Geoscience Applications Research Articles

Explainable deep learning for automatic rock classification

As deep learning (DL) gains popularity for its ability to make accurate predictions in various fields, its applications in geosciences are also on the rise. Many studies focus on achieving high accuracy in DL models by selecting models, developing more complex architectures, and tuning hyperparameters. However, the interpretability of these models, or the ability to understand how they make their predictions, is less frequently discussed. To address the challenge of high accuracy but low interpretability of DL models in geosciences, we study rock classification from thin-section photomicrographs of six types of sedimentary rocks, including quartz arenite, feldspathic arenite, lithic arenite, siltstone, oolitic packstone, and dolomite. These rocks’ characteristic framework grains and grain textures are their distinguishing features, such as the rounded or oval ooids in oolitic packstone. We first train regular DL models, such as ResNet-50, on these photomicrographs and achieve an accuracy of over 0.94. However, these models make classifications based on features like cracks, cements, and scale bars, which are irrelevant for distinguishing sedimentary rocks in real-world applications. We then propose an attention-based dual network incorporating both global (overall photomicrograph) and local (distinguishing framework grains) features to address this issue. Our proposed model achieves not only high accuracy (0.99) but also provides interpretable feature extractions. Our study highlights the need to consider interpretability and geological knowledge in developing DL models, in addition to aiming for high accuracy.

Inter-laboratory re-determination of the atmospheric 22Ne/20Ne

Accurate knowledge of the Ne isotopic composition of air is essential for planetary science. While the uncertainty of the noble gas isotopic composition of air has been drastically reduced to the level of ∼0.1% in the last few years thanks to modern techniques, the most widely accepted value of the 22Ne/20Ne ratio of air (0.102 ± 0.0008, Eberhardt et al., 1965) has an uncertainty of ±0.78% (1σ). Here we present the first multi-laboratory re-determination of the atmospheric 22Ne/20Ne. An artificial, high purity mixture of 20Ne and 22Ne was prepared and the 22Ne/20Ne (0.11888 ± 0.00001, 1σ) and 20Ne/22Ne (8.4118 ± 0.0007, 1σ) determined gravimetrically. This gas was used to determine the mass fractionation of five mass spectrometers allowing the air 22Ne/20Ne to be determined (n = 234 analyses). Each laboratory sampled their own local air, used a different gas preparation system and analysis procedure as well as doing their own expansion of the high-pressure artificial Ne gas. Individual air 22Ne/20Ne determinations have uncertainties in the range of 0.01–0.08%. The overall reproducibility of the calculated 22Ne/20Ne of air between the laboratories shows no overdispersion with respect to the individual uncertainties. We report a global value for the atmospheric 22Ne/20Ne of 0.10196 ± 0.00007 (0.07%, 1σ), equivalent of 20Ne/22Ne of 9.808 ± 0.007. This is almost identical to the Eberhardt et al. (1965) value although its uncertainty shows a 12 times reduction. Our study did not verify any of the other previous determinations of atmospheric 22Ne/20Ne. This highly accurate and precise atmospheric 22Ne/20Ne value provides a new reference for atmospheric 21Ne/20Ne determinations and we recalculate (21Ne/20Ne)air of five recent determinations. While this exercise resulted in no significant change to the absolute values, it gives more confidence with respect to the correctness of (21Ne/20Ne)air. We suggest that the revised value for atmospheric 22Ne/20Ne be used routinely in all geoscience applications.

Perspectives of physics-based machine learning strategies for geoscientific applications governed by partial differential equations

Abstract. An accurate assessment of the physical states of the Earth system is an essential component of many scientific, societal, and economical considerations. These assessments are becoming an increasingly challenging computational task since we aim to resolve models with high resolutions in space and time, to consider complex coupled partial differential equations, and to estimate uncertainties, which often requires many realizations. Machine learning methods are becoming a very popular method for the construction of surrogate models to address these computational issues. However, they also face major challenges in producing explainable, scalable, interpretable, and robust models. In this paper, we evaluate the perspectives of geoscience applications of physics-based machine learning, which combines physics-based and data-driven methods to overcome the limitations of each approach taken alone. Through three designated examples (from the fields of geothermal energy, geodynamics, and hydrology), we show that the non-intrusive reduced-basis method as a physics-based machine learning approach is able to produce highly precise surrogate models that are explainable, scalable, interpretable, and robust.

