Faulted geological structures having unconformities

Abstract

A method can include providing a mesh of a geologic environment that includes conformable sequences and an unconformity; interpolating an implicit function defined with respect to the mesh to provide values for the implicit function; and identifying an iso-surface based on a portion of the values where the iso-surface represents the unconformity as residing between two of the conformable sequences. Various other apparatuses, systems, methods, etc., are also disclosed.

Description

RELATED APPLICATION

This application
where unknowns in the equation are ϕ(a₀), ϕ(a₁), ϕ(a₂) and ϕ(a₃). For example, refer to the control point ϕ(a*), labeled 514 in the cell 512 of the control point constraints formulation 510 of FIG. 5, with corresponding coordinates (x*,y*,z,*); noting a matrix “M” for coordinates of the nodes or vertices for a₀, a₁, a₂ and a₃, (e.g., x₀, y₀, z₀ to x₃, y₃, z₃).

As an example, the number of such constraints of the foregoing type may be based on the number of interpretation points where, for example, interpretation points may be decimated interpretation for improving performance.

As mentioned, a process can include various regularization constraints, for example, for constraining smoothness of interpolated values, of various orders (e.g., constraining smoothness of ϕ or of its gradient ∇ϕ, which may be combined through a weighted least squares scheme.

As an example, a method can include constraining the gradient ∇ϕ in a mesh element (e.g. a tetrahedron, a tetrahedral cell, etc.) to take a (weighted) arithmetic average of values of the gradients of ϕ in with respect to its (topological) neighbors. As an example, one or more weighting schemes may be applied (e.g. by volume of an element) and for defining of a topological neighborhood (e.g., by face adjacency). As an example, two geometrically “touching” mesh elements that are located on different sides of a fault may be deemed not topological neighbors, for example, as a mesh may be “unsewn” along fault surfaces (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 one considers a mesh element m_i that has n neighbors m_j (e.g., for a tetrahedron), one may formulate an equation of the regularization constraint as follows:

$\nabla \phi \left(m_i\right)=\frac{1}{n}\sum _{j=1}^n\nabla \phi \left(m_j\right)$

In such an example of a regularization constraint, solutions for which isovalues of the implicit function would form a “flat layer cake” or “nesting balls” geometries may be considered “perfectly smooth” (i.e. 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 provided on nodes of a mesh (e.g., a control node). In such an example, data may be from force values at the location of well tops. As an example, a control gradient, or control gradient orientation, approach may be implemented to impose dip constraints.

Referring again to FIG. 5, the linear system formulation 530 includes various types of constraints. For example, a formulation may include harmonic equation constraints, control point equation constraints (see, e.g., the control point constraints formulation 510), gradient equation constraints, constant gradient equation constraints, etc. As shown in FIG. 5, a matrix A may include a column for each node and a row for each constraint. Such a matrix may be multiplied by a column vector such as the column vector ϕ(a_i) (e.g., or ϕ), for example, where the index “i” corresponds to a number of nodes, vertices, etc. for a mesh (e.g., a double index may be used, for example, a_ij, where j represents an element or cell index). As shown in the example of FIG. 5, the product of A and the vector ϕ may be equated to a column vector F (e.g., including non-zero entries where appropriate, for example, consider ϕ_{control point} and ϕ_gradient).

FIG. 6 shows a block diagram of an example of a method 610 that includes an input block 620 and output block 680, for example, to output an implicit function equated to a stratigraphic property per a block 682. As to the input block 620, it may include a fault surfaces input block 622 and a horizon points input block 624. As shown in the example of FIG. 6, the input block 620 may provide input to a thickness estimation block 630, a layer block 640 and a background mesh block 652.

As to the layer block 640, it can include a thickness values block 642 for determining or receiving thickness values (e.g., based on or from the thickness estimation block 630) and a computation block 644 for computing control point values (see, e.g., the formulations 510 and 530 of FIG. 5). As shown, the layer block 640 can output control points to a control points block 662, which may be defined with respect to a mesh provided by the background mesh block 652. As an example, the control points of the control points block 662 may account for one or more regularization constraints per a regularization constraint block 654.

As an example, given control point values for layers definable with respect to a mesh and subject to one or more constraints, a method can include calculating values of an implicit function (e.g., or implicit functions). As shown in the example of FIG. 6, an implicit function calculation block 662 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.

As to the output block 680, given calculated values for one or more implicit functions, these may be associated with, for example, a stratigraphic property per the block 682. As an example, one or more iso-surfaces may be extracted based at least in part on the values of the stratigraphic property per an iso-surface extraction block 684, for example, where one or more of the extracted iso-surfaces may be defined to be a horizon surface (e.g., or horizon surfaces) per a horizon surface block 686.

FIG. 6 also shows an example of a method 690 for outputting a volume based model (e.g., a model constructed from a subdivision of a volume of interest in sub-volumes representing stratigraphic layers, fault blocks or segments, etc). As shown, the method 690 includes an input block 691 for inputting information (e.g., sealed fault framework information, horizon interpretation information, etc.), a mesh block 692 for providing or constructing a mesh, a volume attribute interpolation block 693 for interpolating values (e.g., using one or more implicit functions), an iso-surface extraction block 694 for extracting one or more iso-surfaces (e.g., based at least in part on the interpolated values), a subdivision block 695 for subdividing a meshed volume (e.g., based at least in part on one or more of the one or more extracted iso-surfaces) and an output block 696 for outputting a volume based model (e.g., based at least in part on one or more portions of a subdivided meshed volume).

