专利摘要:
The invention relates to a method that can include receiving (510) a mesh that represents a geological environment, the mesh comprising elements; receiving (520) location information for a discontinuity in the geological environment; at least in part depending on the location information, the definition (530) of enrichment equations for a part of the elements, the enrichment equations having a jump function that models the discontinuity; the resolution (540) of a system of equations for an implicit function, the system of equations containing the enrichment equations; and, at least in part depending on the resolution, outputting (550) values for the implicit function with respect to at least a portion of the mesh.
公开号:FR3036210A1
申请号:FR1554222
申请日:2015-05-12
公开日:2016-11-18
发明作者:Thomas Laverne
申请人:Services Petroliers Schlumberger SA；
IPC主号:

专利说明:

[0001] 29469 / 298EN1 1 GEOLOGICAL STRATIGRAPHY BY IMPLICIT FUNCTIONS AND BACKGROUND FUNCTIONS [0001] The phenomena associated with a sedimentary basin can be modeled using a mesh, a grid, etc. As an example, a structural model can be created based on data associated with a sedimentary basin. For example, when a basin has various types of features (eg, stratigraphic layers, faults, etc.), the data associated with these features can be used to create a structural model of the basin. Such a model can form the basis of an analysis, another modeling, etc.
[0002] The various technologies, techniques, etc. described herein relate to structural modeling, structural models, and so on. SUMMARY [0002] A method may comprise the reception of a mesh that represents a geological environment, the mesh comprising elements; receiving location information for a discontinuity in the geological environment; at least in part according to the location information, the definition of enrichment equations for a part of the elements, the enrichment equations having a jump function that models the discontinuity; solving a system of equations for an implicit function, the system of equations containing the enrichment equations; and, at least in part depending on the resolution, outputting values for the implicit function with respect to at least a portion of the mesh. A system may include a processor; a memory functionally coupled to the processor; one or more modules stored in the memory, the module or modules comprising instructions executable by the processor, the instructions comprising instructions for: receiving a mesh that represents a geological environment, the mesh comprising elements; receive location information for a discontinuity in the geological environment; at least in part depending on the location information, define enrichment equations for a part of the elements, the enrichment equations having a jump function that models the discontinuity; solve a system of equations for an implicit function, the system of equations containing the enrichment equations; and outputting values for the implicit function with respect to at least a portion of the mesh. One or more computer readable storage media may include processor executable instructions, the instructions including instructions for requesting a system to: receive a mesh that represents a geological environment, the mesh including elements; receiving location information for a discontinuity in the geological environment; at least in part depending on the location information, define enrichment equations for a part of the elements, the enrichment equations having a jump function that models the discontinuity; solve a system of equations for an implicit function, the system of equations containing the enrichment equations; And outputting values for the implicit function with respect to at least a portion of the mesh. Various other apparatus, systems, methods, etc. are also described. This summary is provided to present a selection of concepts which are more fully described below in the detailed description. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as a medium to limit the scope of the claimed subject matter. BRIEF DESCRIPTION OF THE DRAWINGS [0004] The features and advantages of the implementations described can be more readily understood from the following description taken in conjunction with the accompanying drawings. [0005] FIG. 1 illustrates an exemplary system that comprises various components for simulating a geological environment; [0006] FIG. 2 illustrates an example of a system; [0007] FIG. 3 illustrates examples of a method, a convention, constraints 20 and equations; [0008] FIG. 4 illustrates an example of a system and an example of a method; [0009] FIG. 5 illustrates an example of a method; [0010] FIG. 6 illustrates an example of a mesh; FIG. 7 illustrates an example of a mesh and examples of tetrahedrons; Figure 8 illustrates examples of meshes; [0013] FIG. 9 illustrates an example of a mesh and examples of equations; FIG. 10 illustrates an example of part of a mesh; [0015] FIG. 11 illustrates an example of a part of a mesh; FIG. 12 illustrates an example of part of a mesh; Figure 13 illustrates an example of part of a mesh; [0018] FIG. 14 illustrates an example of a method; FIG. 15 illustrates examples of values of implicit functions; and [0020] Fig. 16 illustrates exemplary components of a system and a networked system. DETAILED DESCRIPTION [0021] The following description includes the best mode currently envisaged for practicing the implementations described. This description should not be considered in a limiting sense, but is merely intended to describe the general principles of the implementations. The scope of the implementations described should be verified by reference to the claims granted. [0022] The phenomena associated with a sedimentary basin (eg, an underground region, whether it is under a land surface, a water surface, etc.) can be modeled using a model or models. As an example, a structural model of a basin can be useful for understanding many processes related to the exploration and production of natural resources (estimation of reserves in place, well drilling, production forecast, etc.). As an example, a structural model can be used as a basis for constructing a model for use with a digital technique. For the application of a numerical technique, equations may be discretized using a grid that includes nodes, cells, and so on. To represent features in a geologic environment, a structural model can help correctly locate nodes, cells, etc., of a grid for use in a simulation employing one or more digital techniques. As an example, a structural model can itself have a mesh, which can sometimes be called a grid. As an example, a structural model may allow analysis possibly without resorting to the creation of a grid adapted to the discretization of equations for a numerical solver (eg, take a structured grid that can reduce computing requirements, etc. .). As for numerical techniques, a numerical technique such as the finite difference method may include discretizing a 1D differential heat equation for the temperature with respect to a spatial coordinate to obtain approximate temperature derivatives. (eg, first order, second order, etc.). When the time is of interest, a derivative of the temperature with respect to time can also be obtained. As for the spatial coordinate, the digital technique may be based on a spatial grid which has various nodes for each of which a temperature will be obtained during the resolution of the heat equation (e.g., depending on the boundary conditions, terms of generation, etc.). Such an example may apply to multiple dimensions in space (e.g., when discretization is applied to multiple dimensions). Thus, a grid may discretize a volume of interest (V01) into elementary elements (eg, grid cells or blocks) that may be affected or associated with properties (eg, porosity, rock type, etc. .), which may relate to the simulation of physical processes (eg, flow of fluid, compaction of a reservoir, etc.). As another example of a numerical technique, consider the finite element method where a space can be represented by one-dimensional or multidimensional "elements". For a spatial dimension, an element can be represented by two nodes positioned along a spatial coordinate. For multiple spatial dimensions, an element may have any number of nodes. In addition, some equations may be represented by some nodes, while others are represented by a smaller number of nodes (eg, take an example for NavierStokes equations where fewer nodes represent pressure) . The finite element method can include obtaining nodes that can define triangular elements (e.g., 3D tetrahedra, higher order simplex in multidimensional spaces, etc.), or quadrilateral elements (e.g. , hexahedra or pyramids in 3D, etc.), or polygonal elements (eg, 3D prisms, etc.). These elements, as defined by corresponding nodes of a grid, can be called grid cells. [0026] Yet another example of a digital technique is the finite volume method. For the finite volume method, values for equation variables of a model can be computed at discrete locations on a grid, for example a grid node that has a "finite volume" surrounding it. The finite volume method can apply the divergence theorem for flow estimation at the surfaces of each finite volume so that the flux entering a given finite volume is equal to that leaving it for one or more volumes. adjacent finishes (eg, to comply with conservation laws). For the finite volume method, nodes in a grid can define grid cells. As mentioned, when a sedimentary basin (eg, an underground region) has various types of features (eg, stratigraphic layers, faults, etc.), nodes, cells, etc. a mesh or grid can represent, or be assigned to, such features. As an example, consider a structural model that can have one or more meshes. Such a model can serve as a basis for forming a grid for discretized equations to represent a sedimentary basin and its characteristics. With respect to a stratigraphic sequence, a sedimentary basin may include sedimentary deposits grouped into stratigraphic units, for example, depending on any of a variety of factors, to approximate or represent time lines that place stratigraphy in a chronostratigraphic setting. Even if sequential stratigraphy is mentioned, lithostratigraphy can be applied, for example, depending on the lithology similarity of rock units (e.g., rather than time-related factors). As an example, a mesh can conform to structural features such as, for example, Y-shaped faults, X-shaped faults, small-angle unconformities, saline bodies, intrusions, etc. . (eg, geological discontinuities), to better understand the complexity of a geological model. As an example, a mesh may optionally conform to a stratigraphy (eg, in addition to one or more geologic discontinuities). Geological discontinuities may include model discontinuities such as one or more model boundaries. As an example, a mesh can be populated with property fields generated, for example, by geostatistical methods. In general, a relationship may exist between the spacing of nodes and a phenomenon or phenomena modeled. Various scales can exist within a geological environment; for example, a molecular scale may be in the range of about 10-9 to about 10-8 meters, a pore scale may be in the range of about 10-6 to about 10-3 meters, a continuum apparent may be in the range of about 10-3 to about 10-2 meters, and a basin scale of about 103 to about 105 meters. As an example, nodes of a mesh can be selected at least in part depending on the type of phenomenon or phenomena being modeled (eg, to select nodes with appropriate spacing or spacings). As an example, nodes in a grid may have a node-to-node spacing of about 10 meters to about 500 meters. In this example, a modeled basin may cover, for example, more than about 103 meters. As an example, a node-to-node space may vary, for example being smaller or larger than the aforementioned spacings. Some data may be involved in the construction of an initial mesh, and subsequently, a model, a corresponding mesh, etc. may optionally be updated in response to the output of a model, changes in time, physical phenomena, additional data, etc. The data may include one or more of the following: depth and thickness maps and geometries and fault chronology from seismic, remote sensing, electromagnetic, gravity, outcrop, and logging data. In addition, the data may include depth and thickness maps derived from facies variations. FIG. 1 shows an example of a system 100 that includes various management components 110 for managing different aspects of a geological environment 150 (eg, an environment that includes a sedimentary basin, a reservoir 151, a or more fractures 153, etc.). For example, the management components 110 may allow direct or indirect management of detection, drilling, injection, extraction, etc., relative to the geological environment 150. In turn, Other environmental information may become available as a feedback 160 (eg, possibly as input to one or more of the management components 110). In the example of FIG. 1, the management components 110 comprise a seismic data component 112, an additional information component 114 (for example, well / logging data), a processing component. 116, a simulation component 120, an attribute component 130, an analysis / visualization component 142 and a process stream component 144. In operation, seismic data and other information provided by the components 112 and 114 can be input into the simulation component 120. In an exemplary embodiment, the simulation component 120 may be based on entities 122. The entities 122 may comprise terrestrial entities or geological objects such as wells, surfaces, tanks, etc. In the system 100, the entities 122 may include virtual representations of real physical entities that are reconstructed for simulation purposes. Entities 122 may include features based on data acquired by detection, observation, etc. (eg, seismic data 112 and other information 114). An entity may be characterized by one or more properties (eg, a geometric pillar grid entity of a terrestrial model may be characterized by a porosity property). These properties can represent one or more measures (eg acquired data), calculations, and so on. In one exemplary embodiment, the simulation component 120 may operate in conjunction with a software infrastructure such as an object-oriented infrastructure. In such an infrastructure, entities may have features based on predefined classes to facilitate modeling and simulation. A commercially available example of an object-oriented infrastructure is the MICROSOFT®. NETTM 25 (Redmond, Washington) infrastructure, which provides a set of extensible object classes. In the .NETTM framework, an object class includes a reusable code module and the associated data structures. Object classes can be used to instantiate object instances for use by a program, script, and so on. For example, borehole classes may define objects for representing boreholes based on well data. In the example of FIG. 1, the simulation component 120 can process information to conform to one or more attributes specified by the attribute component 130, which can comprise an attribute library. This processing may occur prior to entry into the simulation component 120 (eg, take the processing component 116). As an example, the simulation component 120 may perform operations on input information based on one or more attributes specified by the attribute component 130. In an exemplary embodiment, the component 120 can construct one or more models of the geological environment 150, upon which one can rely to simulate the behavior of the geological environment 150 (eg, sensitive to one or more acts, whether natural or artificial). In the example of FIG. 1, the analysis / visualization component 142 may allow interaction with a model or model-based results (e.g., simulation results, etc.). As an example, an output of the simulation component 120 may be an input of one or more other process streams, as indicated by the process stream component 144. [0037] As an example, the simulation component 120 may include a or several features of a simulator such as the ECLIPSETM tank simulator (Schlumberger Limited, Houston Texas), the INTERSECTTM tank simulator (Schlumberger Limited, Houston Texas), etc. As an example, a tank or tanks may be simulated for one or more enhanced recovery techniques (eg, take a thermal process such as SAGD, etc.). In one exemplary embodiment, the management components 110 may include features of a commercially available infrastructure such as the PETREL® seismic simulation software infrastructure (Schlumberger Limited, Houston, Texas). The PETREL® infrastructure provides components that enable the optimization of exploration and reconnaissance operations of a deposit. The PETREL® 20 infrastructure includes seismic simulation software components that can output information to be used to increase tank performance, for example by improving the productivity of the active team. Through the use of such an infrastructure, various professionals (eg geophysicists, geologists, and reservoir engineers) can develop collaborative workflows and integrate operations to streamline processes.
