Seismic inversion method and system based on dynamic change of lagrangian operator

Abstract

The application provides a seismic inversion method and system based on dynamic change of Lagrange operators, and the method comprises the following steps: obtaining a column vector composed of 2n+1 Lagrange operators according to a preset prior velocity model and an initial velocity model, wherein n is a positive integer; substituting the column vector into a preset inversion iteration formula to obtain a corresponding number of inversion velocity models, and obtaining a target function according to the inversion velocity models; determining an inversion velocity model with the minimum function value of the target function as an iteration model, and repeatedly determining the iteration model until the minimum value of the target function reaches a preset value of the target function. The application can facilitate rapid reduction of the target function by using dynamic Lagrange operators in the inversion process, and ensure the speed and accuracy of the inversion result.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of geophysical exploration technology, and in particular to a seismic inversion method based on dynamic changes of Lagrange operators and a system thereof. BACKGROUND

[0002] At present, in the field of seismic inversion technology, the Occam inversion proposed by Constable and DeGroot-Hedlin in 1990 is usually used, the basic idea of which is to obtain the smoothest model by introducing an adaptive regularization factor and model roughness under the premise of data fitting. The basic idea is to define the objective function of inversion as being composed of a data item and a model item, and add a Lagrange operator λ to the model item, thereby obtaining the objective function.

[0003] After obtaining the iteration formula according to the objective function, the inversion process is divided into two stages. The first stage is to calculate the model update under a series of values, and to compare the size of the data fitting difference and to make the data fitting difference reach the expected value (for example, 1.0); once the expected fitting difference is reached, the smoothest model is found by changing different λ values, which is the second stage. Therefore, the given of the Lagrange operator λ has a significant impact on seismic inversion, and at present, it is usually given according to experience, without a clear and scientific way of giving. SUMMARY

[0004] An object of the present application is to provide a seismic inversion method based on dynamic changes of Lagrange operators, which is beneficial to the rapid reduction of the objective function by using a dynamic Lagrange operator in the inversion process, and ensures the speed and accuracy of the inversion result. Another object of the present application is to provide a seismic inversion system based on dynamic changes of Lagrange operators. Still another object of the present application is to provide a computer device. Yet another object of the present application is to provide a readable medium.

[0005] In order to achieve the above objects, the present application discloses a seismic inversion method based on dynamic changes of Lagrange operators, comprising:

[0006] obtaining a column vector composed of 2n+1 Lagrange operators according to a preset prior velocity model and an initial velocity model, n being a positive integer;

[0007] substituting the column vector into a preset inversion iteration formula to obtain a corresponding number of inversion velocity models, and obtaining an objective function according to the inversion velocity models;

[0008] determining the inversion velocity model with the minimum function value of the objective function as an iteration model, and repeating the determination of the iteration model until the minimum value of the objective function reaches a preset value of the objective function.

[0009] Preferably, the column vector composed of 2n+1 Lagrange multipliers obtained according to the preset prior velocity model and the initial velocity model specifically comprises:

[0010] The forward response is calculated according to the preset prior velocity model and the initial velocity model, and the data covariance matrix and the model covariance matrix are calculated;

[0011] The target function data item and the model item are obtained according to the forward response, the data covariance matrix and the model covariance matrix;

[0012] The reference coefficient is obtained according to the target function data item and the model item, and the column vector composed of 2n+1 Lagrange multipliers is calculated according to the reference coefficient.

[0013] Preferably, the data covariance matrix is a diagonal matrix of N*N dimensions, and the model covariance matrix is a full rank matrix of M*M dimensions, wherein M is the total number of element divisions of the underground medium, and N is the total number of data.

[0014] Preferably, the calculation of the model covariance matrix specifically comprises:

[0015] The model covariance matrix is calculated by the finite difference algorithm.

[0016] Preferably, the finite difference algorithm is a central difference algorithm.

[0017] Preferably, n is a positive integer greater than 5.

[0018] Preferably, the column vector is substituted into the preset inversion iteration formula to obtain a corresponding number of inversion velocity models, specifically comprising:

[0019] The column vector is substituted into the preset inversion iteration formula;

[0020] The inversion iteration formula into which the column vector is substituted is solved by the conjugate gradient method to obtain a corresponding number of inversion velocity models.

