CN120009996B - Layered small inclusion position identification method and system based on potential layer potential - Google Patents
Layered small inclusion position identification method and system based on potential layer potentialInfo
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Abstract
The invention belongs to the technical field of object detection, and provides a method and a system for identifying the position of a layered small inclusion based on potential layer potential, wherein the method comprises the steps of obtaining disturbance potential and background potential of an object inclusion to be identified; and respectively carrying out progressive analysis on the obtained disturbance potential and background potential by considering boundary transmission conditions and telescopic transformation, obtaining a difference value of disturbance potential integral expression and background potential integral expression by considering potential layer potential, constructing a potential field analysis model of the layered small inclusion, determining the position relation of the layered small inclusion according to the constructed potential field analysis model, and completing the position identification of the layered small inclusion based on the potential layer potential. The invention constructs a potential field analysis model of the layered small inclusion based on the potential layer potential theory so as to realize accurate identification of the position of the layered small inclusion without considering shape recovery.
Description
Technical Field
The invention belongs to the technical field of object detection, and particularly relates to a layered small inclusion position identification method and system based on potential layer potential.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
In oil and gas exploration, mineral resource exploration or environmental monitoring, it is often necessary to identify small inclusions (e.g., mineral bodies, fluid pockets, fracture zones, etc.) embedded in a subsurface layered medium. The traditional methods mainly depend on resistivity methods, electromagnetic methods or seismic wave technologies, but the methods have limitations in complex layered structures (namely, processing multiparameter and multiscale geological anomalies), wherein the resistivity methods are effective on single-level layered structures, but are difficult to distinguish the spatial distribution of a plurality of small inclusions, particularly when the electrical difference between layered media and the inclusions is small, the resolution is obviously reduced, the electromagnetic methods are greatly influenced by electromagnetic signal attenuation and external interference, high-frequency signals are difficult to penetrate deep media, the boundary positioning precision of the small inclusions is insufficient, the seismic wave technologies depend on acoustic wave impedance differences, the sensitivity of the small inclusions with low impedance difference is low, the equipment cost is high, and the data processing is complex.
Disclosure of Invention
In order to solve the problems, the invention provides a method and a system for identifying the position of a layered small inclusion based on potential layer potential, which construct a potential field analysis model of the layered small inclusion based on potential layer potential theory so as to realize accurate identification of the position of the layered small inclusion without considering shape recovery.
According to some embodiments, the first scheme of the invention provides a layered small inclusion position identification method based on potential layer potential, which adopts the following technical scheme:
A method for identifying the position of a layered small inclusion based on potential layer potential, comprising:
Acquiring disturbance potential and background potential of an object inclusion to be identified;
Carrying out progressive analysis on the obtained disturbance potential and background potential respectively by considering boundary transmission conditions and telescopic transformation, obtaining a difference value of a disturbance potential integral expression and a background potential integral expression by considering potential layer potential, and constructing a potential field analysis model of the layered small inclusion;
and determining the position relation of the layered small inclusion according to the constructed potential field analysis model, and completing the position identification of the layered small inclusion based on the potential layer potential.
As a further technical definition, the acquired disturbance potential and background potential at least satisfy the laplace control equationWherein, the method comprises the steps of,Representing a three-dimensional space,The operator of the degree of divergence is represented,The gradient operator is represented by a gradient operator,Representing an infinitely small amount of the higher order,In order to perturb the potential of the electric field,In order to perturb the potential of the electric field,As a function of the characteristics of the features,For being embedded inMiddle inclusion body and has A smooth boundary is provided between the inner and outer surfaces,The first derivative of the representation function satisfies the heldet condition,As a background space for the light,Is a regionIs a closure of (1)Medium conductivityIn the followingIn (a),Is thatIs used as a basis for the harmonic function of (a),Is a perturbation potential.
Further, the inclusionComprising a plurality of layered small inclusionsThe small lamellar inclusionIs the central region where the electric field is generated, and the position in space changes with time.
