Point spread function calculation method and apparatus, electronic device, and medium
By employing a point spread function calculation method based on local neighborhood high-frequency approximation, the problems of insufficient imaging resolution and difficulty in calculating the Hessian matrix in oil and gas exploration are solved, achieving efficient point spread function solving and high-resolution seismic data processing.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHINA PETROLEUM & CHEMICAL CORP
- Filing Date
- 2021-10-21
- Publication Date
- 2026-05-08
AI Technical Summary
In oil and gas exploration, conventional resolution enhancement techniques cannot fully consider the actual wave field propagation effect, resulting in insufficient imaging resolution. Furthermore, the calculation and storage of the Hessian matrix are difficult, and existing point spread function calculation methods involve huge computational loads, making it difficult to achieve efficient solutions.
A point spread function calculation method based on local neighborhood high-frequency approximation is adopted. By establishing an initial point spread function and setting constraint parameters, the point spread function is quickly solved using the least squares method and high-frequency approximation, simplifying the calculation process of the Hessian matrix.
It enables rapid solution of point spread function, improves the solution efficiency of local neighborhood point spread function, reduces computational cost, and provides high-precision, high-resolution seismic data processing capabilities.
Smart Images
Figure CN116010761B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of geophysical exploration technology, and more specifically, to a method, apparatus, electronic device, and medium for calculating point spread function. Background Technology
[0002] The increasingly refined targets of oil and gas exploration have placed higher demands on high-resolution processing of seismic data. Conventional resolution-enhancing techniques, such as deconvolution, inverse Q-filtering, and spectral extension, are usually based on one-dimensional assumptions, do not consider the actual wavefield propagation effects, cannot fully consider the fidelity of the processing, and cannot improve lateral resolution.
[0003] In fact, high-resolution imaging depends on the resolution of the space wavelet on the imaging profile. Higher space wavelet resolution corresponds to higher imaging resolution. The resolution of the space wavelet is determined by the Hessian matrix (model resolution matrix) of the imaging system. The Hessian matrix corresponds to the response function of a linear imaging system, and is composed of the point spread function (PSF) at each point in the system (each row corresponds to the PSF of one point). For an imaging system, the PSF is different at each point in the model; therefore, the Hessian matrix applied to the subsurface reflectance is equivalent to defining a spatially varied convolution process.
[0004] Mathematically, the difference between least-squares migration results and conventional migration results lies in the inverse of the Hessian matrix. Therefore, the process of solving least-squares imaging is essentially the process of solving for the inverse of the Hessian matrix, and it also involves eliminating the adverse effects of seismic data observation systems, subsurface medium velocity variations, seismic wave geometric spread, and migration imaging formulas on conventional migration imaging results. Because the Hessian matrix is extremely large, its computation and storage are very difficult, so many researchers approximate it. Traditional Hessian matrix approximation methods still primarily rely on implicit solutions, approximating the inverse of the Hessian matrix in the data domain through inversion iterations, gradually approaching the true reflection coefficients from the migration results. Explicitly calculating the Hessian matrix in the imaging domain makes it easier to achieve target-oriented least-squares migration imaging, but the enormous computational and storage requirements remain the biggest challenges. In recent years, point spread function (PSF) algorithms based on discrete point models have been proposed for explicit approximation of the Hessian matrix. These algorithms have improved efficiency to some extent, but they still rely on wave equations, thus still facing significant computational challenges.
[0005] Therefore, it is necessary to develop a method, apparatus, electronic device, and medium for calculating the point spread function based on the local neighborhood high-frequency approximation.
[0006] The information disclosed in the background section of this invention is intended only to enhance the understanding of the general background of this invention, and should not be construed as an admission or in any way implying that such information constitutes prior art known to those skilled in the art. Summary of the Invention
[0007] This invention proposes a method, apparatus, electronic device, and medium for calculating the point spread function. Based on local neighborhood and high-frequency approximation, it achieves rapid solution of the point spread function, which better serves the properties of the Hessian matrix and the high-dimensional forward modeling of seismic data. It also provides new technical ideas for future high-precision, high-efficiency, and high-resolution processing of seismic data and provides strong technical support for practical production applications.