[0021] Preferably, the preset value of the target function is 1.

[0022] The application also discloses a seismic inversion system based on dynamic change of Lagrange multipliers, comprising:

[0023] A data processing module is configured to obtain a column vector composed of 2n+1 Lagrange multipliers according to a preset prior velocity model and an initial velocity model, wherein n is a positive integer;

[0024] A target function determination module is configured to substitute the column vector into a preset inversion iteration formula to obtain a corresponding number of inversion velocity models, and obtain a target function according to the inversion velocity models.

[0025] An iterative solution module is configured to determine an inversion velocity model with a minimum function value of the objective function as an iterative model, and repeatedly determine the iterative model until the minimum value of the objective function reaches a preset value of the objective function.

[0026] The application further discloses a computer device, which comprises a memory, a processor, and a computer program stored in the memory and executable on the processor,

[0027] The processor implements the method described above when executing the program.

[0028] The application further discloses a computer readable medium, which stores a computer program,

[0029] The program is executed by the processor to implement the method described above.

[0030] The application can take into account the weights of the data item and the model item, is beneficial to the rapid reduction of the objective function, guarantees the speed and accuracy of the inversion result, and changes the traditional Occam inversion which needs to be performed in two stages, can effectively reduce the data item and the model item at each iteration, does not need to search for a model for reducing the data item first and then further reduce the model item, and greatly improves the inversion efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0031] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description only show some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained from these drawings without creative labor.

[0032] Figure 1 A flow chart of one specific embodiment of the seismic inversion method based on dynamic changes of Lagrange multipliers of the present application is shown;

[0033] Figure 2 A flow chart of one specific embodiment S100 of the seismic inversion method based on dynamic changes of Lagrange multipliers of the present application is shown;

[0034] Figure 3 A flow chart of one specific embodiment S300 of the seismic inversion method based on dynamic changes of Lagrange multipliers of the present application is shown;

[0035] Figure 4A flow chart showing a specific example of the seismic inversion method based on dynamic change of Lagrange multiplier according to the present application;

[0036] Figure 5 A curve graph showing the change of data items in a specific example of the seismic inversion method based on dynamic change of Lagrange multiplier according to the present application;

[0037] Figure 6 A curve graph showing the change of model items in a specific example of the seismic inversion method based on dynamic change of Lagrange multiplier according to the present application;

[0038] Figure 7 A comparison graph of the objective function in a specific example of the seismic inversion method based on dynamic change of Lagrange multiplier according to the present application and the objective function in the prior art;

[0039] Figure 8 A structure diagram showing a specific embodiment of the seismic inversion system based on dynamic change of Lagrange multiplier according to the present application;

[0040] Figure 9 A structure diagram showing a computer device suitable for implementing the embodiments of the present application. DETAILED DESCRIPTION

[0041] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application.

[0042] In 1990, Occam inversion was proposed by Constable and DeGroot-Hedlin, the basic idea of which is to introduce an adaptive regularization factor and model roughness to obtain the smoothest model under the premise of data fitting. The basic idea is to define the objective function of inversion as composed of data items and model items, and add a Lagrange multiplier λ to the model items. Let the total number of sub-units of the underground medium be M, and the total number of data be N, the objective function is defined as follows:

[0043]

[0044] Where d is the observation data vector, F[m] is the model forward response, C d is the data covariance matrix, λ is the Lagrange multiplier, m is the model vector (which can be a velocity model, a resistivity model, a density model, etc.), m0 is the prior model vector, C m is the model covariance matrix, For the model roughness, the solution of the smoothest model is to make this item as small as possible.

[0045] For the model response of the k+1th iteration, Taylor expansion is made and the high order term is ignored, and the following equation is obtained:

[0046] F[m k+1 ]≈F[m k +Δm]=F[m k ]+J k (m k+1 -m k ) (2)

[0047] Where k represents the iteration number, J k is the Jacobian matrix of the kth iteration, formula (2) is brought into the objective function, and the partial derivative of the model vector is calculated and set to zero, and the following equation is obtained:

[0048]

[0049] The iterative formula of the classic OCCAM can be obtained:

[0050]

[0051] Where X k =d-F[m k ]+J k (m k -m0). It can be seen that when the model change is calculated, a MxM linear equation system is solved, and the right end term is The coefficient matrix is

[0052] After obtaining the iterative formula, the inversion process is divided into two stages. The first stage is to calculate the model update under a series of λ values, and to compare the size of the data fitting difference and to make the data fitting difference reach the expected value (for example, 1.0); once the expected fitting difference is reached, the smoothest model is found by changing different λ values, which is the second stage.

