Multifractal Theory Research Articles

Prediction of hysteretic soil and water characteristic curve of loess based on multifractal theory and improved physical statistics

Soil and water characteristic curve (SWCC) is an important soil parameter which is used to estimate various parameters to describe unsaturated soil hydrodynamic properties. Due to the large span of soil matric suction, this procedure is time-consuming and difficult to measure it in the laboratory. However it is of great significance to find a scientifically efficient and economically viable method to predict SWCC of loess soil. Based on the measurement of soil–water characteristic curves in the laboratory, this study predicted the drying curve (DC) based on the soil particle size distribution (PSD) fractal theory. It also used the domain model to predict the wetting curve (WC) based on the pore distribution, and finally obtained the complete soil–water characteristic curve of loess. These procedures improved the research status which using the drying curve to instead of the wetting curve, and this replace usually leads to a large calculation error and underestimates the safety of the slope. The method proposed in this study can quickly obtain the hysteretic soil–water characteristic curve of loess based on only the soil particle size distribution, improve the correlative calculation accuracy of unsaturated loess, and play an important role in predicting the hydraulic parameters of loess soil.

An Improved Rock Resistivity Model Based on Multi-Fractal Characterization Method for Sandstone Micro-Pore Structure Using Capillary Pressure

Micro-pore structures are an essential factor for the electrical properties of porous rock. Theoretical electrical conductivity models considering pore structure can highly improve the accuracy of reservoir estimation. In this study, a pore structure characterization method based on a multi-fractal theory using capillary pressure is developed. Next, a theoretical electrical conductivity equation is derived based on the new pore structure characterization method. Furthermore, a distinct interrelationship between fractal dimensions of capillary pressure curves (Dv) and of resistivity index curves (Dt and Dr) is obtained. The experimental data of 7 sandstone samples verify that the fitting result by the new pore structure characterization method is highly identical to the experimental capillary pressure curves, and the accuracy of the improved rock resistivity model is higher than the Archie model. In addition, capillary pressure curves can be directly converted to resistivity index curves according to the relationship model between fractal dimensions of capillary pressure curves (Dv) and resistivity index curves (Dt and Dr). This study provides new ideas to improve the accuracy of pore structure characterization and oil saturation calculation; it has good application prospects and guiding significance in reservoir evaluation and rock physical characteristics research.

Analysis and Warning Prediction of Tunnel Deformation Based on Multifractal Theory

To better analyze the fluctuation characteristics and development law of tunnel deformation data, multifractal theory is applied to tunnel deformation analysis. That is, the multifractal detrended fluctuation analysis (MF-DFA) model is first utilized to carry out the multifractal characterization of tunnel deformation data. Further, Mann–Kendall (M–K) analysis is utilized to construct the dual criterion (∆α indicator criterion and ∆f(α) indicator criterion) for the tunnel deformation early warning study. In addition, the particle swarm optimization long-short-term memory (PSO-LSTM) prediction model is used for predicting tunnel settlement. The results show that, in reference to the tunnel warning level criteria and based on the Z-value results of the indicator criterion, the warning level of all four sections is class II. At the same time, through the analysis of tunnel settlement predictions, the PSO-LSTM model has a better prediction effect and stability for tunnel settlement. The predicted results show a slow increase in tunnel settlement over the next 5 days. Finally, the tunnel warning level and the predicted results of tunnel settlement are analyzed in a comprehensive manner. The deformation will increase slowly in the future. Therefore, monitoring and measurement should be strengthened, and disaster preparedness plans should be prepared.