As an example, the input block 691 may include one or more features of the input block 620 of the method 610, the mesh block 692 may include one or more features of the mesh block 652 of the method 610, the volume attribute interpolation block 693 may include one or more features of the implicit function calculation block 664 and/or the stratigraphic property block 682 of the method 610, the iso-surface extraction block 694 may include one or more features of the iso-surface extraction block 684 of the method 610, the sub-division block 695 may include subdividing a meshed volume using one or more horizon surfaces per the horizon surfaces block 686 of the method 610 and the output block 696 may include outputting a volume based model based at least in part on one or more outputs of the output block 680 of the method 610.

As explained with respect to the method 410 of FIG. 4, an implicit function may be provided for performing, for example, interpolation. As an example, an implicit modeling approach can include representing surfaces as iso-values of a volume attribute (e.g., of an implicit function). As an example, such a volume attribute may be referred to as being a “thickness proportion” (e.g., volumetrically filling in space). For example, an implicit function may correspond to the stratigraphic age of formations and, for example, such an implicit function may be embedded and interpolated in a volumetrically filling tetrahedral mesh (e.g., structured, unstructured, etc.).

As an example, a method can include building, a tetrahedral mesh for carrying and interpolating an implicit function. As an example, a 3D boundary-constrained Delaunay mesh generator may be implemented, for example, with constraints such as constraints based on faults affecting considered horizons where such faults may be accounted for as internal boundaries during mesh generation, for example, where some border faces of tetrahedra may match fault geometries in a resulting mesh. As an implicit function may be defined and interpolated on nodes of a tetrahedral mesh, density of the mesh, and therefore the spatial resolution of the implicit function, may be controlled, for example, to include a higher density within a shell at, proximate to or around various data and/or faults (e.g., to maximize degree of freedom of an interpolation at or near various data and/or faults). As an example, a mesh adaptation process may include producing tetrahedra that have a vertical resolution higher than their areal resolution (e.g., to better capture thickness variations in layering). As an example, a resulting mesa (e.g., a built mesh) may be unstructured.

As an example, a method can include interpolating values of an implicit function on nodes of a tetrahedral mesh. As an example, an interpolation process may include using a linear least squares formulation, which may tend to minimize misfit between interpretation data and interpolated surfaces and to minimize variations of dip and thickness of layers.

As an example, a method can include generating surfaces representing individual implicitly modeled horizons. In such an example, as the specific value of the implicit function associated to each of the individual horizons may be known, a method may include using an iso-surfacing algorithm. As an example, resolution of a resulting surface or surfaces may be higher or approximately equal to a local resolution of a tetrahedral mesh around sample points (e.g., which may be user-controllable).

As an example, a method may include a volume based modeling approach that generates a consistent zone model (e.g., a model of interpreted geological layers). For example, such a zone model may include an individual geological layer that may be seen as an interval of values of an implicit function. In such an example, given its value of the implicit function, a method may determine to which layer an arbitrary point belongs, in particular where such arbitrary points correspond to nodes of a mesh supporting the implicit function.

As an example, edges of a tetrahedral mesh may intersect limits of geological layers. In such an example, construction of such intersection points may have been computed where they correspond to nodes of triangulated surfaces representing horizons. Accordingly, zones may be built by cutting edges of the tetrahedral mesh by some iso-surfaces of the implicit function.

As an example, a method can include cutting a volume to produce zones that are sets of tetrahedra. As an example, a method can include cutting volume borders to produce zones that are sets of triangulated patches. As to the latter, it may include cutting volume borders by iso-contours. As noted, one or more implicit functions may be formulated for determination of iso-surfaces and/or iso-contours that do not intersect one another other.

As an example, a volume based modeling approach may be less sensitive to complexity of a fault network and may provide conformable horizons belonging to a common conformable sequence (e.g., which may be modeled simultaneously). As to the latter, by using an implicit approach (e.g., by representing sets of conformable horizons by several iso-values of a common implicit attribute), the approach may avoid crossing of conformable horizons.

As an example, a volume based modeling approach may provide for conformable horizons that constrain geometry of other conformable horizons that belong to a common sequence, which itself may be constrained by geometry. As an example, a volume based modeling approach may be applied in scenarios where data are sparse, for example, consider data from well tops, 2D sections, etc. As an example, one or more surfaces may be modeled using seismic data and, for example, globally adjusted using well top data.

As an example, a volume based modeling approach may include outputting geometry of a horizon as well as volume attribute values, which may be defined within a volume of interest and, for example, represent a stratigraphic age, or relative chronostratigraphic age, of a formation (or formations).

FIG. 7 shows a diagram 700 that represents an example of a cross-sectional view of a geologic environment. As shown, the environment includes four faulted conformable horizons and one unconformity (e.g., an erosion). In the example of FIG. 7, the :limits have also been eroded and are active in the sequence below the erosion. As an example, a method may include defining an implicit function within such an environment (e.g., with respect to a mesh that models the environment) and interpolating, the implicit function to provide implicit function values upon which iso-surfaces, iso-contours, etc., may be extracted.

As an example, such a method may produce correct geometries for the eroded horizons (e.g., similar to those of horizons labeled 1-4) provided that the implicit function is interpolated on a background mesh which upper boundary corresponds to unconformity U of FIG. 7.