[0053] However, there is no relevant theoretical research on how to give the Lagrange operator λ. Some scholars directly translate λ as a penalty factor, which is to balance the weight of the data item and the model item in the objective function. As can be seen from formula (1), if the value of λ is given larger, the weight of the model item in the objective function will be larger, which may cause the "contribution" of the data item to be smaller in the iteration, which may cause the data fitting difference to be larger and larger, leading to the non-convergence of the inversion. On the contrary, if the value of λ is given smaller, the weight of the model item will be smaller, resulting in smaller "contribution" of the model item in the inversion iteration process, which cannot achieve the effect of smoothing the model, and the inversion model is far from the actual situation.

[0054] On the other hand, in the iteration process, the size of the data item and the model item is constantly changing, and the value of lambda must be dynamically adjusted to ensure that the weight of the data item and the model item in the entire objective function is comparable, and more preferably beneficial to the efficiency and accuracy of the inversion algorithm. How to dynamically adjust the value of lambda is currently given according to experience, and there is no explicit formula.

[0055] In addition, the traditional Occam inversion first considers the rapid reduction of the data item, and the second stage can consider the reduction of the model item, which can ensure the smoothness of the final model, but the inversion process is divided into two stages, which often leads to a large number of iterations and low calculation efficiency.

[0056] In order to solve the problems of the prior art, according to one aspect of the present application, the embodiment discloses a seismic inversion method based on dynamic change of Lagrange operator. As shown in the figure, Figure 1 The method comprises the following steps:

[0057] S100: obtaining a column vector composed of 2n+1 Lagrange operators according to a preset prior velocity model m0 and an initial velocity model m1, n is a positive integer.

[0058] S200: substituting the column vector into a preset inversion iteration formula to obtain a corresponding number of inversion velocity models, and obtaining an objective function according to the inversion velocity models.

[0059] S300: determining that the inversion velocity model with the minimum function value of the objective function is an iteration model, and repeatedly determining the iteration model until the minimum value of the objective function reaches a preset value of the objective function.

[0060] The present application can take into account the weight of the data item and the model item by using the reference coefficient to give a plurality of Lagrange operators in each iteration process, and taking the model with the minimum objective function as the inversion result of the iteration, which is beneficial to the rapid reduction of the objective function, ensures the speed and accuracy of the inversion result, and changes the traditional Occam inversion which needs to be divided into two stages. In each iteration, the data item and the model item can be effectively reduced at the same time, and there is no need to search for a model that reduces the data item first and then further reduces the model item, so the efficiency of the inversion is greatly improved.

[0061] In the preferred embodiment, as shown in the figure, Figure 2 The S100 according to the preset prior velocity model and the initial velocity model to obtain the column vector composed of 2n+1 Lagrange operators can specifically comprise:

[0062] S110: Calculate the forward response F[m1] based on the preset prior velocity model m0 and the initial velocity model m1, and calculate the data covariance matrix C. d And the model covariance matrix C m .

[0063] S120: Based on the forward response F[m1] and the data covariance matrix C d And the model covariance matrix C m Obtain the objective function data term W d and model term W m .

[0064] S130: Obtain the reference coefficients ε based on the objective function data terms and model terms, and calculate the column vector λ composed of 2n+1 Lagrange operators based on the reference coefficients.

[0065] Preferably, the data covariance matrix C d The model covariance matrix C is an N×N dimensional diagonal matrix. m Let be an M×M full-rank matrix, where M is the total number of subsurface media subdivision cells and N is the total number of data points. The model covariance matrix C... m The calculation can be performed using a finite difference algorithm, and more preferably, a central difference algorithm. It is understood that, in practical applications, those skilled in the art can also use other feasible methods to obtain the above calculation results, and this invention does not limit such methods.

[0066] Furthermore, based on the forward response F[m1] and the data covariance matrix C... d And the model covariance matrix C m Data items can be determined based on the objective function. and model items The expression is used to calculate the objective function data item W. d and model term W m .