Analysis of the effect of different pretreatment conditions on pore structure heterogeneity of low-rank coal based on multifractal theory

Analysis of the effect of different pretreatment conditions on pore structure heterogeneity of low-rank coal based on multifractal theory

УМОВИ ВИКОРИСТАННЯ КОНФОРМНИХ ВІДОБРАЖЕНЬ ДЛЯ ВИВЧЕННЯ ФРАКТАЛЬНОГО СТИСНЕННЯ ІНФОРМАЦІЇ

To describe the properties of self-similarity and invariance observed in various physical situations, the theory of fractals and multifractals is actively used in modern science. We consider a conformal mapping of the first kind, which is given by the entire linear function w = az + b, where w, z are complex variables, a, b are complex constants, a ≠ 0 . With its help, affine transformations are performed to construct the Sierpinski triangle and the Koch curve by specifying the functions w3(z) and finding the coefficients Re аі, Im аі, Re bi, Im bi, і = 1,2,3 or і = 1,2,3,4. These coefficients encode the image of the object and it can be unambiguously reconstructed by them. It is determined that the method in which self-similar regions in an object are detected and conformal mapping coefficients are found for them works under the condition that each such mapping is compressive. Only then will Banach’s fixed point theorem ensure image collection during decompression. This method of compressing graphic information is called fractal.

Time-Frequency Response of Acoustic Emission and Its Multi-Fractal Analysis for Rocks with Different Brittleness under Uniaxial Compression

The occurrence of rock burst hazards is closely related to the brittleness of rocks. Current research has paid less attention to the in-depth relationship between rock brittleness and acoustic emission (AE) signal characteristics and precursor information caused by rock fracture. Therefore, in order to further improve the accuracy of the AE monitoring of rockburst hazards, uniaxial compression tests were carried out and AE were monitored for rocks with different brittleness (yellow sandstone, white sandstone, marble, and limestone) in this paper. The relationship between the mechanical properties and the time-frequency characteristics of the AE was analyzed. In addition, the multi-fractal theory was introduced to further deconstruct and mine the AE signals, and the multi-fractal characteristics of AE from rocks with different brittleness were investigated. The results show that the stronger the brittleness of the rock, the higher the main frequency and main frequency amplitude of the AE. Brittleness is positively correlated with the multi-fractal parameter Δα (uniformity of data distribution) and negatively correlated with Δf (frequency difference between large and small data). In addition, the dynamics of Δα and Δf provide new indicators for AE monitoring of rock stability, and their abrupt changes can be regarded as precursors of failure. The weaker the brittleness of the rock, the earlier the failure precursor is and the more significant it is. This has potential engineering application value, which can help identify rockburst precursors and take timely protective measures to ensure engineering safety.

Identificating favourable reservoir areas of coalbed methane based on multifractal and gated circulation unit

Identificating favourable reservoir areas of Coalbed methane (CBM) is significant for improving economics of CBM project. However, accurately identification of favourable areas from CBM reservoir with strong heterogeneity of reservoir parameters is challenging. In previous researches, some traditional models were applied to identify favourable areas of CBM reservoir, however there is a widely gap between the evaluation result and reality distribution of high-yield areas of CBM reservoir. For solving above problem, identifying favourable reservoir area with strong heterogeneity is conducted with deep learning and multifractal theory. In identification process, firstly the fracture characteristics of the research area is calculated with multifractal theory to generate weighted data layer. Secondly a deep learning model is constructed with the genetic algorithm and door circulation unit to identify favourable reservoir areas of CBM and is verifyed with the block of Fanzhuang-Zhengzhuang located in the Qinshui coalfield of China. The fitting degree of the above model and the known CBM wells is better than the previous methods, and the accuracy of the model reaches 87%, which indicates that the method is feasible and provides a new way for identificating favourable reservoir areas of CBM under complex geological conditions.

