Complex Geological Models Research Articles

Improved Reservoir Porosity Estimation Using an Enhanced Group Method of Data Handling with Differential Evolution Model and Explainable Artificial Intelligence

Summary Reservoir characterization is critical to the oil and gas industry, influencing field development, production optimization, hydraulic fracturing, and reserves estimation decisions. Accurately estimating porosity is crucial for reservoir characterization, well planning, and production optimization in the oil and gas industry. Traditional porosity determination methods, such as porosimetry, geostatistical, and core analysis, often involve complex geological and geophysical models, which are expensive and time-consuming. This study used the integrated machine learning and optimization model of differential evolution (DE) with group method of data handling (GMDH-DE) to estimate the porosity using integrated well log and core data from the Mpyo oil field, Uganda. The GMDH-DE demonstrates superior performance compared with conventional GMDH, support vector regression (SVR), and random forest (RF), achieving a coefficient of determination (R2) of 0.9925 and a root mean square error (RMSE) of 0.0017 during training, an R² of 0.9845 with an RMSE of 0.0121 during testing, and when validated the R2 was 0.9825 with RMSE of 0.00018. A key novelty of this work is the integration of Shapley additive explanations (SHAP), which provides an interpretable analysis of the model’s input features. SHAP reveals that bulk density (RHOB) and neutron porosity (NPHI) are the most critical parameters for porosity estimation, offering valuable insight into features importance. The proposed GMDH-DE model and SHAP analysis represent a novel and independent approach for accurate porosity estimation and interpretability, significantly enhancing the efficiency and reliability of hydrocarbon exploration and development.

Poynting and polarization vectors mixed imaging condition of source time‐reversal imaging

AbstractSource time‐reversal imaging based on wave equation theory can achieve high‐precision source location in complex geological models. For the time‐reversal imaging method, the imaging condition is critical to the location accuracy and imaging resolution. The most commonly used imaging condition in time‐reversal imaging is the scalar cross correlation imaging condition. However, scalar cross‐correlation imaging condition removes the directional information of the wavefield through modulus operations to avoid the direct dot product of mutually orthogonal P‐ and S‐waves, preventing the imaging condition from leveraging the wavefield propagation direction to suppress imaging artefacts. We previously tackled this issue by substituting the imaging wavefield with the energy current density vectors of the decoupled wavefield, albeit at the cost of increased computational and storage demands. To balance artifact suppression with reduced computational and memory overhead, this work introduces the Poynting and polarization vectors mixed imaging condition. Poynting and polarization vectors mixed imaging condition utilizes the polarization and propagation direction information of the wavefield by directly dot multiplying the undecoupled velocity polarization vector with the Poynting vector, eliminating the need for P‐ and S‐wave decoupling or additional memory. Compared with scalar cross‐correlation imaging condition, this imaging condition can accurately image data with lower signal‐to‐noise ratios. Its performance is generally consistent with previous work but offers higher computational efficiency and lower memory usage. Synthetic data tests on the half‐space model and the three‐dimensional Marmousi model demonstrate the effectiveness of this method in suppressing imaging artefacts, as well as its efficiency and ease of implementation.

High-Resolution 3D Geological Modeling of Three-Phase Zone Coexisting Hydrate, Gas, and Brine

Three-dimensional geological modeling is essential for simulating natural gas hydrate (NGH) productivity and formulating development strategies. Current approaches primarily concentrate on the single-phase modeling of either hydrate or free gas layers. However, an increasing number of instances suggest that the three-phase coexistence zone, which includes hydrate, gas, and water, is common and has become a focal point of international research, as this type of reservoir may present the most viable opportunities for exploitation. At present, there exists a significant gap in the research regarding modeling techniques for such reservoirs. This study undertakes a comprehensive modeling investigation of the three-phase zone reservoir situated in the sand layer of the Qiongdongnan Basin. By employing deterministic complex geological modeling techniques and integrating existing seismic and logging data, we have developed a three-phase coexistence zone model that precisely characterizes the interactions between geological structures and utilizes them as auxiliary constraints. This approach effectively mitigates the potential impact of complex geological conditions on model accuracy. Through a comprehensive analysis of 105 seismic profiles, we enhanced the model’s accuracy, resulting in the creation of a three-phase coexistence zone model comprising 350,000 grids. A comparison between the modeling results and well data indicates a relatively small error margin, offering valuable insights for future development efforts. Furthermore, this method serves as a reference for modeling hydrates in marine environments characterized by three-phase coexistence on a global scale.