Multi-Scalar Oblique Photogrammetry-Supported 3D webGIS Approach to Preventive Mining-Induced Deformation Analysis

Underground coal mining will inevitably cause serious ground deformation, and therefore, preventive mining-induced deformation analysis (MIDA) is of great importance in assisting mining planning and decision-making. Current web-based Geographic Information System (webGIS)-based applications usually use 2D GIS data and lack a holistic framework. This study presents a multi-scalar oblique photogrammetry-supported unified 3D webGIS framework for MIDA applications to fill this gap. The developed web platform uses multiple open-source JavaScript libraries, and the prototype system provides user-friendly interfaces for GIS data collecting and corresponding database establishment, geo-visualization and query, dynamic prediction, and spatial overlapping analysis within the same framework. The proposed framework was tested and evaluated in the Qianyingzi mining area in eastern China. The results demonstrated that multi-scalar oblique photogrammetry balances data quality and acquisition efficiency and provides a good source of GIS datasets, and the web-based platform has a good absolute and relative spatial accuracy verified by two types of validation data. Practical application results proved the feasibility and reliability of the system. The developed web-based MIDA prototype system attains an appealing performance and can be easily extended to similar geoscience applications.

GTWS-MLrec: global terrestrial water storage reconstruction by machine learning from 1940 to present

Abstract. Terrestrial water storage (TWS) includes all forms of water stored on and below the land surface, and is a key determinant of global water and energy budgets. However, TWS data from measurements by the Gravity Recovery and Climate Experiment (GRACE) satellite mission are only available from 2002, limiting global and regional understanding of the long-term trends and variabilities in the terrestrial water cycle under climate change. This study presents long-term (i.e., 1940–2022) and relatively high-resolution (i.e., 0.25∘) monthly time series of TWS anomalies over the global land surface. The reconstruction is achieved by using a set of machine learning models with a large number of predictors, including climatic and hydrological variables, land use/land cover data, and vegetation indicators (e.g., leaf area index). The outcome, machine-learning-reconstructed TWS estimates (i.e., GTWS-MLrec), fits well with the GRACE/GRACE-FO measurements, showing high correlation coefficients and low biases in the GRACE era. We also evaluate GTWS-MLrec with other independent products such as the land–ocean mass budget, atmospheric and terrestrial water budget in 341 large river basins, and streamflow measurements at 10 168 gauges. The results show that our proposed GTWS-MLrec performs overall as well as, or is more reliable than, previous TWS datasets. Moreover, our reconstructions successfully reproduce the consequences of climate variability such as strong El Niño events. The GTWS-MLrec dataset consists of three reconstructions based on (a) mascons of the Jet Propulsion Laboratory of the California Institute of Technology, the Center for Space Research at the University of Texas at Austin, and the Goddard Space Flight Center of NASA; (b) three detrended and de-seasonalized reconstructions; and (c) six global average TWS series over land areas, both with and without Greenland and Antarctica. Along with its extensive attributes, GTWS_MLrec can support a wide range of geoscience applications such as better understanding the global water budget, constraining and evaluating hydrological models, climate-carbon coupling, and water resources management. GTWS-MLrec is available on Zenodo through https://doi.org/10.5281/zenodo.10040927 (Yin, 2023).

