A non-stationary autoregressive regularized seismic data interpolation method and device
By using a non-stationary autoregressive regularization method to process seismic data, the problem of poor performance in processing non-stationary data in existing technologies is solved. This method achieves efficient and accurate data interpolation, adapts to complex geological structures, and improves the efficiency and accuracy of oil and gas exploration.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHINA PETROLEUM & CHEMICAL CORP
- Filing Date
- 2024-12-23
- Publication Date
- 2026-06-23
AI Technical Summary
Existing seismic data interpolation methods are ineffective when dealing with non-stationary data, suffer from aliasing problems, have low computational efficiency, are difficult to select parameters, and lack adaptability, especially in complex geological structures.
A non-stationary autoregressive regularization method is adopted. Seismic data is processed through a non-stationary autoregressive model and a preset regularization operator to obtain the prediction error filter coefficients, reconstruct missing or aliased data, and perform interpolation using the least squares formula.
It improves the accuracy and resolution of seismic data interpolation, reduces computation time, adapts to complex underground structures, and significantly improves the efficiency and accuracy of oil and gas exploration.
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Figure CN122260431A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of seismic exploration technology, and more specifically, to a non-stationary autoregressive regularized seismic data interpolation method and apparatus. Background Technology
[0002] Seismic exploration is a crucial method for oil and gas resource development, with seismic data acquisition and processing being particularly critical. Seismic data is typically sampled in both time and space; however, due to cost and technological limitations, sampling may be uneven or incomplete, leading to aliasing and distortion in the imaging results. To improve imaging quality and resolution, interpolation processing of this data is necessary.
[0003] Currently, traditional processing methods mainly include the following seismic data interpolation methods: Prediction Error Filter (PEF) method: Spitz (1991) proposed a seismic data interpolation technique based on PEF, which uses known data to estimate filter coefficients and then interpolates the missing data. PEF extension in the time domain: Claerbout (1992) extended the PEF method to the time and space domains, improving its ability to handle complex geological structures. Half-step PEF scheme: Porsani (1999) proposed a half-step PEF scheme to improve interpolation efficiency. Interpolation techniques in the frequency-space domain: Gulunay (2003) and Wang (2002) and other researchers proposed methods for seismic data interpolation in the frequency-space domain. Non-stationary PEF method: Crawley et al. (1999) and Fomel (2002) proposed a PEF method for processing non-stationary data, which improves the interpolation effect through local stabilization and smoothing.
[0004] However, the following problems still exist:
[0005] Limitations of Non-Stationary Autoregressive Regularized Seismic Data Interpolation: Most existing methods are based on the assumption of stationary data and are insufficient in handling the non-stationary characteristics of real seismic data. Aliasing Problem: Existing techniques struggle to effectively remove aliasing artifacts when data sampling is sparse or contains significant missing data. Computational Efficiency: Existing methods are computationally inefficient when processing large-scale datasets, especially when frequent iterative optimization is required. Difficult Parameter Selection: In existing techniques, the selection of regularization parameters often relies on experience, lacking intuitive guiding principles. Insufficient Adaptability: Existing methods have limited adaptability to seismic data with complex geological structures and variable geological features.
[0006] Therefore, how to solve the above problems is an urgent issue that needs to be addressed. Summary of the Invention
[0007] This application provides a non-stationary autoregressive regularized seismic data interpolation method and apparatus, aiming to improve the above-mentioned problems.
[0008] Firstly, this application provides a non-stationary autoregressive regularized seismic data interpolation method, the method comprising:
[0009] Acquire earthquake data;
[0010] The seismic data is processed based on a non-stationary autoregressive model to obtain the prediction error filter coefficients;
[0011] Based on the prediction error filter coefficients and the seismic data, the missing or aliased data in the seismic data is reconstructed to obtain the interpolated data.
[0012] In one possible embodiment, the process of processing the seismic data based on a non-stationary autoregressive model to obtain prediction error filter coefficients includes:
[0013] The seismic data is processed based on a non-stationary autoregressive model and a preset regularization operator to obtain the prediction error filter coefficients.
[0014] In one possible embodiment, the seismic data is processed based on a non-stationary autoregressive model and combined with a preset regularization operator to obtain prediction error filter coefficients, including:
[0015] Determine the translation data of the seismic data after a preset translation step size;
[0016] The earthquake data and the translation data are input into a non-stationary autoregressive model, and the prediction error filter coefficients are obtained by combining them with a preset regularization operator.
