A least squares reverse-time migration imaging method, device, equipment and medium
By improving the finite-memory quasi-Newton IL-BFGS method and optimizing the quasi-Newton equation with weight parameters, the problems of low computational efficiency and slow convergence speed in least-squares reverse time migration imaging are solved, and high-precision imaging of underground structures is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- XI'AN POLYTECHNIC UNIVERSITY
- Filing Date
- 2025-12-04
- Publication Date
- 2026-07-14
Smart Images
Figure CN121578374B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of geophysical exploration technology, and in particular to a least-squares reverse time migration imaging method, apparatus, equipment, and medium. Background Technology
[0002] Least-Squares Reverse Time Migration (LSRTM) is a high-precision seismic imaging technique based on the wave equation. It improves the imaging resolution and amplitude fidelity of subsurface structures through iterative optimization. Its core principle is to use the least-squares inversion method to compensate for the limitations of traditional reverse time migration (RTM), such as the period jump problem caused by velocity model errors. LSRTM establishes a linear relationship between observed and simulated data through the Born approximation and uses the conjugate gradient method to solve for the generalized inverse of the Hessian matrix to optimize the imaging results.
[0003] Currently, in least-squares reverse time migration imaging, commonly used optimization methods for solving large-scale nonlinear least-squares problems include the gradient method, Newton's method, and quasi-Newton methods. Newton's method has a second-order convergence speed, but it requires calculating the Hessian matrix and its inverse matrix of the objective function in each iteration, resulting in a huge computational burden. Furthermore, the method may fail when the Hessian matrix is not positive definite. To address this issue, quasi-Newton methods have been introduced, which avoid direct inversion by constructing an approximate inverse of the Hessian matrix. Among these, the BFGS method is widely used due to its numerical stability and superlinear convergence.
[0004] However, the BFGS method requires storing the complete approximate Hessian matrix during the iteration process, and the memory consumption increases sharply with the scale of model parameters, making it unsuitable for large-scale seismic inversion problems. Based on this, the finite-memory BFGS (L-BFGS) method was proposed. This method only retains the vector information of the most recent few iterations, which significantly reduces the storage requirements. However, the L-BFGS method still suffers from slow convergence and low computational efficiency in least squares reverse time migration, especially under complex geological conditions, where its local convergence is low and it is difficult to meet the requirements of high-precision imaging. Summary of the Invention
[0005] This invention provides a least-squares reverse time migration imaging method, apparatus, device, and medium, which can solve the problems existing in the prior art.
[0006] This invention provides a least-squares reverse time migration imaging method, comprising the following steps:
[0007] Acquire seismic wave propagation data of the target area to be imaged. Based on the seismic wave propagation data, obtain the velocity model characterizing the propagation characteristics of the subsurface medium, the observed seismic data, and the migration velocity field used to construct the initial background wavefield in the reverse time migration imaging of the wavefield of the target area.
[0008] The imaging profile from the first wavefield imaging iteration of reverse time migration imaging is set as a reflection coefficient model characterizing the subsurface tectonic process. Based on the velocity model and migration velocity field, simulated seismic data is obtained through Born forward modeling. The difference between the simulated seismic data and the observed seismic data is calculated to obtain the data residuals characterizing the fit between the current model and the real subsurface structure.
[0009] Reverse-time migration imaging is applied to the data residuals for reverse-time propagation to obtain the inverse propagation wavefield. This inverse propagation wavefield is then cross-correlated with the forward propagation wavefield to obtain the gradient of the objective function in the current iteration of the reflection coefficient model. Based on the gradient of the objective function, the approximate matrix of the Hessian inverse matrix, the gradient, and the iteration step size are calculated using the improved finite-memory quasi-Newton IL-BFGS method. The IL-BFGS method involves: by pre-setting an adjustable weight parameter, combining the quasi-Newton equation that matches the gradient to the objective function value during iteration with the quasi-Newton equation that directly adjusts the update amount of the reflection system model using the tuning ratio parameter during iteration, forming an improved quasi-Newton equation. The tuning ratio parameter is then adjusted to be an adaptive combination of the update amount of the reflection system model and the update amount of the residual gradient.