[0008] In a first aspect, embodiments of this disclosure provide a method for calculating a point spread function, including:
[0009] Establish the initial point spread function;
[0010] Set constraint parameters;
[0011] Based on the initial point spread function and the constraint parameters, the final point spread function is obtained and calculated.
[0012] Preferably, establishing the diffusion function includes:
[0013] Establish a linear relationship between seismic observation data and velocity models;
[0014] The objective function is established using the least squares method, thereby obtaining the underground model;
[0015] The initial point diffusion function is determined based on the underground model.
[0016] Preferably, the objective function is:
[0017] Q(m) = ||Lm-d|| 2 (1)
[0018] Where d represents earthquake data, L represents the seismic wave propagation operator, and m represents the subsurface model.
[0019] Preferably, the underground model is:
[0020]
[0021] Where d represents earthquake data, L represents the seismic wave propagation operator, and m represents the subsurface model.
[0022] Preferably, the initial point spread function is:
[0023]
[0024] Where G(.) is the Green's function, f t (t) represents the source wavelet, G T (.) denotes the adjoint operator of the Green's function G(.).
[0025] Preferably, the constraint parameters include local neighborhood range, background velocity, and imaging observation system within the neighborhood range.
[0026] Preferably, the final point spread function is:
[0027] PSF(x0,x)==∫∫∫w(t)w(t-(I(x)-x0) / v(x0))dx S dx R dt (4)
[0028] Where w(.) represents the far-field imaging wavelet corresponding to the underground imaging point under the high-frequency approximation, I(.) represents the constraint function of the illumination angle range, x0 is the imaging point in the neighborhood, and v(x0) is the velocity in the neighborhood.
[0029] As one specific implementation of this disclosure,
[0030] Secondly, embodiments of this disclosure also provide a point spread function calculation apparatus, comprising:
[0031] Initial module, establish the initial point spread function;
[0032] The constraint module allows you to set constraint parameters.
[0033] The calculation module obtains the final point spread function and calculates the solution based on the initial point spread function and the constraint parameters.
[0034] Preferably, establishing the diffusion function includes:
[0035] Establish a linear relationship between seismic observation data and velocity models;
[0036] The objective function is established using the least squares method, thereby obtaining the underground model;
[0037] The initial point diffusion function is determined based on the underground model.
[0038] Preferably, the objective function is:
[0039] Q(m) = ||Lm-d|| 2 (1)
[0040] Where d represents earthquake data, L represents the seismic wave propagation operator, and m represents the subsurface model.
[0041] Preferably, the underground model is:
[0042]
[0043] Where d represents earthquake data, L represents the seismic wave propagation operator, and m represents the subsurface model.
[0044] Preferably, the initial point spread function is:
[0045]
[0046] Where G(.) is the Green's function, f t (t) represents the source wavelet, G T (.) denotes the adjoint operator of the Green's function G(.).
[0047] Preferably, the constraint parameters include local neighborhood range, background velocity, and imaging observation system within the neighborhood range.
[0048] Preferably, the final point spread function is:
[0049] PSF(x0,x)==∫∫∫w(t)w(t-(I(x)-x0) / v(x0))dx S dx R dt (4)
[0050] Where w(.) represents the far-field imaging wavelet corresponding to the underground imaging point under the high-frequency approximation, I(.) represents the constraint function of the illumination angle range, x0 is the imaging point in the neighborhood, and v(x0) is the velocity in the neighborhood.
[0051] Thirdly, embodiments of this disclosure also provide an electronic device, the electronic device comprising:
[0052] Memory, which stores executable instructions;
[0053] A processor that executes the executable instructions in the memory to implement the point spread function calculation method.
[0054] Fourthly, embodiments of this disclosure also provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the point spread function calculation method described above.
[0055] Its beneficial effects are as follows: it realizes the fast solution of point spread function by adopting high frequency approximation and local uniformity algorithm, effectively improves the solution efficiency of local neighborhood point spread function, and under the condition of high frequency approximation, it can effectively approximate the point spread function solution method based on wave-type algorithm with a small computational cost.