Development and application of feature engineered geological layers for ranking magmatic, volcanogenic, and orogenic system components in Archean greenstone belts

Geologically representative feature engineering is a crucial component in geoscientific applications of machine learning. Many commonly applied feature engineering techniques used to produce input variables for machine learning apply geological knowledge to generic data science techniques, which can lead to ambiguity, geological oversimplification, and/or compounding subjective bias. Workflows that utilize minimally processed input variables attempt to overcome these issues, but often lead to convoluted and uninterpretable results. To address these challenges, new and enhanced feature engineering methods were developed by combining geological knowledge, understanding of data limitations, and a variety of data science techniques. These include non-Euclidean fluid pre-deformation path distance, rheological and chemical contrast, geologically constrained interpolation of characteristic host rock geochemistry, interpolation of mobile element gain/loss, assemblages, magnetic intensity, structural complexity, host rock physical properties. These methods were applied to compiled open-source and new field observations from Archean greenstone terranes in the Abitibi and western Wabigoon sub-provinces of the Superior Province near Timmins and Dryden, Ontario, respectively. Resulting feature maps represent conceptually significant components in magmatic, volcanogenic, and orogenic mineral systems. A comparison of ranked feature importance from random forests to conceptual mineral system models show that the feature maps adequately represent system components, with a few exceptions attributed to biased training data or limited constraint data. The study also highlights the shared importance of several highly ranked features for the three mineral systems, indicating that spatially related mineral systems exploit the same features when available. Comparing feature importance when classifying orogenic Au mineralization in Timmins and Dryden provides insights into the possible cause of contrasting endowment being related to fluid source. The study demonstrates that integrative studies leveraging multi-disciplinary data and methodology have the potential to advance geological understanding, maximize data utility, and generate robust exploration targets.

Developing innovative and cost-effective UAS-PPK module for generating high-accuracy digital surface model

Traditional indirect georeferencing requires time-consuming and labor-intensive field surveys to obtain ground control points (GCPs), making it challenging to apply in high-risk areas with limited accessibility. This study proposes a novel and low-cost system for direct georeferencing using unmanned aerial system post-processing kinematics (UAS-PPK), which is less than a quarter of the price of commercially available products. To evaluate the accuracy of the aerial surveys of the custom-built module and digital surface models, we used 15 checkpoints (CPs) and 99 validation points (VPs). The results showed that this UAS-PPK module could deliver high-precision aerial surveys with a root mean square error (RMSE) of less than 4 cm for three dimensions without using control points. After adding one GCP, the RMSE of three dimensions was close to that of traditional aerial survey methods using 12 GCPs, having a vertical accuracy of 2.51 cm. The same 99 VPs were used to evaluate the accuracy of the digital surface model produced using UAS-PPK. The results showed that the accuracy was close to that of traditional aerial survey methods, having an average error of less than 3 cm. We demonstrated the self-made attachable UAS-PPK module to be a reliable and accurate survey tool in geoscience applications.

A comparative analysis of super-resolution techniques for enhancing micro-CT images of carbonate rocks

High-resolution digital rock micro-CT images captured from a wide field of view are essential for various geosystem engineering and geoscience applications. However, the resolution of these images is often constrained by the capabilities of scanners. To overcome this limitation and achieve superior image quality, advanced deep learning techniques have been used. This study compares four different super-resolution techniques, including super-resolution convolutional neural network (SRCNN), efficient sub-pixel convolutional neural networks (ESPCN), enhanced deep residual neural networks (EDRN), and super-resolution generative adversarial networks (SRGAN) to enhance the resolution of micro-CT images obtained from heterogeneous porous media. Our investigation employs a dataset consisting of 5000 micro-CT images acquired from a highly heterogeneous carbonate rock. The performance of each algorithm is evaluated based on its accuracy to reconstruct the pore geometry and connectivity, grain-pore edge sharpness, and preservation of petrophysical properties, such as porosity. Our findings indicate that EDRN outperforms other techniques in terms of the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) index, increased by nearly 4 dB and 17%, respectively, compared to bicubic interpolation. Furthermore, SRGAN exhibits superior performance compared to other techniques in terms of the learned perceptual image patch similarity (LPIPS) index and porosity preservation error. SRGAN shows a nearly 30% reduction in LPIPS compared to bicubic interpolation. Our results provide deeper insights into the practical applications of these techniques in the domain of porous media characterizations, facilitating the selection of optimal super-resolution CNN-based methodologies.