[0010] Based on the approximate matrix, gradient, and iteration step size of the Hessian inverse matrix, the reflection coefficient model is continuously updated and imaging is performed. When the imaging accuracy is higher than the preset imaging accuracy, the inverse time-shifted imaging map at this time is obtained.
[0011] Preferably, the quasi-Newton equation that can match the gradient to the objective function value during iteration is expressed as:
[0012] ;
[0013] The quasi-Newton equation that directly uses the tuning ratio parameter to adjust the update of the reflection system model during iteration is expressed as:
[0014] ;
[0015] ;
[0016] in: H k+1 The matrix that represents the approximate Hessian inverse matrix; Representing the reflection coefficient model Update volume; Represents the residual gradient Update volume; Indicates the tuning ratio parameter; This indicates the current iteration number.
[0017] Preferably, the improved quasi-Newton equation is expressed as:
[0018] ;
[0019] ;
[0020] in: Represents the weight parameters. ;
[0021] when When the value is 0, the equation becomes a quasi-Newton equation that directly adjusts the update of the reflection system model using the tuning ratio parameter during iteration. When the value is 1, the equation becomes a quasi-Newton equation that can match the gradient to the objective function value during iteration.
[0022] Preferably, the equation after adjusting the tuning ratio parameter is expressed as:
[0023] ;
[0024] in: This indicates the tuning ratio parameter.
[0025] Preferably, the equations for obtaining the approximate matrix, gradient, and iteration step size of the Hessian inverse matrix are as follows:
[0026] The gradient of the objective function in the current iteration of the reflection coefficient model Represented as:
[0027]
[0028] in: This represents simulated earthquake data; This represents the imaging result under the first imaging iteration of the reverse time migration imaging method;
[0029] The approximate matrix representation of the Hessian inverse matrix is as follows:
[0030] ;
[0031] The gradient of the Hessian inverse matrix is expressed as:
[0032] ;
[0033] The iteration step size of the Hessian inverse matrix is expressed as:
[0034] ;
[0035] in: H k+1 The matrix that represents the approximate Hessian inverse matrix; d k This represents the gradient of the Hessian inverse matrix; α k This represents the iteration step size of the Hessian inverse matrix; ; ; ; .
[0036] This invention also provides a least-squares reverse time-shift imaging device, comprising:
[0037] The data module is used to acquire seismic wave propagation data of the target area to be imaged. Based on the seismic wave propagation data, it acquires the velocity model characterizing the propagation characteristics of the subsurface medium, the observed seismic data, and the migration velocity field used to construct the initial background wavefield in the reverse time migration imaging of the wavefield of the target area.
[0038] The imaging profile from the first wavefield imaging iteration of reverse time migration imaging is set as a reflection coefficient model characterizing the subsurface tectonic process. Based on the velocity model and migration velocity field, simulated seismic data is obtained through Born forward modeling. The difference between the simulated seismic data and the observed seismic data is calculated to obtain the data residuals characterizing the fit between the current model and the real subsurface structure.
[0039] The forward and inverse evolution module is used to apply inverse time migration imaging to the data residuals for inverse time propagation, obtain the inverse propagation wavefield and perform cross-correlation imaging with the forward propagation wavefield to obtain the gradient of the objective function in the current iteration of the reflection coefficient model. Based on the gradient of the objective function, the approximate matrix of the Hessian inverse matrix, the gradient, and the iteration step size are calculated using the improved finite memory quasi-Newton IL-BFGS method. The IL-BFGS method is as follows: by pre-setting an adjustable weight parameter, the quasi-Newton equation that can match the gradient to the objective function value in the iteration is combined with the quasi-Newton equation that directly adjusts the update amount of the reflection system model using the tuning ratio parameter in the iteration, forming an improved quasi-Newton equation. The tuning ratio parameter is then adjusted to be an adaptive combination of the update amount of the reflection system model and the update amount of the residual gradient.
[0040] The imaging module continuously updates the reflection coefficient model and performs imaging based on the approximate matrix, gradient, and iteration step size of the Hessian inverse matrix. When the imaging accuracy is higher than the preset imaging accuracy, the inverse time-shifted imaging map at this time is obtained.
