A three-dimensional denoising method based on spatio-temporal domain streaming prediction filtering

Abstract

The application is suitable for the field of seismic data processing, and provides a three-dimensional denoising method based on space-time flow prediction filtering, comprising: obtaining three-dimensional seismic data, performing boundary mirror image extension processing to obtain an extended data body; performing adaptive data prediction, introducing space-time variable flow prediction filter coefficients, and obtaining a linear combination form of the space-time variable flow prediction filter coefficients; taking a three-dimensional local smooth regularization equation as a constraint condition to determine a calculation target function of the space-time variable flow prediction filter coefficients; calculating the target function, updating the space-time variable flow prediction filter coefficients, and determining a denoising result of the extended data body. The application converts the space-time adaptive prediction filtering denoising into a mathematical overdetermined problem, analyzes and calculates a target function under a local smooth regularization condition, and uses a flow recursive algorithm to avoid an iterative algorithm in the adaptive prediction filtering, thereby effectively saving the memory cost and operation time in the calculation process.

Description

Technical Field

[0001] This invention belongs to the field of earthquake data processing, and in particular relates to a three-dimensional denoising method based on spatiotemporal domain streaming predictive filtering. Background Technology

[0002] Random noise suppression has always been a crucial aspect of seismic data processing, as improving the signal-to-noise ratio (SNR) can effectively reduce the risks of oil, gas, and mineral resource exploration. Random noise is widespread in seismic data. Complex subsurface media in areas such as piedmont zones and steep geological structures can easily cause energy loss of effective seismic signals. Random noise caused by surface conditions leads to low-quality data acquisition. As the exploration depth increases, the energy of the effective seismic signal weakens, and random noise generally results in a low SNR for deep seismic data. Besides significant environmental noise, coherent noise generated by conventional processing of residual surface waves and efficient mixed-data acquisition exhibits strong random noise characteristics in specially ordered trace sets. Non-stationary seismic data heavily contaminated with random noise makes it difficult to obtain accurate effective wave information, significantly increasing the cost of resource exploration under complex conditions. Effectively removing random noise is a major challenge. Various methods exist for handling random noise, with predictive filtering being one of the most important research directions.

[0003] In 2012, Fomel proposed a streaming computing framework and applied it to the computation of prediction error filters. This method assumes that the updated filter coefficients are approximately equal to the previous filter coefficients, using this condition as a constraint. This reduces computer memory usage and improves computation speed, but it is only applicable to deconvolution and interpolation tasks for one-dimensional and two-dimensional data. In 2018, Liu et al. proposed a two-dimensional streaming orthogonal predictive filtering denoising technique. This method has higher computational efficiency than iterative adaptive predictive filtering algorithms, but the denoising results are slightly worse because it only uses information from two data dimensions. In 2020, Guo Longyu et al. proposed a streaming predictive filter in the fx domain. This method uses a direct complex matrix instead of an iterative algorithm to solve for non-stationary filter coefficients, improving the computational efficiency of the frequency domain adaptive predictive filtering denoising algorithm. In 2022, Liu et al. proposed a three-dimensional streaming predictive filtering algorithm based on the fxy domain and applied it to the problem of random noise suppression in seismic data. This method combines the local similarity of frequency and spatial filtering coefficients in the three-dimensional seismic data volume and has a better effect than the two-dimensional fx domain streaming predictive filtering denoising algorithm. However, the frequency-spatial domain predictive filtering method has an unsolvable problem of spurious phase axis artifacts. Summary of the Invention

[0004] The purpose of this invention is to provide a three-dimensional denoising method based on spatiotemporal domain streaming predictive filtering, which aims to solve the problems of computational complexity, high memory cost, and frequency-spatial domain predictive filtering artifacts in existing adaptive predictive filtering denoising methods.

[0005] The present invention is implemented as follows: a three-dimensional denoising method based on spatiotemporal domain streaming predictive filtering, comprising:

[0006] Acquire 3D seismic data, perform boundary mirroring expansion processing on the 3D seismic data, and obtain the expanded data volume;

[0007] Adaptive data prediction is performed on the expanded data volume, and spatiotemporal variable current prediction filter coefficients are introduced to represent the expanded data volume as a linear combination form containing the spatiotemporal variable current prediction filter coefficients.

[0008] Based on the extended edge data volume in the form of linear combination, and with the three-dimensional local smoothing regularization equation as a constraint, the objective function for calculating the coefficients of the spatiotemporal variable current predictive filter is determined.