Experimental and digital investigations of heterogeneity in lower cretaceous carbonate reservoir using fractal and multifractal concepts

Characterization and prediction of reservoir heterogeneity are crucial for hydrocarbon production. This study applies the multifractal theory using both numerical and experimental data to characterize quantitatively the heterogeneity of pore structures in Lower Cretaceous limestone reservoir from the United Arab Emirates. Fractal dimensions calculated from three dimensional digital images showed good correlation (R2 = + 0.69) with experimental high-pressure mercury injection (HPMI) measurements. Moreover, both experimental and numerical fractal dimensions correlate well with experimental HPMI porosity measurements. Multifractal parameters such as the non-uniformity degree of the pore structures Δα, the asymmetry degree in the vertical axis Δf(α), the concentration of pore size distribution α0 and the asymmetry degree in the horizontal axis Rd estimated from digital and experimental data correlated well and revealed ability to quantitatively describe samples heterogeneity. The ranges of digital and experimental multifractal parameters provided the means to differentiate between homogeneous and heterogeneous samples.

Renyi entropy analysis of a deep convolutional representation for texture recognition

Despite the recent success of convolutional neural networks in computer vision in general, texture images still pose an important challenge to those models, especially when dealing with textures “in the wild”. In this context, deep learning models can benefit from the introduction of features long known to be useful for texture modeling. And that is the case of entropy, a measure of texture regularity that has played an important role in classical computer vision. Based on this observation, here we propose an alternative analysis over deep convolutional neural features based on entropy for texture representation and, particularly, texture classification. More precisely, we couple a module to the convolutional backbone that locally computes the Renyi entropy of the latent representation at multiple levels. The rationale for using Renyi entropy is essentially two-fold: (1) It connects the concept of entropy with multifractal theory, another well explored measure especially in domains of application where we seek some physical interpretation of the descriptors, e.g., in medicine, biology, and others; (2) It has an extra degree of freedom (α parameter) that can be fine-tuned. The main contribution of this study is the development of a strategy that can improve the performance of convolutional neural networks in texture recognition tasks, adding low computational cost. The effectiveness of our method is verified in texture classification of benchmark datasets, as well as in a practical task of plant species identification. Our method achieves a competitive accuracy of 84.5% in the classification of KTH-TIPS-2b and 80.9% in FMD, which are two challenging benchmark databases. Besides, an accuracy of 91.6% is obtained in the plant identification application, to our knowledge outperforming all the results previously published on this task. In both scenarios, the proposed descriptors outperform several approaches from the state-of-the-art, confirming the method potential as a rich and robust solution for texture analysis in general. The results also suggest that information-theoretical measures like entropy can be a reliable source of information to compose a precise and robust latent representation of texture images.

CALCULATION OF MATERIAL QUALITY CRITERIA USING FRACTAL THEORY

Problem statement. Changing the parameters of standard technology can significantly change the properties of rolled iron in a wide range of values. Regulatory and technical industry documentation regulates only the hardness indicators of cast iron rolls, and the requirements for mechanical characteristics and wear resistance are not indicated due to the influence of many technological parameters. Therefore, an important aspect is the prediction for quality indicators of cast iron due to the use of mathematical modeling, in particular the theory of fractals. Materials and methods. Cast iron rolls with a pearlite matrix were studied. The mechanical properties of the working area for cast-iron graded rolled rolls produced by OJSC “Dniprovskyi zavod protnykhnykh valkov”, Dnipro, were determined on standard equipment using INSTRON and CD-40 machines, PSV 5 pendular digger, Shore hardness tester. The microstructure of the rolls was analyzed at a magnification of 200 times. The results of the experiment. As a result of the experiment, it was established that the best among analyzed sensitivity of mechanical properties to dimensional characteristics of carbides is observed for fractal, information and correlation dimensions. Therefore, it is advisable to use these dimensional estimates of carbides in the future to predict the mechanical properties of the working zone for rolled iron with lamellar graphite. To predict the mechanical properties of rolled cast iron with lamellar graphite, it is advisable to use dimensional estimates of graphite and carbides with an increase in the structure of ´200. Conclusions. The analysis of the obtained results showed the promise of using the theory of multifractals for the quantitative assessment of the structural elements of rolled cast iron rolls with a complex geometric shape. This approach makes it possible to use statistical estimates of the dimensions of graphite and carbides to predict and correct the quality indicators of roll metal according to the obtained equations (3-6) along with traditional methods of quantitative metallography, which evaluate their geometric characteristics: shape, distribution, dimensions (length, diameter) and content.

