专利摘要:
The invention relates to a method for predicting the fault activity of an underground volume comprising the steps of obtaining a model of the underground volume on the basis of far field stress tensors, of identifying faults in the field. underground volume, generation of results corresponding to the single contribution of a fault for each of the far-field stress tensors, of selective combination for each of the far-field stress tensors and on the basis of a Boolean vector of activity fault, results in the form of a linearly independent contribution scaled to a superimposed result, calculation of a cost function representing a difference between the superimposed result and a measurement of the underground volume, and minimization of the cost function by iterative adjustment of an optimization parameter for each far field stress tensor and iterative adjustment of the vect Boolean Boolean activity, to generate a prediction of the fault activity of the underground volume.
公开号:FR3023954A1
申请号:FR1456780
申请日:2014-07-15
公开日:2016-01-22
发明作者:Frantz Maerten；Laurent Maerten；Mustapha Lejri；Jean-Pierre Joonnekindt
申请人:Services Petroliers Schlumberger SA；
IPC主号:

专利说明:

[0001] BACKGROUND OF THE INVENTION 100011 A fault can be considered as a complex three-dimensional surface discontinuity in a volume of soil or rock. Fractures including, but not limited to, diaclases, veins, dikes, pressure solution layers containing stylolites, etc., may be intentionally propagated to increase permeability in formations such as shale, in which optimizing the number, location, and size of fractures in the formation increases the yield of resources such as shale gas. The stress in continuous media mechanics can be considered as a measure of internal forces acting within a volume. This constraint can be defined as a measure of the average force per unit area at a surface within the volume on which internal forces act. Internal forces can be produced between the particles contained in the volume in response to external forces applied to the volume. [0003] An understanding of the origin and evolution of faults and the tectonic history of fault regions can be established by linking fault orientation, direction of slip, geological and geodesic data to the state. stress in the earth's crust. In some inverse problems, the directions of the remote principal stresses and a ratio of their magnitudes are constrained by a field data analysis concerning the orientations of the faults and the directions of slip as deduced from artifacts such as streaks appearing on exposed fault surfaces. Also, although many fault surfaces can be interpreted from seismic data, it is well known that, during a given geologic time, some of them were active (or unsealed) and thus slipped. As slip faults have strongly disturbed the stress, and therefore generate associated fracturing, it is important to determine, at a given geological time (past or present), which faults were active and which ones were sealed (ie say inactive).
[0002] SUMMARY OF THE INVENTION [0004] In general, in one aspect, certain embodiments relate to a method of predicting fault activity of an underground volume.  The method includes obtaining a model of the subterranean volume based on a plurality of linearly independent far field stress tensors; identify a plurality of faults in the underground volume; generating a plurality of precomputed results for each of the plurality of linearly independent far field stress tensors, wherein each of the plurality of precomputed results corresponds to the only contribution of one of the plurality of faults in the subterranean volume; selectively combining, for each of the plurality of linearly independent far field stress tensors and on the basis of a Boolean fault activity vector, the plurality of pre-calculated results as a linearly independent contribution to a superimposed result wherein each linearly independent contribution is scaled in the superimposed result by an optimization parameter associated with one of the plurality of corresponding linearly independent far field stress tensors; calculating a cost function representing a difference between the superimposed result and a measurement of the underground volume; and minimizing the cost function by iteratively adjusting the optimization parameter for each of the plurality of linearly independent far field stress tensors and iteratively adjusting the Boolean fault activity vector, wherein the iterative adjustment of the Boolean vector d Fault activity to minimize the cost function generates a prediction of fault activity of the underground volume.  [0005] In a general aspect, embodiments relate to a system for predicting the fault activity of an underground volume.  The system comprising: a detection device configured to obtain a measurement of the underground volume; a constraint, fracture, and fault activity modeling engine configured to: obtain a model of the underground volume based on a plurality of linearly independent far field stress tensors; identify a plurality of faults in the underground volume; generating a plurality of precomputed results for each of the plurality of linearly independent far field stress tensors, wherein each of the plurality of precomputed results corresponds to the single contribution of one of the. . . plurality of faults in the underground volume; selectively combining, for each of the plurality of linearly independent far field stress tensors and on the basis of a Boolean fault activity vector, the plurality of pre-calculated results as a linearly independent contribution to a superimposed result wherein each linearly independent contribution is scaled in the superimposed result by an optimization parameter associated with one of the plurality of corresponding linearly independent far field stress tensors; calculating a cost function representing a difference between the superimposed result and the measurement of the underground volume; and minimizing the cost function by iteratively adjusting the optimization parameter for each of the plurality of linearly independent far field stress tensors and iteratively adjusting the Boolean fault activity vector, wherein the iterative adjustment of the Boolean vector d fault activity to minimize the cost function generates a prediction of fault activity of the underground volume; and a controller configured to generate, based on the prediction of fault activity, a control signal of a field operation in the underground volume.  In a general manner, in one aspect, the invention relates to a non-volatile computer readable medium storing instructions for predicting the fault activity of an underground volume.  The instructions, when executed by a computer processor, include features for: obtaining a model of the underground volume based on a plurality of linearly independent far field stress tensors; identify a plurality of faults in the underground volume; generating a plurality of precomputed results for each of the plurality of linearly independent far field stress tensors, wherein each of the plurality of precomputed results corresponds to the only contribution of one of the plurality of faults in the subterranean volume; selectively combining, for each of the plurality of linearly independent far-field strain tensors and on the basis of a Boolean fault activity vector, the plurality of pre-calculated results [0007] [0008] [0009] [0009] [0011] as a linearly independent contribution to a superimposed result, in which each linearly independent contribution is scaled in the superimposed result by an optimization parameter associated with one of the plurality of field stress tensors. distant linearly independent corresponding; calculating a cost function representing a difference between the superimposed result and a measurement of the underground volume; and minimizing the cost function by iteratively adjusting the optimization parameter for each of the plurality of linearly independent far field stress tensors and iteratively adjusting the Boolean fault activity vector, wherein the iterative adjustment of the Boolean vector d Fault activity to minimize the cost function generates a prediction of fault activity of the underground volume.  This summary is presented with a view to introducing a choice of concepts which are further described hereinafter in the detailed description.  This summary is not intended to identify critical or essential characteristics of the claimed subject matter, nor to be used as a guide to delimit the extent of the claimed subject matter.  BRIEF DESCRIPTION OF THE DRAWINGS Embodiments of the inversion for obtaining fault activity and tectonic stress are described with reference to the following figures.  Like reference numerals are used throughout the figures to denote identical features and components.  Figure 1 is a diagram of an exemplary stress, fracture and fault activity modeling system.  Figure 2 is a block diagram of an example of the computing environment for performing stress, fracture and fault activity modeling using the superposition principle.  Figure 3 is a block diagram of an exemplary constraint, fracture and fault activity modeling engine.  Figure 4 is a block diagram of constraint modeling, fracture and fault activity techniques.  Figure 5 is a diagram of an example of a method applied to fracture and conjugate fault planes using data sets without size information.  FIG. 6 is a flowchart of an exemplary method of stress modeling, fracture and fault activity using the superposition principle.  Fig. 7 is a flowchart of an exemplary method of constraint, fracture and fault activity modeling using the superposition principle and a cost function.  Figure 8, Figure 9, and Figure 10 show an example of constraint modeling, fracture modeling, and fault activity.  DETAILED DESCRIPTION In the following detailed description of embodiments, many specific details are presented to provide a deeper understanding.  However, those skilled in the art will appreciate that embodiments can be implemented without these specific details.  In other cases, well-known features have not been described in detail in order to avoid unnecessarily complicating the description.  Embodiments of inversion for fault activity and tectonic stress to provide a system and method for inverting fault activity over geological time, i.e., to detect faults that were active during a given period of geological time.  