[0009] Based on the objective function for calculating the coefficients of the spatiotemporal variable current predictive filter, the coefficients of the spatiotemporal variable current predictive filter are updated using the least squares analytical algorithm to determine the denoising result of the expanded edge data volume.

[0010] Preferably, in the step of performing boundary mirroring expansion processing on the three-dimensional seismic data to obtain the expanded data volume, the calculation formula for the expanded data volume is:

[0011]

[0012] Where d(t, x, y) represents the three-dimensional seismic data; t = 0, 1, ..., M represents the number of time sampling points of the data; x = 0, 1, ..., N represents the number of sampling points for the transverse or longitudinal seismic lines; and y = 0, 1, ..., L represents the number of sampling points for the longitudinal or transverse seismic lines.

[0013] Preferably, in the step of representing the expanded edge data volume as a linear combination of coefficients of the spatiotemporal variable predictive filter, the specific representation is as follows:

[0014]

[0015] Among them, b i，j，k (t, x, y) are the adaptive filter coefficients; i is the time displacement variable; j is the displacement variable of the transverse or longitudinal survey line; k is the displacement variable of the longitudinal or transverse survey line; d i，j，k (t, x, y) represents the time and space copy of the three-dimensional seismic data d(t, x, y), where α, β, and γ are the filter window size parameters in the time t, space x, and space y directions, respectively.

[0016] Preferably, in the step of determining the objective function for calculating the coefficients of the spatiotemporal variable current predictive filter based on the extended edge data volume in linear combination form, using the three-dimensional local smoothing regularization equation as a constraint, the specific form is as follows:

[0017]

[0018] Where b(t, x, y) represents the filter coefficient vector; These are the estimated values ​​of the filter coefficients; Let represent the filter coefficient vector that is adjacent to B(t, x, y) in both time and space, and as well as D(t, x, y) represents the data copy d. i，j，k A data vector consisting of (t, x, y); λ n The scaling factor controls the degree of variation of the filter coefficients in time t and in the spatial x and y directions; T is the transpose of the matrix.

[0019] Preferably, the step of updating the coefficients of the spatiotemporal variable predictive filter using a least-squares analytical algorithm based on the objective function for calculating the coefficients of the spatiotemporal variable predictive filter, and determining the denoising result of the expanded-edge data volume, includes:

[0020] The objective function for calculating the coefficients of the spatiotemporal variable current predictive filter is calculated, and the least squares solution for the coefficients of the spatiotemporal variable current predictive filter is obtained.

[0021] Based on the least squares solution of the spatiotemporal variable current predictive filter coefficients and the Sherman-Morrison formula, the spatiotemporal variable current predictive filter coefficients representing effective phase axis information in 3D seismic data are determined.

[0022] The spatiotemporal variable current predictive filter coefficients of adjacent calculation points are updated according to the calculation formula of the spatiotemporal variable current predictive filter coefficients to determine the denoising result of the three-dimensional expanded edge data.

[0023] Preferably, the coefficients of the spatiotemporal variable current predictive filter are expressed as follows:

[0024]

[0025] in,

[0026] Preferably, the least squares expression for the coefficients of the spatiotemporal variable predictive filter is:

[0027]

[0028] in,

[0029] The 3D denoising method based on spatiotemporal domain streaming predictive filtering provided in this invention performs boundary mirroring expansion processing on 3D seismic data. It utilizes the predictive relationship between the predictive filter coefficients and the data, introduces spatiotemporally variable predictive filter coefficients, and combines autoregressive analysis with non-stationary local smoothing regularization constraints. Through a streaming computation framework, the spatiotemporally variable streaming predictive filter coefficients are adaptively updated as the data changes, effectively reconstructing non-stationary seismic phase axis information. This invention transforms spatiotemporal domain adaptive predictive filtering denoising into a mathematical overdetermined problem, analytically calculating the objective function under local smoothing regularization conditions. The streaming recursive algorithm avoids iterative algorithms in adaptive predictive filtering, effectively saving memory costs and computation time. Simultaneously, this invention provides excellent spatiotemporally variable seismic phase axis prediction characterization capabilities, effectively recovering non-stationary seismic phase axis information from random noise interference. Attached Figure Description

[0030] Figure 1 A flowchart illustrating the implementation of a three-dimensional denoising method based on spatiotemporal domain streaming predictive filtering, provided in an embodiment of the present invention.