As further technical limitation, the potential field analysis model of the built layered small inclusion adopts progressive behavior represented by integration of disturbance potential and background potential, namely, the obtained disturbance potential is subjected to Taylor expansion by using a Laplacian operator, the conductivity of each layer in the layered small inclusion is considered, and the boundary transmission condition is combined to obtain the difference value of the disturbance potential integration expression and the background potential integration expression, so that the construction of the potential field analysis model of the layered small inclusion is completed.
As a further technical limitation, the position information of the small lamellar inclusion when moving is obtained based on boundary measurement, and the position of the small lamellar inclusion is determined by combining the constructed potential field analysis model, so that the position identification of the small lamellar inclusion is completed.
As a further technical limitation, in the progressive analysis, a single-layer potential operator, a double-layer potential operator and a boundary integral operator of a small inclusion are combined to obtain a jumping relation of the single-layer potential operator, and the obtained jumping relation of the single-layer potential operator is subjected to telescopic transformation to obtain a disturbance potential integral expression.
According to some embodiments, a second aspect of the present invention provides a layered small inclusion position recognition system based on potential layer potential, which adopts the following technical scheme:
A layered small inclusion position identification system based on potential layer potential, comprising:
An acquisition module configured to acquire a disturbance potential and a background potential of an object inclusion to be identified;
The construction module is configured to respectively carry out progressive analysis on the obtained disturbance potential and background potential in consideration of boundary transmission conditions and telescopic transformation, and obtain a difference value of a disturbance potential integral expression and a background potential integral expression in consideration of potential layer potential, so as to construct a potential field analysis model of the layered small inclusion;
and the identification module is configured to determine the position relation of the layered small inclusion according to the constructed potential field analysis model and complete the position identification of the layered small inclusion based on the potential layer potential.
According to some embodiments, a third aspect of the present invention provides a computer-readable storage medium, which adopts the following technical solutions:
a computer-readable storage medium having stored thereon a program which, when executed by a processor, implements the steps in a method for identifying a position of a layered small inclusion based on a potential layer potential according to a first aspect of the present invention.
According to some embodiments, a fourth aspect of the present invention provides an electronic device, which adopts the following technical solutions:
an electronic device comprising a memory, a processor and a program stored on the memory and running on the processor, the processor implementing the steps in a method for identifying a position of a layered small inclusion based on a potential layer potential according to the first aspect of the invention when the program is executed.
According to some embodiments, a fifth aspect of the present invention provides a computer program product, which adopts the following technical aspects:
a computer program product comprising software code, a program in the software code performing the steps of a method for identifying a position of a layered small inclusion based on a potential layer potential according to the first aspect of the invention.
Compared with the prior art, the invention has the beneficial effects that:
The invention constructs a potential field analysis model of the layered small inclusion based on the potential layer potential theory so as to realize accurate identification of the position of the layered small inclusion without considering shape recovery.
The invention establishes a mathematical theory for identifying the lamellar anomalies by utilizing potential data, and based on Laplace system control, uniquely restores the positions of a plurality of changed lamellar small inclusions, namely, the nonlinear relation between a potential field and a conductive lamellar anomaly structure is depicted by using a mathematical model, thereby overcoming the limitation of the traditional method in the process of multi-parameter and multi-scale geological anomalies. The method means that the specific position of the underground lamellar abnormality can be accurately inverted through the disturbance potential difference data obtained through measurement, and solid theoretical basis and technical support can be provided for practical application in the fields of mineral exploration, geological disaster early warning, water resource management and the like.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments and are incorporated in and constitute a part of this specification, illustrate and explain the embodiments and together with the description serve to explain the embodiments.
FIG. 1 is a flow chart of a method for identifying the position of a layered small inclusion based on potential layer potential in a first embodiment of the invention;
FIG. 2 is a detailed schematic diagram of the steps of a method for identifying the position of a layered small inclusion based on potential layer potential according to a first embodiment of the present invention;
FIG. 3 is a schematic diagram of the layered small inclusion in the first embodiment of the present invention;
Fig. 4 is a block diagram of a layered small inclusion position recognition system based on potential layer potential in a second embodiment of the present invention.