[0056] The methods and apparatus of the present invention have other features and advantages that will be apparent from or will be set forth in detail in the accompanying drawings and following detailed description, which together serve to explain the particular principles of the invention. Attached Figure Description
[0057] The above and other objects, features and advantages of the present invention will become more apparent from the more detailed description of exemplary embodiments of the invention in conjunction with the accompanying drawings, wherein the same reference numerals generally represent the same parts.
[0058] Figure 1 A flowchart illustrating the steps of a point spread function calculation method according to an embodiment of the present invention is shown.
[0059] Figure 2 A schematic diagram of an observation system corresponding to the point spread function solution according to an embodiment of the present invention is shown.
[0060] Figure 3 A schematic diagram of an imaging wavelet according to an embodiment of the present invention is shown.
[0061] Figure 4a , Figure 4b , Figure 4c , Figure 4d Schematic diagrams of spatial domain point spread functions with illumination angle ranges of -90 to 90°, -60 to 60°, -45 to 45°, and -30 to 30° according to an embodiment of the present invention are shown respectively.
[0062] Figure 5a , Figure 5b , Figure 5c , Figure 5d Schematic diagrams of wavenumber domain point spread functions for illumination angle ranges of -90 to 90°, -60 to 60°, -45 to 45°, and -30 to 30° according to an embodiment of the present invention are shown respectively.
[0063] Figure 6a , Figure 6b Schematic diagrams of spatial domain point spread functions with an illumination range of -90 to 90° and imaging wavelet frequencies of 25 Hz and 45 Hz, respectively, according to an embodiment of the present invention, are shown.
[0064] Figure 7a , Figure 7b Schematic diagrams of wavenumber domain point spread functions with an illumination range of -90 to 90° and imaging wavelet frequencies of 25 Hz and 45 Hz, respectively, according to an embodiment of the present invention, are shown.
[0065] Figure 8 A block diagram of a point spread function calculation apparatus according to an embodiment of the present invention is shown.
[0066] Explanation of reference numerals in the attached figures:
[0067] 201. Initialization module; 202. Constraint module; 203. Calculation module. Detailed Implementation
[0068] Preferred embodiments of the invention will now be described in more detail. While preferred embodiments of the invention are described below, it should be understood that the invention can be implemented in various forms and should not be limited to the embodiments set forth herein.
[0069] This invention provides a method for calculating the point spread function, comprising:
[0070] Establish the initial point spread function;
[0071] Set constraint parameters;
[0072] Based on the initial point spread function and constraint parameters, the final point spread function is obtained and calculated.
[0073] In one example, establishing the diffusion function includes:
[0074] Establish a linear relationship between seismic observation data and velocity models;
[0075] The objective function is established using the least squares method, thereby obtaining the underground model;
[0076] The initial point diffusion function is determined based on the underground model.
[0077] In one example, the objective function is:
[0078] Q(m) = ||Lm-d|| 2 (1)
[0079] Where d represents earthquake data, L represents the seismic wave propagation operator, and m represents the subsurface model.
[0080] In one example, the underground model is as follows:
[0081]
[0082] Where d represents earthquake data, L represents the seismic wave propagation operator, and m represents the subsurface model.
[0083] In one example, the initial point spread function is:
[0084]
[0085] Where G(.) is the Green's function, f t (t) represents the source wavelet, G T (.) denotes the adjoint operator of the Green's function G(.).
[0086] In one example, the constraint parameters include the local neighborhood range, background velocity, and the imaging observation system within the neighborhood range.
[0087] In one example, the final point spread function is:
[0088] PSF(x0,x)==∫∫∫w(t)w(t-(I(x)-x0) / v(x0))dx S dx R dt (4)
[0089] Where w(.) represents the far-field imaging wavelet corresponding to the underground imaging point under the high-frequency approximation, I(.) represents the constraint function of the illumination angle range, x0 is the imaging point in the neighborhood, and v(x0) is the velocity in the neighborhood.