Hybrid optimization for DC resistivity imaging via intelligible-in-time logic and the interior point method

Geophysical DC resistivity imaging is crucial in subsurface exploration, environmental studies, and resource assessment. However, traditional inversion techniques face challenges in accurately resolving complex subsurface features because of the inherent nonlinearities in geophysical data. To overcome these challenges, we propose a hybrid optimization approach that combines incomprehensible but intelligible-in-time (IbI) logic with the interior point method (IPM). The IbI logic framework leverages complexity and temporal intelligibility, allowing for a dynamic interpretation of subsurface phenomena. By integrating IbI with IPM, our approach benefits from global exploration and local refinement, leading to improved convergence speed and solution quality. The objective function formulated for the inversion process includes data misfit and model regularization terms, which promote accurate and smooth solutions. Our methodology involves the use of the IbI logic algorithm (ILA) for initial global search, which identifies promising regions in the search space. This is followed by the application of IPM for local optimization. This synergy between the two algorithms ensures robustness and efficiency in handling large datasets and complex geological models. We conducted tests using synthetic and real DC resistivity data to validate our approach. The synthetic test demonstrated the accurate reconstruction of subsurface anomalies, whereas the real data test successfully identified fault zones, which is consistent with previous studies. The hybrid optimization algorithm significantly improves the resolution of subsurface structures and enhances geophysical data inversion practices. It balances the exploration and refinement phases effectively, optimizing the computation time and ensuring precise model delineation.

Iterative algorithm for computing magnetic field considering remanent magnetization and demagnetization

SUMMARY Efficient and high-precision methods for performing large-scale numerical calculations under high magnetic susceptibility conditions are essential for magnetic exploration applications. This paper proposes an algorithm for magnetic field modelling considering both demagnetization and remanent magnetization. The 3-D partial differential equation of magnetic potential is reduced to a 1-D ordinary differential equation in the space-wavenumber domain through a 2-D Fourier transform in the horizontal direction. Using the quadratic interpolation finite element method to obtain the pentagonal equation, the chasing method is used to solve the equation efficiently, and a contraction operator based on electromagnetic integral equation method is introduced to ensure stable iteration convergence. The validity of the algorithm was confirmed by comparing it with analytical solutions. Numerical examples demonstrate the importance of considering demagnetization under high magnetization conditions. Test results reveal that magnetic susceptibility is the sole factor affecting convergence among the factors examined. Further analysis showed that, for the same magnetic susceptibility, the algorithm converges with the same number of iterations and higher precision is achieved with an increasing number of nodes. Under the same grid configuration, higher magnetic susceptibility requires more iterations to converge and results in lower algorithm precision. The algorithm presented in this paper shows higher efficiency compared to those based on integral equations. Moreover, we demonstrate the algorithm's high accuracy when applied to models with anomalies near boundaries. Finally, the adaptability of the algorithm to complex geological models and undulating topography is verified by combining model tests with DEM data. This algorithm presents an efficient and high-precision method for magnetic field calculations under conditions of high susceptibility and strong remanent magnetization, offering promising prospects for geoscience applications.