FIG. 8 shows a diagram 800 that represents an example of a model of the geologic environment of FIG. 7. In the example of FIG. 8, the model is built to represent the “real” geologic environment of FIG. 7 via interpolating or extrapolating conformable horizons within a volume of interest (VOI), including the eroded and non-deposited portions, for which no data may exist. As shown, the model of FIG. 8 does not provide a “realistic” representation of the horizons, for example, in part due to the fact that the interpolation domain is not bounded by the erosion surface U.

FIG. 9 shows a diagram 900 that represents an example of a model of the geologic environment of FIG. 7. In the example of FIG. 9, the model may be formed by taking the unconformity (e.g., erosion) into account by computing geometric intersections with the conformable horizons previously modeled as in FIG. 8 and, for example, removing “unreal” portions of the model of FIG. 8. A comparison between the diagram 700 of the geologic environment of FIG. 7 and the model 900 of FIG. 9 shows that inaccuracies exist, especially near the contacts between the unconformity and the conformable horizons. Again, as with the model of FIG. 8, this is due in part to the fact that the domain in which horizons 1-4 were interpolated is not bounded by the erosion surface U.

FIGS. 7, 8 and 9 illustrate that modeling, an unconformity surface before eroded surfaces can enhance a modeling effort and that such an effort may include using an unconformity surface to limit a domain of interpolation of an implicit function. Such an approach may provide for more accurately modeling a real geologic environment, for example, when compared to results achieved via extrapolating fault surfaces to reconstruct their eroded geometry, which may be unpractical and not robustly automated since this eroded geometry may be unknown (e.g., where no subsurface data is available to constrain it) and since the extrapolation may include some interpretative work that may lead to incorrect or unrealistic limit and horizon geometries.

As an example, a method may provide a model of a geologic environment that represents features, for example, more accurately than the approaches described with respect to the diagrams 800 and 900 of FIGS. 8 and 9, respectively. As an example, the method 410 of FIG. 4 may include outputting one or more models (e.g., a mesh or meshes, etc.) that account for various features of a geologic environment, for example, where the output model or models is volume filling (e.g., “watertight” or “sealed”).

As an example, a method may be implemented to create a reservoir model on a “conformable sequence per conformable sequence” basis, for example, where surfaces belonging to a common conformable sequence may be interpolated simultaneously. As an example, a method can include iteratively editing topology of a volume mesh, for example, to control extent of the volume in which an interpolation is performed and continuity of an interpolated implicit function. As an example, a method may include producing layering that is consistent with a geological style of deposition in one or more eroded areas.

As an example, a method can include building a background mesh, for example, where the background volume mesh covers a volume of interest (VOI), which itself may be of a size sufficient to include horizons to be modeled.

FIG. 10 shows an example of a mesh 1010 that includes an unconformity 1012 and a “solid” vertical portion 1014 composed of connected tetrahedra. As indicated in FIG. 10, tetrahedra size may vary within a portion of the mesh 1010, for example, to better fit an interpolation process for building horizons via an implicit scheme. As to the unconformity 1012, it may be defined using seismic data or other data.

FIG. 11 shows an example of a mesh 1110 that includes the unconformity 1012 and the solid vertical portion 1014 where tetrahedra volumetrically fill the mesh 1110. In the example of FIG. 11, the mesh 1110 is also shown along with volume attribute values. In the example of FIG, 11, the volume attribute values may be displayed or represented with respect to a periodic color scale, for example, where the volume attribute or “property” may be monotonously increasing (e.g., corresponding to values of a monotonic implicit function). For example, each “period” of the periodic scale may correspond to a layer in a series of layers defined by input horizons. In such an example, an individual horizon may be conformable to another individual horizon within a common sequence.

FIG. 12 shows a volume 1210 that corresponds to the mesh 1110, however, without lines indicating mesh elements (e.g., mesh cells, etc.). In the example of FIG. 12, eight portions (portions 1 to 8) are shown as an example for purposes of explanation. For example, within these portions, a periodic scale may be repeated as indicated by black and white hatchings: 1221-1, 1222-1, 1223-1, 1224-1, 1225-1, 1221-2, 1222-2, 1222-3, 1224-2, etc., where “−1” corresponds to one portion of the volume 1210 and “−2” corresponds to another portion of the volume 1210. As mentioned, the scale may represent values of an implicit function.

Referring again to FIG. 11, the tetrahedral background mesh 1110 may be used for modeling implicitly an unconformity described by seismic data points such as the unconformity 1012 of the mesh 1010 of FIG. 10. The mesh 1110 also shows an implicit function represented by a periodic scale (e.g., whether black and white, color, etc.) that may be interpolated within the background mesh. As mentioned, FIG. 12 shows the volume 1210 without the mesh lines to more clearly illustrate an example of a periodic scale for an implicit function. As an example, the unconformity 1012 of FIG. 10 may be represented by a specific iso-surface of the implicit function.

As an example, a method may include building a mesh that includes subsets of its facets that match (e.g., in a general sense) elements, of the mesh representing one or more faults. In such an example, the facets may be approximating, in the background mesh, geometry of a fault network. As an example, a mesh may include elements with shape and size that are specified to be suitable for an interpolation process (e.g., shape, size, etc. may be specified depending on one or more characteristics of an interpolation process).

As an example, a mesh may be considered an initial mesh (e.g., or other early stage mesh) that may not include one or more internal borders, for example, that represent one or more discontinuities.