[0031] Figure 2 The flowchart illustrates the steps of updating the coefficients of the spatiotemporal variable predictive filter using the least squares analytical algorithm based on the objective function for calculating the coefficients of the spatiotemporal variable predictive filter, and determining the denoising result of the expanded data volume, as provided in this embodiment of the invention.

[0032] Figure 3 Test data for a three-dimensional theoretical model with fault structure provided in embodiments of the present invention;

[0033] Figure 4 The test data provided in this embodiment of the invention has been processed by the three-dimensional denoising method of the present invention;

[0034] Figure 5 This is a difference graph between the data processed by the three-dimensional denoising method of the present invention and the original theoretical data, provided in an embodiment of the present invention.

[0035] Figure 6 Three-dimensional actual seismic data map provided for embodiments of the present invention;

[0036] Figure 7 The actual seismic data processed by the three-dimensional denoising method of the present invention is provided in the embodiments of the present invention;

[0037] Figure 8 The noise separated by the three-dimensional denoising method provided in the embodiments of the present invention. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0039] To address the problems of computational complexity, numerous iterations, and high memory costs associated with existing methods for removing random noise from 3D seismic data, this invention proposes a 3D denoising method based on spatiotemporal domain streaming predictive filtering using a streaming computing framework. This method involves boundary mirroring of the 3D seismic data, utilizing the predictive relationship between the predictive filter coefficients and the data, and introducing spatiotemporally variable predictive filter coefficients. It combines autoregressive analysis with non-stationary local smoothing regularization constraints. The streaming computing framework enables the spatiotemporally variable streaming predictive filter coefficients to adaptively update as the data changes, effectively reconstructing non-stationary seismic phase axis information. This invention transforms spatiotemporally domain adaptive predictive filtering denoising into a mathematical overdetermined problem, analytically calculating the objective function under local smoothing regularization conditions. The streaming recursive algorithm avoids the iterative algorithms in adaptive predictive filtering, effectively saving memory costs and computation time. Simultaneously, this invention provides excellent spatiotemporally variable seismic phase axis prediction and characterization capabilities, effectively recovering non-stationary seismic phase axis information from random noise interference.

[0040] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structures, features, and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided.

[0041] like Figure 1 The diagram shown is a flowchart of a three-dimensional denoising method based on spatiotemporal domain streaming predictive filtering. For ease of explanation, only the parts relevant to the embodiments of the present invention are shown, and are described in detail below:

[0042] In step S101, the three-dimensional seismic data is subjected to boundary mirroring expansion processing to obtain the expanded data volume.

[0043] In this embodiment of the invention, let d(t, x, y) represent three-dimensional seismic data, t be the number of time sampling points of the data, x be the number of sampling points for the transverse (or longitudinal) survey line, and y be the number of sampling points for the longitudinal (or transverse) survey line. To obtain a three-dimensional denoising result that eliminates boundary effects, the three-dimensional seismic data is first expanded into an expanded data volume through mirror symmetry processing. The expanded data volume can be represented as:

[0044]

[0045] Where M represents the total sampling length of the data in the time direction, N represents the total sampling length of the data in the transverse (or longitudinal) direction, and L represents the total sampling length of the data in the longitudinal (or transverse) direction. The data in the expanded portion is used to calculate the update amount of the initial filtering parameters. If the original 3D seismic data is used directly for denoising, it will cause a certain signal attenuation at the data boundaries. Therefore, in order to reduce the boundary effect, the original 3D seismic data needs to be mirrored and expanded.

[0046] In step S102, adaptive data prediction is performed on the expanded edge data and spatiotemporal variable current prediction filter coefficients are introduced to represent the expanded edge data volume as a linear combination of spatiotemporal variable current prediction filter coefficients.

[0047] In this embodiment of the invention, the three-dimensional seismic data d(t, x, y) is represented by a linear combination of adaptive prediction filter coefficients and spatiotemporal direction data copies as follows:

[0048]

[0049] Among them, b i，j，k (t, x, y) are the adaptive filter coefficients; i is the time displacement variable; j is the displacement variable of the transverse survey line (or longitudinal survey line); k is the displacement variable of the longitudinal survey line (or transverse survey line); d i，j，k (t, x, y) represents the temporal and spatial copies of the 3D seismic data d(t, x, y); α, β, and γ are the filter window sizes in the time (t), spatial (x), and spatial (y) directions, respectively. The above equation can be simplified as:

[0050] d(t, x, y) = D(t, x, y) T B(t, x, y) (3)

[0051] Where, D(t, x, y) T Copy data d i，j，k B(t, x, y) is the transpose of the data vector consisting of (t, x, y), B(t, x, y) is the spatiotemporal variable filter coefficient vector, and T is the transpose of the matrix.