[0003] Such an infrastructure can be considered an application and can be considered as a data-driven application (e.g. when the data is an input for modeling, simulation, etc. ).  In an exemplary embodiment, various aspects of the management components 110 may include add-ons and expansion modules that operate according to the specifications of an infrastructure.  For example, a commercially available infrastructure known as the OCEAN® Infrastructure (Schlumberger Limited, Houston, Texas) allows the integration of additives (or add-ons) into a process flow of the PETREL® infrastructure.  The OCEAN® infrastructure leverages the NET® tools (Microsoft Corporation, Redmond, Washington) and provides stable, user-friendly interfaces for efficient development.  In an exemplary embodiment, various components may be implemented in the form of add-ons (or expansion modules) that conform to and function according to the specifications of an infrastructure ( eg. according to the specifications of an application programming interface (API), etc. ).  FIG. 1 also shows an example of an infrastructure 170 which comprises a model simulation layer 180 with a service layer of the infrastructure 190, a core layer of the infrastructure 195 and a layer of modules. 175.  The infrastructure 170 may include the OCEAN® commercially available infrastructure, the Model 180 simulation layer being the software package centered on the commercially available PETREL® model that hosts OCEAN® infrastructure applications.  In an exemplary embodiment, the PETREL® software can be considered a data-driven application.  PETREL® software may include an infrastructure for building and viewing a model.  Such a model may include one or more grids.  The model simulation layer 180 can provide domain objects 182, act as a data source 184, provide a rendering 186 and provide various user interfaces 188.  The rendering 186 may provide a graphical environment in which applications may display their data, while the user interfaces 188 may provide usual usability for the application user interface components.  In the example of FIG. 1, the domain objects 182 may comprise entity objects, property objects and possibly other objects.  The entity objects can be used to geometrically represent wells, surfaces, reservoirs, etc. , while property objects can be used to provide property values as well as data versions and display settings.  For example, an entity object may represent a well where a property object provides logging information as well as version information and display information (e.g. , to display well 25 as part of a model).  In the example of FIG. 1, data can be stored in one or more data sources (or data stores, generally physical data storage devices), which can be on identical physical sites. or different and be accessible by one or more networks.  The model simulation layer 180 can be configured to model projects.  As such, a particular project can be stored, with the stored project information including entries, templates, results, and folders.  Thus, at the end of a modeling session, a user can store a project.  Subsequently, the project can be recovered and restored using the model simulation layer 180, which can recreate instances of the relevant domain objects.  In the example of FIG. 1, the geological environment 150 may comprise layers (e.g. laminating) which comprise a reservoir 151 and which can be cut by a fault 153.  As an example, the geological environment 150 may be equipped with any of a variety of sensors, detectors, actuators, etc.  For example, the equipment 152 may include a communication circuit for receiving and transmitting information to one or more networks 155.  This information may include information associated with downhole equipment 154, which may be equipment for acquiring information, facilitating recovery of a resource, etc.  Other equipment 156 may be located away from the drilling site and include detection, transmission or other circuits.  This equipment may include a storage and communication circuit for storing and communicating data, instructions, etc.  As an example, one or more satellites may be provided for communication, data acquisition, etc.  For example, FIG. 1 shows a satellite in communication with the network 155 that can be configured for communications, noting that the satellite may, in addition or in replacement, include an imaging circuit (e.g. , spatial, spectral, temporal, radiometric, etc. ).  FIG. 1 also shows the geological environment 150 as possibly comprising equipment 157 and 158 associated with a well which comprises a substantially horizontal portion which can cross one or more fractures 159.  For example, consider a well in a shale formation that may have natural fractures, artificial fractures (eg. , hydraulic fractures) or a combination of natural and artificial fractures.  As an example, a well may be drilled for a laterally extending reservoir.  In this example, lateral variations of properties, constraints, etc.  may exist, an assessment of these variations that may assist planning, operations, etc.  to develop a laterally extending reservoir (e.g. , by fracturing, injection, extraction, etc. ).  As an example, the equipment 157 and / or 158 may comprise components, a system, systems, etc.  for fracturing, seismic detection, seismic data analysis, evaluation of one or more fractures, etc.  As mentioned, the system 100 can be used to perform one or more processing flows.  A process flow can be a process that involves a number of operations.  An operation can act on data, for example to create new data, to update existing data, etc.  As an example, we can act on one or more inputs and generate one or more results, for example on the basis of one or more algorithms.  As an example, a system can include a workflow editor for creating, editing, running, and so on.  a processing flow.  In this example, the process stream editor may allow the selection of one or more predefined operations, one or more custom operations, and so on.  As an example, a process stream may be a process stream that can be implemented in the PETREL® software, which for example acts on seismic data, seismic attribute (s). ), etc.  As an example, a process flow may be a process that can be implemented in the OCEAN® infrastructure.  As an example, a process flow may include one or more operations that access a module such as an extension module (e.g. , external executable code 5, etc. ).  As an example, a method may comprise a structural modeling, for example the construction of a structural model, the editing of a structural model, and so on.  of a geological environment.  As an example, a process flow may include obtaining a structural model prior to constructing a grid (e.g. , using the structural model), which in turn may be suitable for use with one or more digital techniques.  As an example, one or more applications may act on a structural model (e.g. , entry of a structural model).  FIG. 2 shows an example of a system 200 which comprises a block of geological / geophysical data 210, a block of surface models 220 (e.g. for one or more structural models), a block of volume modules 230, an application block 240, a digital processing block 250 and an operational decision block 260.  As shown in the example of FIG. 2, the geological / geophysical data block 210 may include data from borehole or wellheads 212, data from a seismic interpretation 214, data from an interpretation outcrop and possibly data from geological knowledge.  As for the block of surface models 220, it can allow the creation, editing, etc.  one or more surface models based for example on fault surfaces 222, and / or horizon surfaces 224 and / or possibly topological relationships 226.  With respect to the 230 volume template block, it can enable creation, editing, and so on.  one or more volume models based, for example, on boundary representations 232 (e.g. , to form a sealed pattern), and / or structured grids 234, and / or unstructured meshes 236.  As shown in the example of Figure 2, the system 200 may allow the implementation of one or more processing streams, data from the data block 210 being used for example to create, edit, etc..  one or more surface models of the surface pattern block 220, which may be used to create, edit, etc.  one or more volume models of the 230 volume model block.  As shown in the example of FIG. 2, the surface model block 220 can provide one or more structural models, which can be entered into the application block 240.  For example, such a structural model can be provided to one or more applications, possibly without performing one or more processes of volume model block 230 (e.g. for digital processing by the digital processing block 250).  Therefore, the system 200 may be suitable for one or more processing streams for structural modeling (e.g. possibly without performing digital processing with the digital processing block 250).  [0050] As for the application block 240, it may include applications such as a well prognostic application 242, a reserve calculation application 244 and a well stability evaluation application 246.  For digital processing block 250, it may include a process for seismic velocity modeling 251 followed by seismic processing 252, a process for petroleum facies and property interpolation 253 followed by simulation of flow 254, and a process for a geomechanical simulation 255 followed by a geochemical simulation 256.  As indicated, as an example, a process stream may range from the volume template block 230 to the digital processing block 250 and then to the application block 240 and / or the operational decision block 260.  As another example, a process flow may range from surface model block 220 to application block 240 and then to operational decision block 260 (e.g. , take an application that works using a structural model).  In the example of FIG. 2, the operational decision block 260 may include a seismic survey design process 261, a well flow adjustment process 252, a well trajectory planning process. 263, a well completion planning process 264 and a process for one or more surveys, for example to decide to explore, develop, abandon, etc.  a prospection.  Consider again the data block 210, where the wellhead or borehole data 212 may include the spatial location, and possibly the inclination of the surface, of an interface between two geologic formations or an underground discontinuity such as a geological fault; the seismic interpretation data 214 may comprise a set of points, lines or surface pieces interpreted from seismic reflection data, and representing interfaces between media (e.g. geological formations in which the velocity of seismic waves differs) or subterranean discontinuities; the outcrop interpretation data 216 may comprise a set of lines or points, possibly associated with a measured inclination, representing boundaries between geological formations or geological faults, as interpreted on the surface of the Earth; and the geological knowledge data 218 may include, for example, knowledge of the paleotectonic and sedimentary evolution of a region.  [0053] As for the structural model, it may be, for example, a set of grid or meshed surfaces representing one or more interfaces between geological formations (e.g. , horizon surfaces, mismatched surfaces, geological bodies, etc. ) or mechanical discontinuities (fault surfaces) in the subsurface.  As an example, a structural model may include certain information on one or more topological relationships between surfaces (e.g. , a fault A truncates a fault B, a fault B intersects a fault C, etc. ).  As an example, an environment may include one or more matching surfaces and / or one or more mismatched surfaces.  As an example, a mismatch may be a geological surface that is disposed between an older material and a newer material (e.g. , older rock and more recent rock) and which represents a disparity in a geological record.  As an example, such a surface could result from a hiatus in a sediment deposition, possibly combined with erosion, or deformation such as fault formation.  An angular mismatch may be a type of mismatch that separates more recent strata from older eroded, inclined strata.  As an example, a discrepancy may represent a period without deposit, possibly combined with erosion.  As an example, a discrepancy may separate overlying strata from older igneous or metamorphic rocks.  As an example, a process stream may include the analysis and interpretation of one or more mismatches (e.g. at the local, regional and / or global level) and may include the analysis and interpretation of a sequential stratigraphy based at least in part on them.  As an example, a concordant surface may be a concordant horizon surface, for example a horizon surface between a lower horizon and an upper horizon when the horizons have undergone a relatively common geological history, for example deposited successively (eg. , continuously in time).  As an example, in one environment, the horizons may not intersect and each of the horizons may be considered to be concordant with adjacent horizons (e.g. , lower and upper or older and newer).  As an example, erosion may act to strip the rock, for example as a result of physical, chemical and / or biological disruption and / or transport.  Erosion can occur, for example, when material (e.g. liberated from the rock by bad weather, etc. ) is carried by liquids, solids (e.g. , wind, water or ice) or a mass movement (e.g. , as in falling rocks and landslides).  As an example, consider two sequences where a lower sequence may have been eroded and a higher sequence deposited above the lower eroded sequence.  In this example, the boundary between the two sequences can be called erosion; it will be noticed that it is concordant with the more recent superior sequence.  As an example, erosion can act to "truncate" a sequence of horizons and to form a surface on which subsequent material can be deposited (e.g. , possibly in a concordant manner).  As an example, a disordered base overlay can be a type of feature in an environment, for example a prograding bevel or an aggradation bevel.  As an example, a progradation wedge may be a termination of overlying layers plunging sharply against a surface or underlying strata that have lower apparent inclinations.  For example, a progradation wedge may be considered the basis of progradation clinoforms and may represent the progradation of a pelvic margin.  As an aggradation bevel, for example, it may be a termination of more recent strata dipping shallowly against older, sharply dipping strata (e.g. sequential stratigraphy that may occur during periods of transgression).  As an example, a basic type of discrepancy overlay can be considered as a progradation bevel (e.g. lower strata with lower apparent inclinations).  In this example, the base overlap limit on unconformity tends to be consistent with horizons immediately preceding it (lower sequence).  As an example, if we consider three sequences, a discontinuity may exist in the form of a boundary that is not consistent with either older horizons or more recent horizons.  As an example, erosions, base overlaps and discontinuities may be referred to as mismatched mismatches or horizons (eg. , surfaces, layers, etc. ).  As an example, one or more intrusions may exist in an environment.  For example, an intrusion may be a structure or structures formed by a process called sediment injection.  For example, consider sills placed parallel to stratification or dykes that cut stratification.  Strata that include intrusion may be called host strata, and the layer or layers that feed an intrusion may be referred to as the parent bed or parent beds.  As an example, a sand injection characteristic may have a dimensional scale which may for example be of an order in a range of the order of several millimeters to the order of several kilometers.  Proof of a feature may exist in a core, a borehole image record, a seismic section, an outcrop, an aerial photograph, a satellite image, etc.  (eg. , depending on the size scale).  With respect to the representation or representations of the boundaries 232, they may comprise a numerical representation in which a subsurface model is divided into various closed units representing geological layers and fault blocks, an individual unit that can be defined by its limit, and possibly by a set of internal boundaries such as fault surfaces.  As regards the structured grid (s) 234, they may comprise a grid that shares a volume of interest in different elementary volumes (cells), which may for example be indexed according to a predefined repetitive pattern.  As for the unstructured mesh (s) 236, they may comprise a mesh that shares a volume of interest 5 in different elementary volumes, which may, for example, not be easily indexed by following a predefined repetitive pattern (e.g. , take a Cartesian cube with indices I, J, and K along the x, y, and z axes.  As for the seismic velocity modeling 251, it may include the calculation of the seismic wave propagation velocity (e.g. when the seismic velocity depends on the type of seismic wave and the direction of propagation of the wave).  Seismic processing 252 may include a set of processes for identifying the location of seismic reflectors in space, the physical characteristics of the rocks between these reflectors, and the like.  As for the interpolation of facies and petrophysical properties 253, it may include an evaluation of the type of rock and their petrophysical properties (e.g. , porosity, permeability), for example possibly in areas not sampled by well logs or coring.  