[0090] Specifically, according to inversion theory, the relationship between seismic observation data and velocity models can be defined as the following linear relationship:
[0091] d = Lm (5).
[0092] If the least squares method is used to estimate the underground model m, then the objective function can be established as formula (1). From this, the model m estimated by the least squares method can be obtained as formula (2). H in formula (2) is the Hessian matrix, H = L T L, therefore formula (3) can be obtained.
[0093] Formula (3) can be rewritten under the high-frequency approximation condition as follows:
[0094] H(x,y)=∫∫∫[w(t-τ(xs,x)-τ(x,xr))][w(t-τ(xs,y)-τ(y,xr))]dx S dx R dt (6)
[0095] Where w(.) represents the far-field imaging wavelet corresponding to the underground imaging point under the high-frequency approximation. Assuming that the Hessian matrix at a point x0 within a space x is obtained, which is the point spread function at that point, the above equation can be written as:
[0096] H(x0,x)=∫∫∫[w(t-τ(x s ,x0)-τ(x0,x r ))][w(t-τ(x s ,x)-τ(x,x r ))]dxS dx R dt (7)
[0097] If the above space is assumed to be a local neighborhood, and point x0 is the imaging point within this neighborhood, then the velocity within this neighborhood is v(x0), and the above equation can be rewritten as:
[0098] PSF(x0,x)=H(x0,x)=∫∫∫[w(t)][w(t-τ(x,x0))]dx S dx R dt
[0099] =∫∫∫w(t)w(t-τ(x,x0))dx S dx R dt (8)
[0100] =∫∫∫w(t)w(t-(x-x0) / v(x0))dx S dx R dt
[0101] Generally speaking, the observation illumination range corresponding to the point spread function (i.e. the imaging response of point x0 in the neighborhood) is not perfectly illuminated. Therefore, the actual solution process requires an illumination range constraint on the neighborhood range x. The constraint parameters include the local neighborhood range, background velocity, imaging observation system within the neighborhood range, including illumination angle range and imaging wavelet parameters. Therefore, the final point spread function solution formula is formula (4). The point spread function is solved according to formula (4).
[0102] The present invention also provides a point spread function calculation device, comprising:
[0103] Initial module, establish the initial point spread function;
[0104] The constraint module allows you to set constraint parameters.
[0105] The calculation module obtains the final point spread function and calculates the solution based on the initial point spread function and constraint parameters.
[0106] In one example, establishing the diffusion function includes:
[0107] Establish a linear relationship between seismic observation data and velocity models;
[0108] The objective function is established using the least squares method, thereby obtaining the underground model;
[0109] The initial point diffusion function is determined based on the underground model.
[0110] In one example, the objective function is:
[0111] Q(m) = ||Lm-d|| 2 (1)
[0112] Where d represents earthquake data, L represents the seismic wave propagation operator, and m represents the subsurface model.
[0113] In one example, the underground model is as follows:
[0114]
[0115] Where d represents earthquake data, L represents the seismic wave propagation operator, and m represents the subsurface model.
[0116] In one example, the initial point spread function is:
[0117]
[0118] Where G(.) is the Green's function, f t (t) represents the source wavelet, G T (.) denotes the adjoint operator of the Green's function G(.).
[0119] In one example, the constraint parameters include the local neighborhood range, background velocity, and the imaging observation system within the neighborhood range.
[0120] In one example, the final point spread function is:
[0121] PSF(x0,x)==∫∫∫w(t)w(t-(I(x)-x0) / v(x0))dx S dx R dt (4)
[0122] Where w(.) represents the far-field imaging wavelet corresponding to the underground imaging point under the high-frequency approximation, I(.) represents the constraint function of the illumination angle range, x0 is the imaging point in the neighborhood, and v(x0) is the velocity in the neighborhood.
[0123] Specifically, according to inversion theory, the relationship between seismic observation data and velocity models can be defined as the following linear relationship:
[0124] d = Lm (5).
[0125] If the least squares method is used to estimate the underground model m, then the objective function can be established as formula (1). From this, the model m estimated by the least squares method can be obtained as formula (2). H in formula (2) is the Hessian matrix, H = L T L, therefore formula (3) can be obtained.