[0052] In step S103, the objective function for calculating the spatiotemporal domain streaming predictive filter is determined by using the three-dimensional local smoothing regularization equation to form constraints based on the form of the coefficients of the spatiotemporal variable flow predictive filter.

[0053] In this embodiment of the invention, the prediction filter coefficients are spatiotemporally varying parameters. It can be seen that the number of unknowns in formula (3) is greater than the number of equations, which is a mathematically underdetermined problem, and the solution to the equation is not unique. In order to solve the equation effectively, a three-dimensional local smoothing regularization equation is added. At this time, formula (3) can be rewritten as:

[0054]

[0055] in, This represents the filter coefficient vector that is adjacent to B(t, x, y) in the time direction. and Let B(t, x, y) be the filter coefficient vector that is spatially adjacent to B(t, x, y), and as well as λ t , λ x and λ y These are the scaling coefficients that control the degree of change of the filter coefficients in time t, space x, and y, respectively. The above equation transforms into a mathematical overdetermined problem, which can be simplified to a regularized L2 norm objective function:

[0056]

[0057] in, This is the filter estimate.

[0058] In step S104, the coefficients of the spatiotemporal variable flow predictive filter are updated using the least squares analytical algorithm based on the objective function form of the spatiotemporal domain flow predictive filter, and the denoising result of the expanded data volume is determined.

[0059] In embodiments of the present invention, such as Figure 2 As shown, step S104 includes:

[0060] In step S201, the objective function form containing the coefficients of the three-dimensional spatiotemporal variable current predictive filter is calculated, and the least squares solution of the coefficients of the three-dimensional spatiotemporal variable current predictive filter is obtained.

[0061] In this embodiment of the invention, the least squares expression for the coefficients of the three-dimensional spatiotemporal variable predictive filter can be obtained according to formula (5):

[0062]

[0063] in, Regularization coefficient λ n It should have an order of magnitude similar to the data amplitude to provide smoothness control for the three-dimensional spatiotemporal domain streaming prediction filter.

[0064] In step S202, the spatiotemporal domain streaming prediction filter coefficients representing effective phase axis information in the three-dimensional seismic data are determined based on the least squares solution of the coefficients of the three-dimensional spatiotemporal variable flow prediction filter and the Sherman-Morrison formula.

[0065] In this embodiment of the invention, the inverse matrix in formula (6) has a special form that can be solved without using an iterative algorithm. The inverse matrix in formula (6) can be directly calculated analytically using the Sherman-Morrison formula in linear algebra, resulting in the following form:

[0066]

[0067] Where D(t, x, y) is a column vector. T For the row vector formula (7), D(t, x, y) is the denominator on the right side of the equation. T Since D(t, x, y) is a constant, the inverse matrix can be directly converted into regular matrix multiplication, which improves computational efficiency.

[0068] Substituting equation (7) into equation (6) and simplifying, we can obtain the coefficients of the three-dimensional spatiotemporal variable current predictive filter:

[0069]

[0070] As shown in formula (8), the filter coefficients are continuously updated by subtracting a data value scaled to a certain size. This update method is a "pipeline" method. Therefore, this embodiment of the invention implements spatiotemporal streaming predictive filtering. The prediction residual is:

[0071]

[0072] As can be seen from equation (9), the prediction residual has a constant multiple relationship with the filter update scaling factor in equation (8).

[0073] In step S203, the filter coefficients of adjacent calculation points are adaptively updated according to the spatiotemporal domain streaming prediction filter coefficient calculation formula to determine the denoising result of the three-dimensional expanded edge data.

[0074] In this embodiment of the invention, the spatiotemporal streaming prediction filter processes each seismic trace along the time axis of the three-dimensional seismic data, calculates the maximum and minimum amplitude values ​​of the three-dimensional seismic data, and selects an appropriate regularization coefficient λ. n The three initial spatiotemporal variable flow prediction filter coefficients for each seismic trace are set to zero. Steps S201 and S202 are repeated to update the spatiotemporal domain streaming prediction filter coefficients. When random noise follows a Gaussian distribution, the prediction filter coefficients are immune to random noise, and the effective in-phase axis information after denoising can be characterized by the spatiotemporal domain streaming prediction filter coefficients.

