CN110687589B - Numerical simulation method and equipment for exciting Krauklis wave by transverse wave in crack medium - Google Patents
Numerical simulation method and equipment for exciting Krauklis wave by transverse wave in crack medium Download PDFInfo
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Abstract
The embodiment of the invention provides a numerical simulation method and equipment for Krauklis waves excited by transverse waves in a crack medium. Wherein the method comprises the following steps: constructing a finite element discrete equation, and loading a transverse wave incidence boundary condition to the finite element discrete equation to obtain a finite element discrete equation of the loading boundary condition; and constructing a boundary auxiliary matrix, a seismic source auxiliary matrix and a seismic source auxiliary vector, combining an iterative algorithm to obtain an iterative formula, and solving a finite element discrete equation of the loading boundary condition by adopting the iterative formula to realize the numerical simulation of the transverse wave in the crack medium for exciting the Krauklis wave. The numerical simulation method and the numerical simulation equipment for the Krauklis wave excited by the transverse wave in the crack medium, which are provided by the embodiment of the invention, can effectively realize the numerical simulation for the Krauklis wave excited by the transverse wave in the crack medium.
Description
Technical Field
The embodiment of the invention relates to the technical field of Krauklis wave research, in particular to a numerical simulation method and equipment for exciting Krauklis waves by transverse waves in a crack medium.
Background
The Krauklis wave is a guided wave propagating in a fluid saturated fracture and is an important component of a complex wave field of a fracture medium. Krauklis has the characteristics of strong frequency dispersion and strong attenuation, the high-frequency limit of the Krauklis is the Scott wave speed, and the low-frequency limit of the Krauklis is 0. The current research aiming at Krauklis waves always stays in theoretical research based on an ideal infinite-length viscous fluid-containing single fracture model, and the actual underground medium fracture is of finite length, so the theoretical analysis conclusion of the infinite-length fracture model is difficult to use in the actual underground model. Furthermore, the wave equation simulation is mostly based on explosive seismic sources, which contain both longitudinal and shear wave components, which makes the wave field extremely complex. Therefore, a numerical simulation method for transverse wave excitation of Krauklis waves in a crack medium is obtained, so that numerical simulation of transverse wave excitation of Krauklis waves is realized, research on Krauklis waves can be in line with practical research, and the technical problem to be solved in the industry is urgent.
Disclosure of Invention
Aiming at the problems in the prior art, the embodiment of the invention provides a numerical simulation method and equipment for exciting Krauklis waves by transverse waves in a crack medium.
In a first aspect, an embodiment of the present invention provides a method for numerically simulating a transverse-wave-excited Krauklis wave in a fractured medium, including: constructing a finite element discrete equation, and loading a transverse wave incidence boundary condition to the finite element discrete equation to obtain a finite element discrete equation of the loading boundary condition; and constructing a boundary auxiliary matrix, a seismic source auxiliary matrix and a seismic source auxiliary vector, combining an iterative algorithm to obtain an iterative formula, and solving a finite element discrete equation of the loading boundary condition by adopting the iterative formula to realize the numerical simulation of the transverse wave in the crack medium for exciting the Krauklis wave.
Further, on the basis of the content of the above method embodiment, the method for numerically simulating Krauklis wave excited by shear wave in fractured medium provided in the embodiment of the present invention, where the constructing a finite element discrete equation includes: and dispersing the basic equation of the fluid and the viscoelastic medium by adopting a six-node irregular isoparametric triangular unit to construct a finite element dispersion equation.
Further, on the basis of the above description of the method embodiment, in the method for numerically simulating Krauklis wave excited by shear wave in fractured medium provided in the embodiment of the present invention, the finite element discrete equation includes:
Ma+Cv+Ku＝F+R
wherein u is the vibration displacement of the dispersed particles; v is the vibration speed of the dispersed particles; a is the vibration acceleration of the dispersed mass points; m is a quality matrix; c is a damping matrix; k is a stiffness matrix; f is a load term; r is a term related to a boundary condition; rho is the density of the fluid inside the fracture; b is a partial derivative matrix; seIs the area of a discrete region; dvIs the viscosity coefficient; deIs the elastic coefficient; f is the force source load; n is a radical of1To N6Bi-quadratic interpolation polynomials corresponding to six nodes of each unit respectively; sigmaxxStress perpendicular to the direction of propagation of the transverse wave; sigmaxyIs the stress parallel to the direction of propagation of the transverse wave.
