Displays

Modeling the subsurface is a complex task because the data scarcity leads to ambiguous interpretations. As a result, subsurface models are prone to many uncertainties, which can be accounted for by stochastically simulating a large set of possible models. These models are constrained by the data (of various resolution and types), but also by geological knowledge and concepts. Integrating the latter in simulation methods emerges as a key point to reduce uncertainties, although it adds another layer of complexity to the modeling process. In this presentation, I focus on two different geological contexts characterized by specific geobody shapes and connectivity: channelized systems and salt tectonics.

Channelized systems are, indeed, characterized by elongated and sinuous structures, the channels, which evolve through time by continuous lateral and vertical migrations, and abrupt events like avulsion or meander cut-offs. The combination of erosion and deposition processes is an additional source of complexity in the sedimentary records. When considering the 3D reconstruction of channelized systems, honoring data while reproducing the complex spatial architecture of these structures - so their specific connectivity - remains challenging. The various methods we have recently developed can now be combined to achieve such a goal: (i) single channels or channel parts (for avulsion) can be simulated consistently with well-data, probability cubes, or confinement thanks to a method based on Lindenmayer systems; (ii) from a channel path, consistent 3D architectures can be generated with a reverse-time channel migration approach (ChaRMigS) handling the observed abandoned meanders; (iii) to honor well data within this reverse-time reconstruction, the stochastic simulation of abandoned meanders and avulsions offers interesting solutions. The impact of such modelling methodology on connectivity reproduction has been demonstrated using static criteria, and a flow-based evaluation constitutes an obvious next step.

In the case of salt tectonics, one difficulty comes from the highly convoluted shapes taken by salt bodies, incompatible with the hypothesis of minimal surface classically used in geomodeling methods. To tackle this issue, we have developed a dedicated method to stochastically generate various salt envelopes in a pre-defined uncertainty zone. Simulations of welds, i.e. surfaces (or most often thin volumes) resulting from the removal of salt from a former layer or diapir stage, also allow us to reproduce topological singularities between salt and the surrounding sediments. Welds connect the different salt volumes, which let us recover a more geologically-consistent representation of such complex systems. The present method is still in its early days, and further improvements need to be undertaken to fully integrate the diversity of structures actually observed in the field.

How to cite: Collon, P., Rongier, G., Parquer, M., Clausolles, N., and Caumon, G.: Uncertainty assessment in subsurface modeling: considering geobody shape and connectivity in complex systems., EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-5641, https://doi.org/10.5194/egusphere-egu2020-5641, 2020.

3D modelling of complex and irregular geological bodies is an expanding discipline that combines two-dimensional cartographic and structural data managed with GIS technology. This study presents a complete workflow developed to process geological information to build a 3D model of major stratigraphic, structural and tectonic boundaries. The investigated area is located in the western part of the Aar Massif (external Central Alps, Switzerland) characterized by pronounced topographic (600–<4000 m) relief, making it prone for surface based 3D depth constructions. The workflow comprises four major steps:

(1)  Generation of 2D polylines in a map view: a two-dimensional dataset of sequences of polylines has been generated in ArcGIS (10.3.1) defining the starting dataset for the major stratigraphic and tectonic boundaries of the bedrock units. This dataset has been compiled and integrated by using: (i) GeoCover vector datasets 1:25 000 of the Swiss Geological Survey; (ii) The Geological Special Map 1:100 000 of the Aar Massif and the Tavetsch and Gotthard Nappes of the Swiss Geological Survey; (iii) data from literature; and (iv) additional field work conducted for this study in key-locations.

(2) Projection of 2D information onto 3D digital elevation model: with the 3D structural modelling software Move (Petex/Midland Valley; 2019.1) the boundaries have then been projected on a digital elevation model (swissALTI3D) with 2 m resolution.

(3) Construction of tectonic cross sections: the use of geometric arguments as well as structural measurements allows for projection of these boundaries into a dense regularly spaced network of 2D cross-sections.

(4) Interpolation of 3D surfaces: the surface and cross-sections boundaries can be interpolated by applying 3D projection and meshing techniques resulting in a final 3D structural model.

