Low-frequency seismic signal sparse inversion and reconstruction method and system based on spatial structure regularization constraint

Abstract

The invention belongs to the technical field of seismic signals, discloses a spatial structure regularization constrained low-frequency seismic signal sparse inversion and reconstruction method, and aims to recognize and solve the problem of frequency dependence of a seismic reflection spatial structure in a targeted manner. By estimating the space structure from the adjacent higher frequency band of the target low-frequency signal, constraint information which is more similar to and more related to the real space structure of the target low-frequency signal is obtained. Compared with a method for estimating the space structure by directly using broadband data which may have missing target low frequency, the space structure constraint provided by the method is more accurate, the recovery of low-frequency signals can be better guided, and error information introduced due to structure mismatching is avoided. By introducing a more reasonable and more relevant space structure as a strong prior constraint, the method effectively reduces the inherent discomfort and multiplicity of the sparse inversion problem.

Description

Technical Field

[0001] This invention belongs to the field of seismic signal technology, and in particular relates to a method and system for sparse inversion and reconstruction of low-frequency seismic signals with spatial structure regularization constraints. Background Technology

[0002] Low-frequency signals play a crucial role in seismic exploration. First, they possess stronger penetration and greater detection depth, making them essential for imaging deep and ultra-deep targets. Second, the inclusion of low-frequency signals effectively broadens the bandwidth of seismic data, thereby improving resolution. Furthermore, in reservoir parameter prediction techniques such as wave impedance inversion, low-frequency signals provide reliable background trend information, which is vital for the stability and accuracy of the inversion, directly impacting the accuracy of reservoir property characterization. In particular, in full waveform inversion (FWI) velocity modeling, accurate low-frequency signals are key to overcoming the high nonlinearity of FWI and avoiding getting trapped in local minima, providing a foundation for constructing reliable low-wavenumber background velocity models.

[0003] However, low-frequency signals in actual seismic data are often of poor quality. In terms of acquisition, effectively exciting low-frequency signals is inherently difficult, and the receiver's own response characteristics (natural frequency) also suppress these signals. Regarding noise, surface waves are among the most severe interference waves contaminating low-frequency signals in land exploration. Although various surface wave suppression techniques exist, they inevitably damage the effective low-frequency signal during the suppression process. Furthermore, the spectrum of ambient noise in the field is not ideal white noise; its low-frequency components often have stronger energy, further deteriorating the signal-to-noise ratio of low-frequency signals. Therefore, how to effectively recover and reconstruct damaged or even missing low-frequency signals is an important research topic in the field of seismic data processing.

[0004] Existing technologies for low-frequency signal recovery and reconstruction mainly include the following categories: 1. A low-frequency signal recovery method based on mathematical transformation and multichannel filtering.

[0005] These methods aim to extract or enhance low-frequency components from noisy data. Examples include low-frequency recovery based on the maximum variance modulus; frequency-division denoising methods for surface wave interference, estimating denoising operators through frequency band division; improving low-frequency signal recovery accuracy by increasing the coherence radius; inverting the low-frequency trend of the velocity field using the seismic signal envelope (which has lower frequency components and stronger noise resistance); estimating low-frequency components using cascaded differential operations; low-frequency recovery of controllable source signals based on empirical mode decomposition; and low-frequency enhancement through multi-channel filtering in the Radon domain. These methods are essentially signal enhancement or extraction methods, and their recovery effect is limited when the target low-frequency signal has an extremely low signal-to-noise ratio or is completely missing.

[0006] 2. Sparse inversion method based on compressed sensing theory.

[0007] Compressed sensing theory posits that if a signal satisfies sparsity in a certain transform domain (such as the reflection coefficient domain), then frequency components outside the original data, including missing low frequencies, can be recovered from band-limited data through sparse inversion.

[0008] Specific applications include: using the L1 norm to perform sparse inversion of reflection coefficients, and then constructing the low-frequency components of seismic data from the recovered reflection coefficients; developing the L1 norm into a total variational (TV) regularization constraint to improve the accuracy of low-frequency signal reconstruction; and applying it to low-frequency compensation of weak signals in deep carbonate fracture reservoirs.

[0009] This type of method represents a significant advancement in low-frequency signal reconstruction, but as mentioned earlier, its inversion results often exhibit strong ambiguity.

[0010] 3. Low-frequency signal reconstruction method based on machine learning.

[0011] These methods learn and establish nonlinear mappings between low-frequency and high-frequency signals in seismic data by constructing different neural network structures (such as deep learning networks), thereby achieving the recovery and reconstruction of low-frequency components. The main challenge lies in the model's generalization ability; a well-trained model may perform significantly worse when applied to data with different geological conditions or acquisition parameters.

[0012] The technical solution most similar to this invention is a sparse inversion low-frequency signal reconstruction method based on compressed sensing theory, combined with certain spatial structure constraints. However, existing solutions, in applying spatial structure constraints, often directly estimate the spatial structure from the original broadband seismic data, failing to fully consider the frequency dependence of spatial reflection structures; that is, the spatial structures reflected by seismic data from different frequency bands may differ. This leads to a situation where, when the goal is to recover low-frequency signals, using the spatial structure estimated from broadband data (which may have lost the target low frequency) to constrain the inversion of low-frequency signals affects its effectiveness and accuracy. This invention addresses this issue.