As an example, such interpolation may be constrained by logging and core logging interpretations, and prior geological knowledge.  As for the flow simulation 254, as an example, it may comprise the simulation of hydrocarbon flow in the subsurface, for example over geological times (e.g. , in the context of oil system modeling, when attempting to predict the presence or quality of oil in an undrilled formation) or during the operation of a hydrocarbon reservoir (e.g. , when some fluids are pumped from 25 or into the tank).  As regards the geomechanical simulation 255, it may include the simulation of the deformation of rocks under boundary conditions.  Such a simulation can be used, for example, to evaluate the compaction of a reservoir (e.g. , associated with its exhaustion, when the hydrocarbons are pumped from the porous and deformable rock which composes the reservoir).  As an example, a geomechanical simulation can be used for various purposes, for example the prediction of a fracturing, the reconstruction of the reservoir paleogeometries as they were before the tectonic deformations, etc.  As for the geochemical simulation 256, this simulation makes it possible to simulate the evolution of the formation and the hydrocarbon composition throughout the geological history (e.g. , to evaluate the probability of oil accumulation in a particular subterranean formation when exploring new surveys).  As to the various applications of the application block 240, the well prognostic application 242 may include the prediction of the type and characteristics of geological formations that may be encountered by a bit, and where these rocks can meet (eg. , before a well is drilled); the reserve calculation application 244 may include the evaluation of the total amount of hydrocarbons or ore present in an underground environment (e.g. , an estimate of the proportion that can be recovered, according to a set of economic and technical constraints); and the well stability evaluation application 246 may include estimating the risk that a well, already drilled or drilled, will collapse or be damaged by the subterranean stresses.  As for the operational decision block 260, the seismic survey design process 261 may include the decision of where to place seismic sources and receivers to optimize the coverage and quality of the collected seismic information while minimizing the cost of acquisition; the well rate adjustment process 262 may include control of injection and production well schedules and flows (e.g. , 15 to maximize recovery and production); the well trajectory planning process 263 may involve the design of a well trajectory to maximize potential recovery and production while minimizing the risks and costs of drilling; the well trajectory planning process 264 may involve selection of good casing, good coating, and well completion of a well (e.g. to meet the production or injection objectives provided in specified reservoir formations); and the prospecting process 265 may involve making the decision, in the context of exploration, to continue exploration, to begin production or to abandon surveys (eg. , based on an integrated assessment of technical and financial risks against expected benefits).  As an example, a method may include implicit modeling that involves the use of one or more implicit functions.  As an example, such a method may comprise the representation of three-dimensional geological horizons using isosurfaces specific for a field of scalar properties (e.g. , an implicit function) defined on a three-dimensional background grid.  As an example, a method may include representing one or more types of features in addition to or replacing geological horizons.  For example, take a process that involves representing one or more discrepancies or other types of features.  As an example, a process that includes implicit modeling may facilitate the exploration and production of natural resources, for example, hydrocarbons or ores.  As an example, such a method may comprise the modeling of one or more faulty structures that may comprise geological layers whose thickness varies spatially.  As an example, such a method can be used to model large-scale areas (basin), syntectonic deposition, etc.  Figure 3 shows an example of a plot of a geological environment 300 which may be represented in part by a convention 301.  As an example, a method may employ implicit modeling to analyze the geological environment, as shown, for example, in lines 302, 303, 304 and 305.  Figure 3 also shows an example of a control point constraint formulation 310 and an example of a linear equation formulation system 330, which relate to an implicit function (9).  In FIG. 3, the plot of the geological environment 300 may be based at least in part on input data, associated for example with one or more fault surfaces, horizon points, and so on.  As an example, one or more features in this geological environment can be characterized at least in part by a slope.  As an example, an inclination may be specified according to convention 301, as graphically illustrated in FIG. 3.  As convention 301 shows, the three dimensional orientations of a plane can be defined by its inclination and azimuthal direction.  By convention 301, the inclination is the angle of the slope of a plane with respect to a horizontal plane (e.g. , an imaginary plane) measured in a vertical plane in a specific direction.  The inclination can be defined by an amplitude (e.g. , also called angle or quantity) and an azimuth (e.g. , also called direction).  As shown in convention 301 of FIG. 3, various angles indicate a slope angle downwardly, for example from an imaginary horizontal plane (e.g. flat upper surface); while the azimuth refers to the direction to which an inclined plane (eg. , which can be given in degrees, compass directions, etc. ).  In the convention 301, various angles are represented by the Greek letter gamma, while the Greek letter phi appears in association with various examples which include implicit modeling.  Another feature shown in convention 301 of FIG. 3 is the azimuthal direction, which is the orientation of the line created by the intersection of an inclined plane and a horizontal plane (e.g. take the flat top surface as an imaginary horizontal plane).  [0074] Certain additional terms related to inclination and azimuthal direction may apply to an analysis, for example depending on the circumstances, the orientation of the data collected, etc.  A term is "the real dip" (see, eg. , DipR in Convention 301 of Figure 3).  The actual dip is the inclination of a plane measured directly perpendicular to the azimuthal direction (see, e.g. , the line indicated to the north and designated by "azimuthal direction" and the angle a90), but also the maximum possible value of the amplitude of inclination.  Another term is "apparent dip" (see, eg. , DipA in Convention 301 of Figure 3).  The apparent dip may be the inclination of a plane such as measured in any other direction than the actual dipping direction (see, e.g. , yA as DipA for the angle a); however, it is possible that the apparent dip is equal to the actual dip (see, eg. , y when DipA = DipR for the angle coo with respect to the azimuthal direction.  In other words, when the apparent dip term is used (e.g. in a method, an analysis, an algorithm, etc. ) for a particular inclined plane, the apparent dip value may be equivalent to the actual dip of that particular inclined plane.  As shown by the convention 301 of FIG. 3, the inclination of a plane observed in section perpendicular to the azimuthal direction is the actual dip (see, e.g. , the area with y when DipA = DipR for the angle a90 with respect to the azimuthal direction).  As indicated, the slope observed in a section in any other direction is the apparent dip (see, e.g. , the surfaces designated DipA).  Further, as shown in convention 301 of FIG. 3, the apparent dip can be approximately 0 degrees (e.g. , parallel to a horizontal surface when an edge of a secant plane extends in the azimuthal direction).  [0076] Concerning the observation of inclination in boreholes, the actual dip is observed in wells drilled vertically.  In wells drilled in any other orientation (or deviation), the inclinations observed are apparent inclinations (e.g. , which are called by some relative inclinations).  In order to determine actual dip values for planes observed in such boreholes, as an example, a vector calculation (e.g. , based on borehole deviation) can be applied to one or more apparent dip values.  As mentioned, another term that can be used in sedimentological interpretations of borehole images is "relative dip" (e.g. , DipR,).  A true dip value measured from borehole images in rocks deposited in very calm environments can be subtracted (eg. using vector subtraction) inclinations in a sandy body.  In this example, the resulting inclinations are referred to as relative dips and can be used in the interpretation of sandy body orientation.  A convention such as convention 301 can be used in relation to an analysis, an interpretation, an attribute, a model, and so on.  (see, e.g. , the different blocks of the system 100 of Figure 1 and the system 200 of Figure 2).  As an example, various types of features may be described, in part, by an inclination (e.g. , sedimentary stratification, horizons, faults and fractures, cuestas, dykes and igneous sills, metamorphic foliation, etc. ).  A seismic interpretation may be directed to identifying and classifying one or more subterranean boundaries at least in part according to one or more tilt parameters (e.g. , angle or amplitude, azimuth, etc. ).  As an example, various types of features 3036210 29469 / 298F R1 18 (e.g. , sedimentary stratification, horizons, faults and fractures, cuestas, dykes and igneous sills, metamorphic foliation, etc. ) can be described at least in part by an angle, at least in part by an azimuth, etc.  Consider the lines 302, 303, 304 and 305 of FIG. 3, which can represent parts of a process that makes it possible to generate a model of a geological environment such as the geological environment represented in the route 300. .  As an example, a volume-based modeling method may include receiving input data (see, e.g. , plot 300); the creation of a volume mesh, which may be, for example, an unstructured tetrahedral mesh (see, e.g. plot 302); the calculation of implicit function values, which may represent a stratigraphy and which may possibly be displayed using a periodic map (see, e.g. , plot 303 and implicit function cp as represented using periodic mapping); the extraction of one or more horizon surfaces as isosurfaces from the implicit function (see, eg. , plot 304); and producing a sealed geologic layer model, which can optionally be obtained by subdividing a model at least in part through implicit function values (see, e.g. , the route 305).  As an example, an implicit function calculated for a geological environment includes isovalues that can represent the stratigraphy of modeled layers.  For example, deposition interfaces identified by seismic data interpretations (e.g. , signals, reflectors, etc. ) and / or borehole data (e.g. , wellheads, etc. ) can correspond to isosurfaces of the implicit function.  As an example, when reflectors correspond to boundaries of isochronous geological sequences, an implicit function may be a monotonic function of the stratigraphic age of geological formations.  As an example, a method of creating a geologic model may include: constructing an unstructured 2D fault mesh (e.g. , if a goal is to construct a cross section of a model) or a 3D mesh from a tight representation of a network of faults; the representation, according to a volume attribute based on an implicit function, of the stratigraphy by interpolating on the constructed mesh; and the division of the mesh constructed at least in part according to isosurfaces of the attribute to generate a volume representation of geological layers.  Such a process may include outputting one or more portions of the volume representation of the geologic layers (e.g. , for a particular layer, part of a layer, etc. ).  As an example, to represent complex deposition patterns, sequences that can be separated by one or more geologic discrepancies can optionally be modeled using one or more volume attributes.  As an example, a method may include taking into account the timing of the activity of a fault (e.g. , possibly in relation to a deposit) during the construction of a model, for example by locally editing a mesh on which the interpolation is performed (e.g. , Between the treatment of two consecutive concordant sequences).  Consider the formulation of control point constraints 310, where a tetrahedral cell 312 is represented as having a control point 314.  As an example, an implicit function can be a scalar field.  As an example, an implicit function can be represented as a property or an attribute, for example for a volume 10 (e.g. , a volume of interest).  As an example, the aforementioned PETREL® infrastructure may include a volume attribute that has spatially defined values that represent values of an implicit function.  As an example, as indicated with respect to the linear system for equation formulation 330, a function "F" can be defined for (x, y, z) coordinates 15 and associated with an implicit function denoted 9.  As for the stress values, the function F can be such that each entry horizon surface "I" corresponds to a known constant value h, of 9.  For example, Figure 3 shows the nodes (e.g. , vertices) of the cell 312 as comprising ao, ai, az and a3 as well as the corresponding values of 9 (see the column vector).  Concerning the values h, of 9, if a horizon I is younger than a horizon J, then h, 20> h, and, if we note T_ij * an average thickness between the horizons I and J, then (hk - h ,) / (h, - hi) T_ik * / Tij *, in which case a method may include estimating values of T_ij * before an interpolation is performed.  Note that such a method may, for example, accept lower values h, cp for more recent horizons when, for example, a constraint is given, within each concordant sequence, the values h, y vary monotonically with respect to the age of the horizons.  As for the interpolation of "F", as an example, 9 can be interpolated on nodes of a bottom mesh (e.g. , a 2D triangulated surface, a 3D tetrahedral grid, a regular structured grid, quaternary / octary trees, etc. ) according to several constraints that can be met at least in the least squares sense.  In this example, since the background grid may be discontinuous along faults, the interpolation may also be discontinuous; it will be noted that "regularization constraints" can be incorporated, for example to constrain the smoothing of interpolated values.  As an example, a method may include the use of fuzzy control point constraints.  For example, at a location of interpretation points, h, of 9 (see, e.g. point a * in Figure 3).  As an example, an interpretation point may be located at another location than that of a node of a mesh on which an interpolation is performed, for example when a numerical constraint can be expressed as a constraint. linear combination of values from 9 to nodes of a mesh element (e.g. , a tetrahedron, a tetrahedral cell, etc. ) that includes the point of interpretation (eg. , sum coefficients being barycentric coordinates of the interpretation point within the element or cell).  For example, for an interpretation point p of a horizon I located inside a tetrahedron which has vertices a0, a1, a2 and a3 and whose barycentric coordinates are b1, b1, b2 and b3 (e.g. , such that the sum of the barycentric coordinates is approximately equal to 1) in the tetrahedron, an equation can be formulated as follows: ## EQU1 ## = hi where the unknowns in the equation are 9 (ao), 9 (a1), (p (a2) and 9 (a3).  For example, consider control point 9 (a *), designated 314 in cell 312 of the control point constraint formulation 310 of Figure 3, with corresponding coordinates (x *, y *, z * ); we will note a matrix "M" for the coordinates of the nodes or vertices for ao, al, a2 and a3 (for ex. , xo, yo, zo to x3, y3, z3).  As an example, a number of these constraints of the above type may be based on a certain number of interpretation points, the interpretation points being able for example to be intended for a decimated interpretation (e.g. , to improve performance).  As mentioned, a process may comprise the implementation of various regularization constraints, for example to constrain the smoothing of interpolated values of various orders (e.g. to constrain the smoothing of (f) or its VO gradient, which may be combined, for example, by a weighted least squares scheme.  As an example, a method may include the constraint of the V9 gradient in a mesh element (e.g. , a tetrahedron, a tetrahedral cell, etc. ) to take an arithmetic mean of the values of cp gradients (e.g. , a weighted average) relative to its neighbors (eg. , topological neighbors).  As an example, one or more weighting schemes may be applied (e.g. , by volume of an element), which can, for example, include the definition of a topological neighborhood (e.g. , by adjacency of faces).  