Generally, steps (2–4) require iterative adaptations particularly in the case of surface areas being covered by glaciers or unconsolidated Quaternary sediments. In the model, special emphasis is given to visualize the current structural disposition of the western Aar Massif as well as the relative geometric and overprinting relationships of the deformation sequence that shaped the investigated area throughout the Alpine deformation. Finally, since in the investigated area underground data are scarce, an assessment of the relative uncertainties related to input data and is intended to be performed following the approach proposed by Baumberger (2014) and Ferńandez (2005). The workflow presented here offers the chance to gain validation approaches for domains only weakly constrained or with no surface data available, by generating a 3D model that integrates all accessible geological information and background knowledge.

REFERENCES

Baumberger, R. (2014): Quantification of Lineaments: Link between internal 3D structure and surface evolution 328 of the Hasli valley (Aar massif, central alps, Switzerland), University of Bern, PhD Thesis, unpublished.

Ferńandez, O. (2005): Obtaining a best fitting plane through 3D georeferenced data, Journal of Structural Geology 27, pp. 855–858

How to cite: Musso Piantelli, F., Herwegh, M., Berger, A., Wiederkehr, M., Kurmann, E., Möri, A., and Baumberger, R.: 3D geological modelling of the western Aar Massif (external Central Alps, Switzerland), EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-8102, https://doi.org/10.5194/egusphere-egu2020-8102, 2020.

In the central and western parts of the Netherlands, the low-lying areas are vulnerable to flooding by rivers. During times of peak runoff, dikes are essential to keep the land dry and the people safe. Rigorous safety standards are in place to ensure dikes are capable of withstanding extreme water level conditions. Key components for the strength and stability of a dike are the internal structure and composition of the dike and the geology in the subsurface: a sandy aquifer may lead to piping and undercutting of the dike while weak or layered strata under certain hydraulic pressures could potentially lead to collapse and catastrophic failure of the dike.

For the dike reinforcement project ‘Sterke Lekdijk’, the regional water authority ‘Hoogheemraadschap de Stichtse Rijnlanden’ is investigating a 55 km long section of the dike along the right bank of the river Lek. Detailed knowledge about the subsurface is crucial when quantifying the conditions of dikes. Given the very heterogeneous build-up of the Holocene sediments this is not an easy task. For the shallow subsurface (down to 50 m below surface level) TNO – Geological Survey of the Netherlands builds and maintains a nation-wide stochastic 3D geological model called GeoTOP. With a 100x100x0.5 m voxel size this model gives a sense of the overall geology, but lacks the very detailed information below the dikes that is needed for the task at hand.

Construction of a high-resolution geological model requires a high data density. Traditionally, shallow geological models are based on borehole information. However, in the built environment another data source is available in the form of cone penetration tests (CPTs), which are routinely obtained to measure the strength of subsurface sediments for geotechnical purposes. Although classification charts are available to translate CPT measurements into lithological classes, these charts require adjustments for local use and resulting performance remains variable. To enable the use of CPTs for geological modelling an artificial neural network (ANN) was trained to translate CPT measurements to lithological classes. Training of the ANN was done on neighboring borehole-CPT pairs (spaced at max. 10 meters). The ANN produces realistic results, with cross-validation statistics showing a vast increase in performance of the ANN results compared to traditional classification charts.

The disclosure of CPTs for geological modelling greatly increases the data density along man-made structures such as dikes. A local high-resolution version of the GeoTOP model was constructed, with a voxel size of 25x25x0.25 m. This detailed information includes the lithostratigraphical unit the voxel belongs to, the most probable lithological class of the voxel as well as the probability of occurrence of particular lithological classes. The high-resolution model enables the local water authority to better estimate dike stability, better target additional measurements in areas of high uncertainty, and take more location specific reinforcement measures.

How to cite: Dabekaussen, W., de Bruijn, R., Kars, R. H., Meijninger, B. M. L., and Stafleu, J.: Integrating multiple geotechnical data types with machine learning to construct high-resolution 3D geological models, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-8500, https://doi.org/10.5194/egusphere-egu2020-8500, 2020.