Since a fault may have been active from its creation to a given geologic time before becoming inactive (for example, locked by cementation), the interpreted fault surfaces do not necessarily correspond to current or historical active faults.  In one or more of the embodiments, the fault activity and the stress regime (i.e. the stress ratio and the orientation of the the maximum maximum horizontal stress) are reversed together.  [0019] At the end of the inversion process, a far-field constraint (also referred to as a regional or tectonic constraint throughout this document depending on the context) and the activity of the faults at any particular geological time are determined. .  By way of example, the activity of each fault at a particular geological time can be represented by a Boolean variable having a value of 0 or 1, where 0 represents an inactive fault and 1 represents an active fault.  As a result, the activities of multiple faults at the particular geological time can be represented by corresponding Boolean variables in a vector format designated as a Boolean fault activity vector.  In one or more of the embodiments, linearly independent far field stress models are simulated for an underground volume to determine (or calculate) stress, strain and / or displacement values based on the tensor superposition. independent constraints.  In one or more of the embodiments, stress, strain, and / or displacement values are expressed as a sum of contributions of independent strain tensors and individual faults in a Monte Carlo method.  Specifically, the contributions of independent stress tensors and individual faults are scaled / qualified by random coefficient values assigned in the Monte Carlo method to minimize a cost function.  The results of this calculation include tectonic events and fault activity, as well as a stress tensor (represented by a ratio of principal magnitudes and an associated orientation) and a fault activity.  Calculation inputs may include fault geometry, drill data (including fracture orientation and secondary fault plane data), global positioning system (GPS), interferometric synthetic aperture radar (InSAR) ), crimped and faulted horizons, inclinometers, lines and slip-slip streaks, etc.  In addition, the calculation may use different types of geological data from seismic interpretation, wellbore readings, and field observations to provide many results, such as the predicted fracture propagation on the basis of a disturbed stress field.  Definitions [0020] In the description below, certain variables are used to simplify the presentation.  Table 1 below indicates each variable that can be used and the corresponding definition of the variables according to one or more of the embodiments.  Table 1 OR Defmit variable OR Regional far-field strain tensor OH Maximum horizontal principal constraint (extracted from aR) Oh Minimum horizontal principal constraint (extracted from oR) av Main vertical stress (extracted from o-) R Constraint ratio defined by ( - o-2,) / (o-1 - cry) and E [0,1] R 'Other stress ratio e [0,3], defined by Rf -.  R for a normal fault regime, R '= 2 - R for a sink fault regime, and R' = 2 + R for a reverse fault regime Re, ep Rotation matrix defined by the three angles of Euler n Number of triangular elements constituting fault surfaces P Number of observation points or data points Sliding vector on a triangular element of a fault surface 0 Orientation of the regional far-field stress.  In one or more of the embodiments, the orientation is defined to the North and in a clockwise direction. 1 Value of the Maximum Main Constraint of a Stress Tensor Value of the Main Stress Intermediate of a Cree Tensor Constraint Value of the minimum principal stress of a stress tensor R0 Rotation matrix along the z-axis of an angle 6 (see above) k Scale parameter defined in the form cry rj Component (i,}) of a tensor constraint c ~ ci Optimization parameters used for the superposition principle ei, strain tensor calculated at the point P u. P Constraint tensor calculated at the point P up Calculated displacement field at the point P Variable Definition b Sliding vector calculated on the triangular element e A 3x3 matrix connecting a and UR -1.  Normal to a plane at the point P np ep Displacement field calculated at the point P, where the exponent c indicates "calculated" Displacement field calculated at the point P, where the exponent m indicates "measured" A Fault activity of a fault j.  A is a Boolean fault activity variable of value 0 for an inactive fault and 1 for an active flaw.  The multiple fault faults [3 / Pn for faults 1 to n in an underground volume form the Boolean fault activity vector [i] (i.e., [,. . .  (3. 3.  . . .  prj) of the underground volume.  General Discussion 100211 This paper describes the inversion of stress and fault activity using the superposition principle.  Knowing various input data, such as fault geometry, and selectable or optional data sets or data measures, including one or more of a fault rejection, depth line directions or slip streaks , stress measurements, fracture data, secondary fault plane orientations, GPS data, InSAR data, geodetic data from surface inclinometers, laser telemetry, etc. , the system example makes it possible to quickly generate or reconstruct many types of results.  The systems and methods described herein apply the superposition principle to complex geometry fault surfaces in at least three dimensions (3D), the faults being of finite size by nature and not infinite or semi-infinite.  The results may be rendered in real time and may include, for example, one or more stress, strain, and / or real-time displacement parameters in response to one or more of a user's or a user's query. an updated parameter; remote stress states for multiple tectonic events; prediction of expected future fracturing; the differentiation of preexisting fractures with respect to induced fractures; etc.  The various inputs can be derived from wellbore data, seismic interpretation, field observations, and so on.  The following examples of systems and methods can be applied to many different reservoir and subsoil operations, including, without limitation, natural gas exploration and production operations, and other hydrocarbons, natural gas storage, hydraulic fracturing and matrix stimulation to increase reservoir production, water resources management, including development and environmental protection of aquifers and other water resources, capture and underground storage of carbon dioxide (CO2), etc.  In an exemplary embodiment, a system applies a 3D boundary element technique using a superposition principle applying to linear elasticity for isotropic heterogeneous media spanning an entire space (taking into account the effect from the surface of the earth) or a half-space (that is to say, not taking into account the effect of the earth's surface).  On the basis of precalculated values of independent stress tensor contributions and individual faults, the system example 15 makes it possible to evaluate a cost function with a view to generating real-time results, such as stress parameters, strain parameters, and moving for any point in an underground volume.  Specifically, the real-time results are generated by optimizing (for example, minimizing) the cost function using a Monte Carlo method to vary the value of the far-field constraint (for example, by assigning different values to optimization parameters) and enabling or disabling the influence of faults (that is, assigning 1 or 0 to Boolean fault activity variables).  FIG. 1 represents an example of a constraint, fracture and fault activity modeling system 100.  The system example 100 solves a variety of geomechanical problems.  The geometry of the faults can be known (and optionally imposed inequality constraints, for example normal, overlapping, etc.). , can be known), and the fault activity (active faults against inactive faults) of certain faults can be known.  The user may have access to one or more of the data from boreholes (e.g., fracture orientation, in-situ stress measurements, secondary fault planes), geodetic data (e.g., InSAR , GPS, and inclinometer), and / or in the form of interpreted horizons.  An example of a constraint, fracture and fault activity modeling engine 102 and / or examples of corresponding methods make it possible, for example, to reconstruct the regime of the state of stress and remote tectonics for one or more events ( s) relevant tectonics, fault activity over geologic time, and displacement discontinuities on faults, and estimating, for example, displacement and disturbed strain and strain fields in any point within the system.  By using the superposition principle, the example of system 100 or constraint, fracture, and fault activity modeling engine 102 can perform each of three linearly independent simulations of stress tensor models in constant time regardless of whether the complexity of each underlying model.  In other words, the total computation time for three linearly independent simulations is substantially constant regardless of the complexity of each underlying model.  It is not necessary for each model to be recalculated for subsequent operations of the exemplary system 100 or the constraint, fracture, and fault activity modeling engine 102.  Then, as was introduced above, applications of the system example 100 may include one or more of constraint interpolation and fracture modeling, tectonic event (s) restitution. (s) and fault activity, quality control of interpreted faults, real-time computation of disturbed strain and displacement fields when the user performs one or more of a parameters, a prediction of fracture propagation, a distinction between pre-existing fractures and induced fractures, and many other applications.  Example Environment [00261 Figure 2 shows an exemplary system 100 of Figure 1 in the context of a computing environment in which constraint, fracture, and fault activity modeling using the superposition principle may be performed.  In the illustrated example, the computer device 200 is coupledby communication channel via detection devices (and control devices) to a real medium, for example, a real underground terrestrial volume 202, a tank 204, a depot basin, seabed, etc. , and associated wells 206 for producing an oil resource, for water resource management, or for carbon-related services, etc.  