[0126] Formula (3) can be rewritten under the high-frequency approximation condition as follows:
[0127] H(x,y)=∫∫∫[w( t -τ(x s ,x)-τ(x,x r ))][w(t-τ(x s ,y)-τ(y,x r ))]dx S dx R dt (6)
[0128] Where w(.) represents the far-field imaging wavelet corresponding to the underground imaging point under the high-frequency approximation. Assuming that the Hessian matrix at a point x0 within a space x is obtained, which is the point spread function at that point, the above equation can be written as:
[0129] H(x0,x)=∫∫∫[w(t-τ(x s ,x0)-τ(x0,x r ))][w(t-τ(x s ,x)-τ(x,x r ))]dx S dx R dt (7)
[0130] If the above space is assumed to be a local neighborhood, and point x0 is the imaging point within this neighborhood, then the velocity within this neighborhood is v(x0), and the above equation can be rewritten as:
[0131] PSF(x0,x)=H(x0,x)=∫∫∫[w(t)][w(t-τ(x,x0))]dx S dx R dt
[0132] =∫∫∫w(t)w(t-τ(x,x0))dx S dx R dt (8)
[0133] =∫∫∫w(t)w(t-(x-x0) / v(x0))dx S dx R dt
[0134] Generally speaking, the observation illumination range corresponding to the point spread function (i.e. the imaging response of point x0 in the neighborhood) is not perfectly illuminated. Therefore, the actual solution process requires an illumination range constraint on the neighborhood range x. The constraint parameters include the local neighborhood range, background velocity, imaging observation system within the neighborhood range, including illumination angle range and imaging wavelet parameters. Therefore, the final point spread function solution formula is formula (4). The point spread function is solved according to formula (4).
[0135] The present invention also provides an electronic device, comprising: a memory storing executable instructions; and a processor executing the executable instructions in the memory to implement the above-described point spread function calculation method.
[0136] The present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described point spread function calculation method.
[0137] To facilitate understanding of the solutions and effects of the embodiments of the present invention, four specific application examples are given below. Those skilled in the art should understand that these examples are merely for the purpose of understanding the present invention, and any specific details therein are not intended to limit the present invention in any way.
[0138] Example 1
[0139] Figure 1 A flowchart illustrating the steps of a point spread function calculation method according to an embodiment of the present invention is shown.
[0140] like Figure 1 As shown, the point spread function calculation method includes: step 101, establishing an initial point spread function; step 102, setting constraint parameters; step 103, obtaining the final point spread function and calculating the solution based on the initial point spread function and constraint parameters.
[0141] Figure 2 This diagram illustrates an observation system corresponding to the point spread function solution according to an embodiment of the present invention, where the rectangle represents a selected local homogeneous region, the center point of the region is the imaging point x0, S and R are the positions of the shot and receiver points, respectively, and P... S and P R These are the incident and reflected vectors, n. SR It is the normal vector of the imaging point, θ SR It refers to the lighting range.
[0142] Figure 3 A schematic diagram of an imaging wavelet according to an embodiment of the present invention is shown.
[0143] In this embodiment, the size of the local neighborhood is set to nx*nz = 81*81, where dx = dz = 10, and the background velocity within this uniform neighborhood is set to 3000 m / s. Furthermore, the imaging wavelet in this embodiment is set to a Ricker wavelet with a main frequency of 25 Hz, such as... Figure 3 As shown.
[0144] Figure 4a , Figure 4b , Figure 4c , Figure 4dSchematic diagrams of spatial domain point spread functions with illumination angle ranges of -90 to 90°, -60 to 60°, -45 to 45°, and -30 to 30° according to an embodiment of the present invention are shown respectively.
[0145] Figure 5a , Figure 5b , Figure 5c , Figure 5d Schematic diagrams of wavenumber domain point spread functions for illumination angle ranges of -90 to 90°, -60 to 60°, -45 to 45°, and -30 to 30° according to an embodiment of the present invention are shown respectively.