[0075] While the filter is continuously updated, the noise-free effective signal reconstructed by the non-causal predictive filter in three-dimensional space is calculated according to the following formula (10). The denoising result of the three-dimensional expanded edge data is as follows:

[0076]

[0077] in, This is the data for denoising estimation.

[0078] Finally, by removing the extended boundary data in the six directions of the 3D extended data, the same denoised data size as the original 3D seismic data can be restored.

[0079] The 3D denoising method based on spatiotemporal domain streaming predictive filtering provided in this invention expands the boundaries of 3D seismic data by utilizing the predictive relationship between the predictive filter coefficients and the data, and introducing spatiotemporally variable predictive filter coefficients. It combines autoregressive analysis with non-stationary local smoothing regularization constraints, and uses a streaming computation framework to adaptively update the spatiotemporally variable streaming predictive filter coefficients as the data changes, effectively reconstructing non-stationary seismic phase axis information. This invention proposes a 3D local smoothing regularization condition to constrain the adaptive predictive filter equation, transforming spatiotemporal domain streaming predictive filtering denoising into a mathematical overdetermined problem. The Sherman-Morrison formula is used to analytically calculate the least-squares solution of the new objective function, and a streaming recursive algorithm avoids the inefficient iterative algorithm in adaptive predictive filtering, effectively saving memory costs and computation time, making it particularly suitable for processing large-scale high-dimensional seismic data. Furthermore, compared to traditional industry-standard predictive filtering denoising methods, this invention provides excellent spatiotemporally variable seismic phase axis prediction characterization capabilities, effectively recovering non-stationary seismic phase axis information from random noise interference.

[0080] Simulation Example 1

[0081] Figure 3 The 3D seismic record after adding normally distributed random noise to the standard qdome theoretical model contains horizontal strata at the top, Gaussian strata in the middle, dipping strata at the bottom, horizontal unconformities at the boundaries of different strata, and a dome-shaped fault. The strong random noise affects the interpretation of effective seismic phase axis information. The three sides in the figure represent slices at the positions of the marker lines within the 3D seismic data volume (the front side is the cross-scan profile at 0.45 km of the longitudinal line, the right side is the longitudinal line profile at 1.25 km of the cross-scan line, and the top side is a time slice at 0.82 s). Figure 4 The result is the 3D denoising effect after spatiotemporal streaming predictive filtering. During the spatiotemporal streaming predictive filtering estimation, the filter window size was set to 9 samples (time) × 5 samples (space X) × 5 samples (space Y), and the scaling factor was 0.02 (λ). t ), 0.0001(λ x ) and 0.0001(λ y ).from Figure 4 As can be seen, the method of the present invention can separate the effective phase axes that are not stationary from three-dimensional seismic data with low signal-to-noise ratio, and can recover the spatial location information of faults and other structures in a good manner. Figure 5 The image shows the difference between the data processed by the three-dimensional denoising method of this invention and the original theoretical data, i.e., the noise profile. As can be seen from the image, no obvious effective wave information was found in the noise profile, which shows that the method of this invention has high amplitude preservation accuracy.

[0082] Simulation Example 2

[0083] Figure 6 This is actual 3D post-stack data for a certain region, with a data size of 700 samples (time) × 266 samples (spatial X) × 310 samples (spatial Y). Strong random noise caused by the complex surface conditions in this region affects both the near-horizontal phase axis information at shallow locations and the complex phase axis information at deep locations. Figure 7 The signal obtained after processing by the three-dimensional denoising method of this invention is an effective signal. The filter window size parameter is set to 7 samples (time) × 5 samples (space X) × 5 samples (space Y), and the scale factor is 100.0 (λ). t ), 1.0(λ x ) and 1.0(λ y ). Figure 7 The results show that the three-dimensional denoising method based on spatiotemporal streaming prediction filtering has a better signal-to-noise separation effect, and the continuity of the in-phase axis and the geological structure are enhanced in the filtered results. (Noise data) Figure 6 ) and denoising results ( Figure 7 Differences between ) Figure 8 The results show that the noise profile contains very little effective in-phase axis information, indicating that the method of this invention can provide relatively accurate high signal-to-noise ratio signal estimation for complex wavefields even in the presence of strongly curved and structurally tilted in-phase axes. Furthermore, the computation time of the method of this invention is relatively low (99.6s on a single-core 2.3GHz CPU), highlighting its computational efficiency, especially its greater advantage in denoising high-dimensional data.

