CN117237558B - Fracture surface reconstruction method based on variational model and related equipment - Google Patents
Fracture surface reconstruction method based on variational model and related equipment Download PDFInfo
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Abstract
The invention provides a fracture surface reconstruction method and related equipment based on a variation model, wherein the method comprises the following steps: constructing a radial basis function expression of an initial fracture surface model in a three-dimensional geological space according to exploration points on a target fracture surface; determining constraint conditions according to the observation data and the radial basis function expression, and constructing a variation model according to the constraint conditions; converting the data constraint in the variation model into a problem for solving a first-order linear iteration step length of the fracture surface model, and carrying out optimization solution to obtain a plurality of iteration optimized fracture surface models; calculating the error between the fracture surface model after each iteration optimization and the observed data, generating an error curve, taking the fracture surface model output when the oscillation amplitude of the error curve is in the range of the preset minimum oscillation amplitude and the error is smaller than the error threshold value as a reconstruction model, and solving a free curved surface corresponding to the reconstruction model when the value of the reconstruction model is the preset value; the accuracy and the reliability of the deep three-dimensional reconstruction of the fracture surface are improved.
Description
Technical Field
The invention relates to the technical field of three-dimensional geological modeling, in particular to a fracture surface reconstruction method based on a variational model and related equipment.
Background
The three-dimensional geologic modeling technology is a research hotspot in the field of intersecting a three-dimensional geographic information system (Geographic Information System or Geo-Information system, GIS) with a geochemical research. The generalized three-dimensional geologic modeling comprises generation of a model, visualization of the model, spatial analysis of the model, application of the model and the like, and is taken as a tool for geologic analysis, and is a multidisciplinary intersection technology for geologic body under the three-dimensional space of a computer and performing geologic interpretation on the geologic body. The three-dimensional geological model has the advantages that firstly, the three-dimensional geological model can three-dimensionally present the three-dimensional form of a single geological body, fully display the spatial relationship among a plurality of geological bodies, and more truly and intuitively express objective geological bodies; secondly, the established three-dimensional geological model can be subjected to three-dimensional space analysis, such as predicting the possible form of an unknown region, inversion structure evolution history and the like by slicing any position of the model; most importantly, the method expresses various information of a complex underground space completely, is compatible with traditional one-dimensional data such as drilling and the like and two-dimensional profile data such as seismic sounding and the like, realizes scientific management and sharing of geological information, and becomes an integration platform of multi-source data in geological big data age.
However, in the prior art, whether modeling is based on geological data or inversion of a structure based on geophysics, most of the current modeling methods use space discretization inference, complex differential forms are likely to be generated in the calculation process, so that solving is difficult, the accuracy of the reconstructed three-dimensional geological model is seriously dependent on the scale of discrete units, and an actual geological interface is difficult to better simulate, so that the deep resolution of the geological model is lower, and high-accuracy reconstruction of a geological structure surface is difficult to realize.
Disclosure of Invention
The invention provides a fracture surface reconstruction method and related equipment based on a variational model, and aims to avoid discretization of a three-dimensional geological space in a three-dimensional geological modeling process and improve the accuracy and reliability of fracture surface reconstruction.
In order to achieve the above object, the present invention provides a fracture surface reconstruction method based on a variational model, including:
step 1, constructing a radial basis function expression of an initial fracture surface model in a three-dimensional geological space according to exploration points on a target fracture surface;
step 2, determining constraint conditions for reconstructing the target fracture surface according to the obtained observation data related to the target fracture surface and the radial basis function expression, and constructing a variation model of the target fracture surface in a three-dimensional geological space according to the constraint conditions; the observation data comprise drilling data, gravity anomaly observation data and magnetic anomaly observation data;
step 3, converting each item of data constraint in the variational model into a problem for solving a first-order linear iteration step length of the fracture surface model, and carrying out optimization solving on the first-order linear iteration step length of the fracture surface model to obtain a plurality of iteration optimized spatially continuous fracture surface models;
and 4, calculating the error between the fracture surface model after each iteration optimization and the observed data, generating an error curve, and taking the fracture surface model after the iteration optimization output when the oscillation amplitude of the error curve is in a preset minimum oscillation amplitude range and the error is smaller than an error threshold value as a reconstruction model of the target fracture surface in a three-dimensional geological space.
Further, the radial basis function expression of the initial fracture surface model in the three-dimensional geological space is as follows:
wherein,representing the number of exploration points on a target fracture surface in three-dimensional geological space +.>Linear coefficient representing the expression of the radial basis function of the fracture plane,/->Represents a radial basis function which satisfies +.>，/>Representing the exploration point on the target fracture surface.
