fund for Meteorological Research in the Public Interest(Grant No.GYHY201206041)
文摘The multifractality of energy and thermal dissipation of fully developed intermittent turbulence is investigated in the urban canopy layer under unstable conditions by the singularity spectrum for the fractal dimensions of sets of singularities characterizing multifractals. In order to obtain high-order moment properties of smallscale turbulent dissipation in the inertial range, an ultrasonic anemometer with a high sampling frequency of 100 Hz was used. The authors found that the turbulent signal could be singular everywhere. Moreover, the singular exponents of energy and thermal dissipation rates are most frequently encountered at around 0.2, which is significantly smaller than the singular exponents for a wind tunnel at a moderate Reynolds number. The evidence indicates a higher intermittency of turbulence in the urban canopy layer at a high Reynolds number, which is demonstrated by the data with high temporal resolution. Furthermore, the temperature field is more intermittent than the velocity field. In addition, a large amount of samples could be used for verification of the results.
文摘We investigate the approximating capability of Markov modulated Poisson processes (MMPP) for modeling multifractal Internet traffic. The choice of MMPP is motivated by its ability to capture the variability and correlation in moderate time scales while being analytically tractable. Important statistics of traffic burstiness are described and a customized moment-based fitting procedure of MMPP to traffic traces is presented. Our methodology of doing this is to examine whether the MMPP can be used to predict the performance of a queue to which MMPP sample paths and measured traffic traces are fed for comparison respectively, in addition to the goodness-of-fit test of MMPP. Numerical results and simulations show that the fitted MMPP can approximate multifractal traffic quite well, i.e. accurately predict the queueing performance.
基金National Key R&D Program of China(2018YFC1506900,2018YFC1506904)National Natural Science Foundation of China(41875027,41911530242)+1 种基金Key Laboratory of South China Sea Meteorological Disaster Prevention and Mitigation of Hainan Province(SCSF201804,419QN330)Research Program of Key Laboratory of Meteorology and Ecological Environment of Hebei Province(Z201603Z)。
文摘In this article,the Multi-Fractal Detrended Fluctuation Analysis(MF-DFA)method is adopted to study the temperature,i.e.,the maximum temperature(Tmax),mean temperature(Tavg)and minimum(Tmin)air temperature,multifractal characteristics and their formation mechanism,in the typical temperature zones in the coastal regions in Guangdong,Jiangsu and Liaoning Provinces.Following are some terms and concepts used in the present study.Multifractality is defined as a term that characterizes the complexity and self-similarity of objects,and fractal characteristics depict the distribution of probability over the whole set caused by different local conditions or different levels in the process of evolution.Fractality strength denotes the fluctuation range of the data set,and long-range correlation(LRC)measures the stability of the climate system and the trend of climate change in the future.In this research,it is found that the internal stability and feedback mechanism of climate systems in different regions show regional differences.Furthermore,the research also proves that the Tavg,Tmaxand Tminof the above three provinces are highly multifractal.The temperature series multifractality of each province decreases in the order of temperature series multifractality of Liaoning>temperature series multifractality of Guangdong>temperature series multifractality of Jiangsu,and the corresponding long-range correlations follow the same order.It reveals that the most stable temperature series is that of Liaoning,followed by the temperature series of Guangdong,and the most unstable one is that of Jiangsu.Liaoning has the most stable climate system,and it will thus be less responsive to the future climate warming.The stability of the climate system in Jiangsu is the weakest,and its temperature fluctuation will continue to increase in the future,which will probably result in the meteorological disasters of high temperature and heat wave there.Guangdong possesses the strongest degree of multifractal strength,which indicates that its internal temperature series fluctuation is the largest among the three regions.The Tmaxmultifractal strength of Jiangsu is stronger than that of Liaoning,while the Tavgand Tminmultifractal strength of Jiangsu is weaker than that of Liaoning,showing that Jiangsu has a larger internal Tmaxfluctuation than Liaoning does,while it has a smaller fluctuation of Tavgand Tminthan Liaoning does.Guangdong and Liaoning both show the strongest Tminmultifractal strength,followed by Tavgmultifractal strength,and the weakest Tmax multifractal strength.However,Jiangsu has the strongest Tmax,followed by Tavg,and the weakest Tmin.The research findings show that these phenomena are closely related to solar radiation,monsoon strength,topography and some other factors.In addition,the multifractality of the temperature time series results from the negative power-law distribution and long-range correlation,in which the long-range correlation influence of temperature series itself plays the dominant role.With the backdrop of global climate change,this research can provide a theoretical basis for the prediction of the spatial-temporal air temperature variation in the eastern coastal areas of China and help us understand its characteristics and causes,and thus the present study will be significant for the environmental protection of coastal areas.
文摘A multifractal analysis to study the multiparticle dynamics in 60A and 200A GeV, 16O-AgBr collisions has been performed in the pseudorapidity phase space. Multifractal moments, Gq, as the function of pseudorapidity bin size for different order of the moments, q, have been calculated. The power-law behaviour has been observed in the considered data sets. The variations of multifractal dimension, Dq, and the multifractal spectral function, f(aq), with order of the moments, q, have been studied thoroughly. Dq is found to decrease with increasing order of moments, q, indicating thereby a self-similar behaviour in the multiparticle production for the considered collisions. We have also found a concave downward curve of multifractal spectral function with maximum at q = 0.
文摘A systematic analysis of the data on 14.5A GeV/c 28Si-nucleus collisions is carried out to investigate the behaviours of Renyi dimensions, Dq and Multifractal Spectral Function, f(αq). The Renyi dimensions, Dq are observed to decrease with increasing order of the moments, q. However, the Multifractal Spectra are concave downwards with their maxima occurring around αq =1.21±0.01. A continuous curve representing Multifractal Spectral Function, f(αq), characterizes manifestation of fluctuations in the rapidity space.
基金supported by the National Natural Science Foundation of China(Grant No.41202110)Open Fund of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation(Southwest Petroleum University)(Grant No.PLN201612)+1 种基金the Applied Basic Research Projects in Sichuan Province(Grant No.2015JY0200)Open Fund Project from Sichuan Key Laboratory of Natural Gas Geology(Grant No.2015trqdz07)
文摘Pore structure characteristics are important to oil and gas exploration in complex low-permeability reservoirs. Using multifractal theory and nuclear magnetic resonance （NMR）, we studied the pore structure of low-permeability sandstone rocks from the 4th Member （Es4） of the Shahejie Formation in the south slope of the Dongying Sag. We used the existing pore structure data from petrophysics, core slices, and mercury injection tests to classify the pore structure into three categories and five subcategories. Then, the T2 spectra of samples with different pore structures were interpolated, and the one- and three-dimensional fractal dimensions and the multifractal spectrum were obtained. Parameters a （intensity of singularity） andf（a） （density of distribution） were extracted from the multifractal spectra. The differences in the three fractal dimensions suggest that the pore structure types correlate with a andf（a）. The results calculated based on the multifractal spectrum is consistent with that of the core slices and mercury injection. Finally, the proposed method was applied to an actual logging profile to evaluate the pore structure of low-permeability sandstone reservoirs.