Evaluation of vertical accuracy of TanDEM-X Digital Elevation Model in Egypt

The study conducted aimed to examine the accuracy of Digital Elevation Models (DEMs) in Egypt, specifically the TanDEM-X mission's 30 m and 12 m resolution DEMs and the SRTM DEM with a 30 m resolution. The accuracy of DEMs is essential for various civil engineering and surveying applications, especially in geoscience applications. To ensure the comparison's accuracy, the study used ellipsoidal heights instead of orthometric heights, preventing errors caused by global geopotential models in the conversion process. The evaluation of the three DEMs was carried out using 352 GNSS points. The findings indicate that both TanDEM-X DEMs with 30 m and 12 m resolutions outperform the SRTM 30 m in terms of vertical accuracy, making them ideal for geomatic applications that require higher-resolution DEMs. The TanDEM-X 30 m generates a standard deviation (STD) and a Root Mean Square Error (RMSE) of approximately 3.03 m and 3.45 m, respectively. On the other hand, the TanDEM-X 12 m generates an STD and RMSE of approximately 2.86 m and 3.18 m, respectively. Comparatively, the SRTM 30 m produces an STD and RMSE of approximately 4.67 m and 5.35 m, respectively.

Editorial for the Special Issue Entitled Hyperspectral Remote Sensing from Spaceborne and Low-Altitude Aerial/Drone-Based Platforms—Differences in Approaches, Data Processing Methods, and Applications

Nowadays, several hyperspectral remote sensing sensors from spaceborne and low-altitude aerial/drone-based platforms with a variety of spectral and spatial resolutions are available for geoscientific applications [...]

Algebraic multiscale grid coarsening using unsupervised machine learning for subsurface flow simulation

Subsurface flow simulation is vital for many geoscience applications, including geoenergy extraction and gas (energy) storage. Reservoirs are often highly heterogeneous and naturally fractured. Therefore, scalable simulation strategies are crucial to enable efficient and reliable operational strategies. One of these scalable methods, which has also been recently deployed in commercial reservoir simulators, is algebraic multiscale (AMS) solvers. AMS, like all multilevel schemes, is found to be highly sensitive to the types (geometries and size) of coarse grids and local basis functions. Commercial simulators benefit from a graph-based partitioner; e.g., METIS to generate the multiscale coarse grids. METIS minimizes the amount of interfaces between coarse partitions, while keeping them of similar size which may not be the requirement to create a coarse grid. In this work, we employ a novel approach to generate the multiscale coarse grids, using unsupervised learning methods which is based on optimizing different parameter. We specifically use the Louvain algorithm and Multi-level Markov clustering. The Louvain algorithm optimizes modularity, a measure of the strength of network division while Markov clustering simulates random walks between the cells to find clusters. It is found that the AMS performance is improved when compared with the existing METIS-based partitioner on several field-scale test cases. This development has the potential to enable reservoir engineers to run ensembles of thousands of detailed models at a much faster rate.

The FABDEM Outperforms the Global DEMs in Representing Bare Terrain Heights

Many remote sensing and geoscience applications require a high-precision terrain model. In 2022, the Forest And Buildings removed Copernicus digital elevation model (FABDEM) was released, in which trees and buildings were removed at a 30 m resolution. Therefore, it was necessary to make a comprehensive evaluation of this model. This research aims to perform a qualitative and quantitative analysis of fabdem in comparison with the commonly used global dems. We investigated the effect of the terrain slope, aspect, roughness, and land cover types in causing errors in the topographic representation of all dems. The fabdem had the highest overall vertical accuracy of 5.56 m. It was the best dem in representing the terrain roughness. The fabdem and Copernicus dem were equally influenced by the slopes more than the other models and had the worst accuracy of slope representation. In the tree, built, and flooded vegetation areas of the fabdem, the mean errors in elevation have been reduced by approximately 3.34 m, 1.26 m and 1.55 m, respectively. Based on Welch's t-test, there was no significant difference between fabdem and Copernicus dem elevations. However, the slight improvements in the fabdem make it the best filtered dem to represent the terrain heights over different land cover types.

