Log Resolution Research Articles

Improving density logging resolution by VMD-CEEMDAN-ICWT method and its application in thin layer identification

Data identification of density logging is a crucial foundation for logging interpretation. Because of device and other external variables, noise will inevitably be mixed in data acquisition process. Moreover, as the main technique for identifying thin reservoirs, density logging exhibits a low resolution. In this study, a new de-noising and distinguish thin-layer method is proposed, namely VMD-CEEMDAN-ICWT method. The VMD-CEEMDAN-ICWT method is designed to combine an adaptive Improved-Continuous-Wavelet-Transform (ICWT) structure, Variational-Mode-Decomposition (VMD) wavelet decomposition structure, and Complete-Ensemble-Empirical-Mode-Decomposition with Adaptive-Noise (CEEMDAN) wavelet reconstruction structure with global denoising characteristics. It integrates the superiorities of VMD, CEEMDAN and ICWT method. Ultimately, empirical-mode-decomposition (EMD), discrete-wavelet-transform (DWT), continuous-wavelet-transform (CWT) and the proposed method are utilized to analyze real data. The findings indicate that the reconstructed density log by VMD-CEEMDAN-ICWT method shows higher vertical resolution. The density log resolution about thin layer increases from 25 cm to 12 cm. It makes density logging curves more capable of identifying reservoirs, which provides high-quality data for further exploration and exploitation of oil and gas.

Enhancing Reservoir Zonation through Triple Porosity System: A Case Study

Summary The Asmari-Jahrom reservoirs, located in southwest Iran, are recognized as one of the major fractured reservoirs in the world. Understanding the role of fractures in enhancing hydrocarbon flow and permeability is of utmost importance. In this study, petrophysical conventional logs [neutron porosity (NPHI), density (RHOB), sonic (DT), and gamma ray (GR)] and advanced image logs [formation microresistivity imaging (FMI)] were used to investigate the reservoir properties. The novelty of this study lies in the implementation of triple porosity on reservoir quality and identification of flow units in Asmari-Jahrom reservoirs using petrophysical and borehole image logs. By quantifying fracture and vuggy porosity and correlating them with velocity deviation log and fracture parameters [fracture aperture (VAH) and fracture density (VDC)], it was demonstrated that fracture porosity is directly related to VAH. High peaks were observed in fracture parameters, particularly in VAH diagrams where the velocity deviation log was negative and low. Total porosity from density logs was found to match secondary porosity from petrophysical logs, validating FMI results. However, FMI log resolution was higher, enabling clearer identification of fracture porosity peaks. The velocity deviation log indicated that the predominant type of porosity in the reservoir was matrix (primary) porosity. However, fracture and vuggy porosity were also observed in certain zones. Based on indirect evidence such as drilling mud loss, porosity type (matrix, fracture, and vuggy), porosity amount, and oil saturation, 18 zones were identified to determine quality zones with appropriate reservoir quality. Asmari-Jahrum reservoirs were found to possess high storage and flow capacity. The presence of multiple fracture types, especially longitudinal fractures, contributed to the development of secondary porosity and enhanced flow unit quality. Despite their complexity, these fractured carbonate reservoirs were analyzed comprehensively through integrated petrophysical and FMI log interpretation, enabling optimized reservoir performance and facilitating hydrocarbon production.

Arithmetic and geometric deformations of threefolds

AbstractWe show that mixed‐characteristic and equi‐characteristic small deformations of 3‐dimensional canonical (resp., terminal) singularities with perfect residue field of characteristic are canonical (resp., terminal). We discuss applications to arithmetic and geometric families of 3‐dimensional Fano varieties and minimal models with canonical singularities. Our results are contingent upon the existence of log resolutions for fourfolds.

Identification of Shale Lithofacies from FMI Images and ECS Logs Using Machine Learning with GLCM Features