As an example, two geometrically "touching" mesh elements that are located on different sides of a fault can be considered as not being topological neighbors, for example when a mesh can be "disconnected" along Fault 35 (e.g. , to define a set of elements or a mesh on one side of the fault and another set of elements or a mesh on the other side of the fault).  As an example, within a mesh, if we consider a mesh element mi which has n neighbors mj (e.g. , for a tetrahedron), we can formulate an equation of an example of a regularization constraint as follows: 1In V (P (mi) = V (P (nJ) ni = i 5 [0094] In such an example, 'a regularization constraint, the solutions for which the isovalues of the implicit function form "flat millefeuille" or "nested balls" geometries can be considered "perfectly smooth" (c. -to-d.  not violating the regularization constraint), it may be that a first one is targeted.  As an example, one or more constraints may be incorporated into a system in linear form.  For example, hard constraints may be imposed on nodes of a mesh (e.g. , a control node).  In this example, data may be derived from force values at the wellhead location.  As an example, a control gradient approach, or control gradient orientation, can be implemented to impose inclination constraints.  [0096] Consider again Figure 3, where the linear system of equation formulation 330 includes various types of constraints.  For example, a formulation may include constraints of harmonic equations, constraints of control point equations (see, e.g. , the formulation of control point constraints 310), constraints of gradient equations, constraints of constant gradient equations, etc.  As shown in Figure 3, a matrix A may have one column for each node and one row for each constraint.  This matrix can be multiplied by a column vector such as the column vector cp (ai) (e.g. , or (p), the index "i" corresponding for example to a certain number of nodes, vertices, etc.  for a mesh (e.g. , a double index can be used, for example, where j represents an element or cell index).  As shown in Example 25 of Figure 3, the product of A and vector 9 can be associated with a column vector F (e.g. , with non-zero entries where appropriate; take for example r (i) control point and (1) gradient) - (0097) Figure 3 shows an example of a harmonic stress graph 334 and an example of a constant gradient stress graph 338.  As shown in Figure 334, nodes may be constrained by a linear equation of a harmonic stress (e.g. , by topological neighbors of a common node).  As shown in Figure 338, two tetrahedra can share a common (hatched) face, which is constrained to share a common value of a gradient of the implicit function cp which, in the example of Figure 3, constrains the value of cp at the 5 nodes of both tetrahedra.  As an example, regularization constraints can be used to control the interpolation of an implicit function, for example by constraining the variations of a gradient of the implicit function.  As an example, constraints can be implemented by specifying (e.g. , as a linear least squares constraint) that the gradient should be similar in two coincident elements of a mesh or, for example, by specifying that for individual elements of a mesh a gradient of the implicit function 5 should be an average of the gradients of the neighboring elements.  In geological terms, these constraints can result in (1) minimizing the slope and thickness variations of individual layers, horizontally, and (2) minimizing the variation of the relative thicknesses of the layers, vertically.  As an example, the aforementioned effects relating to the minimization of variations and the minimization of changes can influence a resulting model.  As an example, a method may include the application of one or more techniques that can counter such effects, for example by separating a linear system of equation formulation, separating one or more trends, etc.  As an example, one or more of these techniques may be implemented in response to input data (e.g. , seismic interpretation, 15 borehole observations, etc. ) which indicate that variations of inclination, thickness of one or more layers exceed one or more criteria.  For example, take a criterion that acts to rank an inclination as important (eg. , more than about 10 degrees of slope variation of a geological interface), a criterion that acts to classify a thickness as variable (e.g. more than a doubling of one part-to-another layer thickness of a model), etc.  As an example, schematically, the calculation of an implicit function can be performed in a manner that aims to respect two types of constraints: (1) minimizing the difference between the interpretation data and the interpolated surfaces and (2) a regularization constraint that aims to smooth and monotonate an interpolated property.  [00101] As explained, the values of an implicit function at the nodes of a volume mesh can be determined by solving a limited linear system of equations (see, e.g. , the linear system of equation formulation 330 of Figure 3).  As shown in Figure 3, various constraints may be applied, which may for example be selected for the purpose of better constraining one or more characteristics (e.g. , Local inclination of a geological layer, etc. ) by constraining a gradient of the implicit function.  As an example, a solution procedure may include one or more least squares constraints, for example using a weighted least squares scheme that can act to balance the effects of conflicting constraints in a solution for a linear system equations.  As an example, a method may include the relaxation of one or more regularization constraints used to interpolate an implicit function, for example such that the interpolation may account for one or more thickness variations at high frequency.  As an example, a method may include removing one or more trends of low frequency data thickness variations (e.g. , input data, etc. ), possibly before interpolating an implicit function and, for example, reintroducing the trend or trends (e.g. , if any) in the default function.  As an example, such an approach can be applied to complex faulty pools, for example, possibly, independently of fault offsets.  [00104] As an example, one or more methods may be applied to interpolate an implicit function, for example to represent a set of matching layers (e.g. , not crossing each other).  As an example, a method may employ one or more techniques, for example a method may employ a relaxation technique, an extraction technique or a relaxation technique, and an extraction technique.  FIG. 4 shows an example of a system 401 and a method 410.  As shown in FIG. 4, the system 401 includes one or more computers 402, one or more storage devices 405, one or more arrays 406, and one or more modules 407.  With respect to the computer or computers 402, each computer may comprise one or more processors (e.g. , or heart processors) 403 and a memory 404 for storing instructions (e.g. , modules), for example executable by at least one of the processors.  As an example, a computer may have one or more network interfaces (e.g. , wired or wireless), one or more graphics cards, a display interface (e.g. , wired or wireless), etc.  As an example, data may be provided in the storage device (s) 405, the computer (s) 402 capable of accessing the data by the network (s) 406 and processing the data by the module (s) 407, for example such (s) as stored in the memory 404 and executed (s) processor (s) 403.  FIG. 4 also shows a block diagram of the method 410, which comprises an input block 420 and an output block 480, for example to output an implicit function associated with a stratigraphic property by a block 482.  As for the input block 420, it may comprise a fault area input block 422 and an edge point input block 424.  As shown in the example of FIG. 4, the input block 420 can provide an input to a thickness estimation block 430, a layer block 440 and a bottom mesh block 452.  With respect to the layer block 440, it may include a thickness block 442 for determining or receiving thickness values (e.g. based on or derived from the thickness estimation block 430) and a calculation block 444 for calculating control point values (see, e.g. the formulations 310 and 330 of Figure 3).  As shown, the layer block 440 may output control points for a block of control points 462, which may be defined with respect to a mesh provided by the background mesh block 452.  As an example, control points of control point block 4662 may represent one or more regularization constraints through a regularization constraint block 454.  As an example, given control point values for layers that can be defined with respect to a mesh and subjected to one or more constraints, a method can comprise the calculation of values of an implicit function (e.g. , or implicit functions).  As shown in the example of FIG. 4, an implicit function calculation block 462 can receive control points and one or more constraints defined with respect to a mesh (e.g. , elements, cells, nodes, vertices, etc. ), and in turn calculate values for one or more implicit functions.  [00109] As for the output block 480, given values calculated for one or more implicit functions, these can be associated, for example, with a stratigraphic property by the block 482.  As an example, one or more isosurfaces can be extracted at least in part depending on the values of the stratigraphic property by an isosurfaces extraction block 484, one or more of the extracted isosurfaces being able for example to be defined as being a surface of horizon (eg. , or horizon surfaces) by a block 20 of horizon surfaces 486.  As mentioned, particular constraints can influence the ability to model inclination, thickness variations, and so on. for example at least partly because of contradictions.  For example, consider the following three examples of geological situations where types of constraints (eg. , for smoothing data and for regularization) may be contradictory, which may for example lead to unpredictable and / or undesirable behavior of an interpolated implicit function.  In the three examples, large variations of inclination, thickness or relative layer thicknesses exist locally and / or globally.  [00111] With regard to the first example, it relates to a local lifting or thinning of the layers, due for example to a movement of ductile material inside or below the studied zone.  Such characteristics can occur on and / or above salt domes or in the presence of thick layers of shale.  In this case, the change of inclination and / or thickness of the layers may be of limited extent in a model.  [00112] As to the second example, it relates to an overall thickness change, which may be due to a lateral variation of the deposition environment (e.g. , proximal or distal 3036210 29469 / 298F R1 25 of the coast paleolith), associated with differential sedimentation.  As an example, this scenario can occur for large models, at the exploration scale.  [00113] With respect to the third example, it relates to a sudden change in layer thickness across faults, which may be associated with the presence of synsedimentary faults (e.g. faults that were active sediments at the time they deposited).  In this scenario, the changes in thickness may be due to a differential variation of reception space, for example on both sides of a fault.  [00114] FIG. 5 shows an example of a method 500 which comprises a reception block 510 for receiving a mesh which represents a geological environment, the mesh comprising elements; a reception block 520 for receiving location information for a discontinuity in the geological environment; a definition block 530 for, at least in part depending on the location information, defining enrichment equations for a part of the elements, the enrichment equations having a jump function which models the discontinuity; a solution block 540 for solving a system of equations for an implicit function, the system of equations including the enrichment equations; and an output block 550 for, at least in part depending on the resolution of the system of equations (e.g. , a solution), output values for the implicit function with respect to at least a part of the mesh.  As for the enrichment equations of the definition block 530, these can correspond to enrichment equations of the extended finite element method (XFEM).  Thus, the method 500 may include the implementation of the XFEM.  The method 500 is shown in FIG. 5 in association with various computer readable media (CRM) blocks 511, 521, 531, 541, and 551.  These blocks generally include appropriate instructions for execution by one or more processors (or cores) to instruct a device or computer system to perform one or more actions.  Although different blocks are shown, only one medium can be configured with instructions allowing, at least in part, to perform various actions of the method 500.  As an example, a computer readable medium (CRM) may be a computer readable storage medium.  As an example, the blocks 511, 521, 531, 541 and 551 may be provided as one or more modules, for example as the one or more modules 407 of the system 401 of FIG.  As an example, the method 500 may comprise the calculation of values of a stratigraphic attribute which may, for example, represent concordant subterranean structures.  In this example, the mesh may be a volumetric mesh where the discontinuities (e.g. , 35 faults) are not explicitly modeled by elements of the mesh.  For example, a discontinuity may pass through one or more elements without being explicitly modeled by a node of an element, an edge of an element, or a side of an element.  As an example, a mesh may include elements that fill a domain, the domain representing a volume that corresponds to a geological environment (e.g. , a box, etc. ).  As an example, a method may act to relax the mesh dependence on the geometry of one or more faults, for example by introducing enrichment equations that represent the one or more defects as one or more discontinuities within the geometry of one or more faults. a mesh.  As an example, when the modeling can be done without explicitly defining geometrically the grid of a mesh to conform to a discontinuity, modeling can be accelerated.  For example, suppose we are able to represent one or more discontinuities, adjust one or more discontinuities, and so on. , without having to adjust one or more nodes, elements, etc. , and / or introduce nodes, elements, etc.  additional.  In this example, a method can be implemented to quickly build a structural model without introducing complexity into the creation of the mesh as associated with the geometric modeling of a discontinuity.  In such an example, a template can be adjusted, updated, etc. for example to model a fault more precisely, etc.  (eg. , without geometric adjustment on a mesh).  As an example, an approach such as that of method 500 of FIG. 5 may include uncertainty quantization of one or more discontinuities (e.g. , fault geometries), for example with reduced computing requirements compared to an approach that includes explicit geometric modeling of discontinuities in a mesh.  [00118] Figure 6 shows an example of a mesh 602 which has faults such as the flaw 612.  Although the flaw 612 may be three-dimensional in shape, it may be represented by a set of individual two-dimensional polygons (e.g. , triangles).  In this example, the mesh 602 can be volumetrically filled with individual three-dimensional polyhedra (e.g. , tetrahedra).  As an example, a mesh may include simplexes (e.g.  simplexes), which can be n-order simplexes (e.g. , triangles when n = 2, tetrahedra when n = 3, etc. ).  To correctly represent the fault 612 inside the mesh 602, the volumetric elements (e.g. , tetrahedra, etc. ) are arranged such that the flaw 612 is modeled as a surface which is delimited by one set of volumetric elements on one side and another set of volumetric elements on the other side.  In the example of Figure 6, consider the tetrahedrons 622-1 and 622-2 where the tetrahedron 622-1 is positioned on one side of the flaw 612 and where the tetrahedron 622-2 is positioned on the other side of the flank. the flaw 612.  Thus, the flaw 612 can be represented as a surface, for example a triangulated surface where each of the triangles in the triangulated surface has on one side a volumetric element and on the other side a volumetric element.  As an example, a method may comprise the representation of three-dimensional geological horizons by isosurfaces of a scalar attribute (e.g. , stratigraphic attribute or implicit attribute) within a three-dimensional volumetric mesh such as mesh 602.  In this example, the mesh integrates a fault geometry in advance (e.g. , a prion) to capture the flaws as discontinuities in the scalar attribute.  Thus, such a method may comprise an initial phase which involves the creation of a three-dimensional volumetric mesh that conforms to the geometries of the faults.  As shown in FIG. 6, the mesh 602 is faulty and represents these discontinuities.  The creation of a mesh such as the mesh 602 of FIG. 6 can present certain challenges, since each fault surface introduces constraints into the mesh creation process.  In addition, difficulties may arise from certain types of complex fault geometry.  For example, take a complex flaw shape that acts to constrain mesh resolution to a degree that the production of mesh elements (eg. , cells) of acceptable quality presents difficulties.  