[0067] Then, based on data item W d and model term W m Through the expression of the reference coefficient ε The reference coefficient ε can be calculated, where brackets [] denote rounding. Based on the reference coefficient ε, the column vector λ(2n+1) = 10 composed of 2n+1 Lagrange operators is calculated. ε-n 10 ε-n+1 10 ε-n+2 …10 ε+n , where n is a positive integer greater than 1, preferably a positive integer greater than 5.

[0068] In a preferred embodiment, such asFigure 3 As shown, step S300, which substitutes the column vector into a preset inversion iteration formula to obtain a corresponding number of inversion velocity models, may specifically include:

[0069] S310: Substitute the column vector into the preset inversion iteration formula.

[0070] S320: The corresponding number of inversion velocity models are obtained by solving the inversion iterative formula with column vectors substituted into it using the conjugate gradient method.

[0071] Specifically, the column vector λ(2n+1) obtained above can be substituted into the iterative formula. The iterative formula can be solved using the conjugate gradient method. Calculate the 2n+1 inversion velocity models corresponding to the 2n+1 Lagrange operators λ, and then calculate the corresponding 2n+1 objective functions.

[0072] The invention will be further illustrated below with a specific example. In this example, the number of data points N is 100, the total number of subsurface media subdivision units N is 10000, and n is 5. The data covariance matrix C... d The diagonal elements represent the random error of 100 data points, and the random error is white noise with a mean of 0. C m C is calculated using a finite difference algorithm for the properties between each mesh subdivision. In this embodiment, central difference is used to calculate C. m In each iteration, C d Remains unchanged, but C m As the physical properties change during each iteration, recalculation is required.

[0073] Specifically, such as Figure 4 As shown in the specific example, the seismic inversion method based on the dynamic changes of the Lagrange operator includes the following steps:

[0074] S1: Given a prior velocity model m0 and an initial velocity model m1, calculate the forward response F[m1] of the initial velocity model. Calculate the data covariance matrix C. d And the model covariance matrix C m The data covariance matrix C d The model covariance matrix C is an N×N dimensional diagonal matrix. m It is an M×M dimensional full-rank matrix.

[0075] S2: Calculate the data items of the objective function according to the formula. and model items In this embodiment, W is obtained from the first iteration calculation. d =1579.64, Wm = 17.87;

[0076] S3: Calculate the reference coefficient Wherein the square brackets in the formula represent rounding.

[0077] S4: Calculate the column vector λ (2n+1) = 10 composed of 2n+1 = 11 Lagrange multipliers according to the reference coefficient ε -3 ,10 -2 ,10 -1 …10 7 .

[0078] S5: Bring in the iteration formula The conjugate gradient method is used to solve the iteration formula. 11 inversion velocity models corresponding to 11 Lagrange multipliers λ are calculated, and 11 objective function values corresponding to the 11 Lagrange multipliers λ are calculated.

[0079] S6: Take the inversion model with the minimum objective function value as the inversion velocity model of the first iteration.

[0080] S7: Repeat steps S2-S6 until the minimum value of the n+1 objective functions corresponding to the n+1 inversion velocity models of the kth iteration reaches the preset value of the objective function, and the preset value of the objective function is 1.

[0081] Table 1 is the change process of the Lagrange multiplier in the iteration process in this embodiment. The minimum values of the objective functions corresponding to the first, second, third, fourth, fifth, sixth, seventh and thirteenth iterations are 10 3 ,10 6 ,10 1 ,10 -1 ,10 0 ,10 1 ,10 -1 and 10 -1 , respectively.