Further, on the basis of the above description of the method embodiment, in the method for numerically simulating Krauklis wave excited by shear wave in fractured medium provided in the embodiment of the present invention, the loading of the boundary condition of shear wave incidence on the finite element discrete equation, and accordingly, the boundary condition of shear wave incidence, includes:
wherein u isxDisplacement of vibration of mass points in the x direction; u. ofyDisplacement of mass point vibration in y direction; sigmaxxStress perpendicular to the direction of propagation of the transverse wave; sigmaxyStress parallel to the propagation direction of the transverse wave, mu is shear modulus, η is the viscosity coefficient of the fluid inside the crack, NeA unit interpolation matrix is obtained;
is a unit node vector;
is a unit node vector;
is the particle vibration velocity at the unit node;
is the particle vibration velocity at the node of the cell.
Further, on the basis of the content of the above method embodiment, in the numerical simulation method for stimulating Krauklis waves by shear waves in a crack medium provided in the embodiment of the present invention, the boundary auxiliary matrix, the seismic source auxiliary matrix, and the seismic source auxiliary vector are constructed, accordingly, diagonal elements corresponding to y components at boundary nodes of the boundary auxiliary matrix are 0, and the remaining diagonal elements are 1; diagonal elements corresponding to the y component of the seismic source node of the seismic source auxiliary matrix are 0, and the other diagonal elements are 1; the seismic source auxiliary vector is a column vector formed by 0 and 1, the element corresponding to the x component of the seismic source node is 1, and the rest elements are 0.
Further, on the basis of the content of the above method embodiment, the method for numerically simulating Krauklis wave excited by shear wave in a fracture medium provided in the embodiment of the present invention combines an iterative algorithm to obtain an iterative formula, and accordingly, the iterative algorithm employs a β -niemann algorithm, and the iterative formula includes:
wherein u iskDisplacement of particle vibration at time k; u. ofk+1Displacement of particle vibration at the moment of k + 1; BC1A boundary auxiliary matrix; BC2Is a seismic source auxiliary matrix; b0Is a seismic source auxiliary vector; Δ t is a duration interval;
the disturbed damping matrix is obtained;
is a rigidity matrix after disturbance; m is a quality matrix; a iskAcceleration of particle vibration at the moment k; a isk+1Acceleration of particle vibration at the moment of k + 1; w is a seismic wavelet; v. ofkThe velocity of particle vibration at time k; v. ofk+1The velocity of the particle vibration at time k + 1.
Further, on the basis of the above description of the method embodiments, in the method for numerically simulating Krauklis wave excited by shear wave in fractured medium provided in the embodiments of the present invention, the basic equations of the fluid and the viscoelastic medium are discretized, and accordingly, the basic equations of the fluid and the viscoelastic medium include:
wherein K' is volume modulus, mu is shear modulus, η is internal fluid viscosity coefficient of the fracture, rho is internal fluid density of the fracture, axAnd ayAcceleration of vibration of mass points in the x direction and the y direction respectively; v. ofxAnd vyThe vibration speeds of the mass point in the x direction and the y direction are respectively; u. ofxAnd uyDisplacement of the particle vibration in the x-direction and y-direction, respectively.
In a second aspect, an embodiment of the present invention provides a numerical simulation apparatus for exciting Krauklis waves by shear waves in a fractured medium, including:
the finite element discrete equation building module is used for building a finite element discrete equation, and loading the transverse wave incident boundary condition to the finite element discrete equation to obtain a finite element discrete equation of the loaded boundary condition;
and the numerical simulation module is used for constructing a boundary auxiliary matrix, a seismic source auxiliary matrix and a seismic source auxiliary vector, combining an iterative algorithm to obtain an iterative formula, solving the finite element discrete equation of the loading boundary condition by adopting the iterative formula, and realizing numerical simulation of transverse wave excitation Krauklis waves in the crack medium.