[0017] In one possible embodiment, the prediction error filter coefficients satisfy:
[0018]
[0019] Where S(t,x) represents the seismic data at time and spatial location (t,x), S n (t,x) represents the translation data, denoted as S(tm) i dt,xm j dx),m i and m j This refers to the preset translation step size for time and translation operations, where dt and dx are the time and translation step sizes; B n (t,x) represents the prediction error filter coefficients; K represents the preset regularization operator, and ∈ is the regularization parameter.
[0020] In one possible embodiment, the preset regularization operator is a Gaussian smoothing operator.
[0021] In one possible embodiment, the missing or aliased data in the seismic data is reconstructed based on the prediction error filter coefficients and the seismic data to obtain interpolated data, including:
[0022] A least squares formula is constructed based on the prediction error filter coefficients, the seismic data, and the translation data.
[0023] Solve the least squares formula to obtain the interpolated data.
[0024] In one possible embodiment, the interpolated data satisfies:
[0025]
[0026] Among them, S new (t,x) represents the interpolated data.
[0027] Secondly, this application provides a non-stationary autoregressive regularized seismic data interpolation device, the device comprising:
[0028] Acquisition unit, used to acquire seismic data;
[0029] The processing unit is used to process the seismic data based on a non-stationary autoregressive model to obtain the prediction error filter coefficients.
[0030] An interpolation unit is used to reconstruct missing or aliased data in the seismic data based on the prediction error filter coefficients and the seismic data, and obtain interpolated data.
[0031] In one possible embodiment, the processing unit is specifically used for:
[0032] The seismic data is processed based on a non-stationary autoregressive model and a preset regularization operator to obtain the prediction error filter coefficients.
[0033] In one possible embodiment, the seismic data is processed based on a non-stationary autoregressive model and combined with a preset regularization operator to obtain prediction error filter coefficients, including:
[0034] Determine the translation data of the seismic data after a preset translation step size;
[0035] The earthquake data and the translation data are input into a non-stationary autoregressive model, and the prediction error filter coefficients are obtained by combining them with a preset regularization operator.
[0036] The present application provides a non-stationary autoregressive regularized seismic data interpolation method and apparatus. This method involves acquiring seismic data; processing the seismic data based on a non-stationary autoregressive model to obtain prediction error filter coefficients; and reconstructing missing or aliased data from the seismic data using the prediction error filter coefficients and the seismic data itself to obtain interpolated data. This effectively processes seismic data with non-stationary characteristics, improves interpolation accuracy, reduces computation time, and adapts to complex underground structures. Through regularization technology, this invention has broad application potential in the field of seismic exploration, significantly improving the efficiency and accuracy of oil and gas exploration. Attached Figure Description
[0037] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.
[0038] Figure 1 This is a schematic diagram of the structure of an electronic device provided in the first embodiment of this application;
[0039] Figure 2 A flowchart of a non-stationary autoregressive regularized seismic data interpolation method provided in the second embodiment of this application;
[0040] Figure 3 To adopt Figure 2 The diagram shows a comparison of the effects of a non-stationary autoregressive regularized seismic data interpolation method on synthetic seismic data interpolation.
[0041] Figure 4 To adopt Figure 2 The diagram shows a comparison of the effects of a non-stationary autoregressive regularized seismic data interpolation method on actual seismic data interpolation.
[0042] Figure 5 This is a schematic diagram of the functional modules of a non-stationary autoregressive regularized seismic data interpolation device provided in the third embodiment of this application. Detailed Implementation
[0043] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0044] First embodiment:
[0045] Figure 1 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. In this application, it can be... Figure 1 The schematic diagram shown illustrates an example of an electronic device 100 used to implement the non-stationary autoregressive regularized seismic data interpolation method and apparatus of the present application embodiments.
[0046] like Figure 1 The diagram shows the structure of an electronic device 100. The electronic device 100 includes one or more processors 102, one or more storage devices 104, input devices 106, and output devices 108. These components are interconnected via a bus system and / or other forms of connection mechanisms (not shown). It should be noted that... Figure 1 The components and structure of the electronic device 100 shown are merely exemplary and not limiting; the electronic device may have, as needed. Figure 1 The components shown may also have Figure 1 Other components and structures not shown.
[0047] The processor 102 may be a central processing unit (CPU) or other form of processing unit with data processing capabilities and / or instruction execution capabilities, and may control other components in the electronic device 100 to perform desired functions.
[0048] It should be understood that the processor 102 in the embodiments of this application can be a central processing unit (CPU), or it can be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor.
