CN115201913A - Least square reverse time migration imaging method, system and storage medium based on non-grid finite difference method - Google Patents
Least square reverse time migration imaging method, system and storage medium based on non-grid finite difference method Download PDFInfo
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Abstract
The invention relates to the technical field of geophysical exploration, in particular to a least square reverse time migration imaging method and system based on a non-grid finite difference method and a storage medium. According to the method provided by the invention, the grid-free distribution generated according to the target work area underground model is used, the grid-free finite difference method reverse time migration is used for obtaining the initial imaging result, and the least square reverse time migration imaging method is carried out by using the migration and reverse migration operator based on the grid-free finite difference method, so that the accurate description and the efficient imaging of the complex earth surface and the underground irregular structure are realized, and the underground complex geological structure can be finely described under any complex earth surface condition. Meanwhile, the method effectively reduces algorithm calculation and memory requirements, improves imaging precision and can provide more accurate imaging results for seismic exploration.
Description
Technical Field
The invention relates to the technical field of geophysical exploration, in particular to a least square reverse time migration imaging method and system based on a non-grid finite difference method and a storage medium.
Background
With the demand for seismic exploration increasing, the imaging technology in the industry is increasingly required. Among a plurality of offset imaging technologies, the reverse time offset technology based on the two-way wave equation has extremely high imaging precision, can describe the spatial position and the geometric structure of an underground reflection interface of any ray path, and can provide reliable data for constructing fine interpretation and well placement. However, the conventional reverse time shift method has inherent disadvantages of strong low frequency interference, uneven illumination, poor amplitude retention, and the like. The least square reverse time migration method is a wave equation inversion method based on reverse time migration and taking a reflection coefficient as a parameter, can improve various defects and deficiencies in reverse time migration, and effectively improves the precision of seismic wave migration imaging.
However, most of the traditional least square reverse time migration imaging methods adopt a finite difference method of a regular grid to perform seismic wave numerical simulation, and grid units of the method are usually rectangular, so that the positions of a curved interface or an irregular model boundary are difficult to accurately describe, and local refinement in a key area is difficult to realize. This results in scattering noise at irregular boundaries when numerically calculating the subsurface wavefield, which severely affects the accuracy of the wavefield calculation. Although the methods have certain geometric flexibility and can solve the problem of adaptability of a model interface or a boundary, the methods usually need a complex mesh subdivision or mesh mapping process, so that the numerical simulation cost is increased. In addition, the finite element and spectral element methods can also solve the problems to a certain extent, but the requirements for the calculated amount and the calculated memory are far higher than those of the finite difference method, and the method is poor in applicability to the least square reverse time migration method with large calculated amount. The grid-free finite difference method is used as a novel numerical calculation method, can effectively solve the problems of the calculation method, and is primarily applied to the field of seismic exploration. For the least square reverse time migration imaging method, the meshless finite difference method can be effectively applied.
At present, domestic exploration focuses on turning from eastern plain areas to western plateau and mountain areas, and western exploration areas mostly face complex earth surface and underground structures. In order to meet the increasingly improved exploration requirements and solve the problems that the accurate description of irregular earth surfaces and underground interfaces is difficult, and the calculation amount and the memory requirement are overlarge in the conventional least square reverse time migration method, an efficient imaging method capable of accurately describing complex earth surfaces and underground irregular structures is urgently needed, and a high-quality imaging result is provided for geological survey and energy exploration.
Disclosure of Invention
In view of the above, a first object of the present invention is to provide a least square reverse time migration imaging method based on a meshless finite difference method, which achieves accurate description and efficient imaging of complex surface and underground irregular structures by using meshless distribution generated according to a target work area underground model and using migration and anti-migration operators based on the meshless finite difference method.
Based on the same inventive concept, the second purpose of the invention is to provide a least square reverse time migration imaging system based on the meshless finite difference method.
Based on the same inventive concept, a third object of the present invention is to provide a storage medium.