Uncertainties are an inherent part of geological interpretation and immersive rendering has the potential to play a key role in gaining better insights. However, most 3D geological models have a limited possibility of manual, fast and smooth modification in order to make better decisions and interpretations. Here we present examples of parametric surface representations which use control points as a possibility to bring interactivity to geological modelling in immersive frameworks.

In fact, using 2D surfaces of 3D solid objects is a typical representation of 3D models. Two of the major ways for surface representation in computer graphics are implicit representations and parametric surface representations. Parametric surface representations, unlike implicit representations, are based on control points. Manipulating these control points makes it easy and intuitive to modify geological models smoothly and fast, with a potential to more interactive decision-making.

We present two different examples of parametric surface approaches; Spline Surfaces and Subdivision Surfaces. Spline surfaces, e.g. Bezier or NURBS surfaces, are a popular and common standard for CAD (Computer-Aided Design). Also, these surfaces are on the basis of parametric- based curves and a set of weighted control points. Subdivision Surfaces define smooth surfaces after a series of refinement which can be controlled by control points. Subdivision surfaces are not only a popular method for making free form models but also a common tool in animation, computer games and entertainment industry.

Recently, research has been done based on using spline surfaces to model diverse geological structures and reservoirs. Similar to applications in computer graphics, using these methods in geological modelling can have specific considerations. Model refinement (e.g. adding new control points) and the requirement of many patches with geometrical constraints for the representation of complex geometries are some of the main difficulties of using spline surfaces. In this presentation, we will discuss several of these aspects and show two promising and controllable techniques for intuitive use of parametric surface-based representations in 3D geological and reservoir modelling.

How to cite: Moulaeifard, S. and Wellmann, F.: Parametric Surfaced-Based Geological Reservoir Representation: A Computer Graphics Tool for Improved Decision Making in Immersive Environments, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-9761, https://doi.org/10.5194/egusphere-egu2020-9761, 2020.

Graphs are a commonly used and well-studied mathematical abstraction for the modeling of complex systems. Three-dimensional (3D) structural geology is no exception, and graphs have received significant attention in recent years to characterize the connectivity for fracture sets, faults, geological units and reservoir compartments. The basis for these analyzes is to summarize an existing structural model as a graph, and to label the nodes and edges using the geological features of interest. In this sense, structural geologists building a 3D structural model are actually creating a graph. For this, they use geological reasoning to relate the various rock units of the subsurface.  

As a matter of fact, the final graph corresponding to a 3D structural model also relates the input spatial data, such as field measurements or interpretive contact lines. Based on this observation, we have proposed a graph-based framework to stochastically model 3D fault networks from incomplete observations, which randomizes the assignment of fault evidence to fault objects. The geometry of these faults is then determined using existing geomodeling techniques. In this approach, each piece of data is considered as a node of a complete graph called a possibility graph. The edges of the possibility graph are valued by a likelihood that two graph nodes belong to the same fault surface, which makes it possible to quickly remove some edges corresponding the associations deemed impossible. A hierarchical simulation algorithm is then proposed, based on the observation that each fault network corresponds to a possible partitioning of the input graph into distinct cliques. This formulation allows to give upper bounds for the (very large) number of possibilities that can be generated. We give several examples of likelihoods that integrate prior geological knowledge (e.g., the fault size distribution and orientation distribution), and check the consistency of the sampling algorithm when more informative rules are used. These preliminary results show that the simulation method consistently explores the search space, but they also highlight the need to further study the mathematical and computational properties of the sampler. Nonetheless, this approach is promising to efficiently generate and cluster a large set of possible structural scenarios and the associated ensemble of structural models obtained by a combination of data-perturbation, interpolation and or model-perturbation.

How to cite: Caumon, G., Godefroy, G., and Marchal, P.: Fault network uncertainty assessment with a generative graph-based algorithm – Current status and perspectives, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-10359, https://doi.org/10.5194/egusphere-egu2020-10359, 2020.

As the number of underground activities increase, the need for better understanding of the geospatial properties become more and more essential for correct engineering designs and optimal decision making. However, gathering subsurface data is still an extremely costly and imprecise endeavour. Geological modelling has played a crucial role for years helping to understand and correlate the complex geometries encountered underground but single deterministic models fail to capture all possible configurations given the limited data. Probabilistic machine learning allows to integrate domain knowledge and observations of the physical world on a rigorous and consistent manner. Inferences to the probabilistic model implements an automatic learning-from-observations process.