Detailed Description
The invention will be further described with reference to the drawings and examples.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the invention. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present invention. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
In the present invention, terms such as "upper", "lower", "left", "right", "front", "rear", "vertical", "horizontal", "side", "bottom", etc. refer to an orientation or a positional relationship based on that shown in the drawings, and are merely relational terms, which are used for convenience in describing structural relationships of various components or elements of the present invention, and do not denote any one of the components or elements of the present invention, and are not to be construed as limiting the present invention.
Embodiments of the invention and features of the embodiments may be combined with each other without conflict.
Example 1
The embodiment of the invention introduces a layered small inclusion position identification method based on potential layer potential.
The method for identifying the position of the layered small inclusion based on the potential layer potential shown in fig. 1 comprises the following steps:
Acquiring disturbance potential and background potential of an object inclusion to be identified;
Carrying out progressive analysis on the obtained disturbance potential and background potential respectively by considering boundary transmission conditions and telescopic transformation, obtaining a difference value of a disturbance potential integral expression and a background potential integral expression by considering potential layer potential, and constructing a potential field analysis model of the layered small inclusion;
and determining the position relation of the layered small inclusion according to the constructed potential field analysis model, and completing the position identification of the layered small inclusion based on the potential layer potential.
As shown in FIG. 2, the embodiment is based on potential layer potential theory, realizes the position identification of small inclusions under complex geological conditions by establishing a plurality of layered small inclusions and potential field analysis models, establishes potential field analysis solutions of the layered small inclusions under the condition that the external interference signals are small without considering the recovery of the shapes, realizes the decoupling of field source coupling effect, and can accurately identify the positions of the layered small inclusions. In practical application, the wave measuring device is usually deployed at a position far away from the target, and the unique recovery of a plurality of layered small inclusions is proved by using layer potential theory, telescopic transformation, asymptotic analysis and unique continuation theorem.
In the embodiment, only measured potential data are adopted, under the condition that the recovery of the shape is not considered, the potential field analysis and the decoupling of a plurality of layered small inclusions are established by small external interference signals, the decoupling of the field source coupling effect is realized, and the positions of the layered small inclusions can be accurately identified.
The embodiment considers the unique recovery result of the positions of a plurality of lamellar inclusion under the control of the Laplace system, and specifically:
the present embodiment assumes that For being embedded inMiddle inclusion body and has Smooth boundaries; is the space of the background and is used for the display, Is a regionIs a closure of the (c). The medium parameter is defined by conductivityDetermining, inIn (a)In the followingIn (a). Background potentialIs thatIs used as a basis for the harmonic function of (a),For disturbance potential, controlled by Laplace system, the equation is satisfied:
(1)
wherein, the Representing a characteristic function.
Assume thatFor detecting the position of the receiver, is a bounded region and comprises,. The inverse problem of the conductivity problem in equation (1) is at a given background potentialAnd boundary measurementIn the case of (2), the inclusion position is reconstructed.
In the embodiment, the position uniqueness recovery of a plurality of small lamellar inclusion bodies is proved by adopting a layer potential theory, asymptotic analysis and a unique extension theorem.
For the multiple layered inclusion problem, this embodiment first constructs an inclusion model.
As shown in fig. 3, it is assumed that inclusionIs composed of multiple inclusion bodiesThe composition of the composite material comprises the components,The position in space may change over time,Is a central region for generating an electric field, andIs of a layered structure, and has conductivity of. With non-intersecting smooth closed surfacesWill beIs divided intoSubset, satisfyEach of which isSurrounding(s)Area (area)Representing uniform dielectric layers, each layer having electrical conductivityThe conductivity satisfies:
(2)
The transmission conditions are satisfied:
(3)
Wherein the symbols are used To representOutward normals on, and for arbitrary functionsHas the following components
(4)
Based on the description of the plurality of layered small inclusions, the formula (1) can be rewritten as
(5)
In the present embodiment, the total disturbance potentialSolutions of the formula (2), the formula (3) and the formula (5),Is a background potential.