[0146] Based on the above-defined locally uniform model, different observation angle ranges can be set, and the point spread function can be solved using the fast solution algorithm proposed in this invention. Figures 4a to 4d The diagrams show point spread functions for illumination angle ranges of -90 to 90°, -60 to 60°, -45 to 45°, and -30 to 30°, respectively. As can be seen from the diagrams, the point spread function obtained based on this invention can reflect the resolution and focusing properties of the point spread function under different illumination ranges. As the illumination range decreases, the resolution and focusing properties of the point spread function decrease. Figures 5a-5d The diagrams show the wavenumber domain point spread function for illumination angle ranges of -90 to 90°, -60 to 60°, -45 to 45°, and -30 to 30°, respectively. The diagrams clearly show the wavenumber distribution range of the point spread function under different illumination ranges, and the illumination angle distribution under different illumination ranges can be directly seen from the wavenumber spectrum.
[0147] Figure 6a , Figure 6b Schematic diagrams of spatial domain point spread functions with an illumination range of -90 to 90° and imaging wavelet frequencies of 25 Hz and 45 Hz, respectively, according to an embodiment of the present invention, are shown.
[0148] Figure 7a , Figure 7b Schematic diagrams of wavenumber domain point spread functions with an illumination range of -90 to 90° and imaging wavelet frequencies of 25 Hz and 45 Hz, respectively, according to an embodiment of the present invention, are shown.
[0149] To further verify the properties of the point spread function solved by this invention, the properties of the point spread function at different imaging wavelet frequencies are further investigated below. (Comparison) Figure 6a , Figure 6b It is clear that the point spread function at 45Hz has higher resolution and better focusing. (Comparison) Figure 7a , Figure 7b It can also be clearly seen that the wavenumber spectrum of the point spread function corresponding to the 45Hz imaging wavelet has a wider wavenumber range.
[0150] Example 2
[0151] Figure 8 A block diagram of a point spread function calculation apparatus according to an embodiment of the present invention is shown.
[0152] like Figure 8 As shown, the point spread function calculation device includes:
[0153] Initial module, establish the initial point spread function;
[0154] The constraint module allows you to set constraint parameters.
[0155] The calculation module obtains the final point spread function and calculates the solution based on the initial point spread function and constraint parameters.
[0156] As an optional approach, establishing the diffusion function includes:
[0157] Establish a linear relationship between seismic observation data and velocity models;
[0158] The objective function is established using the least squares method, thereby obtaining the underground model;
[0159] The initial point diffusion function is determined based on the underground model.
[0160] As an optional approach, the objective function is:
[0161] Q(m) = ||Lm-d|| 2 (1)
[0162] Where d represents earthquake data, L represents the seismic wave propagation operator, and m represents the subsurface model.
[0163] As an alternative, the underground model is as follows:
[0164]
[0165] Where d represents earthquake data, L represents the seismic wave propagation operator, and m represents the subsurface model.
[0166] As an optional approach, the initial point diffusion function is:
[0167]
[0168] Where G(.) is the Green's function, f t (t) represents the source wavelet, G T (.) denotes the adjoint operator of the Green's function G(.).
[0169] As an optional approach, the constraint parameters include the local neighborhood range, background velocity, and the imaging observation system within the neighborhood range.
[0170] As an optional approach, the final point spread function is:
[0171] PSF(x0,x)==∫∫∫w(t)w(t-(I(x)-x0) / v(x0))dx S dx R dt (4)
[0172] Where w(.) represents the far-field imaging wavelet corresponding to the underground imaging point under the high-frequency approximation, I(.) represents the constraint function of the illumination angle range, x0 is the imaging point in the neighborhood, and v(x0) is the velocity in the neighborhood.
[0173] Example 3
[0174] This disclosure provides an electronic device comprising: a memory storing executable instructions; and a processor executing the executable instructions in the memory to implement the point spread function calculation method described above.
[0175] An electronic device according to an embodiment of the present disclosure includes a memory and a processor.