In a third aspect, an embodiment of the present invention provides an electronic device, including:
at least one processor; and
at least one memory communicatively coupled to the processor, wherein:
the memory stores program instructions executable by the processor, and the processor calls the program instructions to perform the method for numerical simulation of transverse wave excitation of Krauklis waves in a fractured medium provided by any one of the various possible implementations of the first aspect.
In a fourth aspect, embodiments of the present invention provide a non-transitory computer-readable storage medium storing computer instructions for causing a computer to perform a method for numerical simulation of shear-wave-excited Krauklis waves in a fractured medium provided in any one of the various possible implementations of the first aspect.
According to the numerical simulation method and device for the Krauklis wave excited by the transverse wave in the crack medium, provided by the embodiment of the invention, the numerical simulation of the Krauklis wave excited by the transverse wave in the crack medium can be effectively realized by constructing the finite element discrete equation, loading the incident boundary condition of the transverse wave, obtaining the iterative formula according to the boundary auxiliary matrix, the seismic source auxiliary matrix and the seismic source auxiliary vector and combining the iterative algorithm, and then repeatedly calculating the finite element discrete equation loaded with the incident boundary condition of the transverse wave by adopting the iterative formula.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, a brief description will be given below to the drawings required for the description of the embodiments or the prior art, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a flow chart of a method for numerically simulating Krauklis wave excited by transverse waves in a fractured medium according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of the effect of a shear wave seismic source provided by an embodiment of the invention;
FIG. 3 is a schematic diagram of the effect of a Krauklis wave with strong amplitude at different times according to an embodiment of the present invention;
FIG. 4 is a schematic structural diagram of a numerical simulation apparatus for exciting Krauklis waves by shear waves in a fractured medium according to an embodiment of the present invention;
fig. 5 is a schematic physical structure diagram of an electronic device according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention. In addition, technical features of various embodiments or individual embodiments provided by the invention can be arbitrarily combined with each other to form a feasible technical solution, but must be realized by a person skilled in the art, and when the technical solution combination is contradictory or cannot be realized, the technical solution combination is not considered to exist and is not within the protection scope of the present invention.
The embodiment of the invention provides a numerical simulation method for exciting Krauklis waves by transverse waves in a crack medium, and with reference to a figure 1, the method comprises the following steps:
101. constructing a finite element discrete equation, and loading a transverse wave incidence boundary condition to the finite element discrete equation to obtain a finite element discrete equation of the loading boundary condition;
102. and constructing a boundary auxiliary matrix, a seismic source auxiliary matrix and a seismic source auxiliary vector, combining an iterative algorithm to obtain an iterative formula, and solving a finite element discrete equation of the loading boundary condition by adopting the iterative formula to realize the numerical simulation of the transverse wave in the crack medium for exciting the Krauklis wave.
Based on the content of the above method embodiment, as an optional embodiment, the method for numerically simulating Krauklis wave excited by shear wave in fractured medium provided in the embodiment of the present invention, where the constructing a finite element discrete equation, includes: and dispersing the basic equation of the fluid and the viscoelastic medium by adopting a six-node irregular isoparametric triangular unit to construct a finite element dispersion equation.