The first purpose of the invention can be realized by adopting the following technical scheme:
a least square reverse time migration imaging method based on a non-grid finite difference method comprises the following steps:
observing the seismic records, and acquiring an underground speed model of the target work area according to the seismic records obtained by observation;
generating a non-grid node distribution suitable for an underground speed model according to the underground speed model of the target work area, and discretizing the underground speed model;
according to the seismic record obtained by observation and the discretized underground velocity model, applying reverse time migration imaging based on a non-grid finite difference method to obtain an initial imaging result;
according to the initial imaging result or the updated imaging result, calculating to obtain a simulated seismic record by applying a forward operator based on a non-grid finite difference method;
calculating a record residual error between the simulated seismic record and the seismic record obtained by observation;
according to the recorded residual error, applying the recorded residual error to an offset operator of a non-grid finite difference method to obtain an updated gradient of an imaging result corresponding to the recorded residual error, and then obtaining an updated imaging result through a linear inversion solver;
judging whether a preset termination condition is met, and if so, outputting a final imaging result; otherwise, continuously calculating and recording residual errors and updating the imaging result, and performing iteration.
Furthermore, in the target work area underground speed model, the discrete degree of the nodes is positively correlated with the size of the speed field.
Further, generating the distribution without network nodes which is suitable for the underground speed model according to the underground speed model of the target work area, comprising the following steps:
determining the size of a calculation domain according to the underground speed model of the target work area, and determining the mapping relation between the radius of non-grid distributed particles and the size of a speed field;
randomly generating node distribution at the bottom of the underground speed model of the target work area, giving out the density of the node distribution according to a preset value, and defining the node positions as potential node positions;
selecting a potential node position with the lowest position as a new effective node position;
determining a circular area by taking the new effective node as the center of a circle and the particle radius at the effective node as the radius of the circle, and deleting all nodes except the effective node in the circular area;
marking a nearest potential node from the left side and the right side of the circle center respectively, determining the direction of a connecting line of the circle center and the two potential nodes, and placing a plurality of new potential nodes on an arc clamped by the two directions at equal intervals;
and continuously selecting a potential node position with the lowest position as a new effective node position, and repeating the steps until the nodes fill the whole calculation domain.
Further, according to the seismic record obtained by observation and the discretized underground velocity model, the reverse time migration imaging based on the non-grid finite difference method is applied to obtain an initial imaging result, and the method comprises the following steps:
constructing a linear equation set by using the radial basis function, and solving the constructed linear equation set to obtain a grid-free difference coefficient;
constructing a wave equation propagation operator according to the grid-free difference coefficient;
and acquiring the initial imaging result by applying reverse time migration imaging based on a non-grid finite difference method according to a wave equation propagation operator.
Further, a linear equation set constructed by using the radial basis function has a specific form as follows:
wherein, phi (| | X-X) i I |) represents the radial basis function, only in relation to the coordinate position, subscript i =0,1,2 \8230nrepresents the ith node in the difference template, where n represents the number of nodes in the difference template, X represents the space coordinate without grid nodes, | | | · | represents the two-norm,
represents the Laplace operator, c i The non-grid difference coefficient to be solved.
Furthermore, an additional basis function is added in a linear equation set constructed by utilizing the radial basis function, so that static errors are eliminated, and the convergence speed of the errors reaches the highest order of the additionally added polynomial.
Further, the additional basis function added in the linear equation set constructed by using the radial basis function is a Taylor monomial, and the specific form of the obtained linear equation set is as follows:
wherein, c n+1 、c n+2 And c n+3 For auxiliary coefficients, A is a matrix of radial basis functions, c is a matrix of difference coefficients, Δ x i Is X i Node and X 0 Difference in horizontal coordinate of node, Δ z i Is X i Node and X 0 The difference in the vertical-direction coordinates of the nodes,
represents X-X 0 Radial basis function of time.
Further, according to the grid-free difference coefficient, a wave equation propagation operator is constructed, and the method comprises the following steps:
calculating the Laplace operator
And solving a spatial derivative term in the wave equation according to the corresponding difference coefficient, wherein the specific form is as follows:
where v is velocity, p is the seismic wavefield, t is time, c i Is a difference coefficient, p i The wave field value at the ith node in the differential template;
estimating a time derivative term in the wave equation by adopting a second-order central difference format, wherein the specific form is as follows:
where p is the seismic wavefield and p is 0 For the background wavefield, t is time, superscripts-1, 0, and 1 represent the previous, current, and next time instants, respectively, and Δ t is the time step.