The identification of sedimentary structures in lithofacies is of great significance to the exploration and development of Paleogene shale in the Boxing Sag. However, due to the scale mismatch between the thickness of laminae and the vertical resolution of conventional wireline logs, the conventional lithofacies division method fails to realize the accurate classification of sedimentary structures and cannot meet the needs of reservoir research. Therefore, it is necessary to establish a lithofacies identification method with higher precision from advanced logs. In this paper, a method integrating the gray level co-occurrence matrix (GLCM) and random forest (RF) algorithms is proposed to classify shale lithofacies with different sedimentary structures based on formation micro-imager (FMI) imaging logging and elemental capture spectroscopy (ECS) logging. According to the characteristics of shale laminae on FMI images, GLCM, an image texture extraction tool, is utilized to obtain texture features reflecting sedimentary structures from FMI images. It is proven that GLCM can depict shale sedimentary structures efficiently and accurately, and four texture features (contrast, entropy, energy, and homogeneity) are sensitive to shale sedimentary structures. To accommodate the correlation between the four texture features, the random forest algorithm, which has been proven not to be affected by correlated input features, is selected for supervised lithofacies classification. To enhance the model’s ability to differentiate between argillaceous limestone and calcareous mudstone, the carbonate content and clay content calculated from the ECS logs are involved in the input features. Moreover, grid search cross-validation (CV) is implemented to optimize the hyperparameters of the model. The optimized model achieves favorable performance on training data, validation data, and test data, with average accuracies of 0.84, 0.79, and 0.76, respectively. This study also discusses the application of the classification model in lithofacies and production prediction.

A novel physics-based resolution improvement method for neutron-density log

In the later stages of oilfield development, the accurate identification of thin reservoirs become increasingly crucial for oil and gas exploration. However, conventional logs have limited vertical resolution, making it challenging to identify thin reservoirs. This results in potential hydrocarbon layers getting overlooked during exploration. To address this issue, a novel resolution enhancement method for density and neutron porosity logs based on physical constraint optimization is proposed. The proposed method involves three main steps: (1) developing an objective function that relates the true formation density and porosity to the measurement based on the physics of nuclear, (2) setting density neutron cross-constraints using the volumetric model of logging interpretation, and (3) establishing the objective function matrix equations using sliding window technology and solving the matrix equations using the constrained least square method to obtain high-resolution density and neutron porosity logs. The proposed method is evaluated using both synthetic and field logs obtained from compensated density and compensated neutron tools. The results demonstrate an effective improvement in neutron porosity and density log resolution to 15 cm, which is significantly enhanced compared to the typical vertical resolution of 2 ft. This study offers a new perspective for enhancing the resolution of logs and contributes to the exploration and development of thin oil and gas resources. And the proposed method could be used in future exploration and production projects to identify potential hydrocarbon layers that might have been overlooked by conventional logs.

MDFULog: Multi-Feature Deep Fusion of Unstable Log Anomaly Detection Model

Effective log anomaly detection can help operators locate and solve problems quickly, ensure the rapid recovery of the system, and reduce economic losses. However, recent log anomaly detection studies have shown some drawbacks, such as concept drift, noise problems, and fuzzy feature relation extraction, which cause data instability and abnormal misjudgment, leading to significant performance degradation. This paper proposes a multi-feature deep fusion of an unstable log anomaly detection model (MDFULog) for the above problems. The MDFULog model uses a novel log resolution method to eliminate the dynamic interference caused by noise. This paper proposes a feature enhancement mechanism that fully uses the correlation between semantic information, time information, and sequence features to detect various types of log exceptions. The introduced semantic feature extraction model based on Bert preserves the semantics of log messages and maps them to log vectors, effectively eliminating worker randomness and noise injection caused by log template updates. An Informer anomaly detection classification model is proposed to extract practical information from a global perspective and predict outliers quickly and accurately. Experiments were conducted on HDFS, OpenStack, and unstable datasets, showing that the anomaly detection method in this paper performs significantly better than available algorithms.

On the relative minimal model program for fourfolds in positive and mixed characteristic

AbstractWe show the validity of two special cases of the four-dimensional minimal model program (MMP) in characteristic$p>5$: for contractions to${\mathbb {Q}}$-factorial fourfolds and in families over curves (‘semistable MMP’). We also provide their mixed characteristic analogues. As a corollary, we show that liftability of positive characteristic threefolds is stable under the MMP and that liftability of three-dimensional Calabi–Yau varieties is a birational invariant. Our results are partially contingent upon the existence of log resolutions.

Multi-view and multi-scale super-resolution method of logging curves based on fractal theory.

With the increasing development of unconventional reservoirs around the world, there is an increasing need to enhance the level of geological characterization. Obviously, since the well loggings are one of the most important data to obtain a fine-scale reservoir model, obtaining well loggings with sufficiently high vertical resolution has always been an important issue and challenge. Therefore, due to its low cost and less time-consuming, employing an advanced signal processing technique to enhance the vertical resolution of loggings has always been a research hotspot in the relevant literature. However, non-homogeneity of the target reservoir is not taken into account in the traditional methods such as vertical resolution matching and spline function interpolation. Furthermore, for state-of-the-art methods that employ different versions of shallow or deep machine learning models, how to adequately exploit the multi-scale shape and temporal information in the employed loggings has been a very challenging problem. To address the above problems, by combining the fractal theory with the long short-term memory network technique, a novel multi-view and multi-scale logging resolution enhancing method was proposed in this paper to make full use of the self-shape-similarity and temporal correlation information in the logging data. Experimental results show that, compared with bi-cubic linear interpolation, sparse representation, super-resolution convolutional neural network and random forest, more promising supper-resolution results can be obtained using the proposed method.