For displaying the position information of the inclusion, assume that
(6)
Wherein, the ,Representation letThe parameters are small enough to be able to be selected,Is a single connected domain with the origin as the center,Reaction position information.
Inverse problem mathematical models can be described as
(7)
Wherein, the The union is represented by a representation of the union,Representing all small inclusionsA set is formed.
The present embodiment restores the plurality of layered small inclusion positions by monitoring the change in the electric field at boundary ∂ Ω.
For the present embodiment、AndRespectively represent the firstFirst of small inclusionsThe specific expressions of the layer single-layer potential operator, the double-layer potential operator and the boundary integral Neumann-Poincare operator are as follows:
(8)
(9)
(10)
wherein, the The density parameter representing the boundary isA single-layer potential operator in the time of the process,The density parameter representing the boundary isThe two-layer potential operator in the time of the process,The density parameter representing the boundary isNeumann-Poincare operator at the time; for Laplace equation basic solution, then ,Represent the firstFirst of small inclusionsA function of the density of the layer,Representing the cauchy principal value.
The jumping relation of the single-double-layer potential operator in the embodiment is that
(11)
(12)
Wherein, the Is thatIs a companion operator of (a).
Is provided withThen
(13)
(14)
Wherein, the The representation being perpendicular toIs defined by the unit external normal vector of (c),Is expressed as hanging fromIs defined by the unit external normal vector of (c),Is thatIs provided.
Consider,Case, order,Due toDistance tends to infinity, then
(15)
Consider,Case, order,,Due toThen
(16)
In the present embodiment, there is providedIs the solution of equation (7), conductivityFrom equation (2), the transmission condition from equation (3), there is a unique functionSo that the following formula is established
(17)
Wherein the boundary layer potential functionSatisfy the following requirements
(18)
Due to the fact thatThe above is continuous, so that the first condition in the formula (3) is automatically satisfied, and the second condition in the formula (3) is utilized to derive the equation
(19)
The equation can be rewritten as follows using the hopping relationship of the single-layer and double-layer potential operators
(20)
Wherein, the 。
Introduction ofA matrix, which is an n-order matrix operator, further incorporating a token vectorAndI.e.
(21)
(22)
(23)
Formula (20) is rewritable
(24)
Wherein the diagonal matrix。
Substituting equation (13) and equation (14) into equation (24) yields
(25)
Wherein, the Is an identity matrix.
In the present embodiment of the present invention, in the present embodiment,The integral expression of (2) is
(26)
Wherein, the ,。
Specifically, performing Taylor expansion on Laplacian basic solution to obtain
(27)
Wherein, the 。
Is provided withOrder-makingAnd (5) performing variable replacement. By substituting equation (25) into equation (17), we can obtain
(28)
In this embodiment, the unique recognition result after the movement of the plurality of lamellar small inclusions is deduced through boundary measurement. Order theAndIndicating that the position is moved small inclusion and respectively replacing;Respectively replaceAndReaction position information; Is the solution of equation (5).
If it isIs true then,Specifically:
Is comprised of And also the position of the measurement receiver).At the position ofThe upper part is a harmonic function, and combines the principle of uniqueness and continuityCombining equation (26) forThen there is
(29)
Order theBy direct calculation, inOn the other hand, there are
(30)
Wherein the method comprises the steps of,,The value of (2) is。
It should be noted that the values defined in equation (30)In the followingThe above is also a harmonic function. By using analytic extension of the harmonic function, the method can be used forObtained by (1). Definition of the definition, wherein,
(31)
By comparison ofCan be obtained atIn (a). If it isThen fromObtaining the productFrom (a) slave,Can be obtained。
By combining the formula (30), it is possible to obtainIf (1)Then there areThis is true.