The second purpose of the invention can be realized by adopting the following technical scheme:
a least square reverse time migration imaging system based on a meshless finite difference method comprises the following steps:
the velocity model unit is used for observing seismic data and generating an underground velocity model of the target work area according to the observed seismic data;
the non-grid node generation unit is used for generating non-grid node distribution which is suitable for the target work area underground speed model according to the target work area underground speed model and discretizing the underground speed model;
the initial imaging unit is used for applying reverse time migration imaging based on a non-grid finite difference method according to the seismic record obtained by observation and the discretized underground velocity model to obtain an initial imaging result;
a least squares offset imaging unit for imaging using a least squares offset imaging principle, comprising:
according to the initial imaging result or the updated imaging result, calculating to obtain a simulated seismic record by applying a forward operator based on a non-grid finite difference method;
calculating a record residual error between the simulated seismic record and the seismic record obtained by observation;
according to the recorded residual error, applying the residual error to an offset operator of a non-grid finite difference method to obtain an updated gradient of an imaging result, and obtaining an updated imaging result through a linear inversion solver;
judging whether a preset termination condition is met, and if so, outputting a final imaging result; otherwise, continuously calculating and recording residual errors and updating the imaging result, and performing iteration.
The third purpose of the invention can be realized by adopting the following technical scheme:
a storage medium stores a program that, when executed by a processor, implements the above-described least-squares reverse time migration imaging method based on the meshless finite difference method.
Compared with the prior art, the invention has the following beneficial effects:
(1) The grid-free node generation algorithm in the least square reverse time migration imaging method based on the grid-free finite difference method can generate a curved interface and an irregular boundary which are suitable for any model, the node distribution density can be based on the grid-free node distribution preset by the model speed, the generation process is simple and efficient, the algorithm can be guaranteed to have extremely high geometric flexibility without spending high calculation cost, and the demand of the algorithm on a memory can be effectively reduced.
(2) The method for solving the grid-free finite difference coefficient and constructing the wave equation operator ensures the accuracy of wave field calculation under the condition of grid-free node distribution, and meanwhile, because the wave field simulation in the method is not influenced by scattering noise introduced by 'step-shaped' approximation at an irregular boundary, the method provides convenient conditions for the implementation of a high-accuracy least square reverse time migration imaging algorithm and is beneficial to accelerating the convergence efficiency of the imaging algorithm.
(3) Generally speaking, the method provided by the invention can finely depict the underground complex geological structure under any complex surface condition, and compared with the traditional method, the method improves the imaging precision while effectively reducing the algorithm calculation and memory requirements, and can provide more accurate imaging results for seismic exploration.
Drawings
Fig. 1 is a schematic flow chart of a least square reverse time migration imaging method based on a meshless finite difference method according to embodiment 1 of the present invention.
Fig. 2 is a schematic diagram illustrating comparison between regular grid distribution and non-grid distribution provided in embodiment 1 of the present invention.
Fig. 3 is a schematic diagram of a non-grid node distribution fast generation algorithm provided in embodiment 1 of the present invention, where (a) is a schematic diagram of step S220, (b) and (c) are schematic diagrams of step S240, and (d) is a schematic diagram of step S250.
FIG. 4 is a schematic representation of a subsurface velocity model of a target zone having three sets of formations according to example 1 of the present invention.
Fig. 5 is a schematic diagram of the number of nodes required by different node discrete modes when performing offset imaging on the three-layer velocity model in embodiment 1 of the present invention.
Fig. 6 is a schematic diagram of imaging results obtained by performing meshless finite difference least square reverse time migration based on the three-layer velocity model in embodiment 1 of the present invention.
Fig. 7 is a schematic diagram of imaging results obtained by performing conventional finite difference least square reverse time migration based on a regular grid on the three-layer velocity model in embodiment 1 of the present invention.
FIG. 8 is a schematic representation of a subsurface velocity model of a target work area with a complex surface in example 1 of the present invention.
Fig. 9 is a schematic diagram of imaging results obtained by performing a meshless finite difference conventional reverse time migration-based acquisition on the complex earth surface velocity model in embodiment 1 of the present invention.
Fig. 10 is a schematic diagram of imaging results obtained by performing a meshless finite difference least squares reverse time migration based on the complex earth surface velocity model in embodiment 1 of the present invention.