[0013] Low-frequency signals play an irreplaceable and crucial role in seismic exploration for thin-layer structure identification, reservoir prediction, deep imaging, and full-waveform inversion velocity modeling. However, in actual seismic data acquisition, due to limitations in excitation and reception conditions, interference from strong energy noise such as surface waves, and the effects of data processing, low-frequency signals are often severely contaminated, distorted, or even completely missing in certain frequency bands.

[0014] Although sparse inversion methods based on compressed sensing theory can recover and reconstruct missing low-frequency signals to some extent, these methods face the following core technical challenges: The inversion results are highly ambiguous and uncertain: sparse inversion is inherently an ill-posed problem, especially when the low-frequency signal-to-noise ratio is extremely low or completely absent. Relying solely on the sparsity of the reflection coefficient as a constraint often fails to yield a unique, geologically reasonable low-frequency solution. The inversion results may contain multiple possibilities, leading to insufficient reliability of the recovered low-frequency signal.

[0015] Frequency Dependence of Spatial Structure Constraints: Introducing spatial structure information into inversion as a regularization constraint is an effective way to improve inversion stability. However, the spatial structure of seismic reflections (such as the shape and continuity of phase axes) exhibits significant frequency dependence. This is because seismic waves of different frequencies have varying resolution capabilities for the subsurface medium, and the interference effect of seismic reflections varies with frequency. If the spatial structure is directly estimated from raw broadband seismic data that may lack the target low-frequency component, and then used to constrain the inversion of the target low-frequency signal, this spatial structure may differ significantly from the true spatial structure of the target low-frequency signal, leading to poor constraint effectiveness or even introducing erroneous guidance.

[0016] Conventional low-frequency recovery methods are ineffective for severely missing signals: Traditional low-frequency signal recovery methods based on mathematical transformations or multichannel filtering primarily aim to extract low-frequency signals from noise. When the target low-frequency signal has an extremely low signal-to-noise ratio, or when certain frequency bands are completely missing, these methods struggle to achieve ideal recovery results and cannot reconstruct the missing frequency components "out of thin air".

[0017] Based on the above analysis, the problems and shortcomings of the existing technology are as follows: (1) The multiple solutions and instability of sparse inversion.

[0018] Relying solely on the sparsity of the reflection coefficients (such as the L1 norm or Cauchy distribution assumption) as a priori constraint for inversion often results in an ill-posed problem when low-frequency signals are severely lacking or the signal-to-noise ratio is extremely low. Multiple solutions exist that satisfy both data fitting and sparsity requirements. This leads to low reliability of the recovered low-frequency signals, potentially resulting in significant deviations from reality. Furthermore, the inversion results are highly sensitive to the selection of the initial model and regularization parameters, and their stability needs improvement.

[0019] (2) The frequency dependence problem of spatial structure constraints has not been effectively solved.

[0020] While some studies have attempted to incorporate spatial structure into inversion, this is typically done by directly estimating spatial structure information (such as dip and strike) from the input (potentially missing low-frequency) broadband seismic data. The spatial structure of seismic reflections is frequency-dependent due to the interference effect of seismic waves. That is, the stratigraphic details and phase axis morphology revealed by seismic data from different frequency bands may differ. If the spatial structure estimated from broadband data is used to constrain the inversion of the target low-frequency signal, this constraint may be inaccurate, or even introduce erroneous structural information, misleading the low-frequency signal recovery process and reducing recovery accuracy, because the spatial structures of the two frequency bands themselves may not be completely consistent.

[0021] (3) Insufficient adaptability to complex geological conditions.

[0022] In regions with complex geological structures and dramatic stratigraphic changes, the interference effect of seismic waves is more pronounced, and the frequency dependence of spatial structures is also stronger. If existing methods cannot properly address this issue, the effectiveness of recovering low-frequency signals in these regions will further decline.

[0023] The closest existing technology to the scheme in this application is the "Reflection-WaveformInversion Regularized with Structure-Oriented Smoothing Shaping" proposed by Yao et al. Within the framework of Reflection Waveform Inversion (RWI), it first calculates the gradient structure tensor from seismic images, and then constructs a structure-oriented smoothing operator by solving the anisotropic diffusion equation to constrain the background velocity field in the strike direction of the strata. The entire process adopts a three-step iterative alternation of "constructing a temporary reflector - updating long-wave velocity - structure diffusion smoothing", which aims to stabilize the low-frequency-long-wave velocity inversion and reduce the blocky artifacts caused by the finite reflection aperture. Its ability to improve the quality of deep low-frequency imaging has been verified on the Marmousi and Overthrust models.

[0024] However, this technique still has significant shortcomings: First, the ill-conditioning inherent in RWI is not eliminated, and the limited observation aperture and velocity-depth trade-off still lead to columnar or clumped velocity anomalies in the inversion results, especially in areas with strong noise ([researchgate.net][1]); Second, this method focuses on smoothing background velocities along structural directions and does not explicitly recover the ultra-low frequency information lost during the acquisition and processing stages. Low-frequency models still need to be constructed externally and are greatly affected by the sparsity of well points and the reliability of velocity ([ikonscience.com][2]); Third, its structure-guided diffusion depends on the accuracy of the initial structure tensor, and excessive smoothing may mask small-scale geological features such as thin interbedded layers, resulting in decreased resolution and weakened amplitude ([researchgate.net][3]). Summary of the Invention

[0025] To address the problems existing in the prior art, this invention provides a method for sparse inversion and reconstruction of low-frequency seismic signals with spatial structure regularization constraints.