The Effect of Thermal Maturity on the Pore Structure Heterogeneity of Xiamaling Shale by Multifractal Analysis Theory: A Case from Pyrolysis Simulation Experiments

Shale oil and gas, as source-reservoir-type resources, result from organic matter hydrocarbon generation, diagenesis, and nanoscale pore during the evolution processes, which are essential aspects of shale gas enrichment and reservoir formation. To investigate the impact of diagenetic hydrocarbons on shale pore heterogeneity, a thermal simulation of hydrocarbon formation was conducted on immature shale from the Middle Proterozoic Xiamaling Formation in the Zhangjiakou area, covering stages from mature to overmature. Nuclear magnetic resonance (NMR) instruments analyzed the microstructure of the thermally simulated samples, and the multifractal model quantitatively assessed pore development and heterogeneity in the experimental samples. The results reveal that the quartz and clay mineral contents show alternating trends with increasing temperature. Organic matter dissolution intensifies while unstable mineral content decreases, promoting clay mineral content development. Pyrolysis intensity influences Total Organic Carbon (TOC), which reduces as hydrocarbons are generated and released during simulation. Porosity exhibits a decreasing–increasing–decreasing trend during thermal evolution, peaking at high maturity. At maturity, hydrocarbon generation obstructs pore space, resulting in higher levels of bound fluid porosity than those of movable fluid porosity. Conversely, high maturity leads to many organic matter micropores, elevating movable fluid porosity and facilitating seepage. Shale pore heterogeneity significantly increases before 450 °C due to the dissolution of pores and the generation of liquid and gas hydrocarbons. In the highly overmature stage, pore heterogeneity tends to increase slowly, correlated with the generation of numerous micro- and nano-organic matter pores.

Multifractal scaling analyses of the spatial diffusion pattern of COVID-19 pandemic in Chinese mainland

Revealing spatio-temporal evolution regularity in the spatial diffusion of epidemics is helpful for preventing and controlling the spread of epidemics. Based on the real-time COVID-19 datasets by prefecture-level cities, this paper is devoted to exploring the multifractal scaling in spatial diffusion pattern of COVID-19 pandemic and its evolution characteristics in Chinese mainland. The ArcGIS technology and box-counting method are employed to extract spatial data and the least square regression based on rescaling probability (μ-weight method) is used to calculate fractal parameters. The results show multifractal distribution of COVID-19 pandemic in China. The generalized correlation dimension spectrums are inverse S-shaped curves, but the fractal dimension values significantly exceed the Euclidean dimension of embedding space when moment order q«0. The local singularity spectrums are asymmetric unimodal curves, which slant to right. The fractal dimension growth curves are shown as quasi S-shaped curves. From these spectrums and growth curves, the main conclusions can be drawn as follows: First, self-similar patterns developed in the process of COVID-19 pandemic, which seems to be dominated by multifractal scaling law. Second, the spatial pattern of COVID-19 across China can be characterized by global clustering with local disordered diffusion. Third, the spatial diffusion process of COVID-19 in China experienced four stages, i.e., initial stage, the rapid diffusion stage, the hierarchical diffusion stage, and finally the contraction stage. This study suggests that multifractal theory can be utilized to characterize spatio-temporal diffusion of COVID-19 pandemic, and the case analyses may be instructive for further exploring natural laws of spatial diffusion.