Based on the content of the above method embodiment, as an optional embodiment, the method for numerically simulating Krauklis wave excited by shear wave in fractured medium provided in the embodiment of the present invention includes:
Ma+Cv+Ku＝F+R (1)
wherein u is the vibration displacement of the dispersed particles; v is the vibration speed of the dispersed particles; a is the vibration acceleration of the dispersed mass points; m is a quality matrix; c is a damping matrix; k is a stiffness matrix; f is a load term; r is a term related to a boundary condition; rho is the density of the fluid inside the fracture; b is a partial derivative matrix; seIs the area of a discrete region; dvIs the viscosity coefficient; deIs the elastic coefficient; f is the force source load; n is a radical of1To N6Bi-quadratic interpolation polynomials corresponding to six nodes of each unit respectively; sigmaxxStress perpendicular to the direction of propagation of the transverse wave; sigmaxyIs the stress parallel to the direction of propagation of the transverse wave. Specifically, in the finite element discrete equation (1), u, v and a are the vibration displacement, velocity and acceleration vectors of the discrete particles, the coefficient matrix M, C, K is respectively called as a mass matrix, a damping matrix and a stiffness matrix, the right-end term F is a load term, and the right-end term R is the phase of the boundary conditionThe item that is off. In the conventional finite element elastic wave numerical simulation process, the seismic source loading mode is to add a force source term to the load term F in the formula (1). Thus, the seismic source field contains both longitudinal and transverse wave components, but the energy of the longitudinal wave is much stronger. The determined wavefield contains both compressional secondary waves and shear secondary waves, but the compressional secondary waves have much stronger field energy than the shear secondary wavefield. This makes the scattered wave field energy inside the fracture medium extremely strong, making it difficult to observe the Krauklis wave. The embodiment of the invention provides a pure shear wave seismic source loading mode and provides corresponding boundary conditions, the seismic source only contains shear waves but not longitudinal wave components, so that a secondary wave field generated by the shear waves can be discussed separately, the energy of scattered waves generated by the shear waves in a fluid is weaker, the energy of Krauklis waves is relatively stronger, the signal-to-noise ratio of the obtained Krauklis higher, and the wave field is clearer and has obvious characteristics.
Based on the content of the foregoing method embodiment, as an optional embodiment, in the method for numerically simulating a Krauklis wave excited by shear waves in a fractured medium provided in the embodiment of the present invention, the loading a shear wave incident boundary condition to the finite element discrete equation, and accordingly, the shear wave incident boundary condition includes:
wherein u isxDisplacement of vibration of mass points in the x direction; u. ofyDisplacement of mass point vibration in y direction; sigmaxxStress perpendicular to the direction of propagation of the transverse wave; sigmaxyStress parallel to the propagation direction of the transverse wave, mu is shear modulus, η is the viscosity coefficient of the fluid inside the crack, NeA unit interpolation matrix is obtained;
is a unit node vector;
is a unit node vector;
is the particle vibration velocity at the unit node;
is the particle vibration velocity at the node of the cell. Specifically, in order to ensure that the shear wave propagates along the propagation direction without any diffraction on the truncation boundaries parallel to the propagation direction on both sides of the model boundary, the stress in the direction perpendicular to the propagation direction is required to be 0, and the displacement in the direction parallel to the propagation direction is also required to be 0; the shear stress in the direction parallel to the propagation direction is not 0, and the displacement in the direction perpendicular to the propagation direction is not 0. Therefore, when a pure transverse wave is incident, the boundary condition expression thereof can be written as the expressions (2) and (3). Before the boundary conditions are processed, it is assumed that the whole simulation system has no external force input, and when the load term F is equal to 0, only the R term remains at the right end of the equation (1). First to satisfy equation (2), the stress σ in r is requiredxxTo zero, and then the shear stress term σ thereinxyThe expansion is a function of node vibration speed and vibration displacement, and the r term after the replacement is the expression (4).
Based on the content of the method embodiment, as an optional embodiment, in the numerical simulation method for stimulating Krauklis waves by shear waves in a fractured medium provided in the embodiment of the present invention, the boundary auxiliary matrix, the seismic source auxiliary matrix, and the seismic source auxiliary vector are constructed, accordingly, diagonal elements corresponding to y components at boundary nodes of the boundary auxiliary matrix are 0, and the remaining diagonal elements are 1; diagonal elements corresponding to the y component of the seismic source node of the seismic source auxiliary matrix are 0, and the other diagonal elements are 1; the seismic source auxiliary vector is a column vector formed by 0 and 1, the element corresponding to the x component of the seismic source node is 1, and the rest elements are 0. In particular, the introduction of the boundary term R leads to a damping momentDisturbance occurs to the array and the rigidity matrix, and the damping matrix and the rigidity matrix after the disturbance are respectively assumed to be
Then, a boundary auxiliary matrix BETA C was constructed1Seismic source auxiliary matrix BETA C2And an auxiliary vector b0。ΒC1And BETA C2Is a diagonal matrix composed of only 0 and 1, and the arrangement order of the rows and columns thereof is related to the node arrangement order. Aiming at BETA C1Diagonal elements corresponding to y components at all boundary nodes are 0, and the other diagonal elements are 1; BETA C2And BETA C1Similarly, but for the source node y component the corresponding diagonal element is 0 and the remaining diagonal elements are 1. And BETA C1Corresponding displacement vector, BETA C2Corresponding to the velocity vector. b0For a column vector consisting of only 0 and 1, the x component of the source node corresponds to an element of 1, the rest elements are 0, b0Also corresponding to the velocity vector. BETA C after wavelet duration1And BETA C2Invariable, b0And (4) disappearing.