In the implementation shown, a computing device 200 implements a component, such as the constraint, fracture and fault activity modeling engine 102 and the graphical display engine 231.  The constraint, fracture, and fault activity modeling engine 102 and the graphical display engine are illustrated as software, but may be implemented as hardware or as a combination hardware and software instructions.  The constraint, fracture and fault activity modeling engine 102 includes functionalities for performing an analysis, for example using a cost function of a constraint ratio value, a value of orientation, and a Boolean vector of fault activity.  The execution of the analysis is discussed below.  In one or more embodiments, the value of the stress ratio can be defined as (1) in the following equations.  The constraint, fracture, and fault activity modeling engine 102 may further include features for computing, for a particular point in the stress domain diagram, a fracture prediction, a disturbed stress field, an activity. fault, and / or a field of displacement.  When executed, for example on the processor 208, the constraint, fracture and fault activity modeling engine 102 is functionally connected to a graphics display engine 231.  For example, the constraint, fracture, and fault activity modeling engine 102 may be part of the same software application as the graphical display engine 231, the graphical display engine 231 may be an extension module for the constraint, fracture, and fault activity modeling engine 102, or another method may be used to connect the graphical display engine 231 to the stress, fracture, and fault activity modeling engine 102 .  The graphical display engine 231 includes features for displaying various results of the constraint, fracture, and fault activity modeling engine 102.  Referring still to FIG. 2, the graphics display engine 231 further includes features for receiving a point selection, requesting a fracture prediction, a disturbed stress field, and / or a displacement field for the particular to the stress, fracture, and fault activity modeling engine 102 in response to the selection, and present the fracture prediction, the disturbed stress field, and / or the displacement field.  In one or more embodiments, the graphics display engine 231 is operatively connected to the user interface control unit 230 and the display 232.  The computing device 200 may be a computer, a computer network, or another device that includes a processor 208, a memory 210, a data storage unit 212, and other associated hardware such as a computer. network interface 214 and a media reader 216 for reading and writing on a removable storage medium 218.  The removable storage medium 218 may, for example, be a compact disc (CD); a versatile digital disc / digital video disc (DVD); a flash disk, etc.  The removable storage medium 218 contains instructions that, when executed by the computing device 200, cause the computing device 200 to implement one or more exemplary methods described herein.  Accordingly, the removable storage medium 218 may include instructions for implementing and executing the exemplary constraint, fracture, and fault activity modeling engine 102 and / or graphics display engine 231.  At least some portions of the constraint, fracture, and fault activity modeling engine example 102 may be stored as instructions on a given copy of the removable storage medium 218, the removable device, or in a storage unit. local data 212, to be loaded into the memory 210 for execution by the processor 208.  More specifically, software instructions or computer readable program code for implementing embodiments may be stored, either temporarily or permanently, in whole or in part, on a nonvolatile computer readable medium such as a CD, DVD, local or remote storage device, local or remote memory, floppy disk, or other computer-readable storage device.  Although the illustrated examples of constraint, fracture and fault activity modeling engine 102 and graphical display engine 231 are represented in the form of a program resident in memory 210, the engine of FIG. Stress, fracture, and fault activity modeling 102 and / or the graphical display engine 231 may be implemented as hardware, such as an application specific integrated circuit (ASIC) or in the form of hardware. a combination of hardware and software.  In this example system, the computing device 200 receives incoming data 220, such as fault geometry and many other types of data, from multiple sources, such as borehole well measurements 222, observations. field 224, and seismic interpretations 226.  The computing device 200 may receive one or more types of data sets 220 via the network interface 214 which may also receive data from a network (e.g., the Internet 228), such as GPS data and InSAR data.  The computing device 200 can determine (or calculate) and compile modeling results, simulator results, and control results, and a display control unit 230 can output images of geological models and images and simulation data to a display 232.  The images may be a 2D or 3D-234 simulation of stress, fracture, and fault activity using the superposition principle.  The constraint, fracture, and fault activity modeling engine example 102 may also generate one or more visual user interfaces (UIs) to input and / or display data.  The example of stress, fracture and fault activity modeling engine 102 can also generate or finally produce control signals for controlling field operations associated with the underground volume.  For example, field operations can be performed using drilling and exploration equipment, injectors and well control valves, or other control devices during the actual control of the reservoir 204, the transmission and distribution network, surface facilities, etc.  Therefore, an exemplary system 100 may include a computing device 200 and an interactive graphics display unit 232.  The computer environment of the system example 100 as a whole may be simulators, models, and the example of constraint, fracture, and fault activity modeling engine 102.  Example of Engine [0037] FIG. 3 represents the example of constraint, fracture and fault activity modeling engine 102 in more detail than in FIG. 1 and FIG.  The illustrated implementation is an exemplary configuration presented to description fms, in order to introduce features and components of an engine implementing the example of stress modeling, fracture and fault activity. using the superposition principle.  The components shown are examples.  Configurations or combinations of components different from those shown may be used to implement the stress, fracture, and fault activity modeling functions, and different or additional components may also be used.  As was introduced above, the example of stress, fracture and fault activity modeling engine 102 can be implemented in hardware, hardware or software combinations.  The illustrated components are communicatively connected to each other to communicate in the desired manner.  Arrows are shown to indicate a process stream or a data stream, since the components can communicate with each other in the desired manner.  The exemplary constraint, fracture, and fault activity modeling engine 102 illustrated in FIG. 3 includes a buffer for the data sets 302 or at least one access to the data sets 302, an engine for the data set 302, or a data set 302. initialization 304, constraint model simulators 306 or at least access to constraint model simulators 306, an optimization parameter selector 308, a cost evaluation engine 310, and a buffer or an output for the results 312.  These components are represented for descriptive purposes.  Other components, or other arrangement of the components, can lead to various implementations of the exemplary stress modeling, fracture and fault activity engine 102.  The features of the constraint modeling, fracture modeling and fault activity example 102 will be described below.  Operation of System and Motor Example [0039] Fig. 4 shows a method of restoring paleoconstraint and fault activity, including techniques using the superposition principle which reduces the complexity of the model (in some cases , the complexity of the model is greatly reduced).  The exemplary method shown in FIG. 4 can be implemented by the example of stress, fracture and fault activity modeling engine 102.  By way of example, in one embodiment, the initialization engine 304, through the constraint model simulators 306, generates three precalculated models of the far-field constraint associated with an underground volume 202.  These three precomputed models correspond to three linearly independent coordinates (i.e., the north orientation, and (ii) & (iii) the two principal magnitudes) of the underground volume 202, and are designated as the three superimposed models.  In other words, the three superimposed models are superimposed to represent a complete far field stress model of the underground volume , 02.  For each of the three superimposed models, the initialization engine 304 further precalculates certain values, for example, one or more of the displacement, strain, and / or stress values, as a sum of the individual fault contributions.  In one or more embodiments, the displacement, deformation, and / or stress values, as well as the corresponding contributions of individual faults, are precalculated by the initialization engine 304 for each observation point P in a terrestrial volume. underground.  The optimization parameter selector 308 iteratively scales one or more of the displacement, strain, and / or strain values for each superimposed model and selectively activates the faults in order to minimize cost at the same time. cost evaluation engine 310.  In one or more embodiments, the optimization parameter selector 308 scales one or more of the displacement, strain, and / or strain values for each superimposed model by selecting values of the optimization parameters. (crt) for the three superimposed models.  In one or more embodiments, the optimization parameter selector 308 selectively activates the flaws by selecting values of the Boolean fault activity variables (pi).  In particular, a flaw j can be selectively activated (that is, the contribution of the flaw to the model is validated) by selecting 1 for the corresponding value of the Boolean flaw activity variable (/ 3k).  Conversely, a flaw j can be selectively disabled (that is, the fault contribution to the model is invalidated) by selecting 0 for the corresponding value of the Boolean flaw activity variable (p,).  