[0049] The storage device 104 may include one or more computer program products, which may include various forms of computer-readable storage media.
[0050] It should be understood that the storage device 104 in the embodiments of this application may be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. The non-volatile memory may be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory may be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of random access memory (RAM) are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate synchronous DRAM (DDR SDRAM), enhanced synchronous DRAM (ESDRAM), synchronous linked DRAM (SLDRAM), and direct rambus RAM (DR RAM).
[0051] The computer-readable storage medium may store one or more computer program instructions, which the processor 102 may execute to implement the client functions (implemented by the processor) in the embodiments of this application described below, and / or other desired functions. Various applications and various data may also be stored in the computer-readable storage medium, such as various data used and / or generated by the applications.
[0052] The input device 106 may be a device used by a user to input commands, and may include one or more of the following: keyboard, mouse, microphone, and touch screen.
[0053] Second embodiment:
[0054] Reference Figure 2 The flowchart shown represents a non-stationary autoregressive regularized seismic data interpolation method, which specifically includes the following steps:
[0055] Step S201: Obtain earthquake data.
[0056] The earthquake data can be pre-acquired. For example, such as... Figure 3 As shown in Figure a, the acquired seismic data is incomplete.
[0057] Step S202: The seismic data is processed based on a non-stationary autoregressive model to obtain the prediction error filter coefficients.
[0058] It should be understood that in a non-stationary autoregressive model (i.e., RNA model), seismic data is considered as a non-stationary signal that varies with time and space.
[0059] As one implementation method, step S202 includes: processing the seismic data based on a non-stationary autoregressive model and in combination with a preset regularization operator to obtain prediction error filter coefficients.
[0060] Optionally, the seismic data is processed based on a non-stationary autoregressive model and combined with a preset regularization operator to obtain prediction error filter coefficients, including: determining the translation data of the seismic data after a preset translation step size; inputting the seismic data and the translation data into the non-stationary autoregressive model and calculating the prediction error filter coefficients in combination with the preset regularization operator.
[0061] Optionally, the prediction error filter coefficients satisfy:
[0062]
[0063] Where S(t,x) represents the seismic data at time and spatial location (t,x), S n (t,x) represents the translation data, denoted as S(tm) i dt,xm j dx),m i and m j This refers to the preset translation step size for time and translation operations, where dt and dx are the time and translation step sizes; B n (t,x) represents the prediction error filter coefficients; K represents the preset regularization operator, and ∈ is the regularization parameter.
[0064] Optionally, the preset regularization operator is a Gaussian smoothing operator.
[0065] Optionally, the value of the regularization parameter ∈ can be set according to the actual situation, and no specific limitation is made here.
[0066] Of course, in practical use, the preset regularization operator K can also be other smoothing operators, and no specific restrictions are made here.
[0067] Understandably, in the RNA model, earthquake data is treated as a non-stationary signal that varies with time and space, and the problem of estimating the prediction error filter coefficients (PEF coefficients) can be expressed as a global regularized least squares problem, i.e., expressed by the above formula.
[0068] In one possible embodiment, before step S202, the non-stationary autoregressive regularized seismic data interpolation method further includes: determining whether the data distribution of the seismic data is greater than a threshold; if yes, executing step S202; if no, acquiring new seismic data and re-determining whether its data distribution is greater than the threshold.
[0069] Optionally, the threshold is 30%.
[0070] In other words, it is necessary to determine whether the data distribution of the earthquake data before interpolation reaches more than 30% of the complete data after interpolation.
[0071] For example, such as Figure 3 or Figure 4 As shown, assuming that we obtain Figure 3 After processing the earthquake data shown in Figure a, first determine whether its data distribution reaches more than 30% of the complete interpolated data. If it does, continue processing... Figure 3 The seismic data shown in Figure a undergoes further processing.
[0072] Step S203: Reconstruct the missing or aliased data in the seismic data based on the prediction error filter coefficients and the seismic data to obtain the interpolated data.
[0073] As one implementation method, step S203 includes: constructing a least squares formula based on the prediction error filter coefficients, the seismic data, and the translation data; solving the least squares formula to obtain the interpolated data.
[0074] Optionally, the interpolated data satisfies:
[0075]
[0076] Among them, S new (t,x) represents the interpolated data.
[0077] For example, such as Figure 3 or Figure 4 The seismic data shown in 'a' is interpolated using the non-stationary autoregressive regularized seismic data interpolation method provided in this embodiment to obtain the following: Figure 3 or Figure 4The interpolated seismic data is shown in Figure b. Combining the diagrams before and after interpolation, it is clear that the non-stationary autoregressive regularized seismic data interpolation method provided in this embodiment can effectively remove aliasing artifacts from seismic data, thereby improving the accuracy and resolution of data interpolation.