Based on the content of the above method embodiment, as an optional embodiment, the numerical simulation method for exciting Krauklis waves by shear waves in a fracture medium provided in the embodiment of the present invention obtains an iterative formula by combining an iterative algorithm, and accordingly, the iterative algorithm adopts a β -niemann algorithm, and the iterative formula includes:
wherein u iskDisplacement of particle vibration at time k; u. ofk+1Displacement of particle vibration at the moment of k + 1; BC1A boundary auxiliary matrix; BC2Is a seismic source auxiliary matrix; b0Is a seismic source auxiliary vector; Δ t is a duration interval;
the disturbed damping matrix is obtained;
is a rigidity matrix after disturbance; m is a quality matrix; a iskAcceleration of particle vibration at the moment k; a isk+1Acceleration of particle vibration at the moment of k + 1; w is a seismic wavelet; v. ofkThe velocity of particle vibration at time k; v. ofk+1The equation (2), (3) and (4) are combined and integrated into the finite element equation (1), and then an β -Newman algorithm is adopted to derive an iterative solution format of an equation set, wherein delta t is the sampling interval duration, and the displacement, speed and acceleration vectors of the particle vibration at the moment k are u, and a specific expression is shown in an equation (5)k,vk,akThen k +1 moment displacement, velocity, and acceleration vectors uk+1,vk+1,ak+1The calculation formula of (2) is the formula (5).
Are two intermediate variables, corresponding to the velocity vector and the acceleration vector, respectively. The result thus obtained naturally satisfies equation (3).
Based on the content of the foregoing method embodiment, as an optional embodiment, in the method for numerically simulating a Krauklis wave excited by shear waves in a fracture medium provided in the embodiment of the present invention, the basic equations of the fluid and the viscoelastic medium are discretized, and accordingly, the basic equations of the fluid and the viscoelastic medium include:
wherein K' is volume modulus, mu is shear modulus, η is internal fluid viscosity coefficient of the fracture, rho is internal fluid density of the fracture, axAnd ayAcceleration of vibration of mass points in the x direction and the y direction respectively; v. ofxAnd vyThe vibration speeds of the mass point in the x direction and the y direction are respectively; u. ofxAnd uyDisplacement of the particle vibration in the x-direction and y-direction, respectively. Specifically, the formula (6) is discretized by adopting a finite element method, and the element type adopts a six-node irregular equal-parameter triangle element. Such a unitThe division rule is flexible, the complex crack space can be well represented, the corresponding interpolation function is of second-order precision, and the displacement interpolation formula can be written as follows:
wherein the content of the first and second substances,
is a unit node vector; n is a radical ofeA matrix is interpolated for the cells. From this finite element discrete equation (1) can be established.
The numerical simulation method for exciting Krauklis waves by transverse waves in a crack medium provided by the embodiment of the invention can effectively realize the numerical simulation of exciting Krauklis waves by transverse waves in the crack medium by constructing the finite element discrete equation, loading the incident boundary condition of the transverse waves, obtaining the iterative formula according to the boundary auxiliary matrix, the seismic source auxiliary matrix and the seismic source auxiliary vector and combining the iterative algorithm, and then repeatedly calculating the finite element discrete equation loaded with the incident boundary condition of the transverse waves by adopting the iterative formula.