[0082] Table 1: Dynamic search table of Lagrange multiplier in iteration process

[0083] K＝1， K＝2 K＝3 K＝4 K＝5 K＝6 K＝7 …… K＝13 10 -3 ]] 10 -4 ]] 10 -5 ]] 10 -5 ]] 10 -5 ]] 10 -5 ]] 10 -5 ]] …… 10 -5 ]] 10 -2 ]] 10 -3 ]] 10 -4 ]] 10 -4 ]] 10 -4 ]] 10 -4 ]] 10 -4 ]] …… 10 -4 ]] 10 -1 ]] 10 -2 ]] 10 -3 ]] 10 -3 ]] 10 -3 ]] 10 -3 ]] 10 -3 ]] …… 10 -3 ]] 10 0 ]] 10 -1 ]] 10 -2 ]] 10 -2 ]] 10 -2 ]] 10 -2 ]] 10 -2 ]] …… 10 -2 ]] 10 1 ]] 10 0 ]] 10 -1 ]] 10 -1 ]] 10 -1 ]] 10 -1 ]] 10 -1 ]] …… 10 -1 ]] 10 2 ]] 10 1 ]] 10 0 ]] 10 0 ]] 10 0 ]] 10 0 ]] 10 0 ]] …… 10 0 ]] 10 3 ]] 10 2 ]] 10 1 ]] 10 1 ]] 10 1 ]] 10 1 ]] 10 1 ]] …… 10 1 ]] 10 4 ]] 10 3 ]] 10 2 ]] 10 2 ]] 10 2 ]] 10 2 ]] 10 2 ]] …… 10 2 ]] 10 5 ]] 10 4 ]] 10 3 ]] 10 3 ]] 10 3 ]] 10 3 ]] 10 3 ]] …… 10 3 ]] 10 6 ]] 10 5 ]] 10 4 ]] 10 4 ]] 10 4 ]] 10 4 ]] 10 4 ]] …… 10 4 ]] 10 7 ]] 10 6 ]] 10 5 ]] 10 5 ]] 10 5 ]] 10 5 ]] 10 5 ]] …… 10 5 ]]

[0084] From the table, we can see that if fixed Lagrange multipliers are selected in each iteration process, the Lagrange multiplier with the fastest objective function descent cannot be searched. Figure 5 and Figure 6For the embodiment, the curve of the data item and the model item with the increase of the iteration number. Since the order of magnitude changes greatly, the logarithm is taken on the vertical axis. As can be seen from the figure, the data item is monotonously decreasing, and the model item experiences a process of first increasing and then decreasing, because the given model is relatively simple at the beginning, and the initial value of the model item is small. In the iterative search process, the model tends to be complex. When the data item decreases to a certain extent, the search direction makes the model tend to be smooth, and thus it begins to decrease. Figure 7 For the comparison figure of the objective function of the present application and the prior art objective function, the Lagrange coefficient in the prior art is 10 3 Remains unchanged, so it can be seen that, from the second iteration, the decreasing trend of the objective function of the prior art is slower than that of the present application, and the present application converges after 13 iterations, reaching the predetermined value, while the prior art experiences 17 iterations, so it can be seen that the present application has good effect in shortening the calculation time.

[0085] The present application can obtain the following technical effects by obtaining the reference coefficient in the inversion iteration process, giving a plurality of Lagrange operators in each iteration process according to the reference coefficient, and bringing it into the iteration formula.

[0086] (1) The present application can consider the weights of the data item and the model item, so that the contribution of the data item and the model item in the objective function develops in the direction most conducive to the rapid reduction of the objective function.

[0087] (2) The present application can not use a series of Lagrange operators in each iteration process, but give a series of coefficients that dynamically change with the iteration number according to the relative size of the data item and the model item each time, so that the objective function can be rapidly reduced in each iteration process, ensuring the speed and accuracy of the inversion result.

[0088] (3) The present application changes the traditional Occam inversion which needs to be divided into two stages, and can effectively reduce the data item and the model item at the same time in each iteration, without first searching for a model that reduces the data item, and then further reducing the model of the model item, greatly improving the efficiency of the inversion.

[0089] Based on the same principle, the present embodiment also discloses a seismic inversion system based on dynamic change of Lagrange operator. As shown in Figure 8 , the system comprises a data processing module 11, an objective function determination module 12 and an iterative solution module 13.

[0090] Among them, the data processing module 11 is used to obtain a column vector composed of 2n+1 Lagrange operators according to a preset prior velocity model and an initial velocity model, and n is a positive integer.

[0091] The objective function determining module 12 is configured to substitute the column vector into a preset inversion iteration formula to obtain a corresponding number of inversion velocity models, and obtain an objective function according to the inversion velocity models.

[0092] The iterative solving module 13 is configured to determine an inversion velocity model with a minimum function value of the objective function as an iteration model, and repeat the determination of the iteration model until the minimum value of the objective function reaches a preset value of the objective function.