According to the embodiment, the mathematical theory of identifying the lamellar anomalies by utilizing potential data is established, and the positions of the changed lamellar small inclusions are uniquely recovered based on Laplace system control, namely, a mathematical model is used for describing the nonlinear relationship between a potential field and a conductive lamellar anomaly structure, so that the limitation of the traditional method in the process of multi-parameter and multi-scale geological anomalies is overcome. The method means that specific positions of underground lamellar anomalies can be accurately inverted through disturbance potential difference data obtained through measurement, and solid theoretical basis and technical support can be provided for practical application in the fields of mineral exploration, geological disaster early warning, water resource management and the like.
Example two
The second embodiment of the invention introduces a layered small inclusion position recognition system based on potential layer potential.
A layered small inclusion position recognition system based on potential layer potential as shown in fig. 4, comprising:
An acquisition module configured to acquire a disturbance potential and a background potential of an object inclusion to be identified;
The construction module is configured to respectively carry out progressive analysis on the obtained disturbance potential and background potential in consideration of boundary transmission conditions and telescopic transformation, and obtain a difference value of a disturbance potential integral expression and a background potential integral expression in consideration of potential layer potential, so as to construct a potential field analysis model of the layered small inclusion;
and the identification module is configured to determine the position relation of the layered small inclusion according to the constructed potential field analysis model and complete the position identification of the layered small inclusion based on the potential layer potential.
The detailed steps are the same as those of the method for identifying the position of the layered small inclusion based on the potential layer potential provided in the first embodiment, and will not be described herein.
Example III
The third embodiment of the invention provides a computer readable storage medium.
A computer-readable storage medium having stored thereon a program which, when executed by a processor, performs the steps in a method for identifying a position of a layered small inclusion based on a potential layer potential according to an embodiment of the present invention.
The detailed steps are the same as those of the method for identifying the position of the layered small inclusion based on the potential layer potential provided in the first embodiment, and will not be described herein.
Example IV
The fourth embodiment of the invention provides electronic equipment.
An electronic device comprising a memory, a processor and a program stored on the memory and running on the processor, wherein the processor implements the steps of a method for identifying a position of a layered small inclusion based on a potential layer potential according to an embodiment of the present invention when the program is executed by the processor.
The detailed steps are the same as those of the method for identifying the position of the layered small inclusion based on the potential layer potential provided in the first embodiment, and will not be described herein.
Example five
A fifth embodiment of the present invention provides a computer program product.
A computer program product comprising software code for executing the steps of a method for identifying the position of a layered small inclusion based on potential layer potential according to an embodiment of the invention.
The detailed steps are the same as those of the method for identifying the position of the layered small inclusion based on the potential layer potential provided in the first embodiment, and will not be described herein.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein. The scheme in the embodiment of the invention can be realized by adopting various computer languages, such as object-oriented programming language Java, an transliteration script language JavaScript and the like.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. It is therefore intended that the following claims be interpreted as including the preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
The above description is only a preferred embodiment of the present embodiment, and is not intended to limit the present embodiment, and various modifications and variations can be made to the present embodiment by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present embodiment should be included in the protection scope of the present embodiment.