[0041] This invention also provides an electronic device, including a memory and a processor;
[0042] The memory is used to store computer programs;
[0043] When the processor executes the computer program stored in the memory, it implements the steps of the least squares reverse time migration imaging method described above.
[0044] This invention also provides a computer-readable storage medium for storing a computer program, which, when executed by a processor, implements the steps of a least-squares reverse time-shift imaging method as described above.
[0045] This invention provides a least-squares reverse time migration imaging method, apparatus, device, and medium, which have the following advantages compared with the prior art:
[0046] This invention first acquires simulated seismic data in least-squares reverse-time migration imaging using a reflection coefficient model. The difference between the simulated and observed seismic data is used as the residual data, representing the degree of fit between the current model and the actual underground structure. This process first obtains high-precision structural migration residual data. Then, in the process of calculating the Hessian inverse matrix data based on the gradient of the objective function in the current iteration of the reflection coefficient model, that is, in the process of capturing the second-order curvature information of the objective function at the current iteration point, a quasi-Newton equation that matches the gradient to the objective function value during iteration is combined with a quasi-Newton equation that directly adjusts the update amount of the reflection system model using an adaptive adjustment parameter through adjustable weight parameters. This process can simultaneously use the gradient to match the objective function value during iteration and directly adjust the update amount of the reflection system model using an adaptive adjustment parameter. Moreover, the addition combination in this process is a weighted adaptive combination, which can capture the second-order curvature information of the objective function at the current iteration point more accurately with a higher convergence speed. Combined with the adaptive adjustment parameter, the computational efficiency is greatly improved, and finally, high-precision migration imaging is achieved. Attached Figure Description
[0047] Figure 1 This is a schematic diagram of the overall process of a least-squares reverse time migration imaging method provided in an embodiment of the present invention;
[0048] Figure 2 A schematic diagram of the imaging results of a least-squares reverse time migration imaging method with 30 iterations of L-BFGS-LSRTM provided in an embodiment of the present invention;
[0049] Figure 3 A schematic diagram of the imaging results of a least-squares reverse time migration imaging method with 30 iterations using the IL-BFGS-LSRTM method, provided in an embodiment of the present invention;
[0050] Figure 4This is a schematic diagram comparing the convergence curves of normalized data residuals from two least-squares reverse time migration imaging methods, IL-BFGS-LSRTM and L-BFGS-LSRTM, after 30 iterations, provided in an embodiment of the present invention. Detailed Implementation
[0051] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.
[0052] Currently, in least-squares reverse-time migration imaging, Newton's method is a numerical method for optimizing imaging parameters. Its core principle is to improve imaging accuracy by iteratively optimizing an objective function (such as the sum of squared errors). Specifically:
[0053] I. Newton's method.
[0054] objective function Regarding the reflection coefficient model Differentiating the expression, we get:
[0055] .
[0056] in: Defined as the Frechet derivative, denoted as Then the above formula can be written as:
[0057] .
[0058] Because directly calculating the Frechet derivative is computationally very expensive, it is generally not used directly. Therefore, given the background model parameters... Expanding the objective function using the Taylor formula in the vicinity yields:
[0059] .
[0060] in: For the objective function Regarding the background model The first derivative, Let be the Hessian matrix, denoted as the objective function. Regarding the background model The second derivative of , therefore we have:
[0061] .
[0062] It can be seen that, From linear terms and nonlinear terms The two-part structure, the Frechet derivative, is almost independent of the reflection coefficient model under the condition of local linearity, then... The nonlinear term approaches 0, at which point it degenerates into:
[0063] .
[0064] When the error function For the reflection coefficient model When the derivative is 0, the update amount of the model is:
[0065] .
[0066] Then Newton's method updates the reflection coefficient model The iterative formula is:
[0067] .
[0068] Different inversion optimization methods can be obtained by replacing the inverse of the Hessian matrix with different quantities. For example, replacing the inverse of the Hessian with the step size yields gradient-based methods, while using... The approximate matrix that replaces the inverse of Hessian is the quasi-Newton method.
[0069] II. Quasi-Newtonian method.
[0070] Although Newton's method is favored for its rapid convergence, its implementation requires solving for the inverse of the Hessian matrix, a step that is both complex and prone to problems; in particular, Newton's method may not work properly when the Hessian matrix is not positive definite. To address these challenges, the academic community has developed quasi-Newton methods.