Mathematically, the selective activation of the faults of the underground terrestrial model is carried out by selecting the vector value of the Boolean vector of fault activity [A] (that is to say [i Al, where n is the number of faults or of fault zones) in the basement model.  In one or more embodiments, the selected values of the optimization parameters (cry) and the values of the Boolean fault activity vector [A] apply to all the observation points in the subterranean volume.  [0040] In one or more embodiments, a Monte Carlo method is used to minimize the cost function.  Typically, the optimization parameters that change the scale of the displacement, strain, and / or stress values are set to continuous values by the optimization parameter selector (308) using the Monte Carlo method.  In the Monte Carlo method, on the other hand, the Boolean fault activity variables that activate the faults are set to binary values by the optimization parameter selector (308), the binary value 1 representing an active fault and the binary value 0 representing an inactive flaw.  In the Monte Carlo method, the far field stress parameters are modeled and simulated to generate a set of variables for each of the three superimposed models.  For example, the variables may include: displacement over a fault, the field of motion at any data point or observation point, a strain tensor at each point of observation, and tectonic stress.  The optimization parameter selector 308 selects the alpha and beta parameters for each Monte Carlo simulation, that is to say a set of "ai" and "el" for the three superimposed models so that they play the role. modifiable optimization parameters for iterative convergence over values for these variables to minimize one or more cost functions, which will be described hereinafter.  In one implementation, the optimization parameter selector 308 randomly selects optimization parameters and randomly activates the faults to begin the convergence of the scaling, stress, and / or scaling parameters to the lowest value of the cost function.  When the scaled optimization parameters and the Boolean fault activity variables are evaluated to have the lowest cost of the cost function, the deformation, constraint, and / or displacement parameters set to The scale may be applied to generate results 312, such as a new tectonic constraint and a new fault activity.  Since the exemplary method of FIG. 4 uses precalculated values for the individual fault contributions to the three linearly independent stress models, the example of a stress, fracture, and stress modeling method or motor is disclosed. Fault activity 102 can provide results quickly, and even in real time in some cases, by superimposing these precalculated values and selectively activating the individual fault contributions.  As introduced above, the constraint, fracture, and fault activity modeling engine 102 can quickly reconstruct multiple tectonic events and fault activity responsible for the present state of the underground volume 202 as compared to other processes, or to discern pre-existing fracturing-induced fracturing faster than conventional techniques, or to provide real-time parameter estimation as the user varies a stress parameter, or can quickly predict fracturing, etc.  Although some paleostress inversion methods may apply a complete mechanical scenario, the constraint, fracture, and fault activity modeling engine 102 improves some of the techniques by using multiple data types in the sets. 302 to develop the cost function.  The sets of data 302 to be used to develop the cost function are generally of two types: those that provide orientation information (such as fractures, secondary fault planes with an internal friction angle, and fault streaks, etc. ), and those that provide magnitude information (such as fault slip, GPS data, InSAR data, etc.). ).  Some paleostress inversion methods are calculated using slip measurements on fault planes.  The schematized process example in FIG. 4, which can be executed by the constraint, fracture and fault activity modeling engine 102, extends the inversion to many types of data, and provides a much faster modeling engine 102 to reverse tectonic stress and fault activity.  By way of example, a rapid and reliable inversion obtained from stress and fault activity is described below.  The different types of data can be weighted and combined together.  The constraint, fracture, and fault activity modeling engine 102 can quickly reconstruct the tectonic event (s) and the displacement discontinuities on the faults using various sets of data and sources, and then obtain an estimate of displacement and strain and stress field disturbed at any point in the environment, using available data from seismic interpretation, boreholes and field observations.  The application of the superposition principle allows a user to execute a parameter estimate very quickly.  A numerical technique for implementing the exemplary methods is described below.  A reduced remote tensor used for simulation is then described, and then the superposition principle itself is described.  An estimate of the complexity is also described.  10046] In one embodiment, constraint model simulators 306 of the constraint, fracture, and fault activity modeling engine 102 can be executed using IBEM3D, a successor of POLY3D (POLY3D is described by F.  Maerten, P.  BOY WUT.  Resor, D.  D.  Pollard, and L.  Maerten, Inverting for slip on threedimensional fault surfaces using angular dislocations, Bulletin of the Seismological Society of America, 95: 1654-1665, 2005, and by A.  L.  Thomas, Poly3D: a three-dimensional, polygonal element, displacement discontinuity boundary element computer program with applications to fractures, faults, and cavities in the earth's crust, Master's thesis, Stanford University, 1995).  IBEM3D is a boundary element code based on the analytical solution of an inhomogeneous or inhomogeneous angular dislocation in a whole space or half-space.  An iterative solver is used for speed reasons and for parallelization purposes on multi-core architectures (see for example F.  Maerten, L.  Maerten, and M.  Cooke, Solving 3D boundary element problems using constraint iterative approach, Computational Geosciences, 2009).  However, inequality constraints can not be used because they are non-linear and the superposition principle does not apply.  In the selected code, the faults are represented by discontinuous displacement triangular surfaces.  This has the advantage that three-dimensional fault surfaces provide a more accurate approximation of curved-planar surfaces and curved end lines without introducing overlaps or gaps.  Mixed boundary conditions may be prescribed, and when tensile boundary conditions are specified, the initialization engine 304 provides a solution for unknown Burgers components.  After the system has been solved and results of the three superimposed models have been generated, it is possible to determine (or calculate) at any point, within the entire space or the half-space, the displacement, the deformation or the constraint at points of observation as a post-processing consisting of linearly combining results of the three superimposed models.  More precisely, the stress field at any point of observation is given by the disturbed stress field due to the slip faults plus the contribution of the remote stress.  Therefore, obtaining the disturbed stress field due to sliding on the faults is not sufficient.  In addition, the estimate of fault slip from seismic interpretations is given along the tilt direction.  Nothing is known along the sliding direction, and a complete mechanical scenario can be used to reconstruct the unknown components of the slip vector, since it has an effect on the disturbed stress field.  The modification of the imposed far-field constraint (the orientation and / or the relative magnitudes) modifies the slip distribution and consequently the disturbed stress field.  In general, a code such as IBEM3D is well suited for calculating all displacement vectors on faults, and can be optimized using an H matrix technique.  The unknown associated for the purposes of the modeling remains the estimate of the far field stress which must be imposed as boundary conditions in the inversion process.  In one or more embodiments, the magnitude and orientation of the far-field stress are determined in the inversion method based on a given set of fault areas using the Monte Carlo method mentioned above.  More precisely, the set of fault surfaces is described below as being a known fault geometry while the far-field constraint is modeled by mathematical formulations described hereinafter.  In an exemplary method that can be implemented by the constraint and fracture modeling engine 102, a model composed of multiple fault surfaces is subjected to a constant far-field stress tensor 0R defined in FIG. global coordinate system by equation (2) assuming a sub-horizontal far-field stress (but the present methodology is not limited to this case): crh OR = H RT9,4,, q. (2) o-, Since the addition of a hydrostatic stress does not modify aR, the far field stress tensor oR can be written as shown in equation (3), where R0 is the matrix of rotation along the vertical axis (clockwise), with 0 E [0.7r]: CF = ah - aH- g (3) [0049] When using the embodiment above, the definition of a regional constraint has three unknowns, namely (ah - Gy), - av), and 0.  When expressing equation (2) using ai, cs2 and a3 for the three Anderson fault regimes (Anderson, E. , The dynamics of faulting.  Edinburgh Geol.  Soc. , 1905, 8 (3): 387-402), by factoring with (ai-a3) and introducing the stress ratio R = (a2-03) / (a1-03) E [0,1], the The following equation (22) gives the following result: (ai - C13) R0 [-1 R - 1 1RI 'for a normal fault regime JI 15 a R (a - 453) R9 [- R1 - R e RT for a regime [01] R0 [R1 e RT for an Overlapping Fault Ratio [0050] By replacing R with R 'as indicated in the following equation (23), a unique stress form parameter R 'is created for the three combined fault regimes: RE [0, 1] for a normal fault regime 2 - RE [1, 2] for a slip fault regime (23) 2 + RE [2, 3] for a overlapping fault regime R '[0051] When omitting the scale factor (ai - 63), the regional stress tensor indicated in (23) is defined by two parameters, 0 and R'.  This definition can be used as follows to determine (0, R ') according to the data used.
