Three-component seismic data vector Anti-aliasing interpolation reconstruction method and apparatus

Abstract

The present invention relates to the technical field of seismic exploration. Provided are a three-component seismic data vector anti-aliasing interpolation reconstruction method and an apparatus. The method comprises: representing three-component seismic data in a time domain as pure quaternions for vector joint; transforming the pure quaternion data in a time-space domain to a frequency-space domain to obtain frequency-space domain data; transforming the frequency-space domain data into a frequency-wave number domain; in the frequency-wave number domain, using an inclination angle scanning strategy to construct a mask matrix; performing vector anti-aliasing interpolation reconstruction on the frequency-space domain data and the mask matrix, so as to obtain a frequency-space domain reconstruction result; and inversely transforming the frequency-space domain reconstruction result to the time-space domain to obtain a time domain three-component three-dimensional data anti-aliasing reconstruction result. The present invention can effectively solve the problem of vector anti-aliasing reconstruction for three-component seismic data that contain both irregular and regular missing traces, thus improving the accuracy of effective wave event identification.

Description

Method and device for reconstructing three-component seismic data vector anti-aliasing interpolation Technical Field

[0001] The present invention relates to the technical field of seismic exploration, and in particular to a three-component seismic data vector anti-aliasing interpolation reconstruction method and a three-component seismic data vector anti-aliasing interpolation reconstruction device and computer equipment. Background Art

[0002] Seismic data acquisition is constrained by factors such as obstacles, construction environments, and economic costs. This results in sparse or irregularly missing data in spatial directions. For example, onshore seismic data acquisition is affected by obstacles such as mountains, rivers, and urban buildings, making it impossible to collect data on an ideal regular grid. In marine seismic data acquisition, tower steamer (TC) acquisition is affected by plume drift; ocean bottom cable (OBC) acquisition is affected by currents and tides; and ocean bottom node (OBN) seismometers offer high accuracy but are affected by currents and rugged seabed topography, leading to deviations in instrument placement. Furthermore, the removal of waste shots and traces during indoor processing can also result in a certain degree of missing traces. Interpolation and reconstruction of sparse and irregularly missing seismic data can effectively improve migration imaging, suppress spatial aliasing, and enhance the accuracy of seismic data interpretation.

[0003] As oil and gas exploration becomes increasingly challenging, multi-component seismic technology is playing an increasingly important role in the exploration of complex oil and gas reservoirs. Compared to traditional single-component (P-wave) exploration, multi-component seismic exploration simultaneously acquires P-wave and S-wave information, effectively reducing the multi-solution nature of reservoir prediction and improving structural imaging accuracy. It offers significant advantages in reservoir monitoring, fluid prediction, and lithology identification. Current methods for reconstructing multi-component seismic data typically involve reconstructing each component individually. This strategy of separately reconstructing each component compromises the interrelationships between them, destroying the structural characteristics and integrity of the seismic wave vector field, making it difficult to achieve ideal reconstruction results.

[0004] OBN multi-wave, multi-component seismic exploration technology is gaining increasing attention and widespread application in the field of marine exploration. Limited by instrument costs, OBN exploration suffers from the problem of having too many shots and too few channels. Sparse sampling leads to spatial aliasing, which in turn affects the quality of subsequent migration imaging. Existing multi-component seismic data reconstruction methods generally lack anti-aliasing mechanisms, making it impossible to implement channel densification interpolation of three-component OBN sparsely sampled data or to jointly reconstruct multi-component regularly missing channel data. Single-component anti-aliasing reconstruction methods cannot be directly applied to the interpolation and reconstruction of multi-component regularly missing channel data. Therefore, there is an urgent need to develop a vector anti-aliasing interpolation method suitable for multi-component data.

[0005] Summary of the Invention

[0006] The present invention provides a three-component seismic data vector anti-aliasing interpolation reconstruction method and device, which can effectively solve the problem of three-component seismic data vector anti-aliasing reconstruction containing both irregular missing traces and regular missing traces.

[0007] In one aspect, the present invention provides a method for reconstructing three-component seismic data vectors by anti-aliasing interpolation, comprising:

[0008] The three-component seismic data are represented as pure quaternions in the time domain, and the three-component data are vector-joined using pure quaternions;

[0009] Transforming pure quaternion data in the time-space domain into the frequency-space domain to obtain frequency-space domain data;

[0010] Transform frequency-space domain data into frequency-wavenumber domain;

[0011] The mask matrix is ​​constructed using the tilt scanning strategy in the frequency-wavenumber domain;

[0012] Perform vector anti-aliasing interpolation reconstruction based on frequency-space domain data and mask matrix to obtain frequency-space domain reconstruction results;

[0013] The frequency-space domain reconstruction result is inversely transformed into the time-space domain to obtain the anti-aliasing reconstruction result of the three-component three-dimensional data in the time domain.