In this work, we show how by embedding state-of-the-art implicit interpolants into probabilistic frameworks, we can integrate the information of distinct data sets in one single common earth model. We will present results from a minimal working example to introduce Bayesian statistics, to full 3-D probabilistic inversions. All the models used for this demonstration are implemented in the open-source library GemPy ( www.gempy.org) allowing full reproducibility of the results.

How to cite: de la Varga, M. and Wellmann, F.: Probabilistic Machine Learning in Structural Geology, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-10785, https://doi.org/10.5194/egusphere-egu2020-10785, 2020.

Drill core samples have been traditionally used by the mining industry to make resource estimations and to build geological models. The hyperspectral drill core scanning has become a popular tool in mineral exploration because it provides a non-destructive method to rapidly characterise structural features, alteration patterns and rock mineralogy in a cost effective way.

Typically, the hyperspectral sensors cover a wide spectral range from visible and near-infrared (VNIR) to short and long wave infrared (SWIR and LWIR). The spectral features in this range will help to characterize a large number of mineral phases and complement the traditional core logging techniques. The hyperspectral core scanning provide mineralogical information in a millimetre scale for the entire borehole, which fills the gap between the microscopic scale of some of the laboratory analytical methods or the sparse chemical assays and the meter scale from the lithological descriptions.

However, applying this technique to the core samples of an entire ore deposit results in big datasets. Therefore, there is the need of a workflow to build a 3D geological model conditioned by the data applying suitable data reduction methods and appropriate interpolation techniques.

This contribution presents a case study in the combination of traditional core logging and hyperspectral core logging for geological modelling. To attain mineral and alteration maps from the hyperspectral data, unsupervised classification techniques were applied generating a categorical data set. The amount of data was reduced by the application of a domain generation algorithm based on the hyperspectral information. The domain generated by the algorithm is a compositional categorical data set that was then fed to condition the application of stochastic Plurigaussian simulations in the construction of 3D models of geological domains. This technique allows to simulate the spatial distribution of the hyperspectral derived categories, to make a resource estimation and to calculate its associated uncertainty.

How to cite: De La Rosa, R., Khodadadzadeh, M., Contreras, C., Tusa, L., Kirsch, M., Tolosana-Delgado, R., and Gloaguen, R.: 3D modelling of a mineral deposit using drill core hyperspectral data, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-14952, https://doi.org/10.5194/egusphere-egu2020-14952, 2020.

Seismic data plays a key role in developing our understanding of the subsurface by providing 2-D and 3-D indirect imaging. But the resulting data needs to be interpreted by specialists using time-intensive, error-prone and subjective manual labour. While the automation of data classification using Machine Learning algorithms is starting to show promising results in areas of good data quality, the classification of noisy and ambiguous data will continue to require geological reasoning for the foreseeable future. In Schaaf & Bond (2019) we provided a first quantification of the uncertainties involved in the structural interpretation of a 3-D seismic volume by analysing 78 student interpretations of the Gullfaks field in the northern North Sea. Our work also concretized the question of to which degree the seismic data itself could provide useful information towards a prediction of interpretation uncertainty.

We now look at the same dataset in an effort to answer the question if we can adequately reproduce the observed interpretation uncertainties by approximating them as aleatoric uncertainties in a stochastic geomodeling framework. For this we make use of the Python-based open-source 3-D implicit structural geomodeling software GemPy to leverage open-source probabilistic programming frameworks and to allow for scientific reproducibility of our results. We identify potential shortcomings of collapsing interpretation uncertainties into aleatoric uncertainties and present ideas on how to improve stochastic parametrization based on the seismic data at hand.