[0026] This invention is implemented as follows: a method for sparse inversion and reconstruction of low-frequency seismic signals with spatial structure regularization constraints includes: Step 1: Construction and solution of the objective function for sparse pulse seismic inversion.

[0027] Step 2: Spatial structure and frequency dependence analysis of seismic records.

[0028] Step 3: Low-frequency signal inversion based on spatial structure constraints.

[0029] Furthermore, the objective function for sparse pulse seismic inversion is constructed and solved.

[0030] According to the convolution model, the seismic record d can be represented as the convolution of the seismic wavelet w and the reflection coefficient sequence r plus noise n: (1) Where t is the earthquake recording time; written in matrix form as: (2) in, , and These are vectors composed of seismic records, reflection coefficients, and random noise, respectively. It is a matrix composed of seismic wavelets.

[0031] Solving the maximum a posteriori probability density problem is equivalent to minimizing the following objective function: (3) in, The first term is the data fitting term (error term). It is the variance of the data.

[0032] The gradient of the objective function is: (4) in, It is A diagonal matrix whose diagonal elements are (5) If we set the gradient of the objective function to zero, then the solution to the objective function is: (6) Due to the diagonal matrix Including unknown vectors to be inverted This is a nonlinear inversion problem, which is usually solved using an iterative reweighting algorithm: first, given the reflection coefficient... Initial value, calculate From equation (6), we obtain the new Recalculate Then proceed to the next iteration until convergence.

[0033] Furthermore, the spatial structure of the seismic record and its frequency dependence are analyzed.

[0034] The gradient structure tensor (GST) is used to estimate the dip and dip direction of seismic records; for 3D seismic data... Its spatial gradient is (7) The gradient structure tensor (GST) is defined as follows: (8) Eigenvalue decomposition of the structure tensor matrix yields: (9) In the formula, , and These are the three eigenvalues ​​of the structure tensor, which are positive real numbers between 0 and 1. , and These are the eigenvectors corresponding to the three eigenvalues; assuming Then the eigenvector This indicates the direction of maximum gradient, i.e., the direction of the construction tendency. and These represent two directions parallel to the structure; for two-dimensional seismic data, the structure tensor degenerates into a two-dimensional form, having (10) The two eigenvectors at this time and These are respectively perpendicular to the direction of the phase axis and parallel to the direction of the phase axis.

[0035] Furthermore, the low-frequency signal inversion based on spatial structure constraints.

[0036] After completing the analysis of the spatial structure and frequency dependence of the seismic record, low-frequency signal inversion based on spatial structure constraints can be performed; firstly, the single-channel convolution model needs to be extended to a multi-channel convolution model, that is, formula (2) is extended to: (11) in, and It is by A super vector formed by connecting the beginning and end of a seismic trace. It is composed of wavelet matrix The block matrix is ​​formed; at this time, the single-channel sparse inversion objective function represented by equation (3) is expanded into the following multi-channel sparse inversion objective function, which has (12) Introducing the spatial structure of the low-frequency signal into the objective function of low-frequency signal inversion, equation (22) is expanded to: (13) The objective function at this time It consists of three parts: the first part is the error term, which characterizes the error between the actual seismic record and the synthetic seismic record; the second part is the sparse structure regularization term, which characterizes the sparse structure of the reflection coefficient sequence; and the third part is the spatial structure regularization term, which describes the spatial structure followed by the low-frequency signal. and It is the regularization coefficient. It is a high cutoff frequency. The low-pass filter, It is a filtering operator related to spatial structure; the objective function (13) can be solved numerically using a method similar to that of the objective function (3).

[0037] After obtaining a convergent reflection coefficient sequence Then, it is low-pass filtered (high cutoff frequency is...). This is used as the recovered low-frequency seismic signal; then, the recovered low-frequency signal is compared with the high-frequency signals in the original seismic record. The frequency components are merged (through frequency domain replacement or time domain superposition) to obtain the final broadband seismic record after low-frequency recovery.

[0038] Another objective of this invention is to provide a sparse inversion and reconstruction system for low-frequency seismic signals with spatial structure regularization constraints, comprising: The solver module is used for constructing and solving the objective function for sparse pulse seismic inversion.

[0039] The analysis module is used for the spatial structure and frequency dependence analysis of seismic records.

[0040] The inversion module is used for low-frequency signal inversion based on spatial structure constraints.

[0041] Another object of the present invention is to provide a computer device comprising a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the method for sparse inversion and reconstruction of low-frequency seismic signals under spatial structure regularization constraints.

[0042] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the method for sparse inversion and reconstruction of low-frequency seismic signals under spatial structure regularization constraints.

[0043] Another objective of this invention is to provide an information data processing terminal for implementing a low-frequency seismic signal sparse inversion and reconstruction system under the spatial structure regularization constraint.

[0044] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows: First, this invention aims to solve the aforementioned technical problems, particularly addressing the issues of ambiguity and spatial structure-constrained frequency dependence in low-frequency signal recovery through sparse inversion. It proposes a novel spatial structure-regularized method for low-frequency signal sparse inversion. This method estimates more relevant spatial reflection structures from adjacent frequency bands of the target low-frequency signal and incorporates these structures, along with the sparse structure of the reflection coefficients, into the regularization term of the low-frequency signal inversion. This aims to more accurately and stably invert and reconstruct missing or damaged low-frequency signals under the effective driving force of spatial structure, providing reliable foundational data for subsequent seismic inversion and reservoir prediction.