[0093] Since the principle of solving problems of the system is similar to the above method, the implementation of the system can refer to the implementation of the method, which will not be repeated here.

[0094] The system, device, module or unit illustrated in the above embodiments can be specifically implemented by a computer chip or entity, or by a product with certain functions. A typical implementation device is a computer device, and specifically, the computer device can be, for example, a personal computer, a laptop computer, a cellular phone, a camera phone, a smart phone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or a combination of any of these devices.

[0095] In a typical example, the computer device specifically includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the above method when executing the program.

[0096] The following refers to Figure 9 which shows a structural schematic diagram of a computer device 600 suitable for implementing the embodiments of the present application.

[0097] As shown in Figure 9 , the computer device 600 includes a central processing unit (CPU) 601, which can perform various appropriate operations and processes according to programs stored in a read-only memory (ROM) 602 or programs loaded from a storage portion 608 to a random access memory (RAM) 603. In the RAM 603, various programs and data required for the operation of the system 600 are also stored. The CPU 601, the ROM 602, and the RAM 603 are connected to each other through a bus 604. An input / output (I / O) interface 605 is also connected to the bus 604.

[0098] The following components are connected to the I / O interface 605: an input part 606 including a keyboard, a mouse, etc.; an output part 607 including a display such as a cathode ray tube (CRT), a liquid crystal display (LCD), etc., and a speaker, etc.; a storage part 608 including a hard disk, etc.; and a communication part 609 including a network interface card such as a LAN card, a modem, etc. The communication part 609 performs communication processing via a network such as the Internet. A drive 610 is also connected to the I / O interface 605 as necessary. A removable medium 611 such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc. is attached to the drive 610 as necessary, so that a computer program read out therefrom is installed in the storage part 608 as necessary.

[0099] In particular, the processes described above with reference to the flowcharts can be implemented as a computer software program according to embodiments of the present application. For example, embodiments of the present application include a computer program product comprising a computer program tangibly embodied on a machine-readable medium, the computer program comprising program code for executing the methods illustrated by the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via the communication part 609, and / or installed from the removable medium 611.

[0100] Computer readable media includes permanent and non-permanent, removable and non-removable media implemented in any method or technology for storage of information. The information can be computer readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read only memory (ROM), electrically erasable programmable read only memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassette, magnetic tape magnetic disk storage or other magnetic storage devices or any other non-transmission medium that can be used to store information accessible to a computing device. According to the definition herein, computer readable media does not include transitory media such as modulated data signals and carriers.

[0101] For the convenience of description, the above apparatus is described in various units by function. Of course, the functions of each unit can be implemented in the same or 2n+1 software and / or hardware when implementing the present application.

[0102] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks or in conjunction with the flowcharts described above. Figure 1 one or more flowcharts and / or blocks in a flowchart block or blocks. Figure 1 one or more flowcharts and / or blocks in a flowchart block or blocks.

[0103] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks or in conjunction with the flowcharts described above. Figure 1 one or more flowcharts and / or blocks in a flowchart block or blocks. Figure 1 one or more flowcharts and / or blocks in a flowchart block or blocks.

[0104] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks or in conjunction with the flowcharts described above. Figure 1 one or more flowcharts and / or blocks in a flowchart block or blocks. Figure 1 one or more flowcharts and / or blocks in a flowchart block or blocks.

[0105] It is further noted that the terms "comprises", "comprising", or any other variations 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 can also include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by "comprises... a" does not, without more constraints, exclude the existence of additional identical elements in the process, method, article, or apparatus that comprises the element.

[0106] Those skilled in the art will appreciate that embodiments of the present application can be readily used as a method, a system or a computer program product. Accordingly, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application can take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage devices, etc.) embodying computer-usable program code embodied thereon.

[0107] The present application can be described in the general context of computer- executable instructions, such as program modules, being executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. The present application can also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules can be located in both local and remote computer storage media including memory storage devices.

[0108] Each of the embodiments described in this specification has been described taking a progressive approach, and parts that are the same or similar between the embodiments can be mutually referred to, and each embodiment mainly describes differences from other embodiments. In particular, for the system embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the part of the description of the method embodiments.