Further, determining the constraint condition for reconstructing the target fracture surface according to the acquired observation data related to the target fracture surface and the radial basis function expression comprises:
according to the formulaConstraining the exploration point on the target fracture surface to be always located on the target fracture surface, wherein +.>Representing the number of iterative optimisation of the target fracture surface, +.>Representing the exploration point on the target fracture surface, < +.>Characterization of->Radial basis function expression of a subiteratively optimized fracture surface model, whereas +.>Characterizing a radial basis function expression of the initial fracture surface model;
according to the formulaConstraining fracture surface model generation in iterative optimization processTrend of keeping consistent with the observed gravity anomaly field, wherein +.>Matrix representing the spatial position correlation between discrete units and surface observation points in three-dimensional geological space during gravity anomaly forward modeling of fracture surface>Representing the spatial residual density distribution determined by the target fracture plane, < >>An observed gravity anomaly value representing the target fracture surface in the investigation region;
according to the formulaConstraining the trend of the magnetic anomaly field generated by the fracture surface model to remain consistent with the observed magnetic anomaly field during iterative optimization, wherein +.>Matrix representing spatial position correlation between discrete units and earth surface observation points in three-dimensional geological space during forward modeling of magnetic anomalies of fracture surface>Representing the determined spatial permeability distribution of the target fracture plane, < >>The observed value of magnetic anomalies of the target fracture surface in the investigation region is represented.
Further, the variational model of the target fracture surface in the three-dimensional geological space is as follows:
wherein,representation purposeNumber of exploration points on the fracture surface, +.>Representing the number of discrete units in the three-dimensional geological space in which the target fracture surface is located,/for>Shallow constraints used to characterize the target fracture surface,used for representing the fitting degree of the fracture surface model and the gravity anomaly observation data,and the method is used for representing the fitting degree of the fracture surface model and the magnetic anomaly observation data.
Further, step 3 includes:
each item of data constraint in the variational model is converted into a problem for solving a first-order linear iteration step of the fracture surface model by using an objective function, wherein the objective function is as follows:
wherein,representing the position of the exploration point on the target fracture surface, < >>A step length item representing each iteration update of the fracture surface model;
carrying out optimization solving on the objective function to obtain a plurality of spatially continuous fracture surface models, wherein the expressions of the spatially continuous fracture surface models are as follows:
wherein,is the number of iterations in the fracture surface reconstruction process.
Further, step 4 includes:
setting an error threshold according to the scale of the investigation region；
Calculating the error between the fracture surface model and the observed data after each iteration optimization and generating an error curve, when the oscillation amplitude of the error curve is in the preset minimum oscillation amplitude range and the first oscillation amplitude isThe error between the sub-iteratively optimized fracture surface model and the observed data satisfies +.>Stopping the iteration and outputting +.>And taking the fracture surface model after the secondary iteration optimization as a reconstruction model of the target fracture surface in the three-dimensional geological space.
Further, the error between the fracture surface model and the observed data includes the fracture surface position error revealed by shallow drillingError of gravity anomaly field->Magnetic anomaly field error->Error between fracture surface model and observed data +.>Expressed as:
wherein,
wherein,is->The sub-iterations optimize the radial basis functions of the fracture surface model at the exploration point,for radial basis functions of the exploration point on the initial fracture surface model, +.>Representing the number of exploration points on the target fracture surface.
Further, after step 4, the method further comprises:
when the reconstruction model is zero, calculating a free-form surface corresponding to the reconstruction model;
and visualizing the free-form surface to obtain the visualized free-form surface.
The invention also provides a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements a method for fracture surface reconstruction based on a variational model.
The invention also provides a terminal device, which comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the processor realizes a fracture surface reconstruction method based on a variation model when executing the computer program.
The scheme of the invention has the following beneficial effects:
according to the invention, a radial basis function expression of an initial fracture surface model in a three-dimensional geological space is constructed according to exploration points on a target fracture surface; then determining constraint conditions for reconstructing the target fracture surface according to the acquired observation data related to the target fracture surface and the radial basis function expression, and constructing a variation model of the target fracture surface in the three-dimensional geological space according to the constraint conditions; each item of data constraint in the variational model is converted into a problem for solving a first-order linear iteration step length of the fracture surface model, and the first-order linear iteration step length of the fracture surface model is optimized and solved to obtain a plurality of iteration optimized spatially continuous fracture surface models; calculating the error between the fracture surface model after each iteration optimization and the observed data, generating an error curve, and taking the fracture surface model after the iteration optimization output when the oscillation amplitude of the error curve is in the preset minimum oscillation amplitude range and the error is smaller than the error threshold value as a reconstruction model of the target fracture surface in the three-dimensional geological space; compared with the prior art, the method directly determines constraint conditions based on gravity anomaly and magnetic anomaly observation data and deep drilling data, builds the variation model of the target fracture surface in the three-dimensional geological space, converts the variation model into a first-order linear problem to solve the variation model, finally directly obtains the fracture surface model in the three-dimensional geological space, realizes high-precision reconstruction of the fracture surface model from a continuous inference angle, avoids discretization of the three-dimensional geological space in the three-dimensional geological modeling process, effectively breaks through the accuracy limit of discrete inference of the geological model, and improves the accuracy and reliability of deep three-dimensional reconstruction of the fracture surface.