Fig. 11 is a schematic diagram of a least-squares reverse time shift imaging system based on the meshless finite difference method in embodiment 2 of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer and more complete, the technical solutions in the embodiments of the present invention will be described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some embodiments of the present invention, but not all embodiments, and all other embodiments obtained by a person of ordinary skill in the art without creative efforts based on the embodiments of the present invention belong to the protection scope of the present invention.
Example 1:
as shown in fig. 1, the present embodiment provides a least square reverse time migration imaging method based on a meshless finite difference method, including the following steps:
s100, observing seismic records, and acquiring an underground velocity model of a target work area according to the seismic records obtained by observation, wherein the method comprises the following steps:
and S110, observing the seismic records. In this embodiment, the observation seismic records are active source seismic data received by the high-density geophone array, and are triggered by an artificial explosion source (explosive is used in an onshore work area, and an air gun is used in an offshore work area). In order to improve the seismic imaging quality and the record reconstruction effect, the observation seismic data can be subjected to operations such as denoising (removing random noise, surface wave noise, radio interference, adjacent shot interference, linear noise and the like), cutting (cutting refracted wave components in the seismic record), deconvolution and the like.
And S120, acquiring an underground velocity model of the target work area according to the observed seismic records. In the embodiment, according to the seismic records obtained by observation, the underground velocity model with more accurate target work area is obtained by means of tomography or full waveform inversion constant velocity modeling.
S200, as shown in figure 3, generating non-grid node distribution suitable for the underground speed model according to the target work area underground speed model, and discretizing the underground speed model.
The generation of the non-grid node distribution in the step is to disperse the underground speed model, and after the non-grid node distribution is generated, the underground wave field is subjected to discrete numerical solution according to the nodes. The method comprises the following steps:
s210, determining the size of a calculation domain according to the underground speed model of the target work area, and determining the mapping relation between the radius of the non-grid distributed particles and the size of a speed field; in this embodiment, the radius of the non-grid-distributed particles is positively correlated with the size of the velocity field, i.e., the larger the velocity is, the larger the corresponding particle radius is;
s220, as shown in a subgraph (a) of FIG. 3, randomly generating node distribution at the bottom of the underground speed model of the target work area, wherein the density of the node distribution is given according to a preset value, and defining the node positions as potential node positions (PDP);
s230, selecting a potential node position with the lowest position as a new effective node position;
s240, as shown in sub-graphs (b) and (c) of fig. 3, determining a circular region by using the new effective node as a circle center and the particle radius at the effective node as the radius of the circle, and deleting all nodes except the effective node in the circular region;
s250, as shown in a subgraph (d) of FIG. 3, marking a nearest potential node from the left side and the right side of the circle center respectively, determining the direction of a connecting line of the circle center and the two potential nodes, and placing 5 new potential nodes on an arc clamped by the two directions at equal intervals;
s260, continuously selecting a potential node position with the lowest position as a new effective node position, and repeating the steps S240-S260 until the node is filled in the whole calculation domain.
S300, according to the seismic record obtained by observation and the discretized underground velocity model, applying reverse time migration imaging based on a non-grid finite difference method to obtain an initial imaging result, and comprising the following steps of:
s310, constructing a linear equation set by using the radial basis function, and solving the constructed linear equation set to obtain a grid-free difference coefficient.
In this embodiment, a linear equation set constructed by using the radial basis function has a specific form as shown in the following formula:
the above system of linear equations can be abbreviated Ac = L Φ. Wherein phi (| | X-X) i I |) represents a radial basis function, which is a function only related to coordinate positions, subscript i =0,1,2 \8230nrepresents the ith node in the difference template, wherein n represents the number of nodes in the difference template, X represents the space coordinate of the grid-free node generated in step S200, | | | | represents a two-norm,
represents the Laplace operator, c i The non-grid difference coefficient to be solved.
An additional basis function (typically a polynomial) may be added to the linear system of equations constructed using the radial basis functions described above to eliminate static errors and to speed the convergence of the errors to the highest order of the additional polynomial added. In this embodiment, a Taylor monomial is added to the linear equation set to obtain a linear equation set as shown in the following formula:
wherein, c n+1 、c n+2 And c n+3 For auxiliary coefficients, A is a matrix of radial basis functions, c is a matrix of difference coefficients, Δ x i Is X i Node and X 0 Difference in horizontal coordinate of node, Δ z i Is X i Node and X 0 The difference in the vertical-direction coordinates of the nodes,
represents X-X 0 Radial basis function of time.