Multifractal Characteristics of Uranium Grade Distribution and Spatial Regularities in a Sandstone-Type Uranium Deposit in Xinjiang, China

Based on an analysis of the spatial distribution of uranium grade in 338 boreholes of a uranium deposit in Xinjiang, the enrichment and spatial variation of uranium ore in two stopes of the deposit are discussed using multifractal theory. The distribution characteristics of the uranium ore of the two stopes are studied by multifractal parameters: the scaling exponent of mass τ(q), the scaling exponent α(q) of each sub-set and its corresponding fractal dimension f(α), the fractal dimension D0 and information dimension D1. The differences of uranium distribution in the two stopes can be quantified well by using multifractal spectrum and multifractal parameters such as Δα, Δf and R. After a comprehensive multifractal distribution analysis, 10 m × 10 m is defined as a fence unit, and the window sizes ε=3,6,9⋯,45 are set; the singularity exponents α of the two stopes are calculated by using this element concentration–area method. The results show that the multifractal theory and model can organically combine spatial structure information, scale change information and anisotropy information to obtain low-grade and weak mineral resources information and can effectively distinguish complex and superimposed anomalies. This will provide a basis for the local concentration and spatial variation rules of uranium distribution and the design of the parameters of the leaching uranium mining well site.

Analyzing the influence of Cerchar abrasiveness index on particle size distribution in ball milling based on multifractal theory

This study investigates the influence of cerchar abrasiveness index (CAI) on the multifractal parameters of particle size distribution (PSD) in the ball milling from both global and local perspectives. The results indicate that with increase of CAI, the generalized dimension spectrum parameters D(0) and D(1) exhibit three distinct stages, and the concentration of PSD gradually decreases. The variations in singular spectrum parameters Δα and Δf reveal that, for CAI below 1.0, the main variation in milling is dominated by large particle, and the local heterogeneity changes are not significant. As the CAI exceeds 1.0, variability of particle sizes approaches each other, and the local heterogeneity shows a trend of increasing and then decreasing. As CAI increases, the point of maximum heterogeneity in PSD becomes more concentrated towards the later stages of milling. Finally, the micro-mechanisms of differences in CAI and multifractal parameters were discussed by considering mineralogical composition and bond work index of individual minerals.

Characteristics of energy evolution and acoustic emission response of concrete under the action of acidic drying-saturation processes cycle

The continuous fluctuation in the acidic mine water level of the underground reservoir will affect the artificial dam's strength and stability. The uniaxial compression test of C25 concrete under different drying-saturation processes cycle (DSPC) numbers and pH solutions were performed. The degradation mechanism of mechanical properties of concrete under acidic DSPC was investigated; the calculation formula for the elastic strain energy at peak stress has been corrected and the energy evolution law has been obtained; besides, the evolution characteristics of acoustic emission (AE) parameters were studied using multi-fractal theory and the precursor characteristics of concrete failure were obtained. The results revealed that increasing the DSPC times or decreasing the pH caused an increase in the saturation moisture content of the concrete, the strain and elastic strain energy of the concrete at peak stress increased, a drop in the ultrasonic velocity, the uniaxial compressive strength (UCS), the elastic modulus (EM) and the overall input energy. The accumulated ringing count and accumulated energy of AE dramatically increased before the concrete was close to failure, and numerous low-frequency and high-amplitude signals started to appear. The information mentioned above might be considered a short-impending warning of concrete failure. During the plastic deformation, the large increase of the multi-fractal parameter Δα and the significant drop of Δf might be viewed as early warning for concrete failure. This research will offer some theoretical direction for artificial dam design and long-term stability monitoring in underground reservoirs.

Multifractal characteristics of fatigue cracks in the full-scale reinforced concrete hollow-slab beams