Other advantageous effects of the present invention will be described in detail in the detailed description section which follows.
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FIG. 1 is a schematic flow chart of an embodiment of the present invention;
fig. 2 is a schematic diagram of a change trend of a reconstructed model relative to an initial fracture surface model in an embodiment of the present invention.
Detailed Description
In order to make the technical problems, technical solutions and advantages to be solved more apparent, the following detailed description will be given with reference to the accompanying drawings and specific embodiments. It will be apparent that the described embodiments are some, but not all, embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In the description of the present invention, it should be noted that the directions or positional relationships indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. are based on the directions or positional relationships shown in the drawings, are merely for convenience of describing the present invention and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a specific orientation, be configured and operated in a specific orientation, and thus should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present invention, it should be noted that, unless explicitly stated and limited otherwise, the terms "mounted," "connected," and "connected" are to be construed broadly, and may be, for example, a locked connection, a removable connection, or an integral connection; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the above terms in the present invention will be understood in specific cases by those of ordinary skill in the art.
In addition, the technical features of the different embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
Aiming at the existing problems, the invention provides a fracture surface reconstruction method based on a variation model and related equipment.
As shown in fig. 1, an embodiment of the present invention provides a fracture surface reconstruction method based on a variational model, including:
step 1, constructing a radial basis function expression of an initial fracture surface model in a three-dimensional geological space according to shallow exploration points of a target fracture surface in the three-dimensional geological space;
step 2, determining constraint conditions for reconstructing the target fracture surface according to the obtained observation data related to the target fracture surface and the radial basis function expression, and constructing a variation model of the target fracture surface in a three-dimensional geological space according to the constraint conditions; the observation data comprise drilling data, gravity anomaly observation data and magnetic anomaly observation data;
step 3, converting each item of data constraint in the variational model into a problem for solving a first-order linear iteration step length of the fracture surface model, and carrying out optimization solving on the first-order linear iteration step length of the fracture surface model to obtain a plurality of iteration optimized spatially continuous fracture surface models;
and 4, calculating the error between the fracture surface model after each iteration optimization and the observed data, generating an error curve, and taking the fracture surface model after the iteration optimization output when the oscillation amplitude of the error curve is in a preset minimum oscillation amplitude range and the error is smaller than an error threshold value as a reconstruction model of the target fracture surface in the three-dimensional geological space.
Specifically, step 1 includes:
taking the exploration point on the target fracture surface as a shallow exploration point, and taking the exploration point as a three-dimensional geological space according to the shallow exploration pointIn the process, the initial fracture surface model is expressed by using a radial basis function, and in order to ensure continuous inference of fracture surfaces, the initial model is expressed as a functional form, namely:
wherein,representing the number of exploration points on a target fracture surface in three-dimensional geological spaceQuantity (S)>Linear coefficient representing the expression of the radial basis function of the fracture plane,/->Represents a radial basis function which satisfies +.>，/>Representing the exploration point on the target fracture surface, the radial basis functions satisfy:
based on the above relationship, linear coefficients of the radial basis functions can be solved, thereby obtaining a continuous functional expression of the initial fracture surface model in the three-dimensional geological space.