As an example, a method can include identifying one or more conformable sequences. In such an example, an identification process may include identifying a set of conformable sequences from a geological type of stratigraphic horizons, for example, provided by an operator of the system. As an example, consider one or more of the definitions provided with respect to FIG. 3 where: (a) an erosion may be an unconformity that is conformable to one or more horizons immediately younger (e.g., without gaps in the geological record) and not conformable to one or more older horizons (see, e.g., the geologic environment 700 of FIG. 7); (b) a baselap may be an unconformity that is conformable to one or more horizons immediately older (e.g., without gaps in the geological record) and not conformable to one or more younger horizons; and (c) a discontinuity may be an unconformity that is neither conformable to one or more older horizons nor to one or more younger ones. As an example, a conformable horizon may be assumed to be conformable to at least an adjacent younger horizon and at least an adjacent older horizon.

Provided with definitions for a given stratigraphic sequence that includes conformable horizons and unconformities, it may be possible to divide the sequence into subsets of conformable sequences, for example, where an individual horizon (e.g., conformable or unconformity) belongs to a single conformable sequence. For example, consider the following rules: (a) an erosion is the oldest horizon to be modeled in the conformable sequence it belongs to; (b) a baselap is the youngest horizon to be modeled in the conformable sequence it belongs to; and (c) a discontinuity is modeled alone in its “own” conformable sequence, which may be, in such a case, a conformable sequence that is degenerated to a single surface.

Through use of such rules, a produced conformable sequence may include a set of horizons that are conformable to one another, for example, meaning that they do not have any contact with one another and do not intersect one another. In such an example, an individual conformable sequence may be modeled with a single implicit function. As an example, a one-to-one correspondence may exist between conformable sequences and implicit functions.

As an example, a method can include editing a mesh (e.g., a background mesh). For example, an editing process may prepare a mesh for interpolation of an implicit function for modeling a given conformable sequence in the mesh.

FIG. 13 shows an example of a first mesh 1322 for a conformable sequence and a second mesh 1326 for a conformable sequence where the first and second mesh result from splitting of a larger mesh, for example, with respect to an unconformity such as the unconformity 1012, which may be an erosion and according to a rule associated with the younger of the two sequences (e.g., the first mesh 1322).

As mentioned with respect to the method 410 of FIG. 4, editing may include one or more processes. As an example, consider a sub-volume process that can create sub-volumes within a meshed volume of interest (VOI). As an example, sub-volumes may be first created from sub-volumes of a background mesh used to model a prior conformable sequence; noting that where a conformable sequence is a first conformable sequence, such a process may, by definition, not have a prior conformable sequence and may be created directly. As an example, a sub-volume process may include cutting, sub-volumes according to one or more unconformities that may bound a conformable sequence previously modeled. For example, referring to FIG. 13, the mesh 1322 may be a conformable sequence previously modeled after which the mesh 1326 is used to model another conformable sequence.

A sub-volume process may be performed, for example, in a manner that avoids numerical instabilities where unconformities are iso-surfaces of a scalar property field defined within considered sub-volumes. In such an example, geometrical intersections between mesh elements of the unconformity (e.g., which may be triangles or other shaped faces) and the mesh elements of the sub-volumes (e.g., which may be tetrahedra or other volumes), may be one of two kinds: (i) a node of a triangle lying on an edge of a tetrahedron; or (ii) a node of a triangle being collocated with a node of a tetrahedron. Such an approach may, for example, facilitate computation of one or more geometrical intersections.

As an example, an identification process may include identifying one or more sub-volumes as corresponding to a conformable sequence. For example, where a previously modeled unconformity is modeled through a volume of interest and includes a maximum areal extension, it may intersect the volume of interest in a manner that divides the volume of interest into sub-volumes such as, for example, two subsets of new sub-volumes (see, e.g., FIG. 13). As an example, one subset of new sub-volumes may be for a sequence older than an unconformity while another subset of new sub-volumes may be for a sequence younger than the unconformity.

As an example, a method may include computing relative ages by taking an average value of an implicit function having been used to model an unconformity in a sub-volume and comparing it with a value of an iso-surface that represents the unconformity. For example, an iso-surface may be defined along a scale that corresponds to age. As an example, depending on order with which conformable sequences are modeled (e.g., from younger to older or from older to younger), one of two subsets of new sub-volumes may be selected and considered for processing a next conformable sequence. As an example, a periodic scale may be implemented to facilitate visualization of an implicit function (e.g. with respect to one or more features in a sequence).

FIG. 14 shows an example of a volume 1410 with active faults 1412-1, 1412-2, 1412-3, 1412-4 and 1412-5 and an example of a re-meshed volume 1430 to account for the active faults (e.g., mesh refinement in regions near the active faults).

As an example a method may include managing fault activity. For example, a list of faults may be provided that have been set as active for a “current” conformable sequence (e.g., meaning that they are expected to introduce a geometrical discontinuity in one or more modeled layers as in the example of FIG. 13) and compared to a list of faults that were set as active for a previously considered conformable sequence. In such an example, to enforce geological consistency, faults that were active for a younger sequence may be set as active for an older sequence. Given such a comparison, discontinuities may be created or removed in a considered sub-volume or sub-volumes of a background mesh. For example, if a subset of facets exists in the sub-volumes matching the geometry (e.g., mesh elements) of a given fault, a corresponding discontinuity may be formed by duplicating these facets and thus creating an internal border. As an example, one or more discontinuities may be removed by performing for example some local mesh editions on elements of a background mesh,

As to interpolation of an implicit function corresponding to a conformable sequence, as an example, its distribution may be discontinuous across one or more internal borders of a background mesh and continuous elsewhere (see, e.g., FIGS. 11 and 12). As an example, interpolation may be performed in one or more sub-volumes of a background mesh that have been created and identified as corresponding to a “current” conformable sequence. As an example, data points that included in such one or more sub-volumes may be taken into account to constrain an interpolation of an implicit function. As an example, once an interpolation process has been performed to provide values for an implicit function, implicit horizons of the “current” conformable sequence may he transformed into explicit surfaces using one or more iso-surfacing algorithms.