Claims (7)
1. A method for identifying the position of a layered small inclusion based on potential layer potential, which is characterized by comprising the following steps:
Acquiring disturbance potential and background potential of an object inclusion to be identified;
Carrying out progressive analysis on the obtained disturbance potential and background potential respectively by considering boundary transmission conditions and telescopic transformation, obtaining a difference value of a disturbance potential integral expression and a background potential integral expression by considering potential layer potential, and constructing a potential field analysis model of the layered small inclusion;
determining the position relation of the layered small inclusion according to the constructed potential field analysis model, and completing the position identification of the layered small inclusion based on potential layer potential;
The potential field analysis model of the constructed lamellar small inclusion adopts progressive behavior represented by integration of disturbance potential and background potential, namely, the acquired disturbance potential is subjected to Taylor expansion by using a Laplacian operator, the conductivity of each layer in the lamellar small inclusion is considered, and the boundary transmission condition is combined to obtain a difference value of disturbance potential integral expression and background potential integral expression, so that the construction of the potential field analysis model of the lamellar small inclusion is completed;
Acquiring position information of the layered small inclusion when moving based on boundary measurement, and determining the position of the layered small inclusion by combining the constructed potential field analysis model to finish the position identification of the layered small inclusion;
inclusion body Comprising a plurality of layered small inclusionsThe small lamellar inclusionIs a central area for generating an electric field, and the position in space changes with time;
wherein, the ,Representation letThe parameters are small enough to be able to be selected,Is a single connected domain with the origin as the center,Reaction position information;
wherein, the The representation being perpendicular toIs defined by the unit external normal vector of (c),The representation being perpendicular toIs defined by the unit external normal vector of (c),Is thatIs a uniform dielectric layer of (a); The density function representing the boundary is Neumann-Poincare operator at the time; Represent the first First of small inclusionsA density function of the layer; Is that Is a companion operator to;
expressed as a diagonal matrix, specifically:
the n-order matrix operator is represented by the following concrete steps:
wherein, the As a result of the overall perturbation potential,As a background potential,Represent the firstFirst of small inclusionsDensity function of the layer.
2. A method for identifying lamellar small inclusion position based on potential layer potential as claimed in claim 1, characterized in that the obtained disturbance potential and background potential at least meet the laplace control equationWherein, the method comprises the steps of,Representing a three-dimensional space,The operator of the degree of divergence is represented,The gradient operator is represented by a gradient operator,Representing an infinitely small amount of the higher order,As a function of the characteristics of the features,For being embedded inMiddle inclusion body and hasA smooth boundary is provided between the inner and outer surfaces,The first derivative of the representation function satisfies the heldet condition,As a background space for the light,Is a regionIs a closure of (1)Medium conductivityIn the followingIn (a)。
3. The method for identifying the position of a layered small inclusion based on potential layer potential according to claim 1, wherein in the progressive analysis, a single-layer potential operator, a double-layer potential operator and a boundary integral operator of the small inclusion are combined to obtain a jumping relation of the single-layer potential operator and the double-layer potential operator, and the obtained jumping relation of the single-layer potential operator is subjected to telescopic transformation to obtain a disturbance potential integral expression.
4. A potential-layer potential-based layered small inclusion position recognition system employing a potential-layer potential-based layered small inclusion position recognition method as claimed in any one of claims 1 to 3, comprising:
An acquisition module configured to acquire a disturbance potential and a background potential of an object inclusion to be identified;
The construction module is configured to respectively carry out progressive analysis on the obtained disturbance potential and background potential in consideration of boundary transmission conditions and telescopic transformation, and obtain a difference value of a disturbance potential integral expression and a background potential integral expression in consideration of potential layer potential, so as to construct a potential field analysis model of the layered small inclusion;
and the identification module is configured to determine the position relation of the layered small inclusion according to the constructed potential field analysis model and complete the position identification of the layered small inclusion based on the potential layer potential.
5. A computer-readable storage medium, on which a computer program is stored, characterized in that the program, when being executed by a processor, implements the steps of a method for identifying the position of layered small inclusions on the basis of potential layers as claimed in any of claims 1-3.
6. An electronic device comprising a memory, a processor and a computer program stored on the memory and running on the processor, characterized in that the processor implements the steps of a method for identifying the position of a layered small inclusion based on potential layer potentials according to any of claims 1-3 when the program is executed by the processor.
7. A computer program product comprising software code, characterized in that a program in said software code performs the steps of a method for identifying the position of a layered small inclusion based on potential layer potentials according to any of claims 1-3.
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| FR1271769A (en) * | 1959-09-29 | 1961-09-15 | Rca Corp | Method for creating a barrier layer in a semiconductor and semiconductor device thus obtained |
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