In particular, the effect of shear wave sources can be seen in fig. 2. Fig. 2 includes: fluid-containing cracks 201, valleys 202 and peaks 203. The strip transverse to the lower part in fig. 2 is a shear wave source, and the contact position of the shear wave source and the model boundary has no diffracted wave, which shows that the corresponding boundary condition is effective. The black arrows indicate the direction of propagation of the shear wave source. By adopting the numerical simulation method for exciting the Krauklis wave by the transverse wave in the crack medium provided by the embodiment of the invention, the Krauklis wave can be clearly seen at different moments, and particularly, the method can be seen in FIG. 3. As can be seen from fig. 3, at different times (t 3.0ms, t 3.5ms, t 4.0ms, t 4.5ms, t 5.0ms, t 5.5ms), the strong amplitude along both sides of the crack is a Krauklis wave.
The implementation basis of the various embodiments of the present invention is realized by programmed processing performed by a device having a processor function. Therefore, in engineering practice, the technical solutions and functions thereof of the embodiments of the present invention can be packaged into various modules. Based on this actual situation, on the basis of the above embodiments, the embodiments of the present invention provide a numerical simulation apparatus for exciting Krauklis waves by shear waves in a fractured medium, which is used for executing the numerical simulation method for exciting Krauklis waves by shear waves in a fractured medium in the above method embodiments. Referring to fig. 4, the apparatus includes:
a finite element discrete equation constructing module 401, configured to construct a finite element discrete equation, and load the shear wave incident boundary condition on the finite element discrete equation to obtain a finite element discrete equation of the loaded boundary condition;
and the numerical simulation module 402 is used for constructing a boundary auxiliary matrix, a seismic source auxiliary matrix and a seismic source auxiliary vector, obtaining an iterative formula by combining an iterative algorithm, solving the finite element discrete equation of the loading boundary condition by adopting the iterative formula, and realizing numerical simulation of transverse wave excitation Krauklis waves in the crack medium.
The numerical simulation device for exciting Krauklis waves by transverse waves in a crack medium provided by the embodiment of the invention adopts a finite element discrete equation construction module and a numerical simulation module, obtains an iterative formula by constructing a finite element discrete equation and loading incident boundary conditions of the transverse waves, according to a boundary auxiliary matrix, a seismic source auxiliary matrix and a seismic source auxiliary vector and combining an iterative algorithm, and then repeatedly solves the finite element discrete equation loaded with the incident boundary conditions of the transverse waves by adopting the iterative formula, so that the numerical simulation of exciting the Krauklis waves by the transverse waves in the crack medium can be effectively realized.
It should be noted that, the apparatus in the apparatus embodiment provided by the present invention may be used for implementing methods in other method embodiments provided by the present invention, except that corresponding function modules are provided, and the principle of the apparatus embodiment provided by the present invention is basically the same as that of the apparatus embodiment provided by the present invention, so long as a person skilled in the art obtains corresponding technical means by combining technical features on the basis of the apparatus embodiment described above, and obtains a technical solution formed by these technical means, on the premise of ensuring that the technical solution has practicability, the apparatus in the apparatus embodiment described above may be modified, so as to obtain a corresponding apparatus class embodiment, which is used for implementing methods in other method class embodiments. For example:
based on the content of the above device embodiment, as an optional embodiment, the device for numerically simulating Krauklis wave excited by shear wave in fractured medium provided in the embodiment of the present invention further includes: and the six-node irregular equal-parameter triangular unit module is used for adopting the six-node irregular equal-parameter triangular unit to disperse the basic equation of the fluid and the viscoelastic medium to construct a finite element discrete equation.