FIG. 15 shows an example of a method 1510 that includes a provision block 1540 for providing a mesh of a geologic environment that includes conformable sequences and an unconformity (or unconformities); an interpolation block 1550 for interpolating an implicit function defined with respect to the mesh to provide values for the implicit function; and an identification block 1560 for identifying an iso-surface based on a portion of the values where the iso-surface represents the unconformity, for example, as residing between two of the conformable sequences.

As an example, the provision block 1540 may include providing the mesh, building the mesh, editing a mesh, etc. based at least in part on receiving input from an input block 1512 and input from a conformity/unconformity block 1514. As an example, the conformity/unconformity block 1514 may provide for defining one or more unconformities in a mesh, for example, with respect to one or more conformal sequences. As an example, the conformity/unconformity block 1514 may provide data associated with an unconformity, for example, where the data is represented as values, points, etc. in a mesh.

As an example, the interpolation block 1550 may include receiving one or more implicit functions per an implicit function block 1522 and include receiving one or more constraints per a constraints block 1524. As an example, an implicit function (or implicit functions) may be constrained by one or more constraints. As an example, where a mesh includes nodes, one or more constraints may be defined with respect to a portion of those nodes. In such an example, a linear system of equations may be formulated and solved, for example, as part of an interpolation process to provide values for an implicit function (e.g., or implicit functions).

As an example, the identification block 1560 may include receiving one or more algorithms, for example, for forming iso-surfaces given values within a region or regions such as a region or regions of a mesh. For example, an algorithm may receive as input values associated with an implicit function and then define iso-surfaces for at least some of those values. As an example, an iso-surface may correspond to a horizon, an unconformity, etc. As an example, a series of iso-surfaces may correspond to a conformable sequence, for example, where the conformable sequence is at least partially bound by an unconformity, which may be represented itself as an iso-surface.

In the example of FIG. 15, the method 1510 may include a block 1570 for performing one or more additional actions. For example, a model block 1572 may provide for outputting a model based at least in part on the identified iso-surface where such a model may be used for modeling one or more physical phenomena associated with a geologic environment (e.g., including one or more processes applied to the environment such as injection, production, etc.). As an example, the block 1570 may include a splitting block 1574 for splitting or sub-dividing a mesh based at least in part on an identified iso-surface. For example, where the iso-surface corresponds to an unconformity, a mesh may be split into meshes based at least in part on that iso-surface (e.g., to form a first mesh and a second mesh where the unconformity may belong to one of the first mesh or the second mesh). As an example, the block 1570 may include a fault block 1576 for introducing one or more faults, for activation of one or more faults, for deactivation of one or more faults, etc.

As an example, the method 1510 may include a provision block 1580 for providing an updated mesh. For example, where splitting occurs per the splitting block 1574, a mesh may be updated and provided to the interpolation block 1550 for further processing. As an example, the conformity/unconformity block 1514 may provide input for updating a mesh. For example, where a mesh has been split into a first mesh and a second mesh according to a first unconformity, one of the first mesh and the second mesh may be further processed, for example, using data, etc. associated with another unconformity. In the example of FIG. 15, the method 1510 may perform iteratively, for example, by looping to edit a mesh (e.g., whether an initial provided mesh, a subsequent mesh resulting from splitting, etc.) and to perform interpolation of one or more implicit functions with respect to an edited mesh.

The method 1510 is shown in FIG. 15 in association with various computer-readable media (CRM) blocks 1513, 1515, 1523, 1525, 1533, 1541, 1551, 1561, 1571, 1573, 1575, 1577 and 1581. Such blocks generally include instructions suitable for execution by one or more processors (or cores) to instruct a computing device or system to perform one or more actions. While various blocks are shown, a single medium may be configured with instructions to allow for, at least in part, performance of various actions of the method 1510. As an example, a computer-readable medium (CRM) may be a computer-readable storage medium. As an example, the blocks 1513, 1515, 1523, 1525, 1533, 1541, 1551, 1561, 1571, 1573, 1575, 1577 and 1581 may be provided as one or more modules, for example, such as the one or more modules 407 of the system 401 of FIG. 4.

As an example, a method can include providing a mesh of a geologic environment (e.g., a two-dimensional spatial mesh or a three-dimensional spatial mesh) that includes conformable sequences and an unconformity; interpolating an implicit function defined with respect to the mesh to provide values for the implicit function; and identifying an iso-surface based on a portion of the values where the iso-surface represents the unconformity as residing between two of the conformable sequences. In such a method, the iso-surface that represents the unconformity may belong to one of the two of the conformable sequences.

As an example, a method can include using an identified iso-surface to split a mesh, for example, into a first mesh and a second mesh. As an example, a method may include interpolating an implicit function defined with respect to a first mesh or a second mesh to provide values for an implicit function and identifying another iso-surface within the first mesh or the second mesh based on a portion of the values.

As an example, a method can include selecting a first mesh or a second mesh (e.g., resulting from splitting a mesh) based at least in part on a type of unconformity associated with an identified iso-surface used to split the mesh and based at least in part on a portion of values of an implicit function for the identified iso-surface.