Specifically, step 2 includes:
according to the observation data of the target fracture surface, such as drilling data, gravity anomaly observation data and magnetic anomaly observation data, the reconstructed fracture surface model needs to conform to the observation data, and therefore, the reconstructed fracture surface model is set to meet the following constraint conditions:
(1) Reconstructing the fracture surface model needs to ensure that the fracture surface position is unchanged, namely, the exploration points on the fracture surface of the constraint target are always positioned on the fracture surface, and the constraint mainly comprises the following steps:
wherein,representing the number of iterative optimisation of the target fracture surface, +.>Representing the target fracture surfaceThe point of investigation on the surface of the substrate,characterization of->Radial basis function expression of a subiteratively optimized fracture surface model, whereas +.>Characterizing a radial basis function expression of the initial fracture surface model;
(2) Reconstructing the fracture surface model needs to fit the gravity anomaly observation data, namely restraining the trend that the gravity anomaly field generated by the fracture surface model needs to be kept approximately consistent with the observed gravity anomaly field in the iterative optimization process, wherein the restraint mainly comprises the following steps:
wherein,matrix representing spatial position correlation between discrete units and earth surface observation points in three-dimensional geological space during gravity anomaly forward modeling of target fracture surface>Since the spatial residual density distribution determined by the target fracture surface has a significant difference in physical properties between the upper and lower plates of the target fracture surface, it is considered that the spatial residual density distribution can be expressed as a continuous function of the position of the target fracture surface>An observed gravity anomaly value representing the target fracture surface in the investigation region;
(3) The reconstruction of the fracture surface model needs to fit magnetic anomaly observation data, namely, the trend that the magnetic anomaly field generated by the fracture surface model needs to be kept approximately consistent with the observed magnetic anomaly field in the iterative optimization process is restrained, and the restraint mainly comprises the following steps:
wherein,matrix representing spatial position correlation between discrete units and earth surface observation points in three-dimensional geological space during forward modeling of magnetic anomalies of a target fracture surface>The spatial permeability distribution determined by the target fracture surface is represented, and the fracture surface upper and lower plates are considered to have a significant permeability difference, so that the permeability parameter is set as a continuous function related to the target fracture surface position, +.>The observed value of magnetic anomalies of the target fracture surface in the investigation region is represented.
According to constraint conditions obviously required to be met by iterative optimization of fracture surfaces, the continuous high-precision reconstruction problem of the target fracture surfaces can be converted into the minimization of the following variation problems:
wherein,representing the number of exploration points on the target fracture surface, < >>Representing the number of discrete units in the three-dimensional geological space where the target fracture surface is located, setting different residual density values and magnetic permeability values for the discrete units for calculating the gravity anomaly forward value or the magnetic anomaly forward value of the fracture surface model, < >>Shallow constraint for characterizing the target fracture plane, < ->Fitting degree for representing fracture surface model and gravity anomaly observation data, < >>And the method is used for representing the fitting degree of the fracture surface model and the magnetic anomaly observation data.
In the embodiment of the invention, the residual density is constructed because the residual density and the magnetic permeability are possibly different on the upper disc and the lower disc of the three-dimensional structural surface due to the uneven distribution of physical properties of the undergroundAnd magnetic permeability->Radial basis function for fracture surface model>For indicating the value of the physical distribution of the upper and lower discs of the target fracture surface, the continuous function being required to satisfy:
wherein,and->Residual density and permeability of the disc on the target fracture surface, respectively->And->To the target fracture surfaceThe residual density and permeability of the bottom wall.
All the above values can be determined by field measurements and existing research data, since the residual density and permeability have similar properties at the target fracture surface, they can be set as similar spatially continuous functions, namely:
to satisfy the relationship of the physical property distribution, a functionThe requirements are satisfied:
the physical properties of the upper and lower plates of the target fracture surface also have spatial smoothness, i.e., the physical properties are distributed at the position of the target fracture surface and are abrupt, and have transition changes, so the functionAlso not a step function, so here the weave function can be referenced, the continuous function +.>The method comprises the following steps:
specifically, step 3 includes:
the nonlinear variational model in the three-dimensional geological space is converted into a first-order linear problem which is easy to solve by using a Gaussian-Newton algorithm, so that each item of data constraint in the variational model can be converted into a problem for solving a first-order linear iteration step length of the fracture surface model by using an objective function, wherein the objective function is as follows:
wherein,representing the position of the exploration point on the target fracture surface, < >>The step length item for representing each iteration update of the fracture surface model can be used for solving the minimisation form of the variational model by minimizing the step length item so as to realize continuous high-precision reconstruction of the fracture surface model in the three-dimensional geological space.