A Spline-Based Regularized Method for the Reconstruction of Complex Geological Models

A Spline-Based Regularized Method for the Reconstruction of Complex Geological Models

Prediction of geothermal temperature field by multi-attribute neural network

Hot dry rock (HDR) resources are gaining increasing attention as a significant renewable resource due to their low carbon footprint and stable nature. When assessing the potential of a conventional geothermal resource, a temperature field distribution is a crucial factor. However, the available geostatistical and numerical simulations methods are often influenced by data coverage and human factors. In this study, the Convolution Block Attention Module (CBAM) and Bottleneck Architecture were integrated into UNet (CBAM-B-UNet) for simulating the geothermal temperature field. The proposed CBAM-B-UNet takes in a geological model containing parameters such as density, thermal conductivity, and specific heat capacity as input, and it simulates the temperature field by dynamically blending these multiple parameters through the neural network. The bottleneck architectures and CBAM can reduce the computational cost while ensuring accuracy in the simulation. The CBAM-B-UNet was trained using thousands of geological models with various real structures and their corresponding temperature fields. The method’s applicability was verified by employing a complex geological model of hot dry rock. In the final analysis, the simulated temperature field results are compared with the theoretical steady-state crustal ground temperature model of Gonghe Basin. The results indicated a small error between them, further validating the method's superiority. During the temperature field simulation, the thermal evolution law of a symmetrical cooling front formed by low thermal conductivity and high specific heat capacity in the center of the fault zone and on both sides of granite was revealed. The temperature gradually decreases from the center towards the edges.

Numerical simulation analysis of slope stability from rainwater utilizing the Civil3D+Flac3D coupling

Building Information Modeling (BIM) technology serves as an effective means for engineering modeling and information integration, surpassing traditional two-dimensional approaches with its superior spatial analysis capabilities. While BIM has gained widespread applications in slope engineering, a gap persists in the integration between protective design and simulation analysis in terms of slope stability. This study employs literature review, theoretical analysis, software development, and numerical simulation methods to explore the application of BIM models in slope stability analysis. Through the integrated application of BIM model construction, mesh subdivision, and stability analysis, we address the deficiency in three-dimensional slope stability inherent in BIM by coupling Civil3D’s secondary development with Flac3D, a numerical simulation software. This approach not only addresses the shortcomings of numerical analysis software in constructing complex geological models but also employs a collaborative multi-software approach for comparison to validate its suitability in slope engineering. The results demonstrate that models built using BIM software are more comprehensive and possess high precision in numerical simulation, thus exhibiting significant practical value in real-world engineering applications.

A High-Resolution subtle fault mapping in Marlin oilfield, Brazil

Discriminating geological discontinuities is important for reservoir management because they influence storage capacity and fluid flow. Structural heterogeneities, such as faults and fractures, significantly impact the compartmentalization of the reservoir’s facies and affect the flow of hydrocarbons. These structures can act as the pore space for fluid storage, flow-control conduits, or barriers that allow the accumulation of exploitable volumes of oil and gas. Understanding these structures’ spatial and temporal development can significantly impact hydrocarbon exploration. Reservoir characterization is a critical process in the oil and gas industry that aims to comprehensively understand reservoir rocks and their fluid content and distribution. It is a multidisciplinary approach that combines geological, geophysical, and engineering datasets through statistical and deterministic mathematical models. Seismic datasets play a crucial role in reservoir characterization. Interpreters can use seismic data processing and imaging to interpret geological horizons and map faults, building complex geological models. Seismic inversion is also employed to estimate acoustic impedance and other petrophysical properties. Faults and fractures mapping are highly relevant themes in reservoir characterization. Identifying subtle faults and fractures is essential in specifying hydrocarbon migration paths and identifying bypassed oil accumulations. However, traditional seismic amplitude data interpretation should consider these structures more. In this study, we apply a high-resolution fault mapping workflow to map the subtle faults system at the Marlim field in the offshore portion of the Campos Basin. As an outcome, we imaged two separate fault trends inside and outside the Marlim reservoir.