As an example, a method may include creating a model for modeling one or more physical phenomena based at least in part on an identified iso-surface that represents an unconformity. As an example, an unconformity may be one of an erosion, a baselap and a discontinuity; noting, for example, that one or more other types of unconformities may be defined and identified using an implicit function and interpolating values for the implicit function.

As an example, a geologic environment may include one or more faults within a portion of at least one conformable sequences, for example, represented by a mesh (e.g., or meshes).

As an example, a method may include introducing topological discontinuities to represent geological fault surfaces in a provided mesh or an edited version thereof (e.g., which may be a mesh resulting from one or more mesh splitting operations). As an example, a method may include using fault surfaces for constraining geometry and topology of mesh elements of a provided mesh (e.g., or an edited version thereof), for example, prior to introducing a topological discontinuity to the mesh.

As an example, a method may include introducing a topological discontinuity representing a fault to at least one portion of the first mesh or to at least one portion of the second mesh (e.g., where the first mesh and the second mesh result from a splitting operation based at least in part on an iso-surface). In such an example, the method may include identifying the at least one portion of the first mesh or the at least one portion of the second mesh based on, for example, sedimentological and tectonic history (e.g., of one or more regions of a volume interest).

As an example, values of an implicit function may be scalar field values. In such an example, the values may be “property” values, for example, of an attribute (e.g., consider a volume attribute). As an example, continuity of an implicit function may be governed by continuity of a mesh (e.g., of a geologic environment). As an example, a method may include using data to represent an unconformity within a mesh.

As an example, a mesh may include nodes (e.g., vertices, etc.). In such an example, a method may include defining a linear system of equations that includes constraints defined with respect to at least a portion of the nodes. As an example, a method may include interpolating an implicit function at least in part by solving a linear system of equations to provide values of the implicit function.

As an example, a system can include a processor; memory operatively coupled to the processor; and one or more modules stored in the memory that include instructions executable by the processor to instruct the system to: provide a mesh of a geologic environment that includes conformable sequences and at least one unconformity; interpolate an implicit function defined with respect to the mesh to provide values for the implicit function; and identify an iso-surface based on a portion of the values where the iso-surface represents one of the at least one unconformity as residing between two of the conformable sequences. In such an example, one or more modules stored in the memory may include instructions executable by the processor to instruct the system to edit the mesh based at least in part on an identified iso-surface. As an example, one or more modules stored in memory of a system that include instructions executable by the processor may instruct the system to define at least one unconformity as a member selected from a group consisting of an erosion, a baselap and a discontinuity; noting, for example, that one or more other types of unconformities may be defined.

As an example, one or more computer-readable storage media may include computer-executable instructions to instruct a computing device to: provide a mesh of a geologic environment that includes conformable sequences and at least one unconformity; interpolate an implicit function defined with respect to the mesh to provide values for the implicit function; and identify an iso-surface based on a portion of the values where the iso-surface represents one of the at least one unconformity as residing between two of the conformable sequences. In such an example, instructions may be included to instruct a computing device to edit the mesh based at least in part on an identified iso-surface; to instruct a computing device to define at least one of the at least one unconformity as a member selected from a group consisting of an erosion, a baselap and a discontinuity.

As an example, a method may include a performance block for performing a simulation of phenomena associated with a geologic environment using at least a portion of a mesh (e.g., or a model based on a mesh or meshes). As to performing a simulation, such a simulation may include interpolating geological rock types, interpolating petrophysical properties, simulating fluid flow, or other calculating (e.g., or a combination of any of the foregoing).

As an example, a system may include instructions to instruct a processor to perform a simulation of a physical phenomenon using at least a portion of a mesh (e.g., or a model based on a mesh or meshes) and, for example, to output results of the simulation to a display.

FIG. 16 shows components of an example of a computing system 1500 and an example of a networked system 1610. The system 1600 includes one or more processors 1602, memory and/or storage components 1604, one or more input and/or output devices 1606 and a bus 1608. In an example embodiment, instructions may be stored in one or more computer-readable media (e.g., memory/storage components 1604). Such instructions may be read by one or more processors (e.g., the processor(s) 1602) via a communication bus (e.g., the bus 1608), which may be wired or wireless. The one or more processors may execute such instructions to implement (wholly or in part) one or more attributes (e.g., as part of a method). A user may view output from and interact with a process via an I/O device (e.g., the device 1606). In an example 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 package, a memory card, etc. (e.g., a computer-readable storage medium).

In an example embodiment, components may be distributed, such as in the network system 1610. The network system 1610 includes components 1622-1, 1622-2, 1622-3, . . . 1622-N. For example, the components 1622-1 may include the processor(s) 1602 while the component(s) 1622-3 may include memory accessible by the processor(s) 1602. Further, the component(s) 1602-2 may include an I/O device for display and optionally 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 includes one or more network interfaces for communication of information. For example, a mobile device may include a wireless network interface (e.g., operable via IEEE 802.11, ETSI GSM, BLUETOOTH®, satellite, etc.). As an example, a mobile device may include components such as a main processor, memory, a display, display graphics circuitry (e.g., optionally including touch and gesture circuitry), a SIM slot, audio/video circuitry, motion processing circuitry (e.g., accelerometer, gyroscope), wireless LAN circuitry, smart card circuitry, transmitter circuitry, GPS circuitry, and a battery. As an example, a mobile device may be configured as a cell phone, a tablet, etc. As an example, a method may be implemented (e.g., wholly or in part) using a mobile device. As an example, a system may include one or more mobile devices.