As an example, consider a process called tetrahedrisation, which can be implemented to generate a set of tetrahedra for an input domain, a set of points, a polyhedron, and so on. , the tetrahedra meeting at one or more shared characteristics (e.g. , vertices, edges, or triangles).  Compared to triangulation (e.g. , of a surface), tetrahedrisation (e.g. , of a volume) may involve some additional considerations.  As an example, as in two dimensions, a parameter "n" can represent a number of vertices of an input domain (e.g. , a geological environment), tetrahedrisation can introduce tetrahedra that "fill" the input domain, each tetrahedron being defined by four vertices.  In various types of numerical methods, such as the finite element method, a condition may be imposed for a mesh to have no degenerate elements.  When an input domain has characteristics that act as geometric constraints (eg. , objects, surfaces, etc. ), a method that aims to avoid degenerate elements can generate additional computational costs.  As an example, take a process such as "annealing" that can act to adjust node positions, inter-node connections, in order to avoid degenerate elements.  FIG. 7 shows an example of a mesh 702 with a bounding box 704 (e.g. , a domain), various faults such as the fault 712 existing inside the bounding box 704.  As illustrated, an element 714 near the flaw 712 and the bounding box 704 may be deformed for computational purposes.  As an example, a deformed member may be a glitter (e.g. , in terms of form ratio, etc. ), a degenerate simplex, a tetrahedron with a volume of an order of magnitude more or less equal to that of other "acceptable" tetrahedra, etc .;  Figure 7 also shows an example of a 732 tetrahedron and an example of a degenerate tetrahedron 734.  In these examples, a tetrahedron can be analyzed with respect to a volume; for example, consider an analysis which partly evaluates a diameter of a circumference of a tetrahedron, a diameter of the smallest sphere circumscribed by a tetrahedron, and so on.  As mentioned, such an analysis may have associated computational requirements and, as an example, although degenerate tetrahedra may be avoided, when adjusting a mesh (e.g. , by annealing, etc. ), the number of elements (e.g. , vertices, etc. ) can increase, which in turn can lead to an associated increase in computing requirements (eg. , memory, calculation time, etc. ).  In a method such as method 410 of FIG. 4, a digital solver that calculates values of an implicit function (see, e.g. , block 464 of method 410) can cope with numerical errors, floating-point exceptions, and so on. when one or more elements are deformed (e.g. , high form ratio, degeneration, etc. ).  As an example, consider a scenario in which a mesh must be updated.  For example, consider receiving an existing mesh and then updating the existing mesh to incorporate one or more additional fault surfaces, to adjust the existing mesh to accommodate new information on one or more fault surfaces, and so on.  This updating may require various calculation requirements, for example when a method for an updated mesh may include the analysis of the updated mesh (e.g. , "Optimization" of the updated mesh) so that in one or more adjusted regions and / or new elements are not deformed.  Fault geometries, such as underground features, may be subject to various types of uncertainties.  For example, the seismological interpretation of faults may involve uncertainties as to extent, position, and so on.  a fault.  As an example, when a model is intended to model fractures, uncertainty may exist as to extent, position, and so on.  one or more fractures.  When the fractures comprise hydraulic fractures, these fractures can be generated in stages, a mesh must for example be updated after each step.  For various reasons, updating a mesh to conform the mesh to one or more features in a domain may require intensive computations.  A processing flow that involves updating a mesh can degrade the user experience and limit scenario-based approaches, which can have consequences for predictions that can be made at least in part based on a model (e.g. , a structural model of a geological environment).  As an example, as explained with respect to method 500 of FIG. 5, a method may include implementing the extended finite element (XFEM) method.  XFEM is a numerical technique that extends the approach of finite element method 3036210 29469 / 298F R1 29 (FEM) by enriching a solution space with solutions of differential equations with discontinuous functions.  [00128] FIG. 8 shows an example of a mesh 810 which has discontinuities, an example of a mesh 820 which has discontinuities and an example of a mesh 830 5 which comprises a discontinuity (e.g. , a discontinuous characteristic or discontinuity characteristic).  In mesh 810, the elements conform to the discontinuities, whereas in the mesh 820, the discontinuities can intersect elements.  As shown in the example grid 810, the elements can be unstructured, while in the example grid 820 the elements can be structured.  As for the mesh 830, various nodes are identified, including nodes of elements that are cut off by the discontinuity and nodes of elements that are adjacent to one end (e.g. , one end of the discontinuity) or in the vicinity of a tip (e.g. , one end of the discontinuity).  [00129] In FIG. 8, the mesh 810 may be a mesh of the finite element method (FEM), while the mesh 820 may be a mesh of the extended finite element method (XFEM).  [00130] The finite element method (FEM) may include the creation of a mesh of elements, the definition of basic functions (e.g. , shape functions) on "reference" elements and the transfer of reference elements to the elements of the mesh.  The XFEM may include applying a partition of the unit to a topological space X, for example to form a set R of continuous functions from X in a unit interval (e.g. , [0,1]) so that for each point x E X there exists a neighborhood of x where a finite number of functions of R is nonzero (e.g. , where other functions of R are zero), and where the sum of the values of the functions in x is equal to unity (e.g. , E peR p (x) = 1).  The partition of the unit may allow the presence of a discontinuity (eg. or discontinuities) in an element by enriching the degrees of freedom with particular displacement functions.  The XFEM may include so-called "jump" functions, these functions possibly representing discontinuities.  As an example, a discontinuity can be classified as a type of discontinuity.  For example, consider a discontinuity classified as a weak discontinuity or a strong discontinuity.  A low discontinuity may be a type of discontinuity associated with a jump in a gradient of a solution.  In this example, an enrichment function such as the function "abs" can be chosen.  For a strong discontinuity, a jump may be present in a solution.  In this example, an enrichment function such as the "sign" function or the Heaviside function can be chosen.  The function of Heaviside (eg. a unit step function), which may be designated H, is a discontinuous function.  For example, for negative arguments, the value of the Heaviside function can be set to zero, and for positive arguments, the value of the Heaviside function can be set to unity (e.g. , or vice versa, etc. ).  As an example, a method may include the implementation of discontinuous basic functions and polynomial basic functions for nodes that belong to elements that are intersected by a discontinuity, for example, possibly to provide a basis that can be represent displacements of the opening of discontinuities.  As an example, the implementation of XFEM can improve convergence rates and accuracy.  As an example, implementing XFEM to model one or more discontinuities may reduce the integration of representations of one or more of these discontinuities by a mesh (e.g. , concordant triangles, tetrahedra, etc. ).  As an example, take the implementation of the XFEM to reduce the discretization of feature interfaces of discontinuities in a mesh, for example to allow the modeling of the propagation of a discontinuity characteristic.  [00134] FIG. 9 shows an example of a mesh 902 of a domain that has a discontinuity characteristic 910 that includes a portion 912, a characteristic transition portion 914, and a feature tip 916.  The mesh 902 comprises various nodes or vertices.  In the example of Figure 9, equations that can represent various types of nodes can be formulated.  For example, the nodes of the mesh 902 can be classified as belonging to a class or to particular classes: nodes of a model, 20 nodes whose form function support is intersected by the interior of a characteristic (for example: ex. , of characteristic 910), and nodes whose shape function support is intersected by the tip of a feature (e.g. , the characteristic tip 916).  [00135] FIG. 9 shows various equations, which are reproduced below as equations (1) to (4): u (x) = Ei uicki (x) (1) u (x) = Ei ui (x) ) + Ei big)] (x) H (x) (2) u (x) = Ei uicki (x) + Ei bicki (x) H (x) (3) 30 + kk (X) 4 (1CfcF e ( r (X), O (X))) e = 1 [Fe (r,, 0)]: = 1.5 sin (B),. Fr-cos (D, rr sin (D sin 09), cos (B) sin (0) (4) 3036210 29469 / 298F R1 31 [00136] Equation (1) can be applied to the mesh 902; Equation (2) can be applied to mesh 902 with discontinuity characteristic 910 (e.g. , a discontinuous characteristic in the domain represented by the mesh 902); and the equation (3) can be applied to the mesh 902 with the discontinuity characteristic 910 where it has the characteristic tip 916 within the mesh 902, the equation (4) being able to be used, for example, as an enrichment function near the end (eg. , within a radius r).  As indicated, equations (2) and (3) have a jump function such as the Heaviside function, for example.  [00137] As an example, a method may include enriching an interpolation function.  For example, take equations (1), (2) and (3) where the first sum can represent classical shape functions, the second sum can represent one or more elements completely flawed by adding a Heaviside multiplier to the function of shape and the third sum can represent enrichment at an end loop (e.g. , with singular functions such as equation (4), for example).  As an example, a feature in a geological environment can be treated as a stationary feature.  As an example, a feature in a geologic environment can be treated as a dynamic feature.  As an example, for a particular solution (e.g. , at a particular time or during a particular period of time), a characteristic can be treated as a stationary characteristic.
[0004] In this example, one or more parameters can be updated depending on the solution, for example to update the characteristic (eg, for a solution at another time, etc.). FIGS. 10, 11, 12 and 13 show examples of meshes 1010, 1110, 1210 and 1310. In the mesh 1010 of FIG. 10, a fault is shown which passes through various elements (e.g. elements) where enrichment functions can be used. For example, nodes marked with empty squares may represent Heaviside-type enrichment, and nodes marked with dots may represent end-loop enrichment with singular functions. [00140] In the mesh 1110 of FIG. 11, there is shown a fault which includes branching (eg, crisscrossing faults, etc.), a method which may for example employ enrichment of one or more branched faults. As the 1110 mesh shows, an enrichment can be used for the fault going from the top left to the bottom right; as the mesh 1210 shows, an enrichment can be used for the fault going from the center up to the right; and as shown in mesh 1310, enrichment may be employed for joining the two faults (eg, for a point, points, a line, lines, etc.). FIG. 14 shows an example of a method 1410 that includes a production block 1410 for generating a grid and grid equations (e.g., as associated with a digital solver, etc.). .), an enrichment block 1420 to enrich the grid equations (e.g., relative to one or more discontinuities in the grid, etc.), a definition block 1430 to define constraints, a solution block 1440 to solve the constrained equations to provide a solution, an extraction block 1450 for extracting at least one isosurface at least in part depending on the solution and an optional update block 1460 for updating at least one parameter, a dimension, discontinuity, etc. As an example, the method 1410 may include an update by the update block 1450 and the transition to one or more of the other blocks (eg, the production block 1410, the enrichment block 1420, etc.). As an example, the method 1410 can implement an XFEM approach for a domain represented by a grid (e.g., a mesh). For example, the method 1410 may involve implementing the XFEM to solve grid-based and constrained equations to provide a solution and, at least in part depending on the solution, constructing values. a stratigraphic attribute (eg, relative to the grid). In this example, the XFEM approach can be used to model one or more discontinuities in the domain without representing these discontinuities with improvements to a grid. For example, one or more discontinuities in the domain may be represented using enrichment equations where the elements (eg, knots, edges, surfaces, etc.) of the grid do not "align" (eg (eg, model) on the discontinuity (s). In this example, the discontinuities may be, for example, one or more faults. As an example, a grid may be structured or unstructured or may include one or more structured portions and one or more unstructured portions. [00143] The method 1410 is shown in FIG. 14 in association with various computer readable media (CRM) blocks 1411, 1421, 1431, 1441, 1451, and 1461. These blocks generally include appropriate instructions for execution by a user. or multiple processors (or heart processors) to instruct a device or computer system to perform one or more actions. Although different blocks are shown, only one support may be configured with instructions allowing, at least in part, various actions of the method 1410. As an example, a computer readable medium (CRM) may be a readable storage medium by computer. As an example, the blocks 1411, 1421, 1431, 1441, 1451 and 1461 may be provided as one or more modules, for example as the one or more modules 407 of the system 401 of FIG. 4. [00144] 1410 of FIG. 14, as an example, a background grid may cover an area of interest of a model, including, for example, data to be incorporated into a structural model. As an example, the resolution of the grid can be adapted to geological features (horizons, discrepancies and faults). In this example, the resolution may be defined such that a discontinuity extends across a plurality of grid elements (e.g., compared to being wholly within a single element ). As an example, a background grid may be composed of identifiable cells (e.g., elements), the grid may be, or comprise, a regular structured grid, and / or an unstructured irregular grid, and / or a grid tartan, and / or an octary tree, etc. As for the block 1420 of FIG. 14, it may comprise the preparation of an underlying representation by the finite element method (FEM) inside a grid 10 to take into account the discontinuities of the faults. Such an approach may include identifying the cells (eg, elements) of the grid that have a portion of a given discontinuity (eg, a given fault). As an example, various additional degrees of freedom associated with enrichment functions may be added to the FEM representation, for example depending on whether or not the end of a fault belongs to a given cell. In addition, if a branch exists with respect to faults (eg, possibly determined by a detection analysis) and a branch point or a branch line (eg, one or more types of junctions) is located at Within a given cell, another enrichment function may be added to represent the branch point or the branch line. This approach may allow a more coherent representation of individual discontinuities that a fault system can induce, for example, on an implicit function (eg, whose values can be used to compute a stratigraphic attribute). As an example, a method may include representing one or more singularities associated with a discontinuity by one or more enrichment functions (eg, take an end, an end, etc.). As an example, a three-dimensional flaw may include an end defined by a line that traverses at least several elements of a mesh. In this example, appropriate enrichment equations can be defined for these elements. As regards the definition block 1430 of FIG. 14, it may include the expression of constraints, for example in a linear or non-linear algebraic system of equations. For example, a method may include constructing an implicit attribute, the method comprising producing different constraints in a linear or nonlinear algebraic system of equations where the constraints act to impose different properties of the implicit attribute. As an example, consider a condition for which an implicit function 35 must conform to given horizon data; therefore, once a given value has been assigned to an individual horizon, a local algebraic constraint can then be created for individual horizon data points that are in a given cell of a given cell. a grid. As an example, consider smoothing as a constraint. For example, consider introducing some type of smoothing on an implicit function as a constraint on at least one gradient of the implicit function. As