Developing meshing workflows in Gmsh v4.11 for the geologic uncertainty assessment of high-temperature aquifer thermal energy storage

Abstract. Evaluating uncertainties of geological features on fluid temperature and pressure changes in a reservoir plays a crucial role in the safe and sustainable operation of high-temperature aquifer thermal energy storage (HT-ATES). This study introduces a new automated surface fitting function in the Python API (application programming interface) of Gmsh (v4.11) to simulate the impacts of structural barriers and variations of the reservoir geometries on thermohydraulic behaviour in heat storage applications. These structural features cannot always be detected by geophysical exploration but can be present due to geological complexities. A Python workflow is developed to implement an automated mesh generation routine for various geological scenarios. This way, complex geological models and their inherent uncertainties are transferred into reservoir simulations. The developed meshing workflow is applied to two case studies: (1) Greater Geneva Basin with the Upper Jurassic (“Malm”) limestone reservoir and (2) the 5° eastward-tilted DeepStor sandstone reservoir in the Upper Rhine Graben with a uniform thickness of 10 m. In the Greater Geneva Basin example, the top and bottom surfaces of the reservoir are randomly varied by ± 10 and ± 15 m, generating a total variation of up to 25 % from the initially assumed 100 m reservoir thickness. The injected heat plume in this limestone reservoir is independent of the reservoir geometry variation, indicating the limited propagation of the induced thermal signal. In the DeepStor reservoir, a vertical sub-seismic fault juxtaposing the permeable sandstone layers against low permeable clay-marl units is added to the base case model. The fault is located in distances varying from 4 to 118 m to the well to quantify the possible thermohydraulic response within the model. The variation in the distance between the fault and the well resulted in an insignificant change in the thermal recovery (∼ 1.5 %) but up to a ∼ 10.0 % pressure increase for the (shortest) distance of 4 m from the injection well. Modelling the pressure and temperature distribution in the 5° tilted reservoir, with a well placed in the centre of the model, reveals that heat tends to accumulate in the updip direction, while pressure increases in the downdip direction.

Three-dimension holographic numerical simulation of gravity anomalies

In gravity-anomaly-based prospecting, it is difficult to achieve large-scale and high-precision inversion imaging of complex geological models. To address this issue, this paper proposes a three-dimensional holographic numerical simulation method for gravity anomalies. This method transforms the 3D partial differential equation of gravity potential into many independent 1D differential equations with different wavenumbers by performing a 2D Fourier transform along the horizontal direction. It decomposes a large-scale 3D numerical modeling problem into many 1D numerical modeling problems, which greatly reduces the computation and memory requirements of modeling, and each 1D differential equation is independent, so it has high parallelism. The vertical direction is reserved as the spatial domain, which has strict upper and lower boundary conditions; The horizontal 2D Fourier transform uses a holographic Fourier transform (Holo-FT) with a full interval of integration, consistent with the physical boundary in the horizontal direction, thus the physical information of the gravity potential described by the three-dimensional partial differential equation is fully and accurately simulated. Using the high parallelism of the algorithm, the CPU is used for parallel solving ordinary differential equations, while the GPU is used for parallel computing of Holo-FT, which implements the CPU-GPU parallel acceleration scheme and further improves the efficiency of this algorithm.

Construction of knowledge constraints: a case study of 3D structural modeling

The uncertainty of structural interpretation complicates the practical production and application of data-driven complex geological structure modeling technology. Intelligent structural modeling excavates and extracts structural knowledge from structural interpretation through human–machine collaboration and combines structural interpretation to form a new model of complex structural modeling guided by knowledge. Specifically, we focus on utilizing knowledge rule reasoning technology to extract topological semantic knowledge from interpretive data and employ knowledge inference to derive structural constraint information from complex geological structure models, thus effectively constraining the 3D geological structure modeling process. To achieve this, we develop a rule-based knowledge inference system that derives theoretical models consistent with expert cognition from interpretive data and prior knowledge. Additionally, we represent the extracted knowledge as a topological semantic knowledge graph, which facilitates computer recognition and allows estimation of intersection lines during 3D geological modeling, resulting in the creation of accurate models. The applicability of our proposed method to various complex geological structures is validated through application tests using real-world data. Furthermore, our method effectively supports the realization of intelligent structure modeling in real working area.