As an example, a system may be a distributed environment, for example, a so-called “cloud” environment where various devices, components, etc. interact for purposes of data storage, communications, computing, etc. As an example, a device or a system may include one or more components for communication of information via one or more of the Internet (e.g., where communication occurs via one or more Internet protocols), a cellular network, a satellite network, etc. As an example, a method may be implemented in a distributed environment (e.g., wholly or in part as a cloud-based service).

As an example, information may be input from a display (e.g., consider a touchscreen), output to a display or both. As an example, information may be output to a projector, a laser device, a printer, etc. such that the information may be viewed. As an example, information may be output stereographically or holographically. As to a printer, consider a 2D or a 3D printer. As an example, a 3D printer may include one or more substances that can be output to construct 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 may be constructed in 3D (e.g., horizons, etc.), geobodies constructed in 3D, etc. As an example, holes, fractures, etc., may be constructed in 3D (e.g., as positive structures, as negative structures, etc.).

Although only a few example embodiments have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible in the example embodiments. Accordingly, all such modifications are intended to be included within the scope of this disclosure as defined in the following claims. In the claims, means-plus-function clauses are intended to cover the structures described herein as performing the recited function and not only structural equivalents, but also equivalent structures. Thus, although a nail and a screw may not be structural equivalents in that a nail employs a cylindrical surface to secure wooden parts together, whereas a screw employs a helical surface, in the environment of fastening wooden parts, a nail and a screw may be equivalent structures. It is the express intention of the applicant not to invoke 35 U.S.C. §112, paragraph 6 for any limitations of any of the claims herein, except for those in which the claim expressly uses the words “means for” together with an associated function.

The following documents are incorporated by reference herein:

• Mallet, J-L, “Geomodelling”, Cambridge University Press, 2001.
• Ledez, D., “Modelisation d'Objets Naturels par Formulation Implicite”, PhD Dissertation, Institute National Polytechnique de Lorraine, October 2003.
• Frank T., et al., “3D Reconstruction of complex geological interfaces from irregularly distributed and noisy point data”, Computers & Geosciences, Vol. 33, issue 7, July 2007.

Claims

1. A method comprising:

providing a mesh to represent a faulted geological structure in a subterranean formation of a field;

identifying an interface separating a plurality of conformable sequences in the faulted geological structure;

interpolating, by a computer processor and in a first iteration, a first implicit function defined with respect to the mesh to provide values for the first implicit function, wherein the values comprise at least a first iso-value corresponding to the interface;

dividing, based at least on the first iso-value, the mesh into at least a first sub-mesh and a second sub-mesh, wherein each of the first sub-mesh and the second sub-mesh comprises at least one of the plurality of conformable sequences;

interpolating, by the computer processor and in a second iteration, a second implicit function, wherein the extent of interpolating the second implicit function is restricted to within one of the first sub-mesh and the second sub-mesh;

extracting, from the first implicit function and the second implicit function, a surface corresponding to the interface;

creating a model based at least on the surface; and

performing exploration of natural resources in the subterranean formation using the model.

2. The method of claim 1, further comprising:

identifying, based on the first iso-value, a first iso-surface to split the mesh-into the first sub-mesh and the second sub-mesh,

wherein the first iso-surface represents the interface in the first iteration.

3. The method of claim 2, further comprising:

identifying, in response to interpolating the second implicit function, a second iso-surface based on a second iso-value of the second implicit function,

wherein the second iso-surface represents an adjustment to the first iso-surface for representing the interface in the second iteration.

4. The method of claim 2, further comprising introducing a topological discontinuity representing a fault to at least one portion of the first sub-mesh or to at least one portion of the second sub-mesh.

5. The method of claim 4, further comprising identifying the at least one portion of the first sub-mesh or the at least one portion of the second sub-mesh based on sedimentological and tectonic history.

6. The method of claim 1, further comprising selecting the one of the first sub-mesh and the second sub-mesh based at least in part on a type of the interface, wherein the interface comprises a member selected from a group consisting of an erosion, a baselap and a discontinuity.

7. The method of claim 1, further comprising modeling one or more physical phenomena based at least in part on the surface that represents the interface, wherein layering in the model is defined by iso-values of the first implicit function and the second implicit function and is consistent with a geological style of deposition in an eroded area of the faulted geological structure.

8. The method of claim 1, further comprising:

associating the one of the first sub-mesh and the second sub-mesh with a stratigraphic age;

obtaining a list of faults that are active prior to the stratigraphic age;

creating, in the one of the first sub-mesh and the second sub-mesh, internal borders based at least on the list of faults, and

wherein the internal borders are used at least to enforce a discontinuity when interpolating the first implicit function.

9. The method of claim 1, wherein the faulted geological structure comprises one or more faults within a portion of at least one of the plurality of conformable sequences.

10. The method of claim 1, further comprising introducing topological discontinuities to represent geological fault surfaces in the provided mesh or an edited version thereof.

11. The method of claim 1, further comprising using fault surfaces for constraining geometry and topology of mesh elements of the provided mesh, or an edited version thereof, prior to introducing a topological discontinuity to the mesh.

12. The method of claim 1, wherein the values of the first implicit function comprise scalar field values.

13. The method of claim 1, wherein continuity of the first implicit function is governed by continuity of the mesh.

14. The method of claim 1, further comprising using data to represent the interface within the mesh.

15. The method of claim 1, wherein the mesh comprises nodes and wherein the first implicit function is defined using at least a portion of the nodes.