In order to achieve continuous iterative optimization of the reconstructed fracture surface model, the above objective function needs to be converted into a continuous form, where the discrete terms are converted into a continuous form of an integral function by means of a dirac delta function having the following features:
thus, for the first term in the objective function described above, the DiracDelta function can be used to represent:
according to the variational algorithm property, that is, since the minimum value of the objective function is solved, the derivative value of the objective function is 0, the derivative of the objective function can be expressed as:
for the second term of the objective function (gravity anomaly data observation constraint term), taylor's formula can be used first forAnd (3) unfolding, namely:
wherein,is Jacobian matrix with mathematical meaning of function +.>First derivative form of>Updating the error vector between the model forward gravity anomaly and the observed value for each iteration, i.e. +.>According to the gravity forward formula, due to +.>For a matrix of spatial coordinate correlations, in the case of a known spatial discrete unit and observation point, the matrix is a constant matrix, which can be represented here in vector form, i.e./i>Wherein->The number of observation points for surface gravity anomalies, therefore, the jacobian matrix can be expressed as:
the above target expression can thus be written as a derivative form with respect to the residual density function, namely:
in order to regularize the objective function, the smoothness of the gravity anomaly field generated by the fracture surface is considered, namely a smoothing term is added into the objective function:
wherein,for Laplace smoothing terms, the iteration step length is characterized by having the characteristic of internal smoothing in space, and a DiracDelta function is introduced to process discrete terms in the iteration step length so as to construct an analytic function form:
for simplicity of the following formulas, a continuous function is set up hereAnd is subsequently abbreviated as +.>On the basis of this, the above formula can be derived, namely:
further Taylor formula expansion is performed:
wherein for the second term of the formulaA distributed integration method can be used, so this term can be expressed as:
in summary, the variational model under the constraint of gravity anomaly data can be expressed as:
likewise, for the third term (magnetic anomaly data observation constraint term) in the variational model, the Taylor formula pair may also be usedThe function is expanded, namely:
wherein,is Jacobian matrix with mathematical meaning of function +.>First derivative form of>Updating the error vector between the model forward magnetic anomaly value and the observed value for each iteration, i.e.>In the calculation formula of the magnetic anomaly,the spatial position-dependent matrix is also characterized, which can be expressed here as +.>Wherein->The number of observation points of the surface magnetic anomaly is the number of the observation points of the surface magnetic anomaly, so that the variation module of the magnetic anomaly constraintThe jacobian matrix in a pattern can be expressed as:
the above target expression can thus be written as a derivative of the permeability function:
for regularization of the above objective function, the smoothness of the magnetic anomaly field caused by the fracture surface is likewise considered here, i.e. in the objective functionAdding a smoothing term:
wherein,still a laplace smoothing term. Furthermore, for the discrete item in the above target formula +.>Here it is converted into a continuous functional form by means of a dirac delta function:
also, in order to simplify the formulation thereafter, a continuous function is provided hereAnd in the following formula it is abbreviated as +.>The objective function can then be +.>And (3) deriving and performing Taylor expansion to obtain:
also for the second term of the formulaThe distributed integration method is used, and comprises the following steps:
thus, the variational expression under the constraint of magnetically anomalous data can be expressed as:
after obtaining the variational form of each data constraint in the variational model, the objective function can be solved using the Du Bois-Reymond lemons, dubu Watts of the Du Bois-Reymond lemons, which is a theorem that derives that a function is constant from its derivative satisfying a certain integral equation, as known from the Du Bois-Reymond lemons:
wherein,a regularization function solution with smoothing terms can be used and a solution in the form of a linear combination of green's functions is obtained, namely:
therefore, according to the drilling data constraint and the geophysical heavy magnetic data constraint of the fracture surface, the step length of each iteration update in the fracture surface reconstruction process can be obtained by considering the smoothness characteristics of the curved surface, and the step length of each iteration update mainly comprises the following three update items:
wherein,，/>，/>is a linear coefficient and satisfies the following relationship:
wherein,is the number of observation points of surface gravity abnormality +.>For the number of observation points of surface magnetic anomaly +.>The number of shallow exploration points for the target fracture surface.
And (3) carrying out optimization solution on the objective function, thereby calculating the linear coefficient value of the iteration step length to obtain a plurality of spatially continuous fracture surface models, wherein the expression of the spatially continuous fracture surface models is as follows:
wherein,reconstruction for fracture surfaceNumber of iterations in the process.
The green's function in the iteratively updated terms in embodiments of the present invention may use a simple basis functionThe representation is performed.
Specifically, step 4 includes:
setting an error threshold according to the scale of the research area；
Performing iterative optimization on the fracture surface model, and calculating the first stepGenerating an error curve by using the error between the fracture surface model and the observed data after the iteration, and when the oscillation amplitude of the error curve is in the preset minimum oscillation amplitude range and +.>The error between the sub-iteratively optimized fracture surface model and the observed data satisfies +.>Stopping the iteration and outputting +.>And taking the fracture surface model after the iterative optimization as a reconstruction model of the target fracture surface in a three-dimensional geological space. />
In the embodiment of the invention, when the initial fracture surface model starts iterative optimization, the error between the initial fracture surface model and observed data is small due to the fact that the shallow part of the initial fracture surface model is better fitted with the control point and the multi-resolvability of geophysical inversion is possible, so that in actual work, the fracture surface model after the previous 50 times of iterative optimization is needed to be abandoned, namely, when the amplitude of an error curve is in a preset minimum amplitude range, the reconstruction model is output, the preset minimum amplitude range is in the preset minimum amplitude range approaching 0 infinitely, and the error curve is in a stable state, so that the stability and the reliability of the calculation error in the subsequent iterative optimization process are ensured.