Schaaf, A., & Bond, C. E. (2019). Quantification of uncertainty in 3-D seismic interpretation: Implications for deterministic and stochastic geomodeling and machine learning. Solid Earth, 10(4), 1049–1061. https://doi.org/10.5194/se-10-1049-2019

How to cite: Schaaf, A., de la Varga, M., Bond, C. E., and Wellmann, F.: Towards reproducing seismic interpretation uncertainties using open-source stochastic geomodeling in Python, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-18359, https://doi.org/10.5194/egusphere-egu2020-18359, 2020.

Identification and modeling of the carbonate tidal channels is key for finding sweet spots or areas at higher risk to water breakthroughs which have a significant impact on the development and monitoring of reservoir dynamic performance. However, such these channels cannot be easily characterize by conventional seismic attributes. It is important to decipher the complexity of carbonate tidal channel architecture with integrated multisource data and different approaches.

A step wise approach has been taken in this work. First, rock physics model was carried out to ensure that elastic properties can be applied for reservoir characterization from the seismic data. Then, post-stack seismic inversion was carried out on the high resolution of 3D seismic dataset. The seismically derived porosity estimation is undertaken using geostatistical method and multiattributes combination was used. Probabilistic neural network training technique was then performed to improve the results for thick reservoir and the result has been used for seismic conditioning of geological models. Finally, the spatial distribution of porosity volume was cautiously assessed through the comparison between input and blind wells, also validated by core data.

The analysis of rock physics displayed a high correlation between elastic properties and the porosity distribution of the Mishrif channel, three facies were observed. The final interpretation of seismically derived characterization in Mishrif channel, observed a different lateral distribution of inverted elastic properties. These features of Mishrif carbonate tidal channels could be classified into these regions: north, southwest, and east. Related a high porosity with low acoustic impedance appeared mostly in these channels which reflect a good reservoir quality grainstone channels or sholas bodies. While, outside these channels is heavily mud filled by peritidal carbonates and characterized a high acoustic impedance anomaly with low quality of porosity distribution.

The results provided a new insight into the distribution of the petrophysical properties and reservoir architecture of facies with quantification of their influence on dynamic reservoir behavior in the Mishrif channelized systems and also for similar heterogeneous carbonate reservoirs

How to cite: Alali, A. and Stephen, K.: Application of Probabilistic Neural Network and Rock physics Analysis for Carbonate Reservoir Characterization: A Case Study from Onshore Supergiant Oil Field, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-184, https://doi.org/10.5194/egusphere-egu2020-184, 2020.

Uncertainty quantification is an important aspect of geological modelling and model interpretation. Recent developments in geological modelling allow us to view the inversion as a problem in Bayesian inference, incorporating the uncertainties in the observations, the forward models and the prior knowledge from geologists. The sampling method Markov chain Monte Carlo (MCMC) is then often applied to solve this inference problem. However, this stochastic modelling approach is limited as the number of parameters increases to higher dimensions. To ensure an efficient sampling in a high dimensional problem, we take advantage of recent advances using Hessian-based MCMC methods in this work. The Hessian of the negative log posterior with respect to the input parameters is evaluated at the Maximum a Posteriori (MAP) point. A Laplace approximation of the posterior at the MAP is then given by the inverse of the local Hessian. This sampling approach provides a potentially less computationally expensive and more efficient way for high dimensional geological inverse modelling, especially in cases where parameters are highly correlated, a situation that commonly arises in geological modelling.

How to cite: Liang, Z. and Wellmann, F.: Uncertainty quantification in geological modelling by Hessian-informed MCMC, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-20042, https://doi.org/10.5194/egusphere-egu2020-20042, 2020.

Subsurface information is usually a limited resource in geological modelling. This is not the case, however, for the Kraków-Silesian Homocline in central Poland. It was subject to rapid exploitation of ore-bearing clays in the second half of the 20^th century. Exhaustive geological documentation remained after this activity had ceased and it contains thousands of borehole records. A small part of this resource has recently been incorporated to propose a new method for determining the dominant orientation of a selected geological contact. This new method regarded Delaunay triangles as source of local orientations that were then analyzed on stereonets. The geological contacts in this region are inclined gently towards NE, but they are also faulted and indicate some stratigraphic noise which makes the extraction of dominant orientation a challenging task.