an example, a gradient of an implicit attribute may be constrained to be as smooth as possible (eg, within one or more error limits). As an example, one or more other types of constraints can be imposed. For example, take horizon tilt constraints, user constraints on an implicit function (eg, if a user wants to model mismatched events), control of gradient amplitude of an attribute implicit 10 (eg, which can be imposed as a non-linear constraint), etc. As an example, constraints can be represented by local integrals which, once calculated, can be translated into local linear (eg, or nonlinear) algebraic systems involving few degrees of freedom of a background grid. As an example, a method may include defining (eg, imposing) constraints in cells that do not have discontinuity and include defining (eg, enforcing) constraints in cells that have a discontinuity (eg, or discontinuities as in the example of a junction). In the second case, a function of enrichment at the end of a fault (eg, a fault end) can be singular and an integration rule can be adapted accordingly. For example, consider one of the following techniques to address a singularity: Delaunay triangulation of a fault cell; creating a match with equivalent polynomials (eg, integrated using conventional quadrature techniques); and quadrature of Gauss. As an example, once an integration technique has been selected, a method may include calculating constraints expressed as local integrals. [00150] As for the block 1440 of FIG. 14, as an example, depending on the type of constraints used, the system can be linear or non-linear with respect to the degrees of freedom (the discretized field of a stratigraphic attribute). As an example, if a system is non-linear, the gradient descent or Newton method can be used to solve a succession of linear system equations. As an example, for a given linear increment, when grouped together, different constraints can generate a linear, rectangular system of m equations (constraints) involving n unknowns (degrees of freedom,), which can then be solved for Implicit attribute values for this increment (eg, values of an implicit function). [00151] With respect to block 1450 of FIG. 14, due to the additional enrichment functions, the extraction of isosurfaces in a fault cell can be accomplished by a suitable technique. As an example, a method may include an animated cube algorithm, and / or an animated tetrahedron algorithm, and / or one or more other algorithms. As an example, a new mesh of a fault for integration purposes, if used, can be reused to extract the values of a stratigraphic attribute. [00152] Figure 15 shows various example traces 1501, 1502, and 1503 that illustrate the values of an implicit function (eg, as a stratigraphic attribute). As illustrated, various features in a geological environment can be discerned in traces 1501, 1502 and 1503, possibly including one or more discontinuities, etc. As an example, a method may include an embodiment block for one or more uncertainty analyzes (e.g., as part of a processing flow, etc.). In this example, an update may occur as to a description of a discontinuity or discontinuities (eg, a fault, flaws, etc.). As an example, an XFEM-based approach can be used to compute a stratigraphic attribute with reduced computing requirements compared to an approach that involves grid adjustments that conform to the geometry of a fault or fault. For example, an XFEM approach can explore various scenarios (eg, achievements) without having to modify an underlying background grid. Thus, this approach can be implemented for scenario-based analysis (eg, as in uncertainty analysis processing flows). As an example, when few parameters have been derived to parameterize a fault system, a method may include repetition of enrichment, etc., for one or more additional scenarios (given data flaw configurations) with a reduced computational cost. , allowing a user to analyze a considerable number of cases, hypotheses, etc., and for example possibly to evaluate the sensitivity of a structural model to the uncertainty of a fault system. [00154] As for the interpolations, as an example, once a value (p (p) has been assigned to individual control point constraints, an interpolation of the implicit function can be performed, for example, by solving a linear system of equations which may include at least one constraint on the value and / or the gradient of the implicit function and at least one regularization constraint (eg, smooth gradient, constant gradient and / or harmonic stress). For example, the output may have a property (p (a), the value of which can be set to individual nodes (eg, where ci represents an individual node) of a background mesh. interpolation can be done locally within individual elements of the mesh (eg by linear interpolation if the elements of the mesh are simplexes) As an example, a method may employ a cubic Hermite spline or an interpolator of cubic Hermite where the individual parts are third-degree polynomials specified as Hermite (eg, by the values and the first derivatives at the endpoints). As an example, a method may include extracting one or more horizon surfaces (e.g., or the surface of another feature) using a or several isovalues of a stratigraphic property, which may be a stratigraphic function. As an example, horizon surfaces (e.g., as used as input, otherwise, intermediate horizons, etc.) can be extracted from a stratigraphic function, for example by using an algorithm of isosurface. As an example, one or more types of surface can be extracted from a stratigraphic function, for example by using a surface extraction algorithm and / or a volume extraction algorithm. As an example, a surface may be a surface of a mismatch or other type of feature within an environment. As an example, a method may include extracting one or more surfaces that may be horizon surfaces that may be adjacent to, intersected by, shaped by, etc., one or more other types of surfaces and / or volumes (eg, discrepancies, geological bodies, etc.). As an example, a method can be implemented to create, at least in part, a 3D model of a subterranean region, to create a 2D model of an intersect through an underground region, and so on. As an example, a method may include computing the values of a stratigraphic property by formulating a stratigraphic property as a function of an implicit function. For example, a stratigraphic property S (a) can be represented by the equation S (a) = g (9 (a), x, y) where a represents the individual nodes of the mesh, where g () is a function of an implicit function (p (a) for the individual nodes has mesh and where x and y are the spatial coordinates of the individual nodes of the mesh. [00160] As an example, a method may comprise a realization block to perform a simulation of phenomena associated with a geological environment by using at least a part of a mesh (eg, or a model based on a mesh or meshes), and for performing a simulation, this simulation may include interpolation of geological rock types, interpolation of petrophysical properties, simulation of fluid flow, or other calculation (eg, or a combination of any of the preceding elements). 00161] As an example, a system may have instructions for requesting a processor to perform a simulation of a physical phenomenon using at least a portion of a mesh (e.g., or a pattern based on a mesh or meshes) and, for example, to produce output the results of the simulation on a display screen. As an example, a method may comprise the reception of a mesh that represents a geological environment, the mesh comprising elements; receiving location information for a discontinuity in the geological environment; at least partially according to the location information, the definition of enrichment equations for a part of the elements, the enrichment equations including a jump function which models the discontinuity; solving a system of equations for an implicit function, the system of equations containing the enrichment equations; and, at least in part depending on the resolution, outputting values for the implicit function with respect to at least a portion of the mesh. In this example, the mesh can be defined by nodes that have coordinates. For example, nodes can be defined by the coordinates of a coordinate system (eg, a Cartesian coordinate system, a cylindrical coordinate system, a spherical coordinate system, etc.). [00163] As an example, a jump function may be or may include the Heaviside function. As an example, a discontinuity may be or have a flaw. As an example, this flaw can cut at least one element of a mesh. For example, a flaw may be a plane that intersects a volumetric element or, for example, a flaw may be a two-dimensional line that intersects a two-dimensional element. As an example, a fault may include at least one fault end that is at least partially in an element. As an example, a jump function can be implemented to model a fault in at least one intersected element and, for example, a different function can be implemented to model an end of the fault. For example, take a singular enrichment function that can model a fault end as a singularity. As an example, an environment may include a plurality of discontinuities, which may in turn be at least partially within a mesh that represents at least a portion of the environment. As an example, a mesh and the associated equations can be used to obtain the values of an implicit function. In this example, a method may include the definition of constraints that constrain the implicit function. As an example, values for an implicit function may include values that correspond to horizons within a geologic environment. As an example, a horizon can be shaped by, intersected by, etc., one or more other geological features. In this example, the other geological feature (s) may be or act as a discontinuity. As an example, when information about one or more characteristics becomes available (eg, pre-existing features, new natural features, new artificial features, etc.), a method may include updating the location information and the repetition of processes such as definition, resolution and output. As an example, the location information may be or include seismological information from a seismic survey of a geological environment. As an example, a method may include performing one or more enrichment functions of an extended finite element (XFEM) method. For example, a mesh may be a finite element mesh that is suitable for applying the finite element method. In this example, the approach may be extended by incorporating one or more enrichment functions which may, for example, facilitate the modeling of one or more discontinuities within a space, volume, etc. . As an example, a system may include a processor; a memory functionally coupled to the processor; one or more modules stored in the memory, the one or more modules comprising instructions executable by the processor, the instructions comprising instructions for: receiving a mesh that represents a geological environment, the mesh comprising elements; receive location information for a discontinuity in the geological environment; at least in part depending on the location information, defining enrichment equations for a part of the elements, the enrichment equations having a jump function that models the discontinuity; solve a system of equations for an implicit function, the system of equations containing the enrichment equations; and outputting values for the implicit function with respect to at least a portion of the mesh. In this example, the jump function can be or include the Heaviside function. As an example, a discontinuity may be or have a flaw. As an example, the values for an implicit function may include values that correspond to one or more horizons within a geologic environment. As an example, one or more computer readable storage media may include executable instructions by a processor, the instructions including instructions for instructing a system to: receive a mesh that represents a geological environment, the mesh including elements ; receive location information for a discontinuity in the geological environment; at least in part depending on the location information, define enrichment equations for a part of the elements, the enrichment equations having a jump function that models the discontinuity; solve a system of equations for an implicit function, the system of equations 30 including the enrichment equations; and outputting values for the implicit function with respect to at least a portion of the mesh. In this example, the jump function can be or include the Heaviside function. As an example, values for an implicit function can include values that correspond to one or more horizons within a geologic environment. [00170] Fig. 16 shows the components of an example of a computer system 1600 and an example of a networked system 1610. The system 1600 includes one or more processors 1602, storage and / or storage components 1604, one or more input and / or output devices 1606 and a bus 1608. In an exemplary embodiment, instructions may be stored in one or more computer-readable media (eg, memory / storage components 1604). These instructions may be read by one or more processors (eg processor (s) 1602) via a communication bus (eg, bus 1608), which may be wired. or wireless. The processor (s) may execute these instructions to implement (in whole or in part) one or more attributes (eg, as part of a process). A user can view the output of and interact with a process through an I / O device (eg, device 1606). In an exemplary embodiment, a computer readable medium may be a storage component such as a physical memory storage device, for example a chip, a chip on a housing, a memory card, and so on. (eg, a computer-readable storage medium). In an exemplary embodiment, the components may be distributed, as in the network system 1610. The network system 1610 comprises components 1622-1, 1622-2, 1622-3, ..., 1622 -NOT. For example, the components 1622-1 may include the processor (s) 1602, while the component (s) 1622-3 may have a memory accessible by the processor (s). ) 1602. In addition, the component (s) 1602-2 may include an I / O device for display and possibly interaction with a method. The network may be or include the Internet, an intranet, a cellular network, a satellite network, etc. As an example, a device may be a mobile device that has one or more network interfaces for the communication of information. For example, a mobile device may include a wireless network interface (eg, usable via IEEE 802.11, GSM ETSI, BLUETOOTH®, satellite, etc.). As an example, a mobile device may include components such as a main processor, a memory, a display, a display graphics circuit (eg, optionally having a touch and gesture circuit), a SIM slot, a circuit audio / video, a motion processing circuit (eg, accelerometer, gyroscope), a wireless LAN circuit, a smart card circuit, a transmitter circuit, a GPS circuit, and a battery. As an example, a mobile device may be configured as a cell phone, tablet, etc. As an example, a method may be implemented (e.g., in whole or in part) using a mobile device. As an example, a system may include one or more mobile devices. As an example, a system can be a distributed environment, for example a so-called "cloud" environment where various devices, components, and so on. interact for purposes of data storage, communications, computing, etc. As an example, a device or system may include one or more components for information communication via the Internet (e.g., when communication is via one or more Internet protocols), and / or a cellular network, and / or a satellite network, etc. As an example, a method may be implemented in a distributed environment (e.g., wholly or partly in the form of a cloud-based service). As an example, information can be captured from a screen (eg, take a touch screen), output to a screen, or both. As an example, information can be output to a projector, a laser device, a printer, etc., so that the information can be viewed. As an example, information may be displayed by stereography or holography. As for a printer, take a 2D or 3D printer. As an example, a 3D printer may include one or more substances that can be ejected to build a 3D object. For example, data may be provided to a 3D printer to construct a 3D representation of a subterranean formation. As an example, layers can be built in 3D (eg, horizons, etc.), geological bodies built in 3D, and so on. As an example, holes, fractures, etc., can be constructed in 3D (e.g., as positive structures, as negative structures, etc.). Although only a few exemplary embodiments have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible in the exemplary embodiments. Therefore, all of these modifications are intended to fall within the scope of this disclosure as defined in the following claims. In the claims, the means and function clauses are intended to cover the structures described herein as providing the indicated function and not only the structural equivalents, but also the equivalent structures. Thus, although a nail and a screw may not be structural equivalents in that a nail uses a cylindrical surface to secure pieces of wood together, while a screw uses a helical surface, in the environment fastening pieces of wood, a nail and a screw can be equivalent structures.