[0003] Superposition Principle The exemplary constraint, fracture, and fault activity modeling engine 102 can utilize the superposition principle, i.e. a well-known principle in the physics of elasticity linear, in order to reconstruct displacement, deformation and stress at any point of observation P using the precomputed specific values from linearly independent simulations. The superposition principle states that a given value f can be determined by a linear combination of specific solutions. In the constraint, fracture and fault activity modeling engine 102, a reconstruction of a far-field constraint involves a reconstruction of the three parameters (ai, a2, a3). Therefore, the number of linearly independent solutions used is three. In other words, in equation (14): r = Ka) = F (ct (14) (a (1)) where (ai, a2, a3) are real numbers, and ° (for i = 1 to 3) are three linearly independent remote stress tensors In one or more embodiments, the right-hand side of equation (14) (i.e., atfl + a2f2 + a3f3) is designated as being a superimposed result and each of the three terms aifi, a2f2 and a3f3 is designated as being a linearly independent contribution to the superimposed result In particular, each linearly independent contribution is scaled in the superimposed result by a corresponding optimization parameter If F is selected as the Green deformation, stress or displacement functions, then the resulting values E, cr, and u, in P can be expressed as a combination of three specific solutions. , as shown below. formation, stress and displacement field for a tectonic load are a linear combination of the three specific solutions, and are given by equation (15): fZip = Cr iti p Cap = CtiC rp "" Ep = Crlep (1) (1: `,; 5: p + cr3 ep (2., '3Up cr (3) la) re) (15) Similarly, the use of (ai, a2, a3) makes it possible to reconstitute the discontinuities of displacement (i.e., slips) on faults, as indicated in equation (16): the + 2 b ) (16) and any far-field stress is also given in the form of a combination of the three parameters, as shown in equation (17): CFR = (ken a2CF (2) + a3 OEu (3) (17) Faults contributions 10055] Equation (15) can also be decomposed as a sum of fault contributions. For example, £ p, ap and up contain the contributions of each fault, which are summed to give the latter. By way of example, ap is decomposed as follows: f0057] ap = In api [0058] where n is the number of faults in the model, and api is the contribution to the disturbed stress field of the fault i. In the general case, the following notations can be used to formulate the deformation, the stress or the displacement represented by V (P) as a function of the data point P. It is assumed that a, represents the coefficients used. for the superposition (i E [0, 3]). It is assumed that [3j (0 for inactive and 1 for active) is the fault activity of the jst fault or fault zone. (11) Suppose that 1 is the value (scalar, vector or tensor) at the data point P, induced by the jth fault or fault area and from each linearly independent simulation i. It is assumed that V (P) is the value at the data point P induced by all the faults or zones of active faults. Table 1 represents an example of an algorithm for initializing a data structure for storing decomposed values of V (P) for each linearly independent simulation i. As shown in Table 1, for each data point P, each linearly independent simulation i, and each fault Fj, a data storage unit ij is initialized to store T ri / 4 J. In other words, the initial value V, (P) for each linearly independent simulation i must be computed as a sum of vii contributions due to each fault or fault area Fi. If we consider a model consisting of n faults or fault zones, V, (P) combines 3n values at each data point P. For m data points in an underground volume, 3nm values (scalar, vector or tensor) are initialized and stored by the algorithm example shown in Table 1. TABLE 1 ALGO 1: INITIALIZING V (P) for simulation in = number of faults or fault areas P is a data point // Calculate a value, V (P) (the value can be a displacement, a deformation or // a constraint), in P for a given remote stress provided by a For each linearly independent simulation i E [1,3] V4 (P ) (P) + ViF2 (P) V, V, 5 (I)) end If the tectonic stress oR is given and if three independent solutions are known, there exists a unique triplet (ai, a2, a3) for which equation (17) is satisfied, and Equations (15) and (16) can be applied. In matrix form, equation (17) is written according to the format represented in equation (18): (r) a 00 '11/1 "11 - R - ° Ri] 11 or, in the form compact, as indicated in equation (19): Ace = oR (19) [0067] Since the three particular solutions where il) are linearly independent, the system can be inverted, leading to equation (20): R (20) (18) In equation (20), A771 is precalculated by the initialization engine 304. Given a remote constraint selected by the user oR, the constraint modeling model, fracture and fault activity 102 reconstructs the three parameters (ai, a2, a3), then the fault slip (that is to say the discontinuities of displacement on the faults) and the fields of displacement, deformation and constraints are determined (or calculated) in real time using equations (16) and (15), respectively. Displacement, deformation, and stress, and displacement discontinuities, are stored during initialization at each point of observation. In one embodiment, the constraint, fracture, and fault activity modeling engine example 102 allows the user to vary the orientation and magnitude of oR, and to interactively display the deformation and the associated disturbed stress field. Quick calculation of a value (deformation, stress or displacement): Table 2 represents an example of an algorithm making it possible to calculate V (P). Given the coefficient of superposition (that is, the optimization parameter) a. and the Boolean variable of fault activity 13., the value at the data point P is given by: 3 n V (PL.t ~ jF ~ (P} i = zj = i (22) [0070] uF- D.1 with a ER and / 3 E {0,1} In one or more embodiments, ri is precalculated for each i and j More specifically, each linearly independent contribution in the equation (22) to the superimposed result V (P) is a selective combination of n precomputed results, where each precomputed result ViFj (P) corresponds to the only contribution of one of the faults Fj to the subterranean volume.In addition, each linearly independent contribution in the equation ( 22) is scaled in the superimposed result V (P) according to a corresponding optimization parameter ai. [0071] These precomputed V 1 (P) make it possible to quickly calculate the value Vau of the data point P when certain faults or fault zones are activated or deactivated Table 2 ALGO 2: RAPID CALCULATION OF V (P) n faults (or zone s) P is at data point V (P) = 0 For all faults or fault zones, Fj, having an activity fJj V (P) + = (alIff (Fa + a21,1 (Fj) + a3V ; (Fi)) end Inversion of paleoconstraint using datasets [0072] As seen above, the main unknowns, when modeling in a forward direction for the estimation of the distribution of slip on The faults, and therefore the associated disturbed stress field, are the orientation, the relative magnitudes of the far-field constraint oR, and the faults that are active at the particular geological time. As described above, these unknowns (i.e. the relative magnitudes of the far-field constraint oR, and the faults that are active at the particular geological time) can be represented by the triplet (ai, a2 , a3) and the Boolean vector of fault activity ([3i, with j in [1, n]). 100731 If field measurements are known at certain points of observation (eg, displacement, deformation and / or stress, fracture orientation, secondary fault planes formed near major faults, etc.) , in data sets 302), it is then possible to reconstruct the triplet (ai, a2, a3) and the Boolean vector of fault activity 04 with j in [1, nj), and consequently also to reconstitute the tectonic strain cyR and the corresponding tectonic regime. The section below describes the resolution method and the cost functions used to minimize the cost for different types of data sets 302. Resolution process [0074] The application of the Monte Carlo technique makes it possible to find the parameters (ai, a2, a3) and ((3j) that minimize the cost functions for three calculated independent far-field constraints (see equation 15). [0075] A simple sampling method can be implemented considering a domain of dimension (n + 2), i.e. (0 and R) and f3j.This domain (n + 2) is randomly sampled with np points, and the associated cost function is used to determine the Minimum cost point As defined in the following sections with respect to various types of data sets 312, the cost function is a function dependent on optimization parameters (a,) and Boolean variables of activity. In one or more In these embodiments, the Monte Carlo method is used to determine accepted values of the optimization parameters (a,) and Boolean fault activity variables ((3,) by minimizing the cost function. A refinement is then created in the vicinity of the selected point and the process is repeated in a smaller domain. Table 3 shows a simplified version of the sample process, for which no refinement is used. The exemplary sampling method presented here can be significantly optimized by various techniques.
[0004] Table 3 ALGO 3: INVERSION OF FAILLE ACTIVITY cost = 1 Let m be the number of points P For all Monte-Carlo simulations Initialise randomly Pj,. / E [1, n] and p, = o or 1 Initialize randomly at 'i E [1, 3] and a, ER For all data points PV (P) + (a yr (Fi) + a 24 (Fi) + a C + = cost (V (P)) I m end if C <cost cost = C Activity = IO Distant = end fm [0076] Although the above presentation describes an example formulation, other formulations can be used without Datasets The peculiarity of this method is that many different types of data sets 302 can be used to constrain reversal.Two sets of data are presented in the following sections. following: the first includes orientation information and the second includes displacement information and / or magnitudes of the constraint. years of magnitude information from datasets For open fractures (eg, diaclases, veins, dikes), the orientation of the normal to the fracture plane indicates the direction of the direction of least compression stress in 3D (0.3). Similarly, the normals at pressure solution layers and stylolites indicate the direction of the higher compressive stress (cr1). The use of fracture orientation measurements, pressure solution layers, and pen-lites as data sets 312 enables the stress, fracture, and fault activity modeling engine 102 to reconstruct the regime. tectonics that generated these characteristics. In any observation point P, the local perturbed stress field can be determined numerically using three linearly independent simulations. Figure 5 shows the planes of fractures and conjugated faults. Figure 5 (a) shows the orientation of rra with respect to an open fracture (diaclases, veins, dikes) given by its normal 71 in 3D. Figure 5 (b) is a representation similar to Figure 5 (a) except that it relates to an orientation of o-3 with respect to a diaclase given by its projected normal i (eg, its trace on an outcrop). Figures 5 (c) and 5 (d) show the same representation as Figures 5 (a) and 5 (b) except that they show the case of a stylolite. Figure 5 (e) shows the orientation of o-2 and sorting with respect to conjugate fault planes given by one of the normal 7i in 3D and the internal friction angle O. The purpose is to determine the best fit of the far-field constraint orR, and hence the optimization parameters (ai, a2, a3) and the Boolean variables of fault activity ([3,), taken from some orientations of open fractures for which the normals coincide with the directions of the constraint of least th compression in P, or, equivalently, for which the plane of the fracture contains the constraint of greater compression (ai), as illustrated in FIGS. (a) and 5 (b). By varying (ai, a2, a3) and Boolean variables of fault activity (p,), one can quickly determine (or calculate) the state of the stress at any point of observation P in using three pre-calculated models and precomputed contributions of individual faults. The cost function to be minimized is given by equation (22): ff c (22) where "." is the scalar product, t is the normal to a fracture plane, and m is the number of observation points. Since the constraint at a given point P is a function of the activated faults and the far-field constraint, a1 and 62 depend on values of the optimization parameters (ai, a2, a3) and Boolean variables of fault activity ( AT).