[0045] The purpose of this invention is to provide a more accurate and stable method for sparse inversion and reconstruction of low-frequency seismic signals, specifically including: 1. Improve the stability and uniqueness of sparse inversion of low-frequency signals: By introducing more reasonable and relevant spatial structure constraints, the ambiguity of sparse inversion is reduced, making the recovered low-frequency signals more consistent with the actual geological laws.

[0046] 2. Addressing the Frequency Dependence of Spatial Structure Constraints: A novel spatial structure estimation strategy is proposed. Instead of directly estimating the spatial structure from raw, potentially missing, broadband seismic data of the target low-frequency signal, this strategy estimates the spatial reflection structure from seismic data in adjacent frequency bands of the target low-frequency signal. This strategy aims to obtain structural information that is more similar to and related to the spatial structure of the target low-frequency signal, thereby reducing the adverse impact of frequency dependence on the accuracy of spatial structure estimation.

[0047] 3. Construct a joint regularized inversion framework: The sparse structure prior of the reflection coefficient and the spatial structure prior of the low-frequency signal estimated from adjacent frequency bands are simultaneously introduced as regularization terms into the objective function of low-frequency signal inversion to achieve low-frequency signal recovery driven by spatial structure.

[0048] 4. Improve the quality and reliability of low-frequency signal recovery: Through the above improvements, it is expected that low-frequency signals that are contaminated, distorted or even missing due to factors such as acquisition, processing or noise can be recovered and reconstructed more accurately, providing more reliable basic data for subsequent seismic inversion (such as wave impedance inversion) and reservoir prediction.

[0049] Second, the technical solution of the present invention fills the technical gap in the field of low-frequency signal reconstruction based on sparse inversion, which is how to obtain and utilize more accurate spatial structure constraints related to the target low-frequency signal frequency.

[0050] In the field of geophysical exploration, it is widely accepted that introducing spatial structure constraints can effectively reduce the ambiguity of sparse inversion. However, a long-standing technical bottleneck is that the spatial structure of seismic reflections itself is frequency-dependent, meaning that the morphology and structural details of in-phase axes revealed by seismic data from different frequency bands differ. Existing techniques typically estimate the spatial structure directly from raw, potentially missing, broadband data of the target low frequency, and use this to constrain the inversion of the low-frequency signal. This approach ignores the frequency difference between the structural constraints and the target signal, significantly reducing the accuracy and effectiveness of the constraints. Therefore, the industry has long lacked a mature technical solution that can properly handle the frequency dependence of spatial structure and provide more accurate and relevant structural constraints for low-frequency inversion.

[0051] This invention proposes for the first time an innovative spatial structure estimation strategy (as described in claims 3 and 4). Its core principle is to estimate the spatial structure of the target low-frequency signal from adjacent higher-frequency bands, rather than from the original broadband data. The theoretical basis is that the spatial structure similarity between adjacent frequency bands is far greater than the similarity between broadband data and the target low-frequency signal. This method effectively fills the technological gap in the industry regarding how to obtain and apply frequency-related spatial structures for precise constraints in low-frequency signal sparse inversion, paving a completely new path for significantly improving the stability and reliability of low-frequency signal recovery.

[0052] The technical solution of this invention solves the long-standing and unresolved problem of "high ambiguity and insufficient reliability" in the inversion results when reconstructing missing low-frequency signals using sparse inversion methods.

[0053] In the field of seismic data processing, researchers have long sought a stable and reliable method to reconstruct missing low-frequency signals from scratch. While sparse inversion based on compressed sensing is theoretically feasible, in practical applications, especially when low-frequency signals are severely lacking, relying solely on the sparsity of the reflection coefficients as a constraint results in a severely ill-posed inversion problem. This means there are numerous mathematically possible but geologically completely incorrect solutions, making the inversion results extremely sensitive to parameter selection and the initial model. The reconstructed low-frequency signals are unreliable and difficult to trust and apply in production, which has become a core challenge hindering the mature application of this technology.

[0054] This invention successfully overcomes this challenge through its unique "joint regularization" inversion framework (as shown in Equation 13). It no longer relies solely on a single sparse constraint, but creatively introduces a second, more reliable spatial structure constraint driven by adjacent frequency bands. This strong geological constraint significantly compresses the solution space of the inversion, effectively eliminating spurious solutions that do not conform to the continuity of geological structures, and guiding the inversion process towards a unique, geologically most reasonable solution. As shown in the wave impedance inversion results of the model test (…),… Figure 8 When the low frequencies recovered by this invention are missing, the inversion results ( Figure 8 (a) in the model and the real model Figure 8 The differences in part (c) are huge; however, after adding the low frequency recovered by this invention, the inversion results ( Figure 8 Part (b) of the model shows a high degree of agreement with the actual model. This eloquently demonstrates that the present invention has successfully solved the industry-recognized technical problem of unreliable low-frequency recovery results due to ambiguity in sparse inversion. Attached Figure Description

[0055] Figure 1 This is a flowchart of the method for sparse inversion and reconstruction of low-frequency seismic signals with spatial structure regularization constraints provided in this embodiment of the invention.

[0056] Figure 2 This is a block diagram of a low-frequency seismic signal sparse inversion and reconstruction system with spatial structure regularization constraints provided in an embodiment of the present invention.

[0057] Figure 3 This refers to the geological model (a) and the 8-50Hz Sink wavelet synthesized seismic record (b) provided in the embodiments of the present invention.

[0058] Figure 4 The geological model provided in this embodiment of the invention contains the 0-8Hz low-frequency component (a) and the 0-8Hz low-frequency component (b) recovered by the method described herein.