权利要求:
Claims (20)
[0001]
REVENDICATIONS1. A method (500) for modeling a discontinuity in a geological environment, the method comprising: receiving (510) a mesh that represents a geological environment, the mesh including elements; receiving (520) location information for a discontinuity in the geological environment; at least in part according to the location information, a definition (530) of enrichment equations for a part of the elements, the enrichment equations comprising a jump function which models the discontinuity; a resolution (540) of a system of equations for an implicit function, the system of equations including the enrichment equations; and at least partially based on the resolution, outputting (550) values for the implicit function with respect to at least a portion of the mesh.
[0002]
The method of claim 1 wherein the jump function comprises the Heaviside function.
[0003]
3. The method of claim 1 wherein the discontinuity comprises a fault.
[0004]
4. The method of claim 3 wherein the fault intersects at least one of the elements.
[0005]
The method of claim 4 wherein the fault comprises a fault end at least in part in an element.
[0006]
The method of claim 5 wherein the jump function models the fault in the at least one intersected element and wherein a different function models the fault end.
[0007]
The method of claim 6 wherein the different function comprises a singular enrichment function that models the fault end as a singularity.
[0008]
The method of claim 1 comprising a plurality of discontinuities. 3036210 41
[0009]
9. The method of claim 1 further comprising a definition of constraints that constrain the implicit function.
[0010]
The method of claim 1 wherein the values for the implicit function include values that correspond to horizons within the geologic environment.
[0011]
11. The method of claim 1 further comprising updating the location information and a repetition of the steps of definition, resolution and output. 10
[0012]
The method of claim 1 wherein the location information comprises seismic information from a seismic survey of the geological environment. 15
[0013]
The method of claim 1 wherein the enrichment functions include enrichment functions of an extended finite element (XFEM) method.
[0014]
14. System (401) for modeling a discontinuity in a geological environment, the system comprising: a processor (403); a memory (404) operatively coupled to the processor; one or more modules (407) stored in the memory, the one or more modules comprising executable instructions by the processor, the instructions including instructions for: receiving (511) a mesh that represents a geological environment, the mesh including elements; receiving (521) location information for a discontinuity in the geological environment; At least in part depending on the location information, defining (531) enrichment equations for a part of the elements, the enrichment equations comprising a jump function that models the discontinuity; solving (541) a system of equations for an implicit function, the system of equations including the enrichment equations; and outputting (551) values for the implicit function with respect to at least a portion of the mesh. 3036210 42
[0015]
The system of claim 14 wherein the jump function comprises the Heaviside function.
[0016]
The system of claim 14 wherein the discontinuity comprises a fault. 5
[0017]
The system of claim 14 wherein the values for the implicit function include values that correspond to horizons within the geologic environment. 10
[0018]
18. Computer-readable storage medium (s) comprising instructions executable by a processor, the instructions including instructions for instructing a system to: receive (511) a mesh that represents a geological environment, the mesh comprising: elements ; Receiving (521) location information for a discontinuity in the geologic environment; at least in part depending on the location information, defining (531) enrichment equations for a part of the elements, the enrichment equations comprising a jump function that models the discontinuity; Solving (541) a system of equations for an implicit function, the system of equations including the enrichment equations; and outputting (551) values for the implicit function with respect to at least a portion of the mesh. 25
[0019]
19. Computer readable medium (s) according to claim 18 wherein the jump function comprises the Heaviside function.
[0020]
20. Computer readable medium (s) according to claim 18 wherein the values for the implicit function include values which correspond to horizons within the geological environment.