[0005] For example, this dependency can be represented by equation (22) above. As a result, although this is not explicitly stated in equation (22), the cost / frac function depends on both the optimization parameters (ai, a2, a3) and the Boolean fault activity variables. (AT). The minimization of a function of the three parameters is expressed by equation (23): Similarly, for pressurized solution layers and stylolites, the cost function is defined as indicated. to equation (22) using the least compression constraint a3 as in equation (24) (see figure 5 (c) and figure 5 (d)): = (24) As for equation (22) although this is not explicitly stated in equation (24), the fity1 cost function depends on both the optimization parameters (ai, a2, a3) and the Boolean fault activity variables (A). . Ffrac = min arava2 {fen a a3)) (23): Use of secondary fault planes The orientation of secondary fault planes that develop in the vicinity of larger active faults can be estimated using a criterion of Coulomb collapse, defined by equation (25): tan (20) = 11/2 (25) where 0 is the angle of the collapse planes with respect to the maximum principal compressive stress ai and u is the coefficient internal friction. Two conjugate collapse planes intersect along 62 and the orientation of the fault is influenced by the orientation of the main stresses and the value of the friction. The cost function is therefore defined by equation (26): (26) [0086] where cry is the direction of the constraint of greater compression and 62 is the direction of the intermediate principal stress. The first term of the right-hand side of equation (26) maintains an orthogonality between the calculated 62 and the normal to the plane of the fault, while the second term makes the angle between the calculated ai and the plane of the fault Fault is close to 8 (see Figure 5 (e)). As with equation (22), although this is not explicitly represented in equation (26), the cost function depends on both optimization parameters (ai, a2, a3) and Boolean variables. of fault activity (, 8,).
[0006] Use of fault lines [0087] In the case of fault striations, the cost function is defined as indicated in equation (27): cr3) = Ep (1 - (1) (27) cic represents the vector of normalized slip from a simulation for a given set of optimization parameters (ai, a2, a3) and Boolean variables of fault activity (A), and cle represents the measured slip vector. that this is not explicitly represented in equation (27), the iron cost function depends on both the optimization parameters (ai, a2, a3) and the Boolean variables of fault activity ((3, For example, this dependency can be represented by equation (22) above .. Data sets containing magnitude information [0088] The magnitude of displacements can be used to determine the orientation of the constraint , as well as the size of the remote stress tensor, instead of simply use the main stress report. For this purpose, the process is similar to that described above. However, given equations (15) and (16), it is clear that there is a parameter for which the displacement discontinuities calculated on the faults and the fields of displacement, deformation and constraints at the observation points have a scale varying linearly with the far-field constraint imposed. In other words, as indicated in equation (28): Sb, Sep Septi (28) Sup [0090] This leads to the following property: [0091] Property 1: Scaling of the far-field constraint according to 3 ER scales the displacement-discontinuity on the faults as well as the fields of displacement, deformation and constraints at the observation points according to Ô. According to this property, one or more measurements at data points (for example, all measurements) are generally normalized before any calculation and the scale factor is noted (the simulations are also normalized, but the factor d scale is irrelevant). After system resolution, the far-field stress, displacement and stress fields are subjected to inverse scaling by a factor equal to Sm1.
[0007] Using GPS Data [0093] In the case of a GPS data set, the cost function is defined in equation (29): where up is the globally normalized calculated elevation change for a given set of parameters. optimization (ai, a2, a3) and the Boolean variables of fault activity ((3;), and up is the normalized measured elevation globally modified at point P with respect to the horizon. is not explicitly represented in equation (29), the fgps cost function depends on both optimization parameters (ai, a2, a3) and Boolean fault activity variables (A). for example, this dependence can be represented by equation (22) above The first term of the right-hand side of equation (29) represents a minimization of the angle formed between the two displacement vectors, while the second term represents a minimization of the norm difference.
[0008] Using InSAR Data [0094] When using an InSAR dataset, there are two possibilities. Either one determines (or one calculates) the global displacement vectors of the measurements by using the displacement u in the direction of the line of sight of the satellite g, in which case one uses the equation (30): uinsar = us (30) and the same process as used for the GPS data set (above) is applied with the calculated etc, or calculated displacement vectors are calculated along the satellite line of sight, in which case the equation is used (31): c (31) Up = U. S where "." is the dot product. The cost function is therefore given by equation (32): J.7ts © r a2) = 7-1.Epo. (32) As for equation (29), although this is not explicitly represented in equation (32), the fine cost function depends both on the optimization parameters a2, a3) and the variables Booleans of Fault Activity ((3i) Using a Flattened Horizon Using the average plane of a given seismic horizon (flattened horizon), the constraint, fracture and activity modeling engine Fault 102 first determines (or calculates) the variation of the elevation for each point constituting the horizon, then uses the GPS cost function for which the component uZ is obtained, giving the equation (33): fh1, a3 = Eij (In-, 12- 1/2 (33) 'up' As for equation (29), although this is not explicitly represented in equation (33), function of cost, fivrizon depends on both the optimization parameters a2, a3) and Boolean variables of fault activity (f).) If pre-folding or a post-wrinkling of the area is observed, the average plane can no longer be used as an intermediate. Therefore, a smooth and continuous adjustment surface must be developed, which eliminates the deformations generating faults while maintaining the folds. The same process as for the average plane is then used to estimate the paleoconstraint. In certain circumstances, before defining the continuous adjustment surface, a method is used to filter the input horizon to eliminate high frequency noise, such as undulations and bumps, while retaining natural deformations. Conclusion and Prospects The constraint and fault activity modeling engine example 102 applies the superposition property that is inherent to the linear elasticity to perform a real-time computation of the stress field. and disturbed displacement in the vicinity of a complex fault area, and the discontinuity of displacements on faults that are active. Further, the formulation performed by the exemplary stress, fracture, and fault activity modeling engine 102 allows for rapid inversion of paleoconstraint using multiple data types such as orientation data. fractures, secondary fault planes, GPS, InSAR, fault releases, and fault slip streaks. Examples of results 312 are described below. In one embodiment, using the fracture orientation and / or secondary fault planes from boreholes, the constraint, fracture, and fault activity modeling engine 102 restores one or more tectonic events as well as as the fault activity, the constraint tensor restored given the orientation and the ratio of the main quantities. The exemplary constraint, fracture, and fault activity modeling engine 102 and related methods can be used in a wide range of applications, including constraint interpolation in a complex faulted reservoir. fracture prediction, quality control of interpreted faults, real-time calculation of disturbed stress and displacement fields while interactively performing parameter estimation, fracture prediction, discernment of fracturing from pre-existing fractures, etc. Alternatively, another application of the constraint, fracture, and fault activity modeling engine 102 and related methods is an evaluation of the disturbed stress field (and hence of an event / event). (s) tectonics (s)) for the recovery of "shale gas." Because shales have low matrix permeability, commercial gas production can involve fractures to create permeability. This can be done by hydraulic fracturing to create extensive artificial fractures in the vicinity of boreholes, and thus involves a good understanding of how fractures propagate in response to the disturbed stress field. Examples of Methods Although the various blocks of these flowcharts are presented and described sequentially, those skilled in the art will appreciate that some or all of the blocks may be executed in different orders, may be combined or omitted, and that some or all of the blocks can be executed in parallel. In addition, the blocks can be actively or passively executed. By way of example, some blocks may be executed using polling or being interrupted in accordance with one or more embodiments. For example, determination blocks may not involve a processor to process an instruction until an interrupt has been received to indicate that a condition exists, according to one or more embodiments. In another example, determination blocks may be executed by performing a test, such as checking a data value to test whether the value matches the tested condition, in accordance with one or more embodiments. FIG. 6 represents an exemplary method 1200 for modeling stress, fracture and fault activity using the superposition principle. In the flowchart, operations are summarized as individual blocks. The exemplary method 1200 can be implemented in hardware form or by combinations of hardware and software, for example, by the example of constraint modeling model, fracture and fault activity. In block 1202, linearly independent stress models for an underground volume are simulated. In one or more embodiments, the stress, strain, and / or displacement parameters for the subsurface volume are modeled based on a superposition of the linearly independent stress models. As a result, the linearly independent stress models are superimposed according to corresponding optimization parameters to calculate the stress, strain and / or displacement values. In addition, the stress, strain and / or displacement parameters modeled by each of the linearly independent stress models are represented as a sum of the individual fault contributions in the subterranean volume. In one or more embodiments, each fault contribution is qualified (i.e., validated or invalidated to represent the active or inactive state) in accordance with a corresponding fault Boolean variable of activity to calculate the values of stress, deformation and / or displacement. At block 1204, the stress, strain, and / or displacement values are precalculated using each of the linearly independent stress models based on a single individual fault contribution. By way of example, using three linearly independent strain models of an underground volume that has n faults, 3n sets of precalculated values of stress, deformation and / or displacement are generated and stored. In block 1206, an attribute of the subterranean volume is iteratively predicted based on precalculated values of stress, strain, and / or displacement. In one or more embodiments, the stress, strain, and / or displacement parameters are iteratively calculated for a large number of random values. assigned to the optimization parameters and the Boolean activity variable by a Monte Carlo method to minimize a cost function. In one or more embodiments, the cost function represents a difference between a predicted attribute of the underground volume and a field measurement (for example, stored in the form of observed data sets, such as the data sets 312 of Figure 3 above) of the attribute of the underground volume as described in one or more of equations (22), (24), (26), (27), (29), (32) and (33). FIG. 7 represents an exemplary method 1300 for modeling stress, fracture and fault activity using the superposition principle. In the flowchart, operations are summarized as individual blocks. The exemplary method 1300 may be implemented by hardware or combinations of hardware and software, for example, by the example of constraint, fracture modeling and fault activity engine described above. In block 1302, fault geometry for an underground volume is received. In general, multiple faults exist in the underground volume. At block 1304, at least one set of data associated with the underground volume is also received. At block 1306, three models of linearly independent far field stress tensors are simulated in constant time to generate strain, stress and / or displacement values. In one or more embodiments, block 1306 is substantially identical to block 1202 shown in FIG. 6 above. At block 1308, stress, strain and / or displacement values are precalculated using each of the linearly independent stress models based on a single individual fault contribution. In one or more embodiments, each of the linearly independent far-field strain tensor models is decomposed into a sum of values corresponding to faults contributions in the subterranean volume. In particular, the contribution from each fault can be activated or inactivated by assigning a binary value corresponding to the fault activity. Mathematically, the decomposition can be represented as shown in Table 1 above. In block 1310, a postprocessing segment of the method begins, the latter making it possible to determine (or calculate) many real-time results on the basis of the superposition principle. In block 1312, an optimization parameter for each of the three models of linearly independent far field stress tensors and a fault activation binary value for each of the faults are selected. In block 1314, a superposition of the three linearly independent far-field strain tensor models is determined (or calculated) on the basis of selected optimization parameters for each of the three linearly independent far field stress tensor models. and selected fault activation binary values for each fault in the subterranean volume.