[0071] The core concept of the quasi-Newton method lies in utilizing The approximate matrix is used to replace the inverse of the Hessian matrix, thereby simplifying the calculation process and maintaining the efficiency of the method; the assumption function It is differentiable twice consecutively, and it is in The second approximate expansion yields:
[0072] .
[0073] Differentiating the above equation, we get:
[0074] .
[0075] Let the above formula be , , We can obtain:
[0076] .
[0077] Then the approximate matrix of the inverse of Hessian The following relationship must be satisfied:
[0078] .
[0079] This equation is a quasi-Newtonian equation, also known as the secant equation.
[0080] Quasi-Newton methods overcome the limitations of Newton's method in certain situations by simplifying the computation process, and have become an effective tool for solving least squares problems in practical applications. Currently, commonly used quasi-Newton methods include the DFP method and the BFGS method. The BFGS method is particularly outstanding due to its efficiency and practicality; it not only performs well numerically but also quickly approximates the optimal solution. Especially when dealing with minimizing convex functions, it demonstrates excellent global convergence through a precise line search strategy.
[0081] The core idea of the BFGS method is that it calculates the approximate matrix of the Hessian inverse needed for the current iteration by combining the reflection coefficient model parameters, residual gradient information, and the approximate matrix of the Hessian inverse from the previous iteration. The iterative formula is:
[0082] .
[0083] The above equation can be rewritten using the Sherman-Morrison formula as follows:
[0084] .
[0085] .
[0086] in: This is an approximate matrix of the Hessian inverse. For the reflection coefficient model Update volume For residual gradient The update volume is visible. and It is possible and We obtain the matrix that approximates the Hessian inverse. Iteratively obtained.
[0087] Reflection coefficient model and search direction The iterative formula is:
[0088] .
[0089] .
[0090] in: for First The residual gradient of the next iteration. Indicates the search direction.
[0091] Although the BFGS method effectively simplifies the approximate calculation of the Hessian inverse matrix by combining the update direction of the residual gradient with the adjustment of the reflection coefficient model parameters, thus reducing computational costs and memory requirements to some extent, it still requires a significant amount of memory when calculating the approximate Hessian inverse matrix. To further conserve memory, some researchers have proposed a finite-memory BFGS method, namely the L-BFGS method. The L-BFGS method, developed from the BFGS method, aims to reduce memory usage. This method not only inherits the excellent convergence properties of the BFGS method in theory but also successfully solves the problem of high storage and computational resource requirements associated with the BFGS method.
[0092] The main difference between the L-BFGS method and the BFGS method lies in the approximation matrix of the Hessian inverse. In terms of computational methods, the L-BFGS method uses storage vectors and The search direction is directly solved using an iterative method. In this process, it does not need to explicitly calculate or store the approximate Hessian matrix. or The update formula is as follows:
[0093] .
[0094] in: For the current iteration number, and ,when hour, Size ,when hour, Pick , ;
[0095] in The initial matrix and It is usually a scalar matrix. Known as the tuning ratio parameter, it has three main possible values: , or .
[0096] when When the value is 1, it degenerates into the memoryless BFGS method.
[0097] III. Improved L-BFGS method.
[0098] 1. Improved quasi-Newton equations.
[0099] Although the L-BFGS method has low memory requirements and good convergence, its convergence speed is low and its computational efficiency is not high. Therefore, in-depth research and improvement of the L-BFGS method is of great theoretical importance and can also bring significant value to practical applications.
[0100] Typically, the quasi-Newton method follows the quasi-Newton equation in each iteration to ensure the correctness of the calculation, which shows the importance of the quasi-Newton equation in the quasi-Newton method. Therefore, many scholars have studied the quasi-Newton equation and found that by adjusting the quasi-Newton equation, the L-BFGS method can not only maintain the core advantages of the quasi-Newton method, but also identify the second curvature change of the objective function with higher accuracy, thereby improving its computational efficiency.
[0101] In 2006, Wei et al. proposed a BFGS-TYPE method, whose corresponding new quasi-Newton equation is:
[0102] .
[0103] in: Furthermore, the superlinear convergence of this method was proven.