[0059] Figure 5The geological model provided in this embodiment of the invention includes a 0-50Hz synthetic seismic record (a) and a seismic record (b) after low-frequency recovery.

[0060] Figure 6 These are the amplitude spectra of the low-frequency signal before (black dashed line) and after (blue solid line) recovery provided in the embodiments of the present invention.

[0061] Figure 7 These are the actual low-frequency components (red) on the four seismic traces provided in this embodiment of the invention and the low-frequency components (blue) recovered by the method described in this paper.

[0062] Figure 8 The embodiments of the present invention provide the wave impedance model (a) inverted when low frequency is missing, the wave impedance model (b) inverted after low frequency recovery, and the actual wave impedance model (c).

[0063] Figure 9 The embodiments of the present invention provide the following: the low-frequency component of the wave impedance inverted when low frequencies are missing (a), the low-frequency component of the wave impedance inverted after low-frequency recovery (b), and the low-frequency component of the actual wave impedance model (c).

[0064] Figure 10 This is the pre-stack time-migrated seismic profile of region A provided in this embodiment of the invention.

[0065] Figure 11 The low-frequency components below 8Hz of the seismic data of region A in the first (a) and second (b) parts of the application of the method described in this embodiment of the invention are provided. Detailed Implementation

[0066] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0067] This invention proposes a spatial structure regularized method for sparse inversion and reconstruction of low-frequency signals. The core of this method lies in estimating the spatial structure from adjacent frequency bands of the target low-frequency signal and combining this estimation with sparsity constraints on the reflection coefficients to construct a new objective function for inversion, thereby improving the accuracy and stability of low-frequency signal recovery.

[0068] like Figure 1 As shown in the figure, the method for sparse inversion and reconstruction of low-frequency seismic signals with spatial structure regularization constraints provided by this invention includes the following steps: S101, Construction and solution of objective function for sparse pulse seismic inversion.

[0069] S102, Spatial structure and frequency dependence analysis of seismic records.

[0070] S103, Low-frequency signal inversion based on spatial structure constraints.

[0071] The present invention provides a method for constructing and solving the objective function for sparse pulse seismic inversion.

[0072] According to the convolution model, the seismic record d can be represented as the convolution of the seismic wavelet w and the reflection coefficient sequence r plus noise n: (1) Where t is the earthquake recording time; written in matrix form as: (2) in, , and These are vectors composed of seismic records, reflection coefficients, and random noise, respectively. It is a matrix composed of seismic wavelets.

[0073] Seismic inversion requires certain prior assumptions about the probability distribution function of the reflection coefficient, with the Gaussian distribution being the most commonly used mathematical assumption. However, statistical analysis of actual well logging data shows that the probability distribution function of the reflection coefficient is not Gaussian, but rather biased towards a sparse distribution described by the Cauchy function. Based on compressed sensing theory and Bayesian inversion theory, if we assume that the reflection coefficient follows a Cauchy distribution and the noise follows a Gaussian distribution, then solving the maximum a posteriori probability density problem is equivalent to minimizing the following objective function: (3) in, The first term is the data fitting term (error term). It is the variance of the data.

[0074] The gradient of the objective function is: (4) in, It is A diagonal matrix whose diagonal elements are (5) If we set the gradient of the objective function to zero, then the solution to the objective function is: (6) Due to the diagonal matrix Including unknown vectors to be inverted This is a nonlinear inversion problem, which is usually solved using an iterative reweighting algorithm: first, given the reflection coefficient... Initial value, calculate From equation (6), we obtain the new Recalculate Then proceed to the next iteration until convergence.

[0075] The present invention provides an analysis of the spatial structure and frequency dependence of seismic records.

[0076] The second step in pre-stack gather optimization based on multi-dimensional constrained dynamic time warping is to analyze the spatial structure and frequency dependence of seismic records. The spatial structure of seismic records refers to the spatial morphology and trajectory changes of phase axes, commonly described by dip and dip angle. This invention uses the Gradient Structure Tensor (GST) to estimate the dip and dip angle of seismic records. For three-dimensional seismic data... Its spatial gradient is (7) The gradient structure tensor (GST) is defined as follows: (8) Eigenvalue decomposition of the structure tensor matrix yields: (9) In the formula, , and These are the three eigenvalues ​​of the structure tensor, which are positive real numbers between 0 and 1. , and These are the eigenvectors corresponding to the three eigenvalues; assuming Then the eigenvector This indicates the direction of maximum gradient, i.e., the direction of the construction tendency. and These represent two directions parallel to the structure; for two-dimensional seismic data, the structure tensor degenerates into a two-dimensional form, having (10) The two eigenvectors at this time and These are respectively perpendicular to the direction of the phase axis and parallel to the direction of the phase axis.

[0077] Seismic records are the result of the convolution of seismic wavelets and reflection coefficients. Their spatial structure is not only related to geological structures but also depends on the interference effect of seismic reflections. The spatial structure of seismic records in different frequency bands varies significantly. In other words, the spatial structure of seismic records is frequency-dependent, which is particularly evident in complex geological conditions. Therefore, if the spatial structure is directly estimated from the original broadband seismic data, which may have lost the target low frequency, and used as prior information to constrain the inversion of the target low frequency signal, the accuracy of this constraint will be severely affected by the frequency dependence.

[0078] The present invention provides a low-frequency signal inversion based on spatial structure constraints.