[0009] Mathematically, the overlay can be represented as shown in Table 2 above. In block 1316, a cost associated with the stress, deformation and / or displacement values from block 1314 is evaluated with respect to observed data. Mathematically, the evaluation can be represented as shown in Table 3 above. If the cost is not satisfactory, the method then loops back to block 1312 to select new optimization parameters and new fault activation binary values. If the cost is satisfactory, the method then proceeds to block 1318. In block 1318, the strain, stress, and / or displacement values from block 1314 are applied to the subterranean volume, for example, relative to to a query regarding the underground volume or in response to an updated parameter regarding the underground volume. In block 1320, an updated query or parameter relating to the underground volume is received, the latter inoculating or initiating the generation of the post-processing results in the real-time results section (1310) of the method 1300. FIG. 8, FIG. 9 and FIG. 10 represent an example of constraint modeling, fracture modeling and fault activity. More precisely, FIG. 8 represents a perspective view of the underground terrestrial volume 801 comprising multiple faults 802 represented in the form of triangular surfaces. For modeling purposes, the underground terrestrial volume 801 is squared into a number of observation points. These observation points located on the cross section 803 are represented as points. Although not explicitly shown otherwise than in cross-section 803, observation points exist throughout the 801 underground terrestrial volume. As described above, stress, strain, and / or displacement values can be determined (or calculated) for each of these observation points. In addition, as illustrated in FIG. 8, a top view A 804 corresponds to the transverse section 803 and represents the calculated orientation of diaclases A 806 which is represented in the form of lines of the fingerprint type in FIG. 803. As described above, for open fractures (eg, diaclases, veins, dikes), the orientation of the normal to the plane of the fracture indicates the direction of the least stress compression (i.e., a3). More specifically, the calculated orientation of A 806 diaclases is based on the stress field (e.g., a3) calculated using the superposition method as described with reference to FIG. 6 and FIG. above, in which the contributions of all the faults 802 are taken into account. In particular, the calculated orientation of A 806 diaclases is an example of an intermediate result of the cost evaluation engine (310) using the Monte Carlo method with a particular combination of optimization parameters ai. In other words, the cost evaluation engine (310) generates this intermediate result by selecting the combination of optimization parameters ai and selecting all faults (802) as active. Accordingly, the calculated orientation of A 806 diaclases corresponds to the particular combination of optimization parameters ai and the selection of the value "1" for all Boolean fault activity variables of the flaws 802. [00116] furthermore, the top view A 804 is superimposed with segments in bold representing observed diaclase orientations, observed diaclase A (805-1), observed diaclase B (805-2), observed diaclase C (805). -3), and the diaclase observed D (805-4). The set of orientations of these diaclases observed is an example of the data sets 302 illustrated in Figure 3 above. [00117] A comparison of the diaclase orientation calculated at 806 and bold segments representing observed diaclase orientations illustrates the agreement between the calculated orientation and the observed orientation for the observed diaclase B (805-2) and the observed diaclase C (805-3). However, the calculated orientation and the observed orientation are in rough disagreement for the observed diaclase A (805-1) and the observed diaclase D (805-4). Consistent with this visual comparison, the cost evaluation engine 310 determines that selecting the value "1" for the Boolean fault state variables of all the flaws 802 does not result in the lowest cost. Accordingly, the optimization parameter selector 308 selects a different fault state Boolean vector as well as possibly a different combination of optimization parameters ai according to the Monte Carlo method, as shown in FIG. after. FIG. 9 shows that a part (referenced as inactive faults 802-2) of faults 802 are deactivated by selecting the value "0" for their Boolean fault state variables. Similarly, the remaining portion (referred to as the 802-1 active faults) of the faults 802 is enabled by selecting the value "1" for their fault state Boolean variables. The cost evaluation engine 310 recalculates the diaclase orientations based on the revised selections of the Boolean fault activity variables to generate the calculated orientation of B 807 diaclases as illustrated in Figure 10 below. Using the Monte Carlo method, not only the computed orientation of B 807 diaclases corresponds to the revised selections of the Boolean fault activity variables, but also, possibly, to a different combination of optimization parameters a .. [00119 Figure 10 shows that the top view B 808 corresponds to the cross-section 803 and represents the calculated orientation of B 807 diaclases based on the 802-1 active faults. A comparison of the calculated orientation of B 808 diaclases and bold segments representing diaclase orientations observed shows the agreement between the calculated orientation and the observed orientation for all those of the observed diaclase A (805-1), the observed diaclase B (805-2), the observed diaclase C (805-3), and the observed diaclase D (805-4). According to this visual comparison, the cost evaluation engine 310 determines that selecting the 802-1 active faults leads to the lowest cost. As a result, the particular selection of the active flaws 802-1 and the optimization parameters ai is used in the generation of the results 312 shown in FIG. 3 above. Conclusion Although examples of systems and methods have been described in a language specific to the structural characteristics and / or the methodological actions, it should be noted that the object of the invention defined in the appended claims is not not limited to the specific features or actions described. Specific features and actions are described as exemplary embodiments of the claimed systems, methods, and structures. [00121] In addition, although the description presented above relates to a limited number of embodiments, one skilled in the art benefiting from the present disclosure will appreciate that it is possible to design other embodiments of the invention. not departing from the scope of the claims. Although only a small number of embodiments have been described above in detail, those skilled in the art will note that many variants are possible in the exemplary embodiments without departing from it. materially from the field of constraint presentation. Accordingly, all such variations are to be considered within the scope of the present invention as defined in the appended claims. In the claims, means-plus-functions clauses are provided to cover the structures described herein as permitting the cited function and not only the structural equivalents, but also equivalent structures. Therefore, although a nail and a screw may not be structural equivalents, in that a nail uses a cylindrical surface to attach pieces of wood to each other, while a screw uses a helical surface in the environment of fastening wooden parts, a nail and a screw may be equivalent structures.