Specifically, in the process of fracture surface reconstruction, the embodiment of the invention needs to calculate the error between the fracture surface model obtained by each iteration optimization and the observed data, wherein the error mainly comprises the fracture surface position error revealed by shallow drillingError of gravity anomaly field->Magnetic anomaly field error->Error between fracture surface model and observed data +.>Expressed as:
wherein each error can in turn be calculated by:
(1) Position error of fracture surface revealed by shallow drilling:
wherein,is->Radial basis function of fracture surface model after sub-iterative optimization on exploration point, ++>For radial basis functions of the exploration point on the initial fracture surface model, +.>Is the number of exploration points on the target fracture surface.
(2) Gravity anomaly field error:
wherein,for the number of three-dimensional geological space discrete points, +.>Matrix of spatial position correlation of discrete points and gravity anomaly observation points>For the three-dimensional geospatial residual density distribution determined by the position of the target fracture surface +.>Is an abnormal observation of the gravity of the target fracture surface in the research area.
(3) Magnetic anomaly field error:
wherein,for the number of three-dimensional geological space discrete points, +.>Matrix of spatial position correlation of discrete points and magnetic anomaly observation points>For a three-dimensional geospatial permeability distribution determined by the position of the target fracture surface +.>Magnetic anomaly observations are made for the target fracture plane in the investigation region.
For each iteration of the optimized fracture surface model, the error between the fracture surface model and the observed data can be solved according to the formula.
Specifically, after the step 4, the method further includes:
setting the value of the reconstruction model to be zero, and calculating a free curved surface corresponding to the reconstruction model;
and visualizing the free-form surface to obtain the visualized free-form surface.
In an embodiment of the invention, after a fracture surface reconstruction model is known, a three-dimensional surface generation algorithm in a computational geometry algorithm library (Computational Geometry Algorithms Library, CGAL) is used to solve for spatial locations satisfying the following conditions：
The reconstructed fracture surface is thereby spatially visualized in three-dimensional geological space.
In the embodiment of the invention, a self-defined fracture surface model is taken as an example, in the example, the self-defined fracture surface model is taken as a standard model, the shallow part form of the self-defined fracture surface model is extracted as an initial model, so that the initial model and the deep part form of the standard model have larger difference in spreading, the physical property distribution of the upper disc and the lower disc of the standard model is given, and the gravity abnormality and the magnetic abnormality caused by the standard fracture surface are calculated and are taken as constraint data of fracture surface deep part estimation.
In order to verify the accuracy of the method, iterative optimization is performed by using an initial model, the direction and the step length of the optimization of the initial model are regulated by using a variation model based on constraint data, and the change trend of the fracture surface reconstruction model relative to the initial model is shown in fig. 2.
According to the embodiment of the invention, a radial basis function expression of an initial fracture surface model in a three-dimensional geological space is constructed according to exploration points on a target fracture surface; then determining constraint conditions for reconstructing the target fracture surface according to the acquired observation data related to the target fracture surface and the radial basis function expression, and constructing a variation model of the target fracture surface in the three-dimensional geological space according to the constraint conditions; each item of data constraint in the variational model is converted into a problem for solving a first-order linear iteration step length of the fracture surface model, and the first-order linear iteration step length of the fracture surface model is optimized and solved to obtain a plurality of iteration optimized spatially continuous fracture surface models; calculating the error between the fracture surface model after each iteration optimization and the observed data, generating an error curve, and outputting the fracture surface model after the iteration optimization as a reconstruction model of the target fracture surface in the three-dimensional geological space when the oscillation amplitude of the error curve is in a preset minimum oscillation amplitude range and the error is smaller than an error threshold value; compared with the prior art, the method directly determines constraint conditions based on gravity anomaly and magnetic anomaly observation data and deep drilling data, builds the variation model of the target fracture surface in the three-dimensional geological space, converts the variation model into a first-order linear problem to solve the variation model, finally directly obtains the fracture surface model in the three-dimensional geological space, realizes high-precision reconstruction of the fracture surface model from a continuous inference angle, avoids discretization of the three-dimensional geological space in the three-dimensional geological modeling process, effectively breaks through the accuracy limit of discrete inference of the geological model, and improves the accuracy and reliability of deep three-dimensional reconstruction of the fracture surface.