[0104] Yuan proposed a BFGS method for matching function values during iteration, with the quasi-Newton equation as follows:
[0105] .
[0106] Experimental results show that the improved method not only retains the global and local convergence of the original method, but also achieves better numerical results.
[0107] In 2011, by performing a convex combination of the modified quasi-Newton equation proposed by Wei et al. and the modified quasi-Newton equation proposed by Yuan, Saman et al. derived a new quasi-Newton equation:
[0108] .
[0109] .
[0110] Experimental results show that the BFGS optimization method using this quasi-Newton equation outperforms the version previously proposed by Yuan, which verifies the effectiveness of the newly proposed quasi-Newton equation method.
[0111] Furthermore, Li et al. proposed a quasi-Newtonian equation that ensures global convergence even under the non-convex assumption:
[0112] .
[0113] .
[0114] To optimize the numerical results and improve the convergence speed, this invention adopts a weight parameter. By combining the two quasi-Newton equations proposed by Li and Yuan in a convex manner, an innovative improved quasi-Newton equation is proposed, as follows:
[0115] .
[0116] .
[0117] in: , or , ,when When the value is 0, the equation reverts to the method proposed by Li. When the value is 1, the equation reverts to the equation proposed by Yuan.
[0118] 2. Improved L-BFGS method.
[0119] Quasi-Newton equations play a central role in the calculations of the quasi-Newton method, and the improved quasi-Newton equations proposed in this invention can optimize numerical results and improve computational efficiency; therefore, the improved quasi-Newton equations proposed above are used to calculate... replace This study investigates an IL-BFGS method and examines the adjustment parameters in the formula. The possible values are as follows:
[0120] .
[0121] For ease of calculation, the initial value of the iteration is set to... Analysis of the convergence properties of IL-BFGS shows that this method can ensure global convergence while significantly improving the convergence speed, and it achieves this by retaining only the nearest convergence. right Update Instead of storing the entire matrix, it saves data storage space, thus effectively improving computational efficiency.
[0122] IV. Least-squares reverse time migration imaging based on the IL-BFGS method.
[0123] The IL-BFGS method demonstrates the ability to ensure global convergence and saves on storage space. Furthermore, its convergence speed is faster and follows an R-linear trend. Therefore, applying this method to the least squares solution of LSRTM can significantly improve computational efficiency. The LSRTM solution process based on the IL-BFGS method includes:
[0124] Step 1: Calculate the gradient of the objective function :
[0125] .
[0126] Step 2: Use the IL-BFGS method to obtain an approximate matrix of the Hessian inverse. ,gradient and iteration step size :
[0127] .
[0128] .
[0129] .
[0130] Step 3: Update the model:
[0131] .
[0132] Step 4: If satisfied or If the condition is not met, the method terminates and the imaging result is output; otherwise, return to step one.
[0133] Based on the above analysis, the imaging workflow based on IL-BFGS-LSRTM is as follows: Figure 1 As shown, it specifically includes:
[0134] (1) In the initial stage, velocity models and seismic observation data need to be provided. And the offset velocity field.
[0135] (2) Set the initial imaging value of the reflection coefficient model to Therefore, the initial iteration process is essentially the same as the standard reverse time migration process; that is, the result of the initial iteration is equivalent to the imaging output of a conventional reverse time migration (RTM). The output is represented as a profile of the reverse time migration; this result is then used as the reflection coefficient model (i.e., the input data) and fed into the reverse migration method for further processing.
[0136] (3) Obtain simulated seismic data by performing Born forward modeling. .
[0137] (4) The data residual is obtained by calculating the difference between the simulated seismic data and the observed seismic data provided in the initial stage. .
[0138] (5) Using the wavefield residual as input, the reverse-time propagation wavefield is calculated; specifically, the gradient of the objective function is obtained by applying the reverse-time migration technique to the data residual and performing cross-correlation imaging. .
[0139] (6) The approximate matrix of the Hessian inverse is calculated using the IL-BFGS method. A sufficiently descent gradient and iteration step size And continuously update the reflection coefficient model. .