The method of the embodiment of the invention is realized by depending on the electronic equipment, so that the related electronic equipment is necessarily introduced. To this end, an embodiment of the present invention provides an electronic apparatus, as shown in fig. 5, including: at least one processor (processor)501, a communication Interface (Communications Interface)504, at least one memory (memory)502 and a communication bus 503, wherein the at least one processor 501, the communication Interface 504 and the at least one memory 502 are in communication with each other through the communication bus 503. The at least one processor 501 may call logic instructions in the at least one memory 502 to perform the following method: constructing a finite element discrete equation, and loading a transverse wave incidence boundary condition to the finite element discrete equation to obtain a finite element discrete equation of the loading boundary condition; and constructing a boundary auxiliary matrix, a seismic source auxiliary matrix and a seismic source auxiliary vector, combining an iterative algorithm to obtain an iterative formula, and solving a finite element discrete equation of the loading boundary condition by adopting the iterative formula to realize the numerical simulation of the transverse wave in the crack medium for exciting the Krauklis wave.
Furthermore, the logic instructions in the at least one memory 502 may be implemented in software functional units and stored in a computer readable storage medium when sold or used as a stand-alone product. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. Examples include: constructing a finite element discrete equation, and loading a transverse wave incidence boundary condition to the finite element discrete equation to obtain a finite element discrete equation of the loading boundary condition; and constructing a boundary auxiliary matrix, a seismic source auxiliary matrix and a seismic source auxiliary vector, combining an iterative algorithm to obtain an iterative formula, and solving a finite element discrete equation of the loading boundary condition by adopting the iterative formula to realize the numerical simulation of the transverse wave in the crack medium for exciting the Krauklis wave. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
The above-described embodiments of the apparatus are merely illustrative, and the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware. With this understanding in mind, the above-described technical solutions may be embodied in the form of a software product, which can be stored in a computer-readable storage medium such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the methods described in the embodiments or some parts of the embodiments.
The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present invention. Based on this recognition, each block in the flowchart or block diagrams may represent a module, a program segment, or a portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
In this patent, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (8)
1. A numerical simulation method for exciting Krauklis waves by transverse waves in a fracture medium is characterized by comprising the following steps:
constructing a finite element discrete equation, and loading a transverse wave incidence boundary condition to the finite element discrete equation to obtain a finite element discrete equation of the loading boundary condition;
constructing a boundary auxiliary matrix, a seismic source auxiliary matrix and a seismic source auxiliary vector, combining an iterative algorithm to obtain an iterative formula, adopting the iterative formula to solve a finite element discrete equation of the loading boundary condition, and realizing numerical simulation of transverse wave excitation Krauklis waves in the fracture medium;
the iterative algorithm adopts a beta-Newman algorithm, and the iterative formula comprises the following steps:
wherein u iskDisplacement of particle vibration at time k; u. ofk+1Displacement of particle vibration at the moment of k + 1; BC1A boundary auxiliary matrix; BC2Is a seismic source auxiliary matrix; b0Is a seismic source auxiliary vector; Δ t is a duration interval;
to disturbA damping matrix after the motion;
is a rigidity matrix after disturbance; m is a quality matrix; a iskAcceleration of particle vibration at the moment k; a isk+1Acceleration of particle vibration at the moment of k + 1; w is a seismic wavelet; v. ofkThe velocity of particle vibration at time k; v. ofk+1The velocity of particle vibration at the time of k + 1; diagonal elements corresponding to the y component at the boundary nodes of the boundary auxiliary matrix are 0, and the other diagonal elements are 1; diagonal elements corresponding to the y component of the seismic source node of the seismic source auxiliary matrix are 0, and the other diagonal elements are 1; the seismic source auxiliary vector is a column vector formed by 0 and 1, the element corresponding to the x component of the seismic source node is 1, and the rest elements are 0.
2. The method for numerically simulating transverse wave excited Krauklis wave in fractured medium according to claim 1, wherein the constructing a finite element discrete equation comprises:
and dispersing the basic equation of the fluid and the viscoelastic medium by adopting a six-node irregular isoparametric triangular unit to construct a finite element dispersion equation.
3. The method of numerical simulation of transverse-wave-excited Krauklis waves in fractured media of claim 1, wherein the finite element discrete equation comprises:
Ma+Cv+Ku＝F+R
wherein u is the vibration displacement of the dispersed particles; v is the vibration speed of the dispersed particles; a is the vibration acceleration of the dispersed mass points; m is a quality matrix; c is a damping matrix; k is a stiffness matrix; f is a load term; r is a term related to a boundary condition; rho is the density of the fluid inside the fracture; b is a partial derivative matrix; seIs the area of a discrete region; dvIs the viscosity coefficient; deIs the elastic coefficient; f is the force source load; n is a radical of1To N6Bi-quadratic interpolation polynomials corresponding to six nodes of each unit respectively; sigmaxxStress perpendicular to the direction of propagation of the transverse wave; sigmaxyIs the stress parallel to the direction of propagation of the transverse wave.