A Proposed Merging Methods of Digital Elevation Model Based on Artificial Neural Network and Interpolation Techniques for Improved Accuracy

ABSTRACT The digital elevation model (DEM) is one of the most critical sources of terrain elevations, which are essential in various geoscience applications. Most of these applications need precise elevations, which are available at a high cost. Thus, sources like the Shuttle Radar Topography Mission (SRTM) DEM are frequently accessible to all users but with low accuracy. Consequently, many studies have tried to improve the accuracy of DEMs acquired from these free sources. Importantly, using the SRTM DEM is not recommended for an area that partly contains high-accuracy data. Thus, there is a need for a merging technique to produce a merged DEM of the whole area with improved accuracy. In recent years, advancements in geographic information systems (GIS) have improved data analysis by providing tools for applying merging techniques (like the minimum, maximum, last, first, mean, and blend (conventional methods)) to improve DEMs. In this article, DEM merging methods based on artificial neural network (ANN) and interpolation techniques are proposed. The methods are compared with other existing methods in commercial GIS software. The kriging, inverse distance weighted (IDW), and spline interpolation methods were considered for this investigation. The essential step for achieving the merging stage is the correction surface generation, which is used for modifying the SRTM DEM. Moreover, two cases were taken into consideration, i.e., the zeros border and the H border. The findings show that the proposed DEM merging methods (PDMMs) improved the accuracy of the SRTM DEM more than the conventional methods (CDMMs). The findings further show that the PDMMs of the H border achieved higher accuracy than the PDMMs of the zeros border, while kriging outperformed the other interpolation methods in both cases. The ANN outperformed all methods with the highest accuracy. Its improvements in the zeros and H border respectively reached 22.38% and 75.73% in elevation, 34.67% and 54.83% in the slope, and 40.28% and 52.22% in the aspect. Therefore, this approach would be cost-effective, especially in critical engineering projects.

A framework for subsurface monitoring by integrating reservoir simulation with time-lapse seismic surveys

Reservoir simulations for subsurface processes play an important role in successful deployment of geoscience applications such as geothermal energy extraction and geo-storage of fluids. These simulations provide time-lapse dynamics of the coupled poromechanical processes within the reservoir and its over-, under-, and side-burden environments. For more reliable operations, it is crucial to connect these reservoir simulation results with the seismic surveys (i.e., observation data). However, despite being crucial, such integration is challenging due to the fact that the reservoir dynamics alters the seismic parameters. In this work, a coupled reservoir simulation and time-lapse seismic methodology is developed for multiphase flow operations in subsurface reservoirs. To this end, a poromechanical simulator is designed for multiphase flow and connected to a forward seismic modeller. This simulator is then used to assess a novel methodology of seismic monitoring by isolating the reservoir signal from the entire reflection response. This methodology is shown to be able to track the development of the fluid front over time, even in the presence of a highly reflective overburden with strong time-lapse variations. These results suggest that the proposed methodology can contribute to a better understanding of fluid flow in the subsurface. Ultimately, this will lead to improved monitoring of reservoirs for underground energy storage or production.

Satellite gradiometry based on a new generation of accelerometers and its potential contribution to Earth gravity field determination

An accurate model of the Earth’s gravity field is beneficial for practical engineering and many applications in geosciences. European Space Agency (ESA) realized the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) gradiometry mission between 2009 and 2013. However, the low-frequency drift of the onboard electrostatic accelerometers (EA) limits the observation accuracy of the GOCE mission to some extent. Advances in electrostatic and quantum technology offer new measurement concepts for future gradiometry missions. In this study, we evaluate the contributions of several types of accelerometers through numerical closed-loop simulation which rigorously maps the accelerometers’ sensitivities to the gravity field coefficients. In comparison to the simulated results of the GRADIO gradiometer used in GOCE, it is demonstrated that the MicroSTAR-type gradiometer has superior precision within degree and order 100 and provides more signal information in the off-diagonal components of the gravity gradient tensor (GGT). The precision of the gravity field model recovery from a HybridACC-type gradiometer is significantly affected by the noise level of the cold atom interferometry (CAI) accelerometer. A HybridACC-type gradiometer with low CAI performance (1×10-9m·s-2/Hz) only favors the high degree component because of its higher accuracy in the measurement bandwidth (MBW) between 5 mHz and 100 mHz. While a better CAI performance up to 1×10-11m·s-2/Hz will increase retrieval performance remarkably. With an orbital rotation compensation mechanism, the CAI gradiometer performs with greater accuracy overall. Otherwise, the accuracy based on this sort of gradiometer is only superior up to degree 50.