[0084] In summary, this invention provides a three-dimensional denoising method based on spatiotemporal domain streaming predictive filtering, which can accurately characterize the spatiotemporal variation features of non-stationary seismic phase axis information and remove strong amplitude seismic random noise. On the one hand, this invention transforms spatiotemporal domain adaptive predictive filtering denoising into a mathematical overdetermined problem, analytically calculates the objective function under local smoothing regularization conditions, and uses a streaming recursive algorithm to avoid the iterative algorithm in adaptive predictive filtering, effectively saving memory costs and computation time in the calculation process. On the other hand, this invention utilizes local smoothing constraint parameters to autonomously select denoising capabilities according to actual conditions, achieving variable adjustment characteristics between the amplitude preservation capability of spatiotemporally variable non-stationary seismic phase axis and the random noise suppression capability.

[0085] The technical features of the embodiments described above can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification. It should be noted that those skilled in the art can make several 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 patent should be determined by the appended claims.

[0086] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A three-dimensional denoising method based on spatio-temporal domain streaming prediction filtering, characterized in that, The method comprises the following steps: acquiring three-dimensional seismic data, performing boundary mirror extension processing on the three-dimensional seismic data to obtain an extended data volume; performing adaptive data prediction on the extended data volume, introducing time-space variable flow prediction filter coefficients, and representing the extended data volume in a linear combination form containing the time-space variable flow prediction filter coefficients; determining a calculation target function of the time-space variable flow prediction filter coefficients according to the extended data volume in the linear combination form and taking a three-dimensional local smooth regularization equation as a constraint condition; updating the time-space variable flow prediction filter coefficients by using a least square analytical algorithm according to the calculation target function of the time-space variable flow prediction filter coefficients, and determining a denoising result of the extended data volume; In the step of determining the calculation target function of the time-space variable flow prediction filter coefficients according to the extended data volume in the linear combination form and taking the three-dimensional local smooth regularization equation as the constraint condition, the specific representation form is: ； wherein denotes a filter coefficient vector; is a filter coefficient estimate; denotes a filter coefficient vector; are filter coefficient vectors adjacent in time and spatial direction, and , and ; denotes a data copy vector; is a control time and spatial directions; is the transpose of a matrix.

2. The method of claim 1, wherein, In the step of performing boundary mirror extension processing on the three-dimensional seismic data to obtain the extended data volume, the calculation formula of the extended data volume is: ； wherein, is three-dimensional seismic data; t = 0, 1,..., M is the number of time samples of the data; x = 0, 1,..., N is the number of cross-line or in-line samples; and y = 0, 1,..., L is the number of in-line or cross-line samples.

3. The method of claim 1, wherein, In the step of representing the extended data volume in the linear combination form containing the time-space variable flow prediction filter coefficients, the specific representation form is: ； wherein, is an adaptive filter coefficient; is a time shift variable; is a crossline or in-line shift variable; is an in-line or crossline shift variable, is three-dimensional seismic data data is copied in time and spatial directions, , and are filter window size parameters in time , spatial and directions, respectively.

4. The method of claim 1, wherein, The step of updating the time-space variable flow prediction filter coefficients by using the least square analytical algorithm according to the calculation target function of the time-space variable flow prediction filter coefficients and determining the denoising result of the extended data volume comprises the following steps: calculating the calculation target function of the time-space variable flow prediction filter coefficients to solve the least square solution of the time-space variable flow prediction filter coefficients; determining the time-space variable flow prediction filter coefficients representing effective event information in the three-dimensional seismic data according to the least square solution of the time-space variable flow prediction filter coefficients and a Sherman-Morrison formula; updating the time-space variable flow prediction filter coefficients of adjacent calculation points according to a time-space variable flow prediction filter coefficient calculation formula to determine the denoising result of the extended data volume.

5. The method of claim 4, wherein, The time-space variable flow prediction filter coefficient is represented as: ； wherein ; .

6. The method of claim 4, wherein, The least square expression of the time-space variable flow prediction filter coefficient is: wherein , .

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