It is still unknown, however, to which extent the proposed modelling approach is capable of detecting faults and calculating their orientation. This is particularly important for the introduction of a new method for the recognition of faults based on investigating spatial distribution of orientation patterns. This expert-guided methodology assumes to relate orientation trends with genetic trends and investigate them on 2D maps.

In this research, we built synthetic models of faulted contacts to observe the behaviour of triangles intersecting the fault surface. To observe the variability of the orientation at larger scale, and perhaps to constrain it at the same time, we applied a combinatorial algorithm for creating all three-element subsets from an n-element set. The employment of this combinatorial approach allowed to achieve a better clustering effect around the expected orientation. The limitation of the proposed approach can be attributed to some unexpected and unintuitive orientations. Compared to previous studies these singularities seem to be geometrical and not numerical in nature.

How to cite: Michalak, M., Kuzak, R., Gładki, P., and Kulawik, A.: Faulted geological contacts: constraining uncertainty of discontinuities orientation using triangulation and combinatorial algorithm, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-20125, https://doi.org/10.5194/egusphere-egu2020-20125, 2020.

Implicit geological modelling allows for observations of surface location and orientation to be interpolated into continuous 3D surfaces. These surfaces are usually built by finding a function that minimises the misfit between the surface and observations (gradient or value of the implicit function) combined with a regularisation constraint that controls how the surface develops between observations. When modelling complex terranes such as fold series, fault networks or intrusions it is usually necessary to use interpretive constraints for creating the expected geometries. These interpretations are problematic, as the constraints are usually not observations but realisations of the geologists’ subjective interpretation, and are therefore difficult to change and interrogate to better understand the geometry. Recent developments for implicit modelling of folds and faults have built new local coordinate systems using the structural geology of the object being modelled and are termed structural frames. For example, for folds, the structural frame is aligned to the axial surface of the fold and fold axis. For faults, the structural frame is aligned to the fault surface and slip direction. Using structural frames, conceptual models of the fold and fault geometries can be combined with the observations of the surfaces. This means that rather than using the geologists' subjective interpretation to constrain the model geometries, the conceptual model can guide the interpolation where observations are missing. Geological uncertainties in the resulting geometries can be assessed by framing the modelling as an inverse problem and varying the conceptual model parameters to fit the geological observations. In this contribution, we review the use of structural frames for constraining 3D geometry of structurally complex terranes and provide an example of a faulted fold series.

How to cite: Grose, L., Laurent, G., and Ailleres, L.: Using structural frames to integrate structural geology into implicit 3D modelling, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-20819, https://doi.org/10.5194/egusphere-egu2020-20819, 2020.

Kriging is a widely used geostatistical tool to estimate the value of a spatially correlated property at a certain location based on sampled data in the surrounding domain. It creates a weighted average of this data based on the distances to the point that is to be predicted. Interpolated maps and simulated stationary fields play an important role in various geological fields like flow simulation and resource estimation.

Distances between locations in a specified domain thus play an important role in the kriging process and are traditionally measured as straight-line distances. In this work we develop an alternative distance metric to these Euclidian distances normally used in the geostatistical worklflow.

The metric is based on a scalar field that is calculated for 3-D geologic models that are interpolated based on a potential field method implemented in the open-source, implicit geologic modeling tool GemPy.

The measure follows the curvature of the deformation of stratigraphic units, which is relevant when modeling the distribution of a property that developed before deformation. As an undeformed state of the domain is represented by these distances, authorized variogram and covariance models are still valid with the introduced distance metric.

In addition, anisotropies can be modeled in relation to the deformation of a layer by manipulating the new distance metric. The kriging calculations and distance measurements are combined in a Sequential Gaussian Simulation to estimate an entire domain, while adequately modeling the underlying variance. We show first promising results of our work using the newly developed distance metric in different geological settings, including folded and faulted domains.

How to cite: von Harten, J., de la Varga, M., and Wellmann, F.: Geostatistical interpolation and simulation of geological properties considering regional deformation, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-21115, https://doi.org/10.5194/egusphere-egu2020-21115, 2020.

This work shows that the traditional version of geological models of oil and gas fields obtained by a computer approach is not the only possible one and it prevents the development of modeling as a whole, since it is not truly mathematical.