Highway Reinforced concrete (RC) bridges bear the repeated vehicle loads for a long time, promoting cracks' sprouting and development. Establishing a quantitative evolution model of cracks will improve the management and maintenance of similar bridges. Therefore, this paper introduces the multifractal theory into crack characterization and carries out the study on the multifractal characteristics of fatigue cracks in full-scale RC hollow slabs. Firstly, the basic procedure of the multifractal analysis method for concrete cracks is introduced, and the sensitivity of the multifractal spectrum under different influencing factors is analyzed. Secondly, the basic information and scheme of the experimental beam are introduced. The experimental results and the development law of fatigue cracks are analyzed. Finally, the variation law of the multifractal spectrum with cycle number is analyzed based on the multifractal theory, and a simplified evolution model of fractal dimension (FD) under fatigue load is established based on the experimental results. The experimental results prove that the multifractal theory is effective in describing the cracking state of RC members under fatigue load. The fatigue cracks' development of the experimental beam presents an obvious three-stage pattern: rapid stage, stable stage, and destabilized stage. The FDs of fatigue cracks also develop in a three-stage pattern along with cycle number, which can be expressed by a linear equation of cycle percentage. The evolution model can provide technical support for the maintenance decisions of RC bridges in service.

Multifractal estimation of NMR T2 cut-off value in low-permeability rocks considering spectrum kurtosis: SMOTE-based oversampling integrated with machine learning

The transverse relaxation time (T2) cut-off value plays a crucial role in nuclear magnetic resonance for identifying movable and immovable boundaries, evaluating permeability, and determining fluid saturation in petrophysical characterization of petroleum reservoirs. This study focuses on the systematic analysis of T2 spectra and T2 cut-off values in low-permeability reservoir rocks. Analysis of 36 low-permeability cores revealed a wide distribution of T2 cut-off values, ranging from 7 to 50 ms. Additionally, the T2 spectra exhibited multimodal characteristics, predominantly displaying unimodal and bimodal morphologies, with a few trimodal morphologies, which are inherently influenced by different pore types. Fractal characteristics of pore structure in fully water-saturated cores were captured through the T2 spectra, which were calculated using generalized fractal and multifractal theories. To augment the limited dataset of 36 cores, the synthetic minority oversampling technique was employed. Models for evaluating the T2 cut-off value were separately developed based on the classified T2 spectra, considering the number of peaks, and utilizing generalized fractal dimensions at the weight <0 and the singular intensity range. The underlying mechanism is that the singular intensity and generalized fractal dimensions at the weight <0 can detect the T2 spectral shift. However, the T2 spectral shift has negligible effects on multifractal spectrum function difference and generalized fractal dimensions at the weight >0. The primary objective of this work is to gain insights into the relationship between the kurtosis of the T2 spectrum and pore types, as well as to predict the T2 cut-off value of low-permeability rocks using machine learning and data augmentation techniques.

The Effects of Stochastic Circular Pores on Splitting Tensile Behavior of Concrete Based on the Multifractal Theory

Concrete naturally contains a large number of circular-like stochastic pores which weaken the tensile strength of concrete and change the crack propagation path. This study investigates the influences of the size distribution and the spatial distribution of stochastic pores on the fracture behavior of concrete based on the splitting tensile test. The mesoscale model of concrete containing coarse aggregate, mortar, interface transition zone (ITZ), and circular pores is established to simulate the crack initiation, propagation, and coalescence of concrete. Concrete samples with a single hole are prepared to verify the effectiveness of the numerical simulation method. Numerical tests are conducted on numerous mesoscale concrete samples with various porosities, pore size distributions, and pore spatial distributions. The numerical simulation results indicate that the tensile strength decreases with the increase of pore size at the same porosity. Based on multifractal theory, a quantitative indicator to describe the spatial distribution uniformity of concrete stochastic pores is proposed. There is a positive correlation between the spatial distribution uniformity of stochastic pores and the tensile strength. The stochastic circular pores can have a profound effect on the concrete’s fracture pattern, which results in three typical macro-crack patterns in the numerical simulation of the splitting tensile test. The presented results deepen the understanding of the influence of stochastic circular pores on the tensile mechanical properties of concrete and provide a reference for the design of concrete structures.