S320, constructing a wave equation propagation operator according to the grid-free difference coefficient, and comprising the following steps:
s321, obtaining Laplace operator
And solving a spatial derivative term in the wave equation according to the corresponding difference coefficient, wherein the specific form is shown as the following formula:
where v is velocity, p is the seismic wavefield, t is time, c i Is a difference coefficient, p i Is the wave field value at the ith node.
S322, estimating a time derivative term in the wave equation by adopting a second-order central difference format, wherein the specific form is shown as the following formula:
where p is the seismic wavefield, t is time, superscripts-1, 0 and 1 represent the previous, current and next moments, respectively, and p 0 For the background wavefield, Δ t is the time step.
S330, acquiring the initial imaging result by applying reverse time migration imaging based on a non-grid finite difference method according to a wave equation propagation operator, and the method comprises the following steps:
s331, inputting the seismic records obtained by observation through the wave equation propagation operator, and calculating a seismic source wave field and a detection wave field, wherein the specific form is shown as the following formula:
wherein p is s And p r Respectively seismic and wave-detection fields, x s And x r The spatial positions of the seismic source and the demodulator probe, respectively, S is a seismic source function, d obs To observe seismic records.
S332, applying imaging conditions to the seismic source and the detection wave field, wherein in the embodiment, the applied imaging conditions are cross-correlation imaging conditions, and the specific form is shown as the following formula:
I(x)＝∫∫p s (x，x s ，t)p r (x，x r ，t)dtdx s
wherein I represents the imaging result.
S400, according to the initial imaging result or the updated imaging result, calculating to obtain a simulated seismic record by applying a forward operator based on a non-grid finite difference method, wherein the specific form is shown as the following formula:
wherein p is 0 And δ p are the background wavefield and the disturbance wavefield, respectively, and d is the simulated seismic record.
And S500, calculating a recording residual error between the simulated seismic record and the seismic record obtained by observation, wherein in the embodiment, the simulated seismic record obtained in the step S400 is subtracted from the seismic record obtained by observation in the step S110 to obtain the recording residual error.
S600, according to the recorded residual error, applying the recorded residual error to an offset operator of a non-grid finite difference method to obtain an updated gradient of an imaging result corresponding to the recorded residual error, and obtaining an updated imaging result through a linear inversion solver, wherein the method comprises the following steps:
s610, inputting a recorded residual error, and calculating an imaging result by using an offset operator based on a non-grid finite difference method to update a gradient, wherein the specific form is shown as the following formula:
wherein g is the imaging result update gradient and λ is the background wavefield p 0 Of the adjoint wave field, v 0 Is the background velocity field.
And S620, acquiring an updated imaging result through an optimization method, such as a steepest descent method, a conjugate gradient method and the like.
S700, judging whether a preset termination condition is met, and if so, outputting a final imaging result; otherwise, continuously calculating and recording residual errors and updating the imaging result, and performing iteration.
In this embodiment, the method for performing iteration is: the new imaging result acquired in step S620 is input as the imaging result of step S400, and steps S400 to S700 are executed again.
In this embodiment, the preset termination condition is: satisfying any one of the preset conditions, including:
a first preset condition, wherein a target function related to the residual error is smaller than a set threshold value;
and under a second preset condition, the iteration times of the algorithm are greater than a set threshold value.
Fig. 2 is a schematic diagram comparing regular grid distribution and non-grid distribution, and it can be seen that for an irregular interface (curved solid line) in a calculation domain, a "stair-like" approximation (black dotted line) occurs when the regular grid distribution is dispersed, and that the node distribution can be well attached to the interface by the non-grid distribution dispersion, so that scattering noise caused when the "stair-like" approximation is numerically calculated for an underground wave field can be effectively avoided. FIG. 3 is a schematic diagram of a mesh-free node distribution fast generation algorithm, according to which an underground velocity model can be discretized quickly by mesh-free nodes.