[0079] After completing the analysis of the spatial structure and frequency dependence of the seismic record, low-frequency signal inversion based on spatial structure constraints can be performed; firstly, the single-channel convolution model needs to be extended to a multi-channel convolution model, that is, formula (2) is extended to: (11) in, and It is by A super vector formed by connecting the beginning and end of a seismic trace. It is composed of wavelet matrix The block matrix is ​​formed; at this time, the single-channel sparse inversion objective function represented by equation (3) is expanded into the following multi-channel sparse inversion objective function, which has (12) Although the above formula has the same mathematical expression as single-channel inversion, the two have different implementation methods; single-channel inversion is performed channel by channel, while multi-channel inversion is performed simultaneously by multiple seismic channels; since multiple seismic channels are inverted simultaneously, spatial structure can be easily introduced into the regularization constraint of the objective function.

[0080] The objective of this invention is to invert and reconstruct low-frequency signals of a specific target frequency band from band-limited seismic records. To reduce the influence of frequency dependence on spatial structure estimation, this invention does not estimate spatial structure from the original broadband seismic records, but rather from seismic data of adjacent higher frequency bands of the target low-frequency signal. For example, if the goal is to recover a low-frequency signal of 0-8 Hz, the spatial structure can be estimated from the 8-16 Hz (or a slightly wider band adjacent to the target low-frequency band) frequency components of the original seismic records. The assumption is that the spatial structure similarity of adjacent frequency bands is generally higher than the structural similarity between broadband data and the target ultra-low frequency signal. By introducing the spatial structure of the low-frequency signal into the objective function of low-frequency signal inversion, equation (22) is extended to... (13) The objective function at this time It consists of three parts: the first part is the error term, which characterizes the error between the actual seismic record and the synthetic seismic record; the second part is the sparse structure regularization term, which characterizes the sparse structure of the reflection coefficient sequence; and the third part is the spatial structure regularization term, which describes the spatial structure followed by the low-frequency signal. and It is the regularization coefficient. It is a high cutoff frequency. The low-pass filter, It is a filtering operator related to spatial structure; the objective function (13) can be solved numerically using a method similar to that of the objective function (3).

[0081] After obtaining a convergent reflection coefficient sequence Then, it is low-pass filtered (high cutoff frequency is...). This is used as the recovered low-frequency seismic signal; then, the recovered low-frequency signal is compared with the high-frequency signals in the original seismic record. The frequency components are merged (through frequency domain replacement or time domain superposition) to obtain the final broadband seismic record after low-frequency recovery.

[0082] like Figure 2 As shown, an embodiment of the present invention provides a sparse inversion and reconstruction system for low-frequency seismic signals with spatial structure regularization constraints, comprising: The solver module is used for constructing and solving the objective function for sparse pulse seismic inversion.

[0083] The analysis module is used for the spatial structure and frequency dependence analysis of seismic records.

[0084] The inversion module is used for low-frequency signal inversion based on spatial structure constraints.

[0085] Another object of the present invention is to provide a computer device comprising a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the method for sparse inversion and reconstruction of low-frequency seismic signals under spatial structure regularization constraints.

[0086] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the method for sparse inversion and reconstruction of low-frequency seismic signals under spatial structure regularization constraints.

[0087] Another objective of this invention is to provide an information data processing terminal for implementing a low-frequency seismic signal sparse inversion and reconstruction system under the spatial structure regularization constraint.

[0088] Specific implementation of the present invention: 1. A sparse inversion method based on spatial structure regularization for low-frequency signal recovery from seismic data, the core feature of which lies in the estimation strategy of spatial structure information: This method does not directly estimate the spatial structure from the original broadband seismic data that may be missing the target low frequency, but extracts spatial reflection structure information (such as dip angle and dip direction, which can be obtained through methods such as gradient structure tensor) from the seismic data of the adjacent higher frequency band of the target low frequency signal.

[0089] 2. By combining the spatial structure information estimated by the adjacent frequency bands with the sparsity assumption of the reflection coefficient, a new joint regularization inversion objective function (Equation 13) is constructed: This objective function includes a data fitting term, a reflection coefficient sparsity constraint term, and a key low-frequency signal spatial structure regularization term driven by the spatial structure estimated by the adjacent frequency bands.

[0090] 3. Specific implementation of the spatial structure regularization term for low-frequency signals: A filter operator or constraint operator related to the spatial structure (such as tilt angle and dip) estimated from adjacent frequency bands is applied to the target low-frequency signal synthesized from the reflection coefficients obtained by the current inversion, so as to make the recovered low-frequency signal follow the structural characteristics inferred from adjacent frequency bands in space.

[0091] 4. Multichannel simultaneous inversion iterative solution algorithm based on the joint regularization objective function: The objective function (13) is solved by nonlinear optimization techniques such as iterative reweighted least squares (IRLS) to obtain a reflection coefficient sequence that satisfies data fitting, sparsity of reflection coefficients and consistency of spatial structure.

[0092] Compared with existing low-frequency signal inversion methods that mainly rely on the sparsity constraints of reflection coefficients, or methods that directly use broadband data to estimate spatial structure for constraints, the spatial structure regularized low-frequency signal sparse inversion and reconstruction method proposed in this invention has the following significant advantages: 1. More accurately and effectively overcome the frequency dependence problem of spatial structure constraints, and improve the effectiveness of constraints.

[0093] (1) This invention recognizes and specifically solves the problem of frequency dependence of spatial structure in earthquake reflection. By estimating the spatial structure from the adjacent higher frequency bands of the target low-frequency signal, constraint information that is more similar to and more relevant to the actual spatial structure of the target low-frequency signal is obtained.