Application of Multifractal Theory for Determination of Fluid Movability of Coal-Measure Sedimentary Rocks Using Nuclear Magnetic Resonance (NMR)

A precise evaluation of the fluid movability of coal sedimentary rock is crucial to the effective and secure utilization of coal measures gas reserves. Furthermore, its complex pore structure and diverse mineral components impact the flow properties of fluids in pore structures, causing accurate evaluation of fluid mobility to be extremely challenging. Nuclear magnetic resonance (NMR) technology is currently a prevalent technique to assess unconventional reservoirs due to its capacity to acquire abundant reservoir physical property data and determine fluid details. The free-fluid volume index (FFI) is a crucial factor in assessing fluid movability in the application of NMR technology, which can only be derived through intricate NMR saturation and centrifugation experiments This research utilized nuclear magnetic resonance (NMR) tests on 13 classic coal-measure sedimentary rock samples of three lithologies to reveal the FFI value. Moreover, the association between mineral components, pore structure parameters, and FFI was then extensively analyzed, and a prediction model for FFI was constructed. The results indicate that the T2 spectra of sandstone and shale own a bimodal distribution, with the principal point between 0.1 and 10 ms and the secondary peak between 10 and 100 ms. The majority of the T2 spectra of mudstone samples provide a unimodal distribution, with the main peak distribution range spanning between 0.1 and 10 ms, demonstrating that the most of the experimental samples are micropores and transition pores. The calculated results of the FFI range from 7.65% to 18.36%, and depict evident multifractal properties. Porosity, the content of kaolinite, multifractal dimension (Dq), and the FFI are linearly positively correlated. In contrast, the content of chlorite, illite, multifractal dimension subtraction (Dmin − Dmax), multifractal dimension proportion (Dmin/Dmax), and singularity strength (Δα) possess a negative linear correlation with the FFI, which can be further used for modeling. On the basis of the aforementioned influencing factors and the FFI experimental values of eight core samples, an FFI prediction model was constructed through multiple linear regression analysis. The accuracy of the prediction model was validated by utilizing this approach to five samples not included in the model development. It was revealed that the prediction model produced accurate predictions, and the research findings may serve as a guide for the classification and estimation of fluid types in coal reservoirs.

Multifractal analysis of the heterogeneity of nanopores in tight reservoirs based on boosting machine learning algorithms

Exploring the geological factors that affect fluid flow has always been a hot topic. For tight reservoirs, the pore structure and characteristics of different lithofacies reveal the storage status of fluids in different reservoir environments. The size, connectivity, and distribution of fillers in different sedimentary environments have always posed a challenge in studying the microscopic heterogeneity. In this paper, six logging curves (gamma-ray, density, acoustic, compensated neutron, shallow resistivity, and deep resistivity) in two marker wells, namely, J1 and J2, of the Permian Lucaogou Formation in the Jimsar Basin are tested by using four reinforcement learning algorithms: LogitBoost, GBM, XGBoost, and KNN. The total percent correct of training well J2 is 96%, 96%, 96%, and 96%, and the total percent correct of validation well J1 is 75%, 68%, 72%, and 75%, respectively. Based on the lithofacies classification obtained by using reinforcement learning algorithm, micropores, mesopores, and macropores are comprehensively described by high-pressure mercury injection and low-pressure nitrogen gas adsorption tests. The multifractal theory servers for the quantitative characterization of the pore distribution heterogeneity regarding different lithofacies samples, and as observed, the higher probability measure area of the generalized fractal spectrum affects the heterogeneity of the local interval of mesopores and macropores of the estuary dam. In the micropore and mesopore, the heterogeneity of the evaporation lake showed a large variation due to the influence of the higher probability measure area, and in the mesopore and macropore, the heterogeneity of the evaporation lake was controlled by the lower probability measure area. According to the correlation analysis, the single-fractal dimension is well related to the multifractal parameters, and the individual fitting degree reaches up to 99%, which can serve for characterizing the pore size distribution uniformity. The combination of boosting machine learning and multifractal can help to better characterize the micro-heterogeneity under different sedimentary environments and different pore size distribution ranges, which is helpful in the exploration and development of oil fields.