[0078] Understandably, in this embodiment, by minimizing the prediction error including the regularization term to estimate the adaptive prediction error filter coefficients, and then using these coefficients for interpolation, it is possible to effectively handle seismic data with non-stationary characteristics, improve interpolation accuracy, reduce computation time, and adapt to complex subsurface structures. Through this shaping regularization technique, the present invention has broad application potential in the field of seismic exploration, and can significantly improve the efficiency and accuracy of oil and gas exploration.
[0079] Third embodiment:
[0080] See Figure 5 The diagram illustrates a non-stationary autoregressive regularized seismic data interpolation device. This device includes an acquisition unit 510, a processing unit 520, and an interpolation unit 530. The specific functions of each unit are as follows:
[0081] Acquisition unit 510 is used to acquire seismic data;
[0082] The processing unit 520 is used to process the seismic data based on a non-stationary autoregressive model to obtain the prediction error filter coefficients.
[0083] Interpolation unit 530 is used to reconstruct missing or aliased data in the seismic data based on the prediction error filter coefficients and the seismic data to obtain interpolated data.
[0084] Optionally, the processing unit 520 is specifically used to: process the seismic data based on a non-stationary autoregressive model and in combination with a preset regularization operator to obtain prediction error filter coefficients.
[0085] Optionally, the seismic data is processed based on a non-stationary autoregressive model and combined with a preset regularization operator to obtain prediction error filter coefficients, including: determining the translation data of the seismic data after a preset translation step size; inputting the seismic data and the translation data into the non-stationary autoregressive model and calculating the prediction error filter coefficients in combination with the preset regularization operator.
[0086] Optionally, the prediction error filter coefficients satisfy:
[0087]
[0088] Where S(t,x) represents the seismic data at time and spatial location (t,x), S n (t,x) represents the translation data, denoted as S(tm) i dt,xm j dx),m i and m j This refers to the preset translation step size for time and translation operations, where dt and dx are the time and translation step sizes; B n (t,x) represents the prediction error filter coefficients; K represents the preset regularization operator, and ∈ is the regularization parameter.
[0089] Optionally, the preset regularization operator is a Gaussian smoothing operator.
[0090] Optionally, the value of the regularization parameter ∈ can be set according to the actual situation, and no specific limitation is made here.
[0091] Of course, in practical use, the preset regularization operator K can also be other smoothing operators, and no specific restrictions are made here.
[0092] Understandably, in the RNA model, earthquake data is treated as a non-stationary signal that varies with time and space, and the problem of estimating the prediction error filter coefficients (PEF coefficients) can be expressed as a global regularized least squares problem, i.e., expressed by the above formula.
[0093] In one possible embodiment, the non-stationary autoregressive regularized seismic data interpolation device further includes: a filtering unit, which is used to determine whether the data distribution of the seismic data is greater than a threshold before processing the seismic data based on the non-stationary autoregressive model to obtain the prediction error filter coefficients; if yes, the processing unit 520 performs the step of processing the seismic data based on the non-stationary autoregressive model to obtain the prediction error filter coefficients; if no, it acquires new seismic data and re-determines whether its data distribution is greater than the threshold.
[0094] Optionally, the threshold is 30%.
[0095] In other words, it is necessary to determine whether the data distribution of the earthquake data before interpolation reaches more than 30% of the complete data after interpolation.
[0096] Optionally, the interpolation unit is specifically used to: construct a least squares formula based on the prediction error filter coefficients, the seismic data, and the translation data; solve the least squares formula to obtain the interpolated data.
[0097] Optionally, the interpolated data satisfies:
[0098]
[0099] Among them, S new (t,x) represents the interpolated data.
[0100] Furthermore, this embodiment also provides a computer-readable storage medium storing a computer program. When the computer program is run by a processing device, it executes the steps of any of the non-stationary autoregressive regularized seismic data interpolation methods provided in Embodiment 2 above.
[0101] The computer program product of the non-stationary autoregressive regularized seismic data interpolation method and apparatus provided in this application includes a computer-readable storage medium storing program code. The instructions included in the program code can be used to execute the methods described in the preceding method embodiments. For specific implementation details, please refer to the method embodiments, which will not be repeated here.