Upper Bounds for Roots of $b$-Functions, following Kashiwara and Lichtin

By building on a method introduced by Kashiwara (Invent. Math. 38 (1976/77), 33–53) and refined by Lichtin (Ark. Mat. 27 (1989), 283–304), we give upper bounds for the roots of certain b -functions associated to a regular function f in terms of a log resolution of singularities. As applications, we recover with more elementary methods a result of Budur and Saito (J. Algebraic Geom. 14 (2005), 269–282) describing the multiplier ideals of f in terms of the V -filtration of f and a result of the second-named author with Popa (Forum Math. Sigma 8 (2020), Paper No. e19, 41) giving a lower bound for the minimal exponent of f in terms of a log resolution.

Quantifying Centimeter- to Microscale Heterogeneities in Sedimentary, Compositional, and Geomechanical Properties of Siltstone Deposits in the Lower Triassic Montney Formation, Northeastern British Columbia, Canada

Abstract Geological and geomechanical heterogeneities exist at multiple scales in fine-grained rocks; however, the complexity of characteristics at the centimeter- to microscale heterogeneities remains poorly understood. In this study, 10 representative samples composed of three centimeter-scale sedimentary fabrics (massive siltstone (F1), stratified siltstone (F2), and bioturbated siltstone (F3)) were analyzed from the Lower Triassic Montney Formation in the Western Canada Sedimentary Basin to describe sedimentological heterogeneity based on sedimentary fabric, compositional, and geomechanical properties. Sedimentary fabric was determined based on grainsize and the distribution of bedforms, which subdivide the facies into four μm- to mm-scale microfacies (massive siltstone (MF1), pinstriped laminated siltstone (MF2), planar- to cross-stratified siltstone (MF3), and bioturbated siltstone (MF4)). Microscale analysis using a scanning electron microscope was used to characterize microfacies and their respective mineralogical makeup (matrix, cement, and framework grains). To quantify heterogeneity, sedimentary fabric was assessed using a CT scan complemented by elemental composition (using X-ray fluorescence), and geomechanical hardness (using Equotip Piccolo Bambino handheld microhardness tool) was collected within a 1 cm by 1 cm grid within each sample. Datasets were compared using a discriminant analysis (DA) to recognize trends between multiple properties and suggest that sedimentary fabric with the highest centimeter-scale aluminum content from XRF (avg. 11%) comprises microfacies that are comparatively matrix-rich consisting of micas, negligible calcite cement, and exhibit the lowest handheld hardness values (<770). Alternatively, sedimentary fabric with a higher elemental calcium component (avg. 18%) comprises microfacies that are matrix-poor, cemented by carbonate (calcite and dolomite) and quartz, and overall exhibit a positive trend with hardness measurement (770–850). Furthermore, to relate the elemental and geomechanical proxies to controls on rock mechanics, natural calcite-filled fractures within the studied core intervals were characterized. Fractures were subdivided into three types—brecciated, bed-parallel, and vertical to subvertical fractures with each type being constrained to a specific sedimentary fabric. Based on centimeter gridding, microscale analysis and the degree of fabric interbedding play a primary role on the variability in mechanical hardness and the geometry and termination of natural fractures. Collectively, this dataset provides insight into the influence that sedimentary fabric and the distribution of elemental composition has on mechanical properties and natural fractures below well log resolution. These findings can be used to better model and predict fine-grained deposit characteristics before undergoing hydraulic stimulation.

Bogomolov-Sommese vanishing and liftability for surface pairs in positive characteristic

We show that the Bogomolov-Sommese vanishing theorem holds for a log canonical projective surface (X,B) in large characteristic unless the Iitaka dimension of KX+⌊B⌋ is not equal to two. As an application, we prove that a log resolution of a pair of a normal projective surface and a reduced divisor in large characteristic lifts to the ring of Witt vectors when the Iitaka dimension of the log canonical divisor is less than or equal to zero. Moreover, we give explicit and optimal bounds on the characteristic unless their Iitaka dimensions are equal to zero.