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WO2016183043A1|2016-11-17|

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法律状态:
2016-04-12| PLFP| Fee payment|Year of fee payment: 2 |

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2016-11-18| PLSC| Publication of the preliminary search report|Effective date: 20161118 |

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2017-05-29| PLFP| Fee payment|Year of fee payment: 3 |

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2018-05-25| PLFP| Fee payment|Year of fee payment: 4 |

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2021-04-12| PLFP| Fee payment|Year of fee payment: 7 |

优先权:

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申请号 | 申请日 | 专利标题

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FR1554222|2015-05-12|

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FR1554222A|FR3036210B1|2015-05-12|2015-05-12|GEOLOGICAL STRATIGRAPHY BY IMPLICIT AND JUMPING FUNCTIONS|FR1554222A| FR3036210B1|2015-05-12|2015-05-12|GEOLOGICAL STRATIGRAPHY BY IMPLICIT AND JUMPING FUNCTIONS|

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US15/572,457| US11175434B2|2015-05-12|2016-05-10|Geologic stratigraphy via implicit and jump functions|

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PCT/US2016/031553| WO2016183043A1|2015-05-12|2016-05-10|Geologic stratigraphy via implicit and jump functions|

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CA2985743A| CA2985743A1|2015-05-12|2016-05-10|Geologic stratigraphy via implicit and jump functions|

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NO20171868A| NO20171868A1|2015-05-12|2017-11-22|Geologic stratigraphy via implicit and jump functions|