[0140] (7) Evaluate the accuracy of the reflection coefficient model to determine whether it meets the accuracy requirements of imaging or whether the number of iterations has reached the preset upper limit; if it meets the requirements, stop the inversion process and output the final image obtained by least squares reverse time migration; otherwise, if the conditions are not met, the process will return to step (3) for further iteration.
[0141] This invention focuses on the Limited Memory Broyden Fletcher Goldfarb Shanno (L-BFGS) method, a local optimization method derived from Newton's algorithm and its improvements. Addressing its slow convergence speed and low computational efficiency, an improved L-BFGS Least Squares Reverse Time Migration (IL-BFGS-LSRTM) imaging method is proposed. By studying quasi-Newton equations and employing a weighting parameter to convexly combine two quasi-Newton equations to more accurately capture their second-order curvature characteristics, a new quasi-Newton equation is obtained. The improved IL-BFGS method achieves higher computational efficiency while maintaining global convergence. The proposed IL-BFGS-LSRTM method improves image quality, achieves faster convergence, and lower convergence values. Its normalized data residuals are reduced by approximately 9.07% compared to L-BFGS-LSRTM, while computational efficiency is improved by approximately 11.83%.
[0142] To verify the feasibility of the IL-BFGS-LSRTM method, this invention uses a leveling velocity model for testing. Figure 2 The images were obtained after 30 iterations of L-BFGS-LSRTM. Figure 3The images are the results of 30 iterations using the IL-BFGS-LSRTM method; from Figure 2 It can be seen that the in-phase axis of L-BFGS-LSRTM after 30 iterations is quite blurry, with significant crosstalk noise, and the imaging effect on both sides of the model is poor. Figure 2 The red arrow points to; by Figure 3 It can be seen that the crosstalk noise of IL-BFGS-LSRTM after 30 iterations is significantly suppressed, the in-phase axis is clearer, and the imaging resolution on both sides of the model is higher.
[0143] To compare the convergence speed performance of IL-BFGS-LSRTM and L-BFGS-LSRTM, Figure 4 A comparison chart of the convergence curves of the normalized data residuals after 30 iterations for these two methods is presented. Figure 4 As can be seen, the convergence speed of IL-BFGS-LSRTM is faster than that of L-BFGS-LSRTM, and the residual can converge to a lower value after 30 iterations, which improves the computational efficiency and verifies the effectiveness of the method of the present invention.
[0144] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.
Claims
1. A least-squares reverse-time migration imaging method, characterized in that, Includes the following steps: Acquire seismic wave propagation data of the target area to be imaged. Based on the seismic wave propagation data, obtain the velocity model characterizing the propagation characteristics of the subsurface medium, the observed seismic data, and the migration velocity field used to construct the initial background wavefield in the reverse time migration imaging of the wavefield of the target area. The imaging profile from the first wavefield imaging iteration of reverse time migration imaging was set as a reflection coefficient model characterizing the subsurface tectonic process, and simulated seismic data were obtained through Born forward modeling based on the velocity model and migration velocity field. The difference between simulated earthquake data and observed earthquake data is calculated to obtain the data residuals that characterize the degree of fit between the current model and the actual underground structure; Reverse-time migration imaging is applied to the data residuals for reverse-time propagation to obtain the inverse propagation wavefield. This inverse propagation wavefield is then cross-correlated with the forward propagation wavefield to obtain the gradient of the objective function in the current iteration of the reflection coefficient model. Based on the gradient of the objective function, the approximate matrix of the Hessian inverse matrix, the gradient, and the iteration step size are calculated using the improved finite-memory quasi-Newton IL-BFGS method. The IL-BFGS method involves: by pre-setting an adjustable weight parameter, combining the quasi-Newton equation that matches the gradient to the objective function value during iteration with the quasi-Newton equation that directly adjusts the update amount of the reflection system model using the tuning ratio parameter during iteration, forming an improved quasi-Newton equation. The tuning ratio parameter is then adjusted to be an adaptive combination of the update amount of the reflection system model and the update amount of the residual gradient. Based on the approximate matrix, gradient, and iteration step size of the Hessian inverse matrix, the reflection coefficient model is continuously updated and imaging is performed. When the imaging accuracy is higher than the preset imaging accuracy, the inverse time-shifted imaging map at this time is obtained.