Fractal characteristics of fractures in crystalline basement rocks: Insights from depth-dependent correlation analyses to 5 km depth

The scaling laws describing the spatial arrangement of fractures along six deep boreholes penetrating the crystalline rocks in the Rhine Graben were derived using a correlation analysis. Five of the wells, two to 5 km depth, were located at the Soultz geothermal site and one well to 5 km depth was located at Basel, some 150 km from Soultz. Five datasets were derived from borehole imaging logs, whilst one stemmed from the analysis of 810 m of continuous core at Soultz. The two differed inasmuch as the core dataset included essentially all fractures, whereas the image log dataset had few fractures narrower than 1–3 mm. The results of the analysis for all image datasets showed that the spatial arrangement of fractures followed fractal behavior at all scales from meters to several hundred meters, the largest scale amenable to assessment, and that the fractal dimensions were confined to the narrow range 0.85–0.9. However, the core dataset showed significant deviation from fractal behavior, the best-fit fractal dimension of 0.8 being somewhat lower than values obtained from imaging logs in neighboring wells. Eliminating fractures with apertures less than 1 mm from the core dataset to improve comparability led to even lower fractal dimension estimates, indicating the discrepancy was not due to imaging log resolution. Analysis of successive depth sections of the core log suggested the discrepancy was due to the presence of a localized zone between 1750 and 2070 m where the fractal organization is disturbed or takes a lower dimension than elsewhere. Aside from this zone, no systematic variation of fractal dimension with depth was observed in any dataset, implying that a single exponent together with intensity adequately describes the arrangement of fractures along the entire length of the boreholes. The results are relevant to the parameterization of DFN models of deep rock masses. • The fracture population derived from image logs followed fractal statistic with very similiar fractal dimensions. • The core-derived fracture dataset showed significant deviation from fractal behavior. • No systematic variations of fractal dimension with depth were observed in any of the datasets.

Cohomology of contact loci

We construct a spectral sequence converging to the cohomology with compact support of the m-th contact locus of a complex polynomial. The first page is explicitly described in terms of a log resolution and coincides with the first page of McLean’s spectral sequence converging to the Floer cohomology of the $m$‑th iterate of the monodromy, when the polynomial has an isolated singularity. Inspired by this connection, we conjecture that if two germs of holomorphic functions are embedded topologically equivalent, then the Milnor fibers of their tangent cones are homotopy equivalent.

Monodromy conjecture for log generic polynomials

A log generic hypersurface in $$\mathbb {P}^n$$ with respect to a birational modification of $$\mathbb {P}^n$$ is by definition the image of a generic element of a high power of an ample linear series on the modification. A log very-generic hypersurface is defined similarly but restricting to line bundles satisfying a non-resonance condition. Fixing a log resolution of a product $$f=f_1\ldots f_p$$ of polynomials, we show that the monodromy conjecture, relating the motivic zeta function with the complex monodromy, holds for the tuple $$(f_1,\ldots ,f_p,g)$$ and for the product fg, if g is log generic. We also show that the stronger version of the monodromy conjecture, relating the motivic zeta function with the Bernstein–Sato ideal, holds for the tuple $$(f_1,\ldots ,f_p,g)$$ and for the product fg, if g is log very-generic. Even the case $$f=1$$ is intricate, the proof depending on nontrivial properties of Bernstein–Sato ideals, and it singles out the class of log (very-) generic hypersurfaces as an interesting class of singularities on its own.

Hodge filtration on local cohomology, Du Bois complex and local cohomological dimension

Abstract We study the Hodge filtration on the local cohomology sheaves of a smooth complex algebraic variety along a closed subscheme Z in terms of log resolutions and derive applications regarding the local cohomological dimension, the Du Bois complex, local vanishing and reflexive differentials associated to Z.

Taming the Thunder Horse With Axes and Vectors

The Thunder Horse Field targets Middle Miocene deepwater turbiditic reservoirs. Despite being prolific, the mapping of the ~180 m thick, partly amalgamated reservoir sandstones is challenging. Seismic quality is reduced by the presence of salt structures. The salt overburden and high formation pressure require the use of heavy mud weights and oil-based drilling fluids, which limit the resolution and interpretation potential of borehole image logs (BHI). Halokinetic movements caused significant post-depositional deformation of the already complex gravity-driven sediment stack, and the reservoir beds drape against an E-W oriented salt wall. Consequently, the assessment and removal of the structural dip component are not trivial, and the evaluation of paleo-transport directions is considerably more complicated compared to undisturbed deepwater reservoirs. This paper illustrates the potential of eigenvector methods to BHI from Ruehlicke et al. (2019) for reconstructing the depositional slope and the architecture of mass transport complexes in the case of chaotic depositional settings and uncertain structural dip. Figures from Henry et al. (2018) are used wherein part axial analysis was performed on data from a group of Thunder Horse wells and presented in more detail.