Fig. 4 is a target work area underground velocity model with three sets of strata adopted in this embodiment, the size of the model is 3km × 2km, fig. 5 shows the number of nodes required for respectively performing regular grid discretization and non-grid discretization on the three-layer velocity model, and it can be seen that the velocity model can be discretized only by the number of nodes of 2/3 of the regular grid discretization without grid, which means that the calculation and memory requirements required by the algorithm are correspondingly reduced when the imaging algorithm is calculated.
Fig. 6 and 7 are imaging results obtained by using the mesh-free finite difference-based least-squares reverse time migration imaging method and the conventional regular-mesh finite difference-based least-squares reverse time migration imaging method in the present embodiment, respectively. It can be seen that both can describe the subsurface structure and provide amplitude information similar to the true reflectivity model. However, due to the stepped approximation of the regular grid, the in-phase axis continuity in the imaging results of fig. 7 is poor, which may be more severe and even affect algorithm convergence when imaging more complex subsurface formations. While the imaging results of fig. 5 may describe the morphology of the subsurface formations almost perfectly. Through comparison of the imaging results of fig. 6 and 7, it can be found that the least square reverse time migration imaging method based on the meshless finite difference in the embodiment can provide a more accurate underground imaging result on the premise of effectively reducing algorithm calculation and memory requirements.
Fig. 8 is a model of the subsurface velocity of the target site with a complex surface, which is 4.16km × 2.49km, as used in this example. Fig. 9 and 10 are imaging results obtained by using a conventional reverse time migration imaging method and a least square reverse time migration imaging method based on meshless finite difference in the embodiment of the present invention, respectively. It can be seen that the imaging precision at the earth surface is high in the imaging result, and compared with the imaging result in fig. 9, the imaging result in fig. 10 has obviously higher resolution, and can provide a more reliable reflectivity model for the construction and lithology interpretation. The adaptability of the grid-free finite difference-based least square reverse time migration imaging method to the complex surface condition is verified, and the capability of providing high-precision imaging results for seismic exploration under the complex geological condition is shown.
Therefore, the non-grid node generation algorithm in the least square reverse time migration imaging method based on the non-grid finite difference method provided by the embodiment can generate the non-grid node distribution which is suitable for the curved interface and the irregular boundary of any model and the node distribution density of which can be preset based on the model speed, the generation process is simple and efficient, the algorithm can be ensured to have extremely high geometric flexibility without spending higher calculation cost, and the demand of the algorithm on the memory can be effectively reduced; meanwhile, the method for solving the grid-free finite difference coefficient and constructing the wave equation operator adopted by the embodiment ensures the accuracy of wave field calculation under the grid-free node distribution, and meanwhile, because the wave field simulation in the method is not influenced by scattering noise introduced by the step-like approximation at an irregular boundary, convenience is provided for the implementation of a high-accuracy least square reverse time migration imaging algorithm, and the convergence efficiency of the imaging algorithm is favorably accelerated; generally speaking, the method provided by the embodiment can finely depict the underground complex geological structure under any complex surface condition, compared with the traditional method, the method effectively reduces algorithm calculation and memory requirements, improves imaging precision and can provide a more accurate imaging result for seismic exploration.
Example 2:
as shown in fig. 11, the present embodiment provides a least-squares reverse time migration imaging system based on the meshless finite difference method, including:
the velocity model unit 1101 is used for observing seismic data and generating an underground velocity model of the target work area according to the observed seismic data;
a non-grid node generation unit 1102, which generates non-grid node distribution adapted to an underground speed model according to the target work area underground speed model, and discretizes the underground speed model;
the initial imaging unit 1103 is used for applying reverse time migration imaging based on a non-grid finite difference method according to the observed seismic record and the discretized underground velocity model to obtain an initial imaging result;
a least squares offset imaging unit 1104 for imaging using a least squares offset imaging principle, comprising:
according to the imaging result, calculating to obtain a simulated seismic record by applying a forward operator based on a non-grid finite difference method;
calculating a recording residual error between the simulated seismic record and the seismic record obtained by observation;
according to the residual error, applying the residual error to an offset operator of a non-grid finite difference method to obtain an updated gradient of an imaging result, and obtaining an updated imaging result through a linear inversion solver;
judging whether a preset termination condition is met, and if so, outputting an imaging result; otherwise, the residual error and the imaging result are continuously calculated, and iteration is carried out.