The embodiment of the invention also provides a computer readable storage medium, on which a computer program is stored, which when being executed by a processor, implements a fracture surface reconstruction method based on a variational model.
The integrated units, if implemented in the form of software functional units and sold or used as stand-alone products, may be stored in a computer readable storage medium. Based on such understanding, the implementation of all or part of the flow of the method of the foregoing embodiments of the present invention may be accomplished by a computer program to instruct related hardware, where the computer program may be stored in a computer readable storage medium, and the computer program may implement the steps of each of the foregoing method embodiments when executed by a processor. Wherein the computer program comprises computer program code which may be in source code form, object code form, executable file or some intermediate form etc. The computer readable medium may include at least: any entity or device capable of carrying computer program code to construct an apparatus/terminal equipment, recording medium, computer memory, read-Only memory (ROm), random access memory (RAm, random Access memory), electrical carrier signal, telecommunications signal, and software distribution media. Such as a U-disk, removable hard disk, magnetic or optical disk, etc. In some jurisdictions, computer readable media may not be electrical carrier signals and telecommunications signals in accordance with legislation and patent practice.
The embodiment of the invention also provides a terminal device which comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the processor realizes a fracture surface reconstruction method based on a variation model when executing the computer program.
It should be noted that the terminal device may be a mobile phone, a tablet computer, a notebook computer, an Ultra mobile personal computer (Ultra-mobile Personal Computer), a netbook, a personal digital assistant (PDA, personal Digital Assistant), or the like, and the terminal device may be a station (ST, station) in a WLAN, for example, a cellular phone, a cordless phone, a session initiation protocol (SiP, session initiation Protocol) phone, a wireless local loop (WLL, wireless Local Loop) station, a personal digital processing (PDA, personal Digital Assistant) device, a handheld device having a wireless communication function, a computing device, or other processing device connected to a wireless modem, a computer, a laptop computer, a handheld communication device, a handheld computing device, a satellite wireless device, or the like. The embodiment of the invention does not limit the specific type of the terminal equipment.
The processor may be a central processing unit (CPU, central Processing Unit), but may also be other general purpose processors, digital signal processors (DSP, digital Signal Processor), application specific integrated circuits (ASiC, application Specific integrated Circuit), off-the-shelf programmable gate arrays (FPGA, field-Programmable Gate Array) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory may in some embodiments be an internal storage unit of the terminal device, such as a hard disk or a memory of the terminal device. The memory may in other embodiments also be an external storage device of the terminal device, such as a plug-in hard disk provided on the terminal device, a Smart media Card (SmC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), etc. Further, the memory may also include both an internal storage unit and an external storage device of the terminal device. The memory is used to store an operating system, application programs, boot loader (BootLoader), data, and other programs, etc., such as program code for the computer program, etc. The memory may also be used to temporarily store data that has been output or is to be output.
It should be noted that, because the content of information interaction and execution process between the above devices/units is based on the same concept as the method embodiment of the present invention, specific functions and technical effects thereof may be found in the method embodiment section, and will not be described herein.
While the foregoing is directed to the preferred embodiments of the present invention, it will be appreciated by those skilled in the art that various modifications and adaptations can be made without departing from the principles of the present invention, and such modifications and adaptations are intended to be comprehended within the scope of the present invention.
Claims (10)
1. The fracture surface reconstruction method based on the variational model is characterized by comprising the following steps of:
step 1, constructing a radial basis function expression of an initial fracture surface model in a three-dimensional geological space according to exploration points on a target fracture surface;
step 2, determining constraint conditions for reconstructing the target fracture surface according to the observation data of the target fracture surface and the radial basis function expression, and constructing a variation model of the target fracture surface in a three-dimensional geological space according to the constraint conditions; the observation data comprise drilling data, gravity anomaly observation data and magnetic anomaly observation data;
step 3, converting each item of data constraint in the variational model into a problem for solving a first-order linear iteration step length of the fracture surface model, and carrying out optimization solving on the first-order linear iteration step length of the fracture surface model to obtain a plurality of spatially continuous fracture surface models after iterative optimization;
and 4, calculating the error between the fracture surface model after each iteration optimization and the observed data, generating an error curve, and taking the fracture surface model after the iteration optimization output when the oscillation amplitude of the error curve is in a preset minimum oscillation amplitude range and the error is smaller than an error threshold value as a reconstruction model of the target fracture surface in a three-dimensional geological space.