[0176] This memory is used to store non-transitory computer-readable instructions. Specifically, the memory may include one or more computer program products, which may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may, for example, include random access memory (RAM) and / or cache memory. The non-volatile memory may, for example, include read-only memory (ROM), hard disk, flash memory, etc.
[0177] The processor 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 to perform desired functions. In one embodiment of this disclosure, the processor is used to execute computer-readable instructions stored in the memory.
[0178] Those skilled in the art will understand that, in order to solve the technical problem of how to achieve a good user experience, this embodiment may also include well-known structures such as communication buses and interfaces, and these well-known structures should also be included within the protection scope of this disclosure.
[0179] For a detailed description of this embodiment, please refer to the corresponding descriptions in the foregoing embodiments, which will not be repeated here.
[0180] Example 4
[0181] This disclosure provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the point spread function calculation method.
[0182] A computer-readable storage medium according to embodiments of the present disclosure stores non-transitory computer-readable instructions. When these non-transitory computer-readable instructions are executed by a processor, all or part of the steps of the methods described in the foregoing embodiments of the present disclosure are performed.
[0183] The aforementioned computer-readable storage media include, but are not limited to: optical storage media (e.g., CD-ROM and DVD), magneto-optical storage media (e.g., MO), magnetic storage media (e.g., magnetic tape or portable hard drive), media with built-in rewritable non-volatile memory (e.g., memory card), and media with built-in ROM (e.g., ROM cartridge).
[0184] Those skilled in the art should understand that the above description of the embodiments of the present invention is only intended to illustrate the beneficial effects of the embodiments of the present invention, and is not intended to limit the embodiments of the present invention to any of the examples given.
[0185] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.
Claims
1. A method for calculating the point spread function, characterized in that, include: Establish the initial point spread function; Set constraint parameters; Based on the initial point spread function and the constraint parameters, the final point spread function is obtained and calculated. The establishment of the initial point spread function includes: Establish a linear relationship between seismic observation data and velocity models; The objective function is established using the least squares method, thereby obtaining the underground model; The initial point diffusion function is determined based on the underground model; The objective function is: （1） Where d represents seismic data, L represents the seismic wave propagation operator, and m represents the subsurface model; The underground model is as follows: （2） in, For the estimated underground model, H is the Hessian matrix; The initial point spread function is: （3） in, For Green's function, Represents the source wavelet. Representing the Green's function The adjoint operator; The constraint parameters include the local neighborhood range, background velocity, illumination angle range of the imaging observation system within the neighborhood range, and imaging wavelet; The final point spread function is: （4） in, This represents the far-field imaging wavelet corresponding to the underground imaging point under the high-frequency approximation. A constraint function representing the range of illumination angles. x 0 represents the imaging point in the neighborhood. v ( x 0) represents the velocity within the neighborhood.
2. A point spread function calculation device, characterized in that, include: Initial module, establish the initial point spread function; The constraint module allows you to set constraint parameters. The calculation module obtains the final point spread function and calculates the solution based on the initial point spread function and the constraint parameters. The establishment of the initial point spread function includes: Establish a linear relationship between seismic observation data and velocity models; The objective function is established using the least squares method, thereby obtaining the underground model; The initial point diffusion function is determined based on the underground model; The objective function is: （1） Where d represents seismic data, L represents the seismic wave propagation operator, and m represents the subsurface model; The underground model is as follows: （2） in, For the estimated underground model, H is the Hessian matrix; The initial point spread function is: （3） in, For Green's function, Represents the source wavelet. Representing the Green's function The adjoint operator; The constraint parameters include the local neighborhood range, background velocity, illumination angle range of the imaging observation system within the neighborhood range, and imaging wavelet; The final point spread function is: （4） in, This represents the far-field imaging wavelet corresponding to the underground imaging point under the high-frequency approximation. A constraint function representing the range of illumination angles. x 0 represents the imaging point in the neighborhood. v ( x 0) represents the velocity within the neighborhood.
3. An electronic device, characterized in that, The electronic device includes: Memory, which stores executable instructions; A processor that executes the executable instructions in the memory to implement the point spread function calculation method of claim 1.
4. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the point spread function calculation method of claim 1.