16. The method of claim 15, further comprising defining a linear system of equations that comprises constraints defined with respect to at least a portion of the nodes wherein interpolating the first implicit function comprises solving the linear system of equations to provide the values of the first implicit function.

17. A system comprising:

a processor;

memory operatively coupled to the processor; and

one or more modules stored in the memory that comprise instructions executable by the processor to instruct the system to:

provide a mesh to represent a faulted geological structure in a subterranean formation of a field;

identify an interface separating a plurality of conformable sequences in the faulted geological structure;

interpolate, in a first iteration, a first implicit function defined with respect to the mesh to provide values for the first implicit function, wherein the values comprise at least a first iso-value corresponding to the interface;

divide, based at least on the first iso-value, the mesh into at least a first sub-mesh and a second sub-mesh, wherein each of the first sub-mesh and the second sub-mesh comprises at least one of the plurality of conformable sequences;

interpolate, in a second iteration, a second implicit function, wherein the extent of interpolating the second implicit function is restricted to within one of the first sub-mesh and the second sub-mesh;

extract, from the first implicit function and the second implicit function, a surface corresponding to the interface;

create a model based at least on the surface; and

perform exploration of natural resources in the subterranean formation using the model.

18. The system of claim 17, further comprising one or more modules stored in the memory that comprise instructions executable by the processor to instruct the system to edit the mesh based at least in part on an identified iso-surface defined by the first iso-value.

19. One or more non-transitory computer-readable storage media comprising computer-executable instructions to instruct a computing device to:

provide a mesh to represent a faulted geological structure in a subterranean formation of a field;

identify an interface separating a plurality of conformable sequences in the faulted geological structure;

interpolate, in a first iteration, a first implicit function defined with respect to the mesh to provide values for the first implicit function, wherein the values comprise at least a first iso-value corresponding to the interface;

divide, based at least on the first iso-value, the mesh into at least a first sub-mesh and a second sub-mesh, wherein each of the first sub-mesh and the second sub-mesh comprises at least one of the plurality of conformable sequences;

interpolate, in a second iteration, a second implicit function, wherein the extent of interpolating the second implicit function is restricted to within one of the first sub-mesh and the second sub-mesh;

extract, from the first implicit function and the second implicit function, a surface corresponding to the interface;

create a model based at least on the surface; and

perform exploration of natural resources in the subterranean formation using the model.

20. The one or more non-transitory computer-readable storage media of claim 19, further comprising computer-executable instructions to instruct the computing device to edit the mesh based at least in part on an identified iso-surface defined by the first iso-value.

21. A method, comprising:

providing a mesh to represent a faulted geological structure in a subterranean formation;

interpolating, by a computer processor at a first time and in a first iteration, a first implicit function on the mesh to provide an iso-value corresponding to an interface between conformable sequences in the faulted geological structure;

dividing, based at least on the iso-value, the mesh into at least a first sub-mesh and a second sub-mesh, wherein each of the first sub-mesh and the second sub-mesh comprises at least one of the conformable sequences;

interpolating, by the computer processor at a second time and in a second iteration, a second implicit function, wherein the interpolating the second implicit function is restricted to within the first sub-mesh or the second sub-mesh;

creating a model of a geological environment based on an iso-surface extracted from the first and second implicit functions; and

performing exploration of natural resources in the subterranean formation using the model.

22. The method of claim 21, wherein the step of creating includes outputting geometry of a horizon.

23. The method of claim 21, further comprising simulating a physical phenomenon using the model and outputting the results of the simulation to a display.

24. The method of claim 21, wherein the dividing includes dividing the mesh based at least in part on a horizon surface.

25. The method of claim 21, wherein the implicit function is interpolated in a volumetrically filling tetrahedral mesh.

26. The method of claim 21, further comprising:

identifying, in response to interpolating the second implicit function, a second iso-surface based on a second iso-value of the second implicit function,

wherein the second iso-surface represents an adjustment to the first iso-surface for representing the interface in the second iteration.

27. The method of claim 21, further comprising introducing a topological discontinuity representing a fault to at least one portion of the first sub-mesh or to at least one portion of the second sub-mesh.

28. The method of claim 21, further comprising constraining geometry and topology of mesh elements of the provided mesh, or an edited version thereof, using fault surfaces prior to introducing a topological discontinuity to the mesh.

29. The method of claim 21, further comprising editing the mesh based at least in part on the iso-surface.

30. A non-transitory computer readable medium containing instructions that when executed by a processor cause the processor to perform the method of claim 21.

31. A system, comprising:

a processor;

memory operatively coupled to a processor; and

one or more modules stored in the memory that comprise instructions executable by the processor to instruct the system to:

provide a mesh to represent a faulted geological structure in a subterranean formation;

interpolate at a first time and in a first iteration a first implicit function on the mesh to provide an iso-value corresponding to an interface between conformable sequences in the faulted geological structure;

divide, based at least on the iso-value, the mesh into at least a first sub-mesh and a second sub-mesh, wherein each of the first sub-mesh and the second sub-mesh comprises at least one of the conformable sequences;

interpolate at a second time and in a second iteration a second implicit function, wherein the interpolating the second implicit function is restricted to within the first sub-mesh or the second sub-mesh;

create a model of a geological environment based on an iso-surface extracted from the first and second implicit functions; and

perform exploration of natural resources in the subterranean formation using the model.

32. The system of claim 31, further comprising one or more modules stored in the memory that comprise instructions executable by the processor to instruct the system to edit the mesh based at least in part on the iso-surface.