[0102] In summary, this embodiment provides a non-stationary autoregressive regularized seismic data interpolation method and apparatus. First, seismic data is acquired; then, the seismic data is processed based on a non-stationary autoregressive model to obtain prediction error filter coefficients; finally, missing or aliased data in the seismic data is reconstructed based on the prediction error filter coefficients and the seismic data to obtain the interpolated data. This effectively processes seismic data with non-stationary characteristics, improves interpolation accuracy, reduces computation time, and adapts to complex subsurface structures. Furthermore, through the shaping regularization technique, this invention has broad application potential in the field of seismic exploration, significantly improving the efficiency and accuracy of oil and gas exploration.
[0103] It should be noted that the above embodiments can be implemented, in whole or in part, by software, hardware (such as circuits), firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, in the form of a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more sets of available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium. A semiconductor medium can be a solid-state drive.
[0104] It should be understood that the term "and / or" in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. A and B can be singular or plural. Additionally, the character " / " in this article generally indicates an "or" relationship between the preceding and following related objects, but it can also represent an "and / or" relationship. Please refer to the context for a more accurate understanding.
[0105] In this application, "at least one" means one or more, and "more than one" means two or more. "At least one of the following" or similar expressions refer to any combination of these items, including any combination of single or multiple items. For example, at least one of a, b, or c can mean: a, b, c, ab, ac, bc, or abc, where a, b, and c can be single or multiple.
[0106] It should be understood that in the various embodiments of this application, the order of the above-mentioned processes does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.
[0107] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.
[0108] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.
[0109] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.
[0110] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.
[0111] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.
[0112] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application. It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.
Claims
1. A non-stationary autoregressive regularized seismic data interpolation method, characterized in that, The method includes: Acquire earthquake data; The seismic data is processed based on a non-stationary autoregressive model to obtain the prediction error filter coefficients; Based on the prediction error filter coefficients and the seismic data, the missing or aliased data in the seismic data is reconstructed to obtain the interpolated data.
2. The method according to claim 1, characterized in that, The process of processing the seismic data based on the non-stationary autoregressive model to obtain the prediction error filter coefficients includes: The seismic data is processed based on a non-stationary autoregressive model and a preset regularization operator to obtain the prediction error filter coefficients.
3. The method according to claim 2, characterized in that, Based on a non-stationary autoregressive model and combined with a preset regularization operator, the seismic data is processed to obtain prediction error filter coefficients, including: Determine the translation data of the seismic data after a preset translation step size; The earthquake data and the translation data are input into a non-stationary autoregressive model, and the prediction error filter coefficients are obtained by combining them with a preset regularization operator.
4. The method according to claim 3, characterized in that, The prediction error filter coefficients satisfy: Where S(t,x) represents the seismic data at time and spatial location (t,x), S n (t,x) represents the translation data, denoted as S(tm) i dt,xm j dx),m i and m j This refers to the preset translation step size for time and translation operations, where dt and dx are the time and translation step sizes; B n (t,x) represents the prediction error filter coefficients; K represents the preset regularization operator, and ∈ is the regularization parameter.
5. The method according to claim 4, characterized in that, The preset regularization operator is a Gaussian smoothing operator.
6. The method according to claim 5, characterized in that, Based on the prediction error filter coefficients and the seismic data, the missing or aliased data in the seismic data is reconstructed to obtain the interpolated data, including: A least squares formula is constructed based on the prediction error filter coefficients, the seismic data, and the translation data. Solve the least squares formula to obtain the interpolated data.
7. The method according to claim 6, characterized in that, The interpolated data satisfies: Among them, S new (t,x) represents the interpolated data.
8. A non-stationary autoregressive regularized seismic data interpolation device, characterized in that, The device includes: Acquisition unit, used to acquire seismic data; The processing unit is used to process the seismic data based on a non-stationary autoregressive model to obtain the prediction error filter coefficients. An interpolation unit is used to reconstruct missing or aliased data in the seismic data based on the prediction error filter coefficients and the seismic data, and obtain interpolated data.
9. The apparatus according to claim 8, characterized in that, The processing unit is specifically used for: The seismic data is processed based on a non-stationary autoregressive model and a preset regularization operator to obtain the prediction error filter coefficients.
10. The apparatus according to claim 9, characterized in that, Based on a non-stationary autoregressive model and combined with a preset regularization operator, the seismic data is processed to obtain prediction error filter coefficients, including: Determine the translation data of the seismic data after a preset translation step size; The earthquake data and the translation data are input into a non-stationary autoregressive model, and the prediction error filter coefficients are obtained by combining them with a preset regularization operator.