Stochastic reconstruction of geological reservoir models based on a concurrent multi-stage U-Net generative adversarial network

For complex geological reservoir modeling, some numerical-simulation-based methods, such as traditional multiple-point statistics (MPS), cannot extract nonstationary patterns of training images (TIs) effectively. CPU-intensive calculations require that variables information only be stored in RAM instead of other storage mediums to avoid huge time consumption if many simulations are performed successively. Generative Adversarial Network (GAN) modeling methods are able to overcome these issues, but when the training datasets are limited, mode collapse easily occurs. Meanwhile, fixed receptive fields might cause the problem that the corresponding reconstruction cannot take local features and global features of the TIs into account simultaneously. Therefore, we propose the Concurrent Multi-Stage U-Net GAN (Con-MSUGAN) based on a single TI. The pyramid structure is used for spatial pattern multi-scale representation in Con-MSUGAN, which can capture the corresponding feature information of TIs under different scales. Meanwhile, concurrent training patterns can make network parameters in adjacent stages correlated with each other to accelerate network convergence speed, thereby realizing stochastic multi-scale reconstructions. Stationary channel and nonstationary delta facies TIs were used to verify the performance of Con-MSUGAN. Results show that simulation of different datasets using this method are more similar in terms of spatial variance, connectivity degree and facies type frequency distribution to the original TIs. Meanwhile, muti-dimensional-scaling (MDS) plots show small discrepancies between simulation results and the corresponding TI. It indicates that Con-MSUGAN can overcome the problem that complex spatial patterns are hard to reproduce. In addition, saved network parameters can be reused. A variety of equiprobability simulation results can be obtained rapidly, thereby realizing stochastic reconstruction of geological reservoir models.

Wykorzystanie ilościowych wskaźników form strukturalnych do geologicznego i statystycznego modelowania struktur o złożonej budowie

Computer processing of geological data is widely used to process geological information. Therefore, an assessment of the structures as potential reservoir traps for oil and gas was carried out on the basis of quantitative parameter analysis. This approach made it possible to reasonably confirm certain regularities. To identify these regularities in the relationships between the numerical parameters of complex structures, computer geological and statistical modeling of the studied objects of the Boryslav-Pokuttya zone was carried out using correlation and cluster analysis. In general, correlation analysis allows analyzing the set of determined values and is aimed at identifying and studying the systems that form some values included in this set. Classification of any objects by meaningful groups is carried out by the method of cluster analysis. To model the processes that formed local structures and to determine the patterns of their spread, a large volume of quantitative indicators was processed. On the basis of quantitative indicators, it was possible to evaluate the results of studies of the tectonic stresses and deformations distribution, which will contribute to more reliable determination of reservoir potential for oil and gas. In turn, this will significantly increase the geological effectiveness of oil and gas exploration in the Boryslav-Pokuttya area. The contemporary form of structures and their spatial arrangement result from the long-termimpact of tectonic forces over geological time. Different manifestations of tectonic activity in successive geological epochs leads to specific changes in the structural plan of geological formations, influencing the potential oil and gas content within them (formation, unforming, and re-forming of traps and, accordingly, hydrocarbon reservoirs). The structures of the Boryslav-Pokuttya zone have undergone a complex and lengthy formation process: from the formation of flysch folds to very complex structural forms. This complexity is contributed to the influence of the magnitude and nature of the tectonic forces. The morphological diversity of the structures, can be described by numerical parameters, which can be used as a basis for classifying these structures in the Boryslav-Pokuttya zone.