权利要求:
Claims (15)
[0001]
REVENDICATIONS1. A method of predicting the fault activity of an underground volume, comprising the steps of: - obtaining, from the underground volume and using a detection device, a measurement of the underground volume; - obtain a model of the underground volume on the basis of a plurality of linearly independent far field stress tensors; - identify a plurality of faults in the underground volume; generating a plurality of precalculated results for each of the plurality of linearly independent far field stress tensors, wherein each of the plurality of precomputed results corresponds to the only contribution of one of the plurality of faults in the subterranean volume ; selectively combining, for each of the plurality of linearly independent far field stress tensors and on the basis of a Boolean fault activity vector, the plurality of precomputed results as a linearly independent contribution to a superimposed result, wherein each linearly independent contribution is scaled in the superimposed result by an optimization parameter associated with the corresponding one of the plurality of linearly independent far field stress tensors; calculating a cost function representing a difference between the superimposed result and the measurement of the underground volume; minimizing the cost function by iterative adjustment of the optimization parameter for each of the plurality of linearly independent far field stress tensors and iterative adjustment of the Boolean fault activity vector, wherein the iterative adjustment of the Boolean vector d fault activity to minimize the cost function generates a prediction of fault activity of the underground volume; and - control a field operation associated with the underground volume based on the prediction of fault activity of the underground volume.
[0002]
The method of claim 1, wherein the iterative adjustment of the optimization parameter for each of the plurality of linearly independent far field stress tensors to minimize the cost function generates a prediction of tectonic stress in the volume. underground.
[0003]
The method of claim 1, wherein minimizing the cost function comprises using a Monte Carlo method by assigning random values to the optimization parameter for each of the plurality of far field stress tensors. linearly independent and Boolean fault activity vector.
[0004]
The method of claim 1, wherein the cost function is iteratively minimized to adjust in real time a local disturbed stress field to a far field stress value in the subterranean volume.
[0005]
The method of claim 1, wherein the subterranean volume measurement comprises at least one selected from a group consisting of seismic interpretation data, wellbore data, and field observation data.
[0006]
The method of claim 1, wherein the subsurface volume measurement comprises at least one data item selected from a group consisting of fault geometry, fracture orientation data, stylolite orientation data, data data. secondary fault plane, fault rejection data, slip streak data, global positioning system (GPS) data, interferometric synthetic aperture radar (InSAR) data, laser telemetry data , inclinometer data, displacement data for a geological fault, and constraint magnitude data for the geological fault.
[0007]
The method of claim 2, further comprising the steps of: - generating, by iterative adjustment of the optimization parameter for each of the plurality of linearly independent far field stress tensors and iterative fit of the Boolean activity vector of a prediction of an underground volume constraint attribute, wherein the constraint attribute comprises at least one attribute selected from a group consisting of a constraint inversion, a constraint field, a value far field stress, constraint interpolation in a complex faulty reservoir, disturbed stress field, stress ratio and associated orientation, one or more tectonic events, discontinuity of a fault, a fault slip, an estimated displacement, a disturbed deformation, a distribution of the slip on the faults, a control the quality of the interpreted faults, a fracture prediction, a fracture propagation prediction according to a disturbed stress field, a real-time computation of disturbed stress and displacement fields while performing an interactive estimation of parameters, or of discernment of an induced fracture compared to a pre-existing fracture. 10
[0008]
A prediction system for fault activity of an underground volume, comprising: - a detection device configured to obtain a measurement of the underground volume; a constraint, fracture, and fault activity modeling engine, configured to: - obtain a model of the subsurface volume based on a plurality of linearly independent far field stress tensors; - identify a plurality of faults in the underground volume; generating a plurality of precomputed results for each of the plurality of linearly independent far field stress tensors, wherein each of the plurality of precomputed results corresponds to the only contribution of one of the plurality of faults in the subterranean volume ; selectively combining, for each of the plurality of linearly independent far field stress tensors and on the basis of a Boolean fault activity vector, the plurality of pre-calculated results as a linearly independent contribution to a superimposed result, wherein each linearly independent contribution is scaled in the superimposed result by an optimization parameter associated with the corresponding one of the plurality of linearly independent far field stress tensors; - calculating a cost function representing a difference between the superimposed result and the measurement of the underground volume; and- minimizing the cost function by iteratively adjusting the optimization parameter for each of the plurality of linearly independent far field stress tensors and iteratively adjusting the Boolean fault activity vector, wherein the iterative adjustment of the Boolean vector of fault activity in order to minimize the cost function generates a prediction of fault activity of the underground volume; and a control device configured to generate, based on the fault activity prediction, a control signal of the field operations in the underground volume.
[0009]
The system of claim 8, wherein the iterative adjustment of the optimization parameter for each of the plurality of linearly independent far field stress tensors to minimize the cost function generates a prediction of the tectonic stress in the underground volume.
[0010]
The system of claim 8, wherein minimizing the cost function comprises using a Monte Carlo method by assigning random values to the optimization parameter for each of the plurality of far-field stress tensors. 15 linearly independent and Boolean fault activity vector.
[0011]
The system of claim 8, wherein the cost function is iteratively minimized to adjust a local disturbed stress field in real time to a far field stress value in the subterranean volume.
[0012]
The system of claim 8, wherein the subsurface volume measurement comprises at least one selected from a group consisting of seismic interpretation data, wellbore data, and field observation data.
[0013]
The system of claim 8, wherein the subsurface volume measurement comprises at least one data item selected from a group consisting of fault geometry data, fracture orientation data, stylolite orientation data, data data. secondary fault plane, fault rejection data, slip stripe data, global positioning system (GPS) data, interferometric synthetic aperture radar (InSAR) data, telemetry data laser, inclinometer data, displacement data for a geological fault, and constraint magnitude data for the geological fault.
[0014]
The system of claim 9, further comprising: generating, by iterative adjustment of the optimization parameter for each of the plurality of linearly independent far field stress tensors and iterative fit of the Boolean fault activity vector; a prediction of a constraint attribute of the subterranean volume, wherein the constraint attribute comprises at least one attribute selected from a group consisting of a constraint inversion, a constraint field, a constraint value far field, a constraint interpolation in a complex faulty reservoir, a disturbed stress field, a stress ratio and an associated orientation, one or more tectonic events, a displacement of a fault, a fault slip, an estimated displacement, a disturbed deformation, a distribution of the slip on the faults, a quality control interpreted faults, a fracture prediction, a fracture propagation prediction according to a disturbed stress field, a real-time calculation of disturbed stress and displacement fields while performing an interactive estimation of parameters, or discernment of an induced fracture with respect to a pre-existing fracture.
[0015]
15. Nonvolatile computer-readable medium storing instructions for prediction of fault activity of an underground volume, the instructions, when executed by a computer processor, including features for: - obtaining, from the underground volume and using a detection device, a measurement of the underground volume - obtain a model of the underground volume on the basis of a plurality of linearly independent far field stress tensors; - identify a plurality of faults in the underground volume; generating a plurality of precomputed results for each of the plurality of linearly independent far field stress tensors, wherein each of the plurality of precalculated results corresponds to the only contribution of one of the plurality of faults in the subterranean volume; selectively combining, for each of the plurality of linearly independent far field stress tensors and on the basis of a Boolean fault activity vector, the plurality of pre-calculated results as a linearly independent contribution to a superimposed result, wherein each linearly independent contribution is scaled in the superimposed result by an optimization parameter associated with the corresponding one of the plurality of linearly independent far field stress tensors; calculating a cost function representing a difference between the superimposed result and the measurement of the underground volume; minimizing the cost function by iterative adjustment of the optimization parameter for each of the plurality of linearly independent far field stress tensors and iterative adjustment of the Boolean fault activity vector, wherein the iterative adjustment of the Boolean vector d fault activity to minimize the cost function generates a prediction of fault activity of the underground volume; and - control a field operation associated with the underground volume based on the prediction of fault activity of the underground volume.

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2016-01-22| PLSC| Search report ready|Effective date: 20160122 |

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优先权:

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申请号 | 申请日 | 专利标题

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FR1456780|2014-07-15|

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FR1456780A|FR3023954B1|2014-07-15|2014-07-15|METHOD FOR INVERTING THE ACTIVITY OF A FAILED AND THE TECTONIC CONSTRAINT|FR1456780A| FR3023954B1|2014-07-15|2014-07-15|METHOD FOR INVERTING THE ACTIVITY OF A FAILED AND THE TECTONIC CONSTRAINT|

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EP15175712.7A| EP2975437B1|2014-07-15|2015-07-07|Method and system to invert for fault activity and tectonic stress|

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US14/794,216| US20160018542A1|2014-07-15|2015-07-08|Method to invert for fault activity and tectonic stress|

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CA2897304A| CA2897304A1|2014-07-15|2015-07-14|Method to invert for fault activity and tectonic stress|