Global sensitivity analysis using multi-resolution polynomial chaos expansion for coupled Stokes–Darcy flow problems

Determination of relevant model parameters is crucial for accurate mathematical modelling and efficient numerical simulation of a wide spectrum of applications in geosciences. The conventional method of choice is the global sensitivity analysis (GSA). Unfortunately, at least the classical Monte-Carlo based GSA requires a high number of model runs. Response surfaces based techniques, e.g. arbitrary Polynomial Chaos (aPC) expansion, can reduce computational effort, however, they suffer from the Gibbs phenomena and high hardware requirements for higher accuracy. We introduce GSA for arbitrary Multi-Resolution Polynomial Chaos (aMR-PC) which is a localized aPC based data-driven polynomial discretization. The aMR-PC allows to reduce the Gibbs phenomena by construction and to achieve higher accuracy by means of localization also for lower polynomial degrees. We apply these techniques to perform the sensitivity analysis for the Stokes–Darcy problem which describes fluid flow in coupled free-flow and porous-medium systems. We consider the Stokes equations in the free-flow region, Darcy’s law in the porous-medium domain and the classical interface conditions across the fluid–porous interface including the conservation of mass, the balance of normal forces and the Beavers–Joseph condition for the tangential velocity. This coupled problem formulation contains four uncertain parameters: the exact location of the interface, the permeability, the Beavers–Joseph slip coefficient and the uncertainty in the boundary conditions. We carry out the sensitivity analysis of the coupled model with respect to these parameters using the Sobol indices on the aMR-PC expansion and conduct the corresponding numerical simulations.

Using Smartphones as a Measurement Platform in Geoscience Applications

Most modern smartphones come with a variety of sensors. Among them are the gyroscope, accelerometer, magnetometer, GNSS (Global Navigation Satellite Systems) receiver, and from 2020, most modern devices are also coupled with a Lidar (Light Detection and Ranging) sensor. These specific sensors allow to acquire data that enables the location and spatial orientation of the smartphone in relation to other objects, and also measure them. For this, it is important to understand how the principle of operation of these sensors occurs, as well as the respective raw data obtained and how to use these data from the sensors to get measurements of the elements of the physical surface of the Earth. This article aims to present a state of the art about the working principle of these sensors and presents the raw data from them. In addition, this article seeks to present an initial test on the quality of the orientation sensor, based on the comparison between the data obtained from this sensor and a total station with high angular precision (1 second). It was noted the occurrence of a systematic error in the observations of the horizontal directions, and an average discrepancy of 5.20° between the observations of the vertical angle. The use of sensors attached to smartphones can support in several activities of geoscience application, such as carrying out a prior survey of a given area of study, aiming to do a pre-analysis of geodetic networks, to carry out measurements of angles and distances for applications in terrain measurements, or even to assist the Geographic Information System (GIS) development.