A Multi-Point Geostatistical Modeling Method Based on 2D Training Image Partition Simulation

In this paper, a multi-point geostatistical (MPS) method based on variational function partition simulation is proposed to solve the key problem of MPS 3D modeling using 2D training images. The new method uses the FILTERSIM algorithm framework, and the variational function is used to construct simulation partitions and training image sequences, and only a small number of training images close to the unknown nodes are used in the partition simulation to participate in the MPS simulation. To enhance the reliability, a new covariance filter is also designed to capture the diverse features of the training patterns and allow the filter to downsize the training patterns from any direction; in addition, an information entropy method is used to reconstruct the whole 3D space by selecting the global optimal solution from several locally similar training patterns. The stability and applicability of the new method in complex geological modeling are demonstrated by analyzing the parameter sensitivity and algorithm performance. A geological model of a uranium deposit is simulated to test the pumping of five reserved drill holes, and the results show that the accuracy of the simulation results of the new method is improved by 11.36% compared with the traditional MPS method.

Using Bayesian Neural Networks for Uncertainty Assessment of Ore Type Boundaries in Complex Geological Models

AbstractBuilding an orebody model is a key step in the design and operation of a mine because it provides the basis for follow-up mine decisions. Recently, it was shown that convolutional neural networks can successfully reproduce the manual geological interpretation of a complex ore deposit. The deep learning approach mitigates the shortcomings of a labor-intensive process that greatly limits the speed at which geological resources can be updated. However, convolutional neural network architectures lack the ability to measure the confidence of their predictions. In this study, we tried to assess the uncertainty of the boundaries of these domains so that the characterization of metal grades within them can account for this uncertainty. We explored and compared Monte Carlo Dropout and Bayesian neural networks to assess the uncertainty of deep convolutional neural network models trained to predict geological domains conditioned to drill-hole data. Monte Carlo Dropout uncertainty maps reflect the uncertainty in geological interpretations. The uncertainty is highest in areas where the interpreter/geologist had more difficulty delineating the boundaries of geological bodies. This is known as geological interpretation uncertainty. In contrast, Bayesian neural network uncertainty is visible depending on ore type frequency, complexity, and heterogeneity. Bayesian neural networks are able to better represent the uncertainty regarding the unknown. The application example here is a real case study of several ore types from a polymetallic sulfide orebody located in the south of Portugal.

An advanced inverse modeling framework for efficient and flexible adjoint-based history matching of geothermal fields

In this study, we present an efficient and flexible adjoint-based framework for history matching and forecasting geothermal energy extraction at a large scale. In this framework, we applied the Principal Component Analysis to reduce the parameter space for representing the complex geological model. The adjoint method is implemented for gradient calculation to speed up the history-matching iteration process. Operator-based linearization (OBL) used in this framework makes the calculation of the physical state and its derivatives very efficient and facilitates the matrix assembly in the adjoint method. This study primarily focuses on history matching based on combined observation of well production and in-situ electromagnetic measurements to predict the temperature front. However, different types of misfit terms can be added to the objective function based on practical considerations. For example, our history-matching case studies include model misfit terms applied for regularization purposes. The measurement data is extracted from the true model, and realistic measurement errors are considered. Also, in this work, we propose an optimal weighting strategy for the terms of the objective function to balance their sensitivity with respect to the model control variables. The high efficiency of the framework is demonstrated for the geothermal doublet model implemented at the heterogeneous reservoir with multiple realizations. The framework allows for generating posterior Randomized Maximum Likelihood (RML) estimates of the entire ensemble of the realizations with a reasonable computational cost. Results show that the framework can achieve reliable history-matching results based on the doublets production data and the reservoir electromagnetic measurement.

Fast large-scale gravity modeling using a high-order compact cascadic multigrid strategy

A new high-order compact (HOC) cascadic multigrid (MG) strategy is developed for modeling large-scale complex gravity problems on nonuniform rectilinear grids. First, the governing 3D Poisson’s gravitational potential equation is discretized by a novel HOC difference scheme, which allows for Robin boundary conditions to further reduce the computational domain. Then, the resulting asymmetric linear system of equations is solved by a generalized extrapolation cascadic MG (gEXCMG) method augmented with a novel MG prolongation operator. The quartic interpolation and completed Richardson extrapolation assist this MG prolongation operator to produce a good initial guess for the biconjugate gradient stabilized smoother. Two synthetic and SEG/EAGE salt models are examined to verify the presented approach. Results indicate that our algorithm can efficiently and accurately produce the gravity signals for complex geologic models. Moreover, the comparisons with the state-of-the-art algebraic MG solvers demonstrate that our gEXCMG solver offers substantially better efficiency with significantly less memory consumption. Therefore, our newly developed method has the potential for serving as a forward engine in large-scale gravity inversions.