4. The method of numerical simulation of transverse-wave-excited Krauklis waves in fractured media of claim 1, wherein the loading of the finite element discrete equations with transverse-wave incident boundary conditions, respectively, comprises:
wherein u isxDisplacement of vibration of mass points in the x direction; u. ofyDisplacement of mass point vibration in y direction; sigmaxxStress perpendicular to the direction of propagation of the transverse wave; sigmaxyStress parallel to the propagation direction of the transverse wave, mu is shear modulus, η is the viscosity coefficient of the fluid inside the crack, NeA unit interpolation matrix is obtained;
is a unit node vector;
is a unit node vector;
is the particle vibration velocity at the unit node;
is the particle vibration velocity at the node of the cell.
5. The method for numerically simulating transverse wave excited Krauklis wave in fracture medium according to claim 2, wherein the discretizing of the fundamental equations of fluid and viscoelastic medium, and accordingly, the fundamental equations of fluid and viscoelastic medium comprise:
wherein K' is volume modulus, mu is shear modulus, η is internal fluid viscosity coefficient of the fracture, rho is internal fluid density of the fracture, axAnd ayAcceleration of vibration of mass points in the x direction and the y direction respectively; v. ofxAnd vyThe vibration speeds of the mass point in the x direction and the y direction are respectively; u. ofxAnd uyThe particles vibrating in the x-direction and y-direction, respectivelyAnd (4) moving displacement.
6. A numerical simulation device for exciting Krauklis waves by transverse waves in a fracture medium is characterized by comprising:
the finite element discrete equation building module is used for building a finite element discrete equation, and loading the transverse wave incident boundary condition to the finite element discrete equation to obtain a finite element discrete equation of the loaded boundary condition;
the numerical simulation module is used for constructing a boundary auxiliary matrix, a seismic source auxiliary matrix and a seismic source auxiliary vector, combining an iterative algorithm to obtain an iterative formula, solving a finite element discrete equation of the loading boundary condition by adopting the iterative formula, and realizing numerical simulation of transverse wave excitation Krauklis waves in a crack medium;
the iterative algorithm adopts a beta-Newman algorithm, and the iterative formula comprises the following steps:
wherein u iskDisplacement of particle vibration at time k; u. ofk+1Displacement of particle vibration at the moment of k + 1; BC1A boundary auxiliary matrix; BC2Is a seismic source auxiliary matrix; b0Is a seismic source auxiliary vector; Δ t is a duration interval;
the disturbed damping matrix is obtained;
is a rigidity matrix after disturbance; m is a quality matrix; a iskAcceleration of particle vibration at the moment k; a isk+1Acceleration of particle vibration at the moment of k + 1; w is a seismic wavelet; v. ofkThe velocity of particle vibration at time k; v. ofk+1The velocity of particle vibration at the time of k + 1; diagonal elements corresponding to the y component at the boundary nodes of the boundary auxiliary matrix are 0, and the other diagonal elements are 1; diagonal elements corresponding to the y component of the seismic source node of the seismic source auxiliary matrix are 0, and the other diagonal elements are 1; the seismic source auxiliary vector is a column vector formed by 0 and 1, the element corresponding to the x component of the seismic source node is 1, and the rest elements are 0.
7. An electronic device, comprising:
at least one processor, at least one memory, a communication interface, and a bus; wherein the content of the first and second substances,
the processor, the memory and the communication interface complete mutual communication through the bus;
the memory stores program instructions executable by the processor, the processor calling the program instructions to perform the method of any of claims 1 to 5.
8. A non-transitory computer-readable storage medium storing computer instructions that cause a computer to perform the method of any one of claims 1 to 5.
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