2. The least-squares reverse-time migration imaging method according to claim 1, characterized in that, The quasi-Newton equation that can match the gradient to the objective function value in the iteration is expressed as: ； The quasi-Newton equation that directly uses the tuning ratio parameter to adjust the update of the reflection system model during iteration is expressed as: ； ； in: H k+1 The matrix that represents the approximate Hessian inverse matrix; Representing the reflection coefficient model Update volume; Represents the residual gradient Update volume; Indicates the tuning ratio parameter; This indicates the current iteration number.
3. The least-squares reverse-time migration imaging method according to claim 2, characterized in that, The improved quasi-Newton equation is expressed as: ； ； in: Represents the weight parameters. ; when When the value is 0, the equation becomes a quasi-Newton equation that directly adjusts the update of the reflection system model using the tuning ratio parameter during iteration. When the value is 1, the equation becomes a quasi-Newton equation that can match the gradient to the objective function value during iteration.
4. The least-squares reverse-time migration imaging method according to claim 3, characterized in that, The equation after adjusting the tuning ratio parameter is expressed as follows: ； in: This indicates the tuning ratio parameter.
5. The least-squares reverse-time migration imaging method according to claim 3, characterized in that, The equations for obtaining the approximate matrix, gradient, and iteration step size of the Hessian inverse matrix are as follows: The gradient of the objective function in the current iteration of the reflection coefficient model Represented as: in: This represents the simulated seismic data from the first imaging iteration of the reverse time migration imaging method; This represents the imaging result under the first imaging iteration of the reverse time migration imaging method; The approximate matrix representation of the Hessian inverse matrix is as follows: ； The gradient of the Hessian inverse matrix is expressed as: ； The iteration step size of the Hessian inverse matrix is expressed as: ； in: H k+1 The matrix that represents the approximate Hessian inverse matrix; d k This represents the gradient of the Hessian inverse matrix; α k This represents the iteration step size of the Hessian inverse matrix; ; ; ; .
6. A least-squares reverse-time migration imaging device, characterized in that, include: The data module is used to acquire seismic wave propagation data of the target area to be imaged. Based on the seismic wave propagation data, it acquires the velocity model characterizing the propagation characteristics of the subsurface medium, the observed seismic data, and the migration velocity field used to construct the initial background wavefield in the reverse time migration imaging of the wavefield of the target area. The imaging profile from the first wavefield imaging iteration of reverse time migration imaging was set as a reflection coefficient model characterizing the subsurface tectonic process, and simulated seismic data were obtained through Born forward modeling based on the velocity model and migration velocity field. The difference between simulated earthquake data and observed earthquake data is calculated to obtain the data residuals that characterize the degree of fit between the current model and the actual underground structure; The forward and inverse evolution module is used to apply inverse time migration imaging to the data residuals for inverse time propagation, obtain the inverse propagation wavefield and perform cross-correlation imaging with the forward propagation wavefield to obtain the gradient of the objective function in the current iteration of the reflection coefficient model. Based on the gradient of the objective function, the approximate matrix of the Hessian inverse matrix, the gradient, and the iteration step size are calculated using the improved finite memory quasi-Newton IL-BFGS method. The IL-BFGS method is as follows: by pre-setting an adjustable weight parameter, the quasi-Newton equation that can match the gradient to the objective function value in the iteration is combined with the quasi-Newton equation that directly adjusts the update amount of the reflection system model using the tuning ratio parameter in the iteration, forming an improved quasi-Newton equation. The tuning ratio parameter is then adjusted to be an adaptive combination of the update amount of the reflection system model and the update amount of the residual gradient. The imaging module continuously updates the reflection coefficient model and performs imaging based on the approximate matrix, gradient, and iteration step size of the Hessian inverse matrix. When the imaging accuracy is higher than the preset imaging accuracy, the inverse time-shifted imaging map at this time is obtained.
7. An electronic device, characterized in that, include: Memory and processor; The memory is used to store computer programs; When the processor executes the computer program stored in the memory, it implements the steps of the least squares reverse time migration imaging method as described in any one of claims 1 to 5.
8. A computer-readable storage medium, characterized in that, Used to store a computer program, which, when executed by a processor, implements the steps of a least-squares reverse time-shifting imaging method as described in any one of claims 1 to 5.