[0109] The embodiments described above are only embodiments of the present application, and are not intended to limit the present application. The present application can have various modifications and changes for those skilled in the art. Any modification, equivalent replacement, improvement, etc. within the spirit and principle of the present application shall be included in the scope of the claims of the present application.

Claims

1. A method of seismic inversion based on dynamic changes in Lagrangian operators, characterized in that, The method comprises the steps of: obtaining a column vector composed of 2n+1 Lagrange multipliers according to a preset prior velocity model and an initial velocity model, n being a positive integer; substituting the column vector into a preset inversion iteration formula to obtain a corresponding number of inversion velocity models, and obtaining a target function according to the inversion velocity models; determining an inversion velocity model with a minimum function value of the target function as an iteration model, and repeatedly determining the iteration model until a minimum value of the target function reaches a preset value of the target function; the step of obtaining the column vector composed of 2n+1 Lagrange multipliers according to the preset prior velocity model and the initial velocity model specifically comprises the steps of: calculating a forward response according to the preset prior velocity model and the initial velocity model, and calculating a data covariance matrix and a model covariance matrix; obtaining a target function data item and a model item according to the forward response, the data covariance matrix and the model covariance matrix; obtaining a reference coefficient according to the target function data item and the model item, and calculating the column vector composed of 2n+1 Lagrange multipliers according to the reference coefficient; The data item is: d is the actual observed data, F[m1] is the forward response of the initial velocity model, C d is the data covariance matrix; The model term is: m is a current model, m0 is a preset prior velocity model, C m is a model covariance matrix; The reference coefficient is: W d is a data item, W m is a model item.

2. The dynamically varying seismic inversion method based on Lagrangian operators of claim 1, wherein, the data covariance matrix is a diagonal matrix of N×N dimensions, and the model covariance matrix is a full-rank matrix of M×M dimensions, wherein M is the total number of element divisions of the underground medium, and N is the total number of data.

3. The Lagrangian operator-based dynamically-varying seismic inversion method of claim 1, wherein, The step of calculating the model covariance matrix specifically comprises the steps of: calculating the model covariance matrix by a finite difference algorithm.

4. The dynamically varying seismic inversion method based on Lagrangian operators of claim 3, wherein, The finite difference algorithm is a central difference algorithm.

5. The Lagrangian operator-based dynamically-varying seismic inversion method of claim 1, wherein, n is a positive integer greater than 5.

6. The dynamically varying seismic inversion method based on Lagrangian operators of claim 1, wherein, the step of substituting the column vector into the preset inversion iteration formula to obtain the corresponding number of inversion velocity models specifically comprises the steps of: substituting the column vector into the preset inversion iteration formula; obtaining the corresponding number of inversion velocity models by solving the inversion iteration formula into which the column vector is substituted by a conjugate gradient method.

7. The Lagrangian operator-based dynamically-varying seismic inversion method of claim 1, wherein, The preset value of the target function is 1.

8. A system for seismic inversion based on dynamic changes in Lagrangian operators, characterized in that, The method comprises the steps of: a data processing module is configured to obtain a column vector composed of 2n+1 Lagrange multipliers according to a preset prior velocity model and an initial velocity model, n being a positive integer; a target function determining module is configured to substitute the column vector into a preset inversion iteration formula to obtain a corresponding number of inversion velocity models, and obtain a target function according to the inversion velocity models; an iteration solving module is configured to determine an inversion velocity model with a minimum function value of the target function as an iteration model, and repeatedly determine the iteration model until a minimum value of the target function reaches a preset value of the target function; the data processing module is further configured to calculate a forward response according to the preset prior velocity model and the initial velocity model, and calculate a data covariance matrix and a model covariance matrix; obtain a target function data item and a model item according to the forward response, the data covariance matrix and the model covariance matrix; obtain a reference coefficient according to the target function data item and the model item, and calculate the column vector composed of 2n+1 Lagrange multipliers according to the reference coefficient; wherein the data item is: d is the actual observed data, F[m1] is the forward response of the initial velocity model, C d is the data covariance matrix; The model term is: m is a current model, m0 is a preset prior velocity model, C m is a model covariance matrix; The reference coefficient is: W d is a data item, W m is a model item. 9.A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the method of any one of claims 1-7 when executing the program. 10.A computer readable medium having a computer program stored thereon, wherein When the program is executed by the processor, it implements the method as described in any one of claims 1-7.

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