Mining and geological models of virtual complex ore blocks of the bench

Purpose. Creation of mining and geological models of virtual complex ore blocks of a bench to develop a basic methodology for determining the geological structure of complex structural sections of mineral deposits. Methodology. In the scientific and technical substantiation of mining and geological, mining and technical indicators of complex structural blocks in terms of ore saturation and complexity of the morphological structure of blocks of ledges, methods of complex and abstract-logical analysis, synthesis, systematization, the method of theoretical generalization, generalization of information sources and world experience in the field of geoinformation of complex structural deposits, statistical analysis, mathematical modeling, mining and geological modeling of mineral deposits were applied. Findings. Mining and geological models of virtual complex structure ore blocks (CSOB) of the bench have been created. The mining and geological characteristics of the blocks are analytically interconnected with the geometric parameters of the scattered ore bodies and the dimensions of the layer of admixed rock or lost ore. They determine the degree of complexity of the geological structure of the CSOB. According to the given sizes and location of disparate solid and dispersed ore bodies of virtual complex structural blocks, the numerical values of the mining and geological characteristics of ore blocks were calculated using the developed method. CSOB are subdivided into more ore-saturated, moderately ore-saturated, less ore-saturated as well as complex structural and more complex structural ones. Originality. For the first time in mining, the concepts of “virtual complex-structural ore blocks of a bench” and “mining and geological models of virtual complex-structural ore blocks of a bench” have been introduced. The set of geometrical parameters of the scattered ore bodies of the block and their mining and geological characteristics are presented as mining and geological models of the virtual CSOB of the bench. The developed models make it possible to establish patterns of changes in the mining and geological characteristics of complex ore blocks. Practical value. The developed mining and geological models of virtual complex structural blocks serve as the basis for creating mining and geological models of real complex ore blocks, models of CSOB in a blasted state. They will make it possible to develop a methodology for rationing losses and impoverishment of ores for real complex-structural blocks, to choose rational parameters for mining technologies for disparate ore bodies in specific mining and geological conditions, and to expand the use of waste-free, low-waste technologies in the development of complex-structural mineral deposits.

P- and S-wave energy current density vectors dot product imaging condition of source time-reversal imaging

SUMMARY Source time-reversal imaging (TRI) based on decoupled elastic wave equation can utilize vector P- and S-wave time differences and achieve high-precision source location in complex geological models. The imaging condition is critical for TRI. However, because of the orthogonally polarized properties of P and S waves, traditional vector dot product imaging condition directly applied to TRI will decrease the effective imaging values. In contrast, the energy current density vectors of P and S waves represent the propagation directions of the wavefields and are almost parallel. Their dot product can result in the maximum imaging energy. Based on this principle, we propose a P- and S-wave energy current density vectors dot product imaging condition (PSEDPIC), which uses the propagation direction information of P and S waves at the source point to suppress imaging artefacts generated by waves with inconsistent propagation directions. Numerical tests reveal that PSEDPIC can (1) reduce the image artefacts, (2) improve the imaging spatial resolution and (3) allow a shallower imaging region. In addition, if the numerical simulation algorithm used in TRI can reconstruct the seismic wavefield accurately in the presence of surface topography, the impact of an observation system with elevation differences on imaging can be eliminated automatically. For this reason, we use the curvilinear grid finite-difference method to directly reconstruct the wavefield in TRI to solve the problem of data elevation correction. The test results of 3-D synthetic and field data for microseismic monitoring demonstrate the effectiveness of the proposed method.