Example 3:
the present embodiment provides a storage medium, which is a computer-readable storage medium, and stores a computer program, and when the computer program is executed by a processor, the method for implementing the least square reverse time migration imaging method based on the meshless finite difference method of embodiment 1 is specifically as follows:
observing the seismic records, and acquiring an underground velocity model of the target work area according to the seismic records obtained by observation;
generating a non-grid node distribution suitable for an underground speed model according to the underground speed model of the target work area, and discretizing the underground speed model;
according to the seismic record obtained by observation and the discretized underground velocity model, applying reverse time migration imaging based on a non-grid finite difference method to obtain an initial imaging result;
calculating to obtain a simulated seismic record by applying a forward operator based on a non-grid finite difference method according to the initial imaging result or the updated imaging result;
calculating a record residual error between the simulated seismic record and the seismic record obtained by observation;
according to the recorded residual error, applying the recorded residual error to an offset operator of a non-grid finite difference method to obtain an updated gradient of an imaging result corresponding to the recorded residual error, and then obtaining an updated imaging result through a linear inversion solver;
judging whether a preset termination condition is met, and if so, outputting a final imaging result; otherwise, continuously calculating and recording residual errors and updating imaging results, and performing iteration.
It should be noted that the computer readable storage medium of the present embodiment may be a computer readable signal medium or a computer readable storage medium or any combination of the two. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the foregoing. More specific examples of the computer readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.
In the present embodiment, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. In this embodiment, however, a computer readable signal medium may include a propagated data signal with a computer readable program embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated data signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may also be any computer readable storage medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. The computer program embodied on the computer readable storage medium may be transmitted using any appropriate medium, including but not limited to: electrical wires, optical cables, RF (radio frequency), etc., or any suitable combination of the foregoing.
The computer-readable storage medium may be written with a computer program for performing the present embodiments in one or more programming languages, including an object oriented programming language such as Java, python, C + +, and conventional procedural programming languages, such as C, or similar programming languages, or combinations thereof. The program may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any type of network, including a Local Area Network (LAN) or a Wide Area Network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet service provider).
It is to be understood that the embodiments described above are only a few embodiments of the present invention, rather than all embodiments, and that the present invention is not limited to the details of the above embodiments, and that any suitable changes or modifications thereof, which may occur to those skilled in the art, are deemed to be within the scope of the present invention.
Claims (10)
1. A least square reverse time migration imaging method based on a meshless finite difference method is characterized by comprising the following steps:
observing the seismic records, and acquiring an underground velocity model of the target work area according to the seismic records obtained by observation;
generating non-grid node distribution suitable for an underground speed model according to the underground speed model of the target work area, and discretizing the underground speed model;
according to the seismic record obtained by observation and the discretized underground velocity model, applying reverse time migration imaging based on a non-grid finite difference method to obtain an initial imaging result;
calculating to obtain a simulated seismic record by applying a forward operator based on a non-grid finite difference method according to the initial imaging result or the updated imaging result;
calculating a recording residual error between the simulated seismic record and the seismic record obtained by observation;
according to the recorded residual error, applying the recorded residual error to an offset operator of a non-grid finite difference method to obtain an updated gradient of an imaging result corresponding to the recorded residual error, and obtaining an updated imaging result through a linear inversion solver;
judging whether a preset termination condition is met, and if so, outputting a final imaging result; otherwise, continuously calculating and recording residual errors and updating the imaging result, and performing iteration.
2. The grid-free finite difference method-based least square reverse time migration imaging method according to claim 1, wherein in the target work area underground velocity model, the discrete degree of the nodes is positively correlated with the size of the velocity field.
3. The least square reverse time migration imaging method based on the meshless finite difference method as claimed in claim 1, wherein a meshless node distribution adapted to the underground velocity model is generated according to the target work area underground velocity model, comprising the steps of:
determining the size of a calculation domain according to the underground speed model of the target work area, and determining the mapping relation between the radius of the non-grid distributed particles and the size of a speed field;
randomly generating node distribution at the bottom of the underground speed model of the target work area, giving out the density of the node distribution according to a preset value, and defining the positions of the nodes as potential node positions;
selecting a potential node position with the lowest position as a new effective node position;
determining a circular area by taking the new effective node as the center of a circle and the particle radius at the effective node as the radius of the circle, and deleting all nodes except the effective node in the circular area;
marking a nearest potential node from the left side and the right side of the circle center respectively, determining the direction of a connecting line of the circle center and the two potential nodes, and placing a plurality of new potential nodes on an arc clamped by the two directions at equal intervals;
and continuously selecting a potential node position with the lowest position as a new effective node position, and repeating the steps until the nodes fill the whole calculation domain.