[0094] (2) Compared with directly using broadband data that may have missing target low frequencies to estimate spatial structure, the spatial structure constraints provided by this method are more accurate and can better guide the recovery of low frequency signals, avoiding erroneous information introduced by structural mismatch.

[0095] 2. Significantly enhances the stability and reliability of sparse inversion of low-frequency signals and reduces multiple solutions.

[0096] like Figure 3 (1) By introducing a more reasonable and relevant spatial structure as a strong prior constraint, this invention effectively reduces the inherent ill-posedness and multiple solutions of the sparse inversion problem itself.

[0097] (2) Even when the original low-frequency signal is severely contaminated, distorted, or even missing, the driving force of spatial structure can help the inversion converge to a solution that better conforms to geological laws, thus improving the reliability of the recovered low-frequency signal. Both model data and actual data tests show that the recovered low-frequency signal has a higher degree of agreement with the actual situation (or expected geological features) (e.g., Figure 4 , Figure 10 , Figure 11 The data quality is higher after restoring low-frequency data. Figure 5 ).

[0098] 3. Improve the accuracy of low-frequency signal recovery and its value for subsequent applications.

[0099] (1) Due to the improved stability and accuracy of the inversion, the low-frequency signal recovered by this method is of higher quality. Model experiments show that the similarity coefficient between the recovered low-frequency components and the true low-frequency components is high ( Figure 7 The amplitude spectrum is effectively compensated. Figure 6 ).

[0100] (2) More accurate low-frequency signals provide a more reliable background trend for subsequent seismic inversion (such as wave impedance inversion), thereby significantly improving the accuracy of reservoir parameter prediction and the reliability of geological interpretation (e.g. Figure 8 , Figure 9 (Comparison of wave impedance inversion).

[0101] 4. It is more adaptable to complex geological conditions.

[0102] In regions with complex geological structures and rapid stratigraphic changes, the frequency dependence of spatial structure is more pronounced. This invention, by acquiring spatial structure from adjacent frequency bands, can better adapt to these complex conditions and maintain the effectiveness of low-frequency recovery.

[0103] 5. The method has good practicality and operability.

[0104] Although spatial structure constraints are introduced, the overall solution can still be achieved within the framework of sparse inversion, for example, by using iterative reweighted least squares. The estimation of spatial structure in adjacent frequency bands can also employ mature techniques such as structure tensors.

[0105] In summary, this invention significantly improves the low-frequency signal recovery technology based on sparse inversion through innovative spatial structure estimation and application strategies. It outperforms existing technologies in terms of accuracy, stability, and adaptability to complex geological conditions, providing a more effective solution to the problem of missing low-frequency seismic data.

[0106] I. Specific application areas or related products of this invention.

[0107] The sparse inversion and reconstruction method for low-frequency seismic signals based on the spatial structure regularization constraints proposed in this invention can be widely applied to the following fields or related products: Low-frequency compensation in seismic data processing: As a core application, it is directly used in the seismic data processing workflow to restore and reconstruct low-frequency signals (such as 0-8Hz) that are missing or damaged due to acquisition, noise suppression, etc., thereby widening the seismic data frequency band and improving imaging quality.

[0108] Reservoir prediction and lithological inversion: The recovered low-frequency signal provides a reliable background trend model for techniques such as wave impedance inversion, which can significantly improve the accuracy and reliability of predictions of oil and gas reservoirs and favorable facies zones.

[0109] Deep / ultra-deep target exploration: Low-frequency signals have strong penetrating power, and their effective recovery is crucial for imaging and exploration of complex tectonic areas such as deep layers and piedmont zones.

[0110] Full Waveform Inversion (FWI) Velocity Modeling: FWI is highly dependent on the low-frequency components of the initial model. This invention can provide FWI with a more accurate and reliable initial velocity model, helping it overcome the period jump problem and move towards wider practical applications.

[0111] Related products: The method of this invention can be seamlessly integrated as a key functional module into various commercial or scientific geophysical exploration data processing and inversion software platforms, providing users with an advanced tool specifically designed for high-quality low-frequency signal recovery.

[0112] II. Evidence related to the technical effects obtained by the embodiments of the present invention.

[0113] This invention obtains sufficient and direct evidence of technical effectiveness by using accurate geological model forward simulation and processing of actual seismic data from the work area, and by systematically comparing the results with those without low-frequency signals, thus demonstrating the significant technical progress of this invention.

[0114] 1. It can recover missing low-frequency signals with high precision.

[0115] In model testing, the raw data contained absolutely no low-frequency signals (e.g., 0-8Hz). Figure 3 (part (b) of the present invention). After applying the method of the present invention, the recovered 0-8Hz low-frequency component ( Figure 4 (b) in the text) and the low-frequency components of the actual geological model ( Figure 4 Part (a) in the diagram is highly consistent in terms of the shape, continuity, and spatial distribution of the in-phase axes. For example... Figure 7 As shown, the comparison of the extracted single-channel waveforms also shows that the recovered low-frequency waveform (blue) matches the real low-frequency waveform (red) with a very high degree of consistency, proving the accuracy of the low-frequency signal recovery of the present invention.

[0116] 2. It effectively broadened the frequency band of seismic data.