Performance evaluation of DFT based speckle reduction framework for synthetic aperture radar (SAR) images at different frequencies and image regions

Polarimetric Synthetic Aperture Radar (PolSAR) images are widely used for remote sensing and geoscience applications. However, the coherent processing of radar signals in PolSAR imaging leads to the presence of speckle noise, which can significantly degrade image quality and limit the accuracy of subsequent analyses. To address this issue, speckle reduction frameworks are often applied to PolSAR images to reduce the noise level and enhance image quality. In this paper, the performance of Discrete Fourier Transform (DFT) based speckle reduction framework is evaluated on different bands (L, C, and P band) against various evaluation metrics like CV, SD, SNR, ENL, SSI and SMPI. The proposed framework is evaluated by comparing filtered and unfiltered images across different parameters, such as mean, standard deviation, coefficient of variation, equivalent number of looks (ENL), variance, and signal-to-noise ratio (SNR) on all three bands for the diagonal elements (T11, T22, and T33) of T3 matrix. These metrics provide a comprehensive evaluation of the proposed framework’s ability to (i) smoothen homogeneous regions, (ii) preserve contours, and (iii) retain polarimetric information. The framework’s ability to reduce speckle noise and improve image quality is demonstrated through a significant reduction in standard deviation, coefficient of variation, and improvement in SNR and ENL values. The proposed framework successfully preserved polarimetric information while effectively suppressing speckle noise. These results suggest that the proposed framework could be a valuable tool for improving PolSAR image quality and enhancing subsequent processing of PolSAR data.

External gravitational field of a homogeneous ellipsoidal shell: a reference for testing gravity modelling software

There are numerous applications in geodesy and other geo-sciences in which the gravitational potential effect or other functions of the potential are computed by forward modelling from a given mass distribution. Different volume discretisations, e.g. prisms, tesseroids or mass layers are used. In order to control the numerical realisation of the forward calculation in the practical application, e.g. in reduction tasks, these evaluation programs should be verified against rigorous analytical solutions. In this contribution, a closed analytical solution for the potential of an ellipsoidal shell as a test body is presented. Furthermore, we derive the respective closed formulae for the gravity vector and the gravity gradient tensor. Program implementations of the tesseroid approach are compared on the basis of this ellipsoidal mass arrangement. For the practical usage, fast-converging expansions in spherical harmonics are provided in addition. The derivation of the formulae is based on a closed solution of the potential of a homogeneous ellipsoid for computation points situated on the rotation axis, which then is extended to the external space.

Using deep-learning to predict Dunham textures and depositional facies of carbonate rocks from thin sections

Petrographic analysis of thin sections is one of the most important and routinely used methods in a wide range of energy, earth and environmental science applications. There has been a growing motivation for computer-aided automated analysis of thin sections due to an inherent subjectivity of interpretation by geologists and the ever-increasing need for analysis of new and legacy thin section petrography data. Particularly in carbonate reservoirs, Dunham texture classification and depositional facies prediction based on thin sections are crucial for accurate description and modeling of the reservoir, but these two tasks are labor and time-intensive and their accuracy is highly dependent on the experience and the ability of the interpreter. This study addresses these challenges by exploring deep learning methods in two case studies to predict Dunham textures and depositional facies using thin sections. The proposed methodologies were applied to 1038 thin sections collected from outcrop analogues of the Upper Jurassic Hanifa Formation. To accelerate the learning speed, transfer learning was applied based on various pre-trained models provided by PyTorch. We used a pre-trained DenseNet model to classify Dunham textures from RGB images of thin sections. For the prediction of depositional facies we applied an integrated methodology consisting of two VGG models and a U-Net model. First, one VGG model was used to classify thin sections into three groups, namely, grain-dominated, mud-dominated, and stromatoporoid facies. Then the U-Net model was used to identify oncoids to further classify oncoidal facies from grain-dominated facies. Finally, another VGG model was applied to classify the peloid-rich facies from the left grain-dominated facies. The Dunham classification model resulted in a prediction accuracy of 89%. The most frequent misclassification was mainly from the identification of packstone, particularly mud-supported packstone, which the model misclassified as wackestone. The depositional facies prediction model achieved final accuracy of 86% where the misclassification was often due to oncoids identification. Overall, the results of this study demonstrate the potential of our proposed workflow to obtain automated prediction of petrographic features from a large number of thin sections. Deep learning offers a promising way forward for rapid and accurate prediction of petrographic features for geoscience applications, while minimizing bias associated with manual interpretation.