Fracture permeability estimation utilizing conventional well logs and flow zone indicator

Characteristics of the natural open fractures on the oil and gas reservoirs is crucial in drilling and production planning. Direct methods of fractures studies such as core analysis and image log interpretation are usually not performed in all drilled wells in a field. Therefore, in absence of these data, the indirect methods can play an important role. In this study, an integrated algorithm is introduced to identify the fractures and estimate its permeability employing conventional well logs. First, open fractures were identified and their properties including density, aperture, porosity and permeability were estimated using FMI log. Subsequently, the fracture index log (FR_Index) was estimated utilizing conventional logs including density, micro-resistivity, sonic (compressional, shear and stoneley slownesses), and caliper logs. After that, the fracture index permeability was estimated by improving the FZI permeability equation. The coherence coefficient between two estimated fracture permeability logs is 0.66. A good correlation is observed on the high permeability zones, but the lower correlation on the low permeability zones. It is notified that, in the high fracture permeability zones, the conventional logs are heavily impacted by fracture permeability. However, due to lower vertical resolution of conventional logs compared with the image logs, the conventional logs are less influenced by less dense fracture zones. However, this algorithm can be used with acceptable accuracy in all uncored and image log wells.

A correction method based on geometric factor for resistivity log response of thinly laminated sand reservoirs: A case study

The log response of thin oil layers is greatly subject to environmental factors such as shoulder beds, resulting in errors high enough to influence the appraisal of rock lithology and fluid properties and increasing the difficulty of interpretation of logging curves and the effective evaluation of thinly laminated sand. The development of high-resolution logging instruments and logging curve processing technology improves the resolution and accuracy of logs, but with some limitations. So far, the geometric factor theory has been an effective approximate approach for induction logging correction. Based on the working principle of the induction/resistivity log and on previous studies, we have developed a new model to correct the resistivity log response of thin layers by taking advantage of the geometric factor. This method can improve the accuracy of the resistivity log for the calculation of porosity and water saturation. Our case study indicates that more reliable resistivity can be acquired to better characterize thin layers.

On subregular slices of the elliptic Grothendieck–Springer resolution

In \cite{davis19}, the author constructed an elliptic version of the Grothendieck-Springer resolution for the stack $\mathrm{Bun}_G$ of principal bundles under a simply connected simple group $G$ on an elliptic curve $E$. This is a simultaneous log resolution of a map from $\mathrm{Bun}_G$ to the union of the coarse moduli space of semistable $G$-bundles and a single stacky point. In this paper, we study singularities, resolutions and deformations coming from subregular slices of this elliptic Grothendieck-Springer resolution. More precisely, we construct explicit slices of $\mathrm{Bun}_G$ through all subregular unstable bundles, for every $G$. For $G \neq SL_2$, we describe the pullbacks of the elliptic Grothendieck-Springer resolution to these slices as concrete varieties, extending and refining earlier work of I. Grojnowski and N. Shepherd-Barron, who related these varieties to del Pezzo surfaces in type $E$. We use the resolutions to identify the singularities of the unstable locus of the subregular slices, and prove that that the extended coarse moduli space map gives deformations that are miniversal among torus-equivariant deformations with appropriate weights.

Natural fracture prediction in Keshen 2 ultra-deep tight gas reservoir based on R/S analysis, Kuqa Depression, Tarim Basin

Within ultra-deep tight sandstone gas reservoirs, natural fractures indicate significant effects on reservoir performance because they can serve as storage spaces for hydrocarbons and improve the permeability. Accurate prediction of natural fractures in ultra-deep reservoirs is critical to the exploration and development of tight gas in Keshen 2 Block of Kuqa Depression. In this study, several conventional logs are selected and the R/S analysis method is introduced to predict the development and distribution of natural fractures in ultra-deep tight sandstone reservoirs. Fracture development coefficient Q is calculated based on the second derivatives of lg(R/S) function and corresponding weight of each log parameter, which matches well with linear fracture density measured from image logs. There is a positive correlation between parameter Q and fracture density, higher Q values usually indicate larger fracture density. Factors causing mismatches between calculated parameter Q and fracture density are also analyzed. Fracture dip angle, fracture filling condition, vertical resolution of logs, multiple interpretations of conventional logs, and lateral detection difference between image and conventional logs may contribute to generate those false appearances. The results in this study are expected to provide new geological references for the exploration and development of ultra-deep tight gas in Keshen 2 Block of Kuqa Depression.