Given that computers do not work with images, but with numbers, a novel approach is presented for the construction of truly mathematical geological models. The proposed model has an unusual appearance and is not intended for visual analysis, but it is more effective for forecasting. The mathematical basis of the novel approach is the cascades of fuzzy-logical matrices, which are formed from spatial coordinates and considered geological parameters.

Suppose that for each point in the geological grid there is a coordinate vector, in the simplest case these are the lateral coordinates X and Y, as well as the vertical coordinate Z. There is also a set of points (wells) at which the specified coordinates and the values of considered geological parameter, for example, porosity or oil saturation are determined. If some seismic parameter is added to them, which can be taken from grids constructed according to seismic data at the points of the wells, then four coordinates become available.

Preliminary, all considered geological parameters should be normalized in the range from -1.0 to + 1.0 in order to standardize and equalize them.

Four coordinates give six independent pairs. A matrix is constructed for each of these pairs. The matrix size can be different - from 100 per 100 to 1000 per 1000.

Next, the values of the considered geological parameter at the well points determined by four coordinates are applied to these matrices. Certainly, such points are much smaller than the points in the matrix, therefore, to fill the entire polygon of the matrix, the interpolation method is used, based on the idea of the lattice Boltzmann equations.

The number of fuzzy-logical matrices in one geological model can reach several hundreds.

Using the obtained matrices, one can construct membership functions and predict the values of the selected geological parameters, as well as the distribution of initial hydrocarbon reserves or the effectiveness of new drilling at the field.

The novel approach to geological modeling based on the cascades of fuzzy-logical matrices may seem complicated. However, the calculation of these cascades is carried out completely automatically, since they are the truly mathematical functions, and not the illustrations of the geological structure of the filed, and they are directly used in forecasting calculations.

The cascades of fuzzy-logical matrices can be considered as a new form of machine learning algorithms, for which it is advisable to use big data sets. It opens up the additional possibilities for the application of machine learning methods in geological modeling of oil and gas fields with conventional and unconventional reserves.

How to cite: Ursegov, S. and Zakharian, A.: Novel Approach to Geological Modeling with Combination of Machine Learning, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-21739, https://doi.org/10.5194/egusphere-egu2020-21739, 2020.

Sharp interfaces often separate regions in the subsurface with distinctively different properties due to processes in geological evolution – and these   interfaces are relevant for a variety of scientific investigations, as well as practical applications.  The delineation of these layers with different properties is commonly attempted on the basis of geological and geophysical data, for example as picks in  prevalent seismic reflectors, interpreted from potential field measurements, and derived from observations in drillholes. 

We evaluate here a specific method to determine the position and shape of such an interface using measurements of state variables related to a physical flow field described with an elliptic PDE. A typical example is the measurement of temperatures related to heat flow through zones with distinctively different thermal conductivities. We use a level-set function to describe the interface and determine the optimal interface shape for a 2-D case. This type of shape inversion has been successfully attempted before, and we extend on this previous work by including additional shape constraints on orientation, interface, and observations of specific segmentation outcomes. These constrains are motivated by geological information that may be available, for example as derived and interpreted from additional geophysical measurements. 

We model this as an image segmentation problem, where we are looking for a segmentation of the image domain whose induced temperature minimizes the squared L² distance to temperature measurements on a lower dimensional set. From an optimal control perspective, the segmentation is the control and the temperature the state.  Numerically, the segmentation is represented by a level set and the minimization is done using a gradient flow, where the derivative with respect to the level set is computed using dualization. Moreover, we include additional geologically motivated constraints by adding soft penalties to the objective function.

We test our method with several conceptual examples to determine the feasibility and limitations, especially with regard to different interface shapes and the amount of available information and additional geological constraints, as well as the influence of noise on the detection  accuracy. Results show that these additional constraints help determining an interface. However, measurement noise and a non-homogeneous spatial distribution of physical properties reduces the accuracy of the derived interface. 

How to cite: Wellmann, F. and Berkels, B.: Detecting subsurface interfaces with a physics-based level-set segmentation and additional geological constraints, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-22526, https://doi.org/10.5194/egusphere-egu2020-22526, 2020.