4. The method of claim 1, wherein a reverse time migration imaging based on the meshless finite difference method is applied according to the observed seismic record and the discretized subsurface velocity model to obtain an initial imaging result, comprising the steps of:
constructing a linear equation set by using the radial basis function, and solving the constructed linear equation set to obtain a non-grid differential coefficient;
constructing a wave equation propagation operator according to the non-grid difference coefficient;
and acquiring the initial imaging result by applying reverse time migration imaging based on a non-grid finite difference method according to a wave equation propagation operator.
5. The grid-free finite difference method-based least square reverse time migration imaging method according to claim 4, wherein the linear equation set constructed by using the radial basis function is in a specific form:
wherein, phi (| | X-X) i I |) represents the radial basis function, only in relation to the coordinate position, subscript i =0,1,2 \8230nrepresents the ith node in the difference template, where n represents the number of nodes in the difference template, X represents the space coordinate without grid nodes, | | | · | represents the two-norm,
represents the Laplace operator, c i The non-grid difference coefficient to be solved.
6. The method of claim 5, wherein an additional basis function is added to the linear system of equations constructed using radial basis functions to eliminate static errors and to increase the convergence rate of errors to the highest order of the additional polynomial.
7. The method of claim 6, wherein the additional basis functions added to the linear system of equations constructed using radial basis functions are Taylor monomials, and the linear system of equations obtained by the method has the specific form:
wherein, c n+1 、c n+2 And c n+3 For auxiliary coefficients, A is a matrix of radial basis functions, c is a matrix of difference coefficients, Δ x i Is X i Node and X 0 Difference in horizontal coordinate of node, Δ z i Is X i Node and X 0 Vertical coordinate difference of node, phi (| X-X) 0 ||)|x 0 Represents X-X 0 Radial basis function of time.
8. The grid-free finite difference method-based least square reverse time migration imaging method according to claim 4, wherein a wave equation propagation operator is constructed according to the grid-free difference coefficient, comprising the following steps:
calculating laplacian
And solving a spatial derivative term in the wave equation according to the corresponding difference coefficient, wherein the specific form is as follows:
where v is velocity, p is the seismic wavefield, t is time, c i Is a difference coefficient, p i The wave field value at the ith node in the differential template;
estimating a time derivative term in the wave equation by adopting a second-order central difference format, wherein the specific form is as follows:
where p is the seismic wavefield and p is 0 For the background wavefield, t is time, and the superscripts-1, 0, and 1 represent the previous time, the current time, and the next time, respectively.
9. A least square reverse time migration imaging system based on a non-grid finite difference method is characterized by comprising the following steps:
the velocity model unit is used for observing seismic data and generating an underground velocity model of the target work area according to the observed seismic data;
the non-grid node generation unit is used for generating non-grid node distribution which is suitable for the target work area underground speed model according to the target work area underground speed model and discretizing the underground speed model;
the initial imaging unit is used for applying reverse time migration imaging based on a non-grid finite difference method according to the seismic record obtained by observation and the discretized underground velocity model to obtain an initial imaging result;
a least squares offset imaging unit for imaging using the least squares offset imaging principle, comprising:
calculating to obtain a simulated seismic record by applying a forward operator based on a non-grid finite difference method according to the initial imaging result or the updated imaging result;
calculating a recording residual error between the simulated seismic record and the seismic record obtained by observation;
according to the recorded residual error, applying the recorded residual error to an offset operator of a non-grid finite difference method to obtain an updated gradient of an imaging result corresponding to the recorded residual error, and obtaining an updated imaging result through a linear inversion solver;
judging whether a preset termination condition is met, and if so, outputting a final imaging result; otherwise, continuously calculating and recording residual errors and updating the imaging result, and performing iteration.
10. A storage medium storing a program which, when executed by a processor, realizes the least-squares reverse-time migration imaging method based on the meshless finite difference method according to any one of claims 1 to 8.
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