[0117] like Figure 6 As shown in the amplitude spectrum, the original record with low frequencies removed (black dashed line) exhibits rapid energy decay below approximately 10 Hz. After processing by this invention, the energy in the final seismic record (blue solid line) in the 0-10 Hz frequency band is effectively compensated, and its spectral shape almost completely overlaps with the original full-band record (red solid line), achieving a perfect reconstruction of the missing frequency band.

[0118] 3. Significantly improved the accuracy of subsequent key applications (wave impedance inversion).

[0119] This is the most compelling evidence proving the value of this invention. For example... Figure 8 As shown, when using missing low-frequency data for wave impedance inversion, the results are ( Figure 8 Part (a) in the data can only reflect the general outline of the strata and cannot provide accurate background trends. However, when the low-frequency data recovered by this invention is used for inversion, the results are much better. Figure 8 Part (b) of the model is not only rich in detail, but its low-frequency background trends also match those of the real model. Figure 8 The (c) part is highly consistent with the content. Figure 9 A separate comparison of low-frequency trends more clearly demonstrates this significant advantage, proving that the present invention provides a reliable basis for reservoir prediction.

[0120] 4. Its application in actual seismic data has shown significant results.

[0121] In the actual pre-stack time migration profile of region A ( Figure 10 In the processing of ), the low-frequency components of the original data ( Figure 11 The energy in part (a) is weak, disordered, and contains almost no useful structural information. After applying the method of this invention, the recovered low-frequency component ( Figure 11 The signal-to-noise ratio of (b) in the data is extremely high, the stratigraphic phase axis is clear and continuous, and the structural morphology is well-defined, demonstrating the powerful capability and robustness of this invention in processing real and complex data.

[0122] In conclusion, a wealth of evidence from models and real-world data irrefutably demonstrates, from multiple dimensions such as the accuracy of the recovered signal, the integrity of the spectrum, and the improved accuracy of subsequent applications (wave impedance inversion), that this invention has achieved decisive success in solving the problem of missing low-frequency signals, and has significant advantages and beneficial effects compared to existing technologies.

[0123] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0124] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for sparse inversion and reconstruction of low-frequency seismic signals with spatial structure regularization constraints, characterized in that, Includes the following steps: Step 1: Establish a sparse pulse seismic inversion objective function with the difference between seismic records and synthetic records as the data fitting term and the logarithmic super-Laplace form as the sparse regularization term. Based on the convolution model, the seismic record is represented as a discrete convolution of wavelet and reflection coefficient sequence, while random noise is added. Step 2: Minimize the objective function using an iterative reweighting algorithm to obtain the initial reflection coefficient sequence; Step 3: Calculate the spatial gradient of the seismic record and construct the gradient structure tensor. Obtain the dip direction vector and horizontal structural components through eigenvalue decomposition to describe the spatial structure and its frequency correlation. Step 4: Under the multi-channel convolution model, the spatial structure description is combined with the low-pass filter operator to form a low-frequency signal inversion objective function containing error terms, sparse regularization terms, and spatial structure regularization terms. The iterative reweighting algorithm is then used again to solve for the converged reflection coefficient sequence. Step 5: Apply low-pass filtering to the reflection coefficient sequence to obtain the recovered low-frequency signal, and then synthesize it with the high-frequency components in the original seismic record through frequency domain substitution or time domain superposition to obtain a broadband seismic record.

2. The method according to claim 1, characterized in that, The sparse regularization term adopts an adaptive weight form that includes noise variance. The weight is updated in each iteration based on the current reflection coefficient value to enhance the sparse constraint effect.

3. The method according to claim 1, characterized in that, The gradient structure tensor contains three positive real eigenvalues ​​and corresponding eigenvectors, where the eigenvector corresponding to the largest eigenvalue indicates the dip direction of the strata, and the other eigenvectors indicate directions parallel to the strike of the strata.

4. The method according to claim 1, characterized in that, In step four, a first regularization coefficient is set to control sparsity, a second regularization coefficient is set to control spatial structure consistency, and a low-pass filter with a high cutoff frequency as a preset threshold is used to limit the effective frequency band of the inversion.

5. A sparse inversion and reconstruction system for low-frequency seismic signals with spatial structure regularization constraints, characterized in that, include: The solution module is used to construct a sparse pulse seismic inversion objective function that includes a data fitting term and a sparse regularization term, and to solve the reflection coefficient sequence using an iterative reweighting algorithm; The analysis module is used to calculate the spatial gradient of seismic records, generate gradient structure tensors, and extract eigenvalues ​​and eigenvectors to form a spatial structure description. The inversion module is used to combine the spatial structure description with a low-pass filter under a multichannel convolution model, construct and solve a low-frequency signal inversion objective function that includes a spatial structure regularization term, and output a broadband seismic record.

6. The system according to claim 5, characterized in that, The solution module updates the diagonal weight matrix based on the current reflection coefficient sequence and resolves the linear equations in each iteration until the convergence threshold is met.

7. The system according to claim 5, characterized in that, The analysis module calculates the first-order gradients of the seismic data on the spatial and time axes to form a spatial gradient vector, and generates a gradient structure tensor based on the outer product of this vector.

8. A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the method according to any one of claims 1 to 4.

9. The computer-readable storage medium according to claim 8, characterized in that, The program employs an adaptive weighting form that includes noise variance when performing the step of establishing the objective function for sparse pulse seismic inversion, in order to improve the robustness of reflection coefficient estimation.

10. A computing device comprising a processor and a memory, the memory storing a computer program of claim 8, the processor being configured to execute the program to generate broadband seismic records.

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