2. The variational model-based fracture surface reconstruction method of claim 1, wherein the radial basis function expression of the initial fracture surface model in three-dimensional geological space is:
wherein,representing the number of exploration points on a target fracture surface in three-dimensional geological space +.>Linear coefficient representing the expression of the radial basis function of the fracture plane,/->Represents a radial basis function which satisfies +.>，/>Representing the exploration point on the target fracture surface.
3. The variational model-based fracture surface reconstruction method of claim 2, wherein said determining constraints for reconstructing said target fracture surface from said observed data of said target fracture surface and said radial basis function expression comprises:
according to the formulaConstraining the exploration point on the target fracture surface to be always located on the target fracture surface, wherein +.>Representing the number of iterative optimisation of the target fracture surface, +.>Representing the exploration point on the target fracture surface, < +.>Characterization of->Radial basis function expression of a subiteratively optimized fracture surface model, whereas +.>Characterizing a radial basis function expression of the initial fracture surface model;
according to the formulaConstraining the trend of the gravity anomaly field generated by the fracture surface model to be consistent with the observed gravity anomaly field in the iterative optimization process, wherein ∈>Matrix representing the spatial position correlation between discrete units and surface observation points in three-dimensional geological space during gravity anomaly forward modeling of fracture surface>Representing the spatial residual density distribution determined by the target fracture plane, < >>An observed gravity anomaly value representing the target fracture surface in the investigation region;
according to the formulaConstraining the trend of the magnetic anomaly field generated by the fracture surface model to be consistent with the observed magnetic anomaly field in an iterative optimization process, wherein ∈>Matrix representing spatial position correlation between discrete units and earth surface observation points in three-dimensional geological space during forward modeling of magnetic anomalies of fracture surface>Representing the determined spatial permeability distribution of the target fracture plane, < >>The observed value of magnetic anomalies of the target fracture surface in the investigation region is represented.
4. A method of reconstructing a fracture surface based on a variational model as claimed in claim 3, wherein the variational model of the target fracture surface in three-dimensional geological space is:
wherein,representing the number of exploration points on the target fracture surface, < >>Representing the number of discrete units in the three-dimensional geological space in which the target fracture surface is located,/for>Shallow constraints used to characterize the target fracture surface,used for representing the fitting degree of the fracture surface model and the gravity anomaly observation data,and the method is used for representing the fitting degree of the fracture surface model and the magnetic anomaly observation data.
5. The method for reconstructing a fracture surface based on a variational model as set forth in claim 4, wherein said step 3 comprises:
each data constraint in the variational model is converted into a problem for solving a first-order linear iteration step of the fracture surface model by using an objective function, wherein the objective function is as follows:
wherein,representing the position of the exploration point on the target fracture surface, < >>A step length item representing each iteration update of the fracture surface model;
and carrying out optimization solution on the objective function to obtain a plurality of spatially continuous fracture surface models, wherein the expression of the spatially continuous fracture surface models is as follows:
wherein,is the number of iterations in the fracture surface reconstruction process.
6. The method of reconstruction of fracture surfaces based on a variational model as set forth in claim 5, wherein said step 4 includes:
setting an error threshold according to the scale of the research area；
Calculating the error between the fracture surface model after each iterative optimization and the observed data and generating an error curve, when the oscillation amplitude of the error curve is in a preset minimum oscillation amplitude range and the first oscillation amplitude is within a preset minimum oscillation amplitude rangeError between the sub-iteratively optimized fracture surface model and the observed data satisfies +.>Stopping the iteration and outputting +.>And taking the fracture surface model after the iterative optimization as a reconstruction model of the target fracture surface in a three-dimensional geological space.
7. The variational model-based fracture surface reconstruction method of claim 6, wherein the error between said iterated fracture surface model and said observed data comprises a fracture surface position error revealed by shallow drillingError of gravity anomaly field->Magnetic anomaly field error->Error between the fracture surface model and the observed data +.>Expressed as:
wherein,
wherein,is->Optimizing the radial basis function of the fracture surface model at the exploration point by sub-iteration, < >>For radial basis functions of the exploration point on the initial fracture surface model, +.>Is the number of exploration points on the target fracture surface.
8. The method of claim 7, further comprising, after the step 4:
setting the value of the reconstruction model to be zero, and calculating a free-form surface corresponding to the reconstruction model;
and visualizing the free-form surface to obtain the visualized free-form surface.
9. A computer readable storage medium, on which a computer program is stored, characterized in that the method of reconstruction of fracture surfaces based on a variational model as claimed in any one of claims 1 to 8 is implemented when the computer program is executed by a processor.
10. Terminal device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that the processor implements the method for fracture surface reconstruction based on a variational model as claimed in any one of claims 1 to 8 when executing the computer program.
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