[0014] In an embodiment of the present invention, the transformation of pure quaternion data in the time-space domain to the frequency-space domain includes: performing a one-dimensional real quaternion Fourier transform on the pure quaternion data along the time variable, transforming the pure quaternion data from the time domain to the frequency domain, and obtaining quaternion frequency-space domain data.

[0015] In an embodiment of the present invention, the transforming of the frequency-space domain data into the frequency-wavenumber domain includes: performing a two-dimensional real quaternion Fourier transform of the spatial dimension on the quaternion frequency-space domain data to obtain the quaternion frequency-wavenumber domain.

[0016] In an embodiment of the present invention, the method of constructing a mask matrix using a tilt scanning strategy in the frequency-wavenumber domain includes: using a tilt scanning strategy in the frequency-wavenumber domain, starting from zero wavenumber, performing linear scanning along different tilt angles, calculating the energy spectrum corresponding to different tilt angles and the negative second-order derivative of the energy spectrum; and calculating the mask matrix corresponding to each frequency slice using the maximum point of the negative second-order derivative of the energy spectrum.

[0017] In the embodiment of the present invention, the expression of the energy spectrum is:

[0018] The expression of the negative second-order derivative of the energy spectrum is:

[0019] Among them, p x and p y is the quaternion ω-k x -k y The slope of the linear ray in the domain, ω n 、k x and k y is the normalized frequency and wave number, satisfying 0<ω n <0.5,-0.5<k x <0.5,-0.5<k y <0.5, ω represents the frequency, n represents the frequency slice number, N ω Indicates the number of frequency slices, Represents the Fourier spectrum coefficient value of the quaternion observation data in the frequency-wavenumber domain, Represents the floor operator.

[0020] In the embodiment of the present invention, the method of constructing the mask matrix in the frequency-wavenumber domain using the tilt scanning strategy further includes: widening and edging the mask matrix using a Gaussian window function to obtain an updated mask matrix.

[0021] In the embodiment of the present invention, the step of calculating the mask matrix corresponding to each frequency slice using the maximum point of the negative second-order derivative of the energy spectrum includes:

[0022] Take the inclination slope corresponding to the first L maximum values ​​of the negative second-order derivative of the energy spectrum to generate each frequency slice ω n The corresponding mask matrix M(ω n ,k x ,k y );

[0023] The values ​​of the elements at the inclination angles corresponding to the first L maximum energy values ​​in the mask matrix are all 1, and the remaining elements are 0. The expression for calculating the mask matrix is:

[0024] Among them, the spatial two-dimensional Gaussian function is used as the window function to widen and edge the range containing 1 elements in the mask matrix. The expression of the spatial two-dimensional Gaussian function G(x,y) is:

[0025] x∈[0,2N x ],y∈[0,2N y ];

[0026] The expression of the rimmed window function W(x,y) is:

[0027] Among them, N x 、N y Respectively represent the edge length of the Gaussian window function in the x and y directions, L x 、L y Respectively represent the length of the central part of the window function in the x and y directions, h x and h y It is a constant in the Gaussian function. The larger its value is, the smaller the slope of the window edge is and the smoother the slope of the window edge is.

[0028] Apply W(x,y) to the mask matrix M(ω n ,k x ,k y ), so that it widens and edges the range containing 1 elements, and the updated mask matrix is ​​recorded as Its expression is:

[0029] In an embodiment of the present invention, the vector anti-aliasing interpolation reconstruction based on frequency-space domain data and a mask matrix includes: reconstructing the frequency slice data in the frequency-space domain data using a vector convex set projection iterative algorithm, and placing the mask matrix corresponding to the frequency slice into the iterative reconstruction expression in each iteration to achieve vector anti-aliasing interpolation reconstruction.

[0030] In an embodiment of the present invention, the frequency slice data in the frequency-space domain data is reconstructed using a vector convex set projection iterative algorithm, and a mask matrix corresponding to the frequency slice is placed into an iterative reconstruction expression at each iteration to implement vector anti-aliasing interpolation reconstruction, including:

[0031] For each frequency slice data of the positive and negative frequency parts of the frequency-space domain data, the vector convex set projection iterative algorithm based on real quaternion Fourier transform is used to reconstruct the mask matrix Abbreviated as Insert vector convex set projection iterative reconstruction expression to suppress spatial aliasing and realize anti-alias channel encryption interpolation;

[0032] Among them, the expression of vector anti-aliasing convex set projection iterative interpolation is:

[0033] represents the reconstruction result of the lth iteration, is the quaternion Q obs (t, x, y) is the result of performing a one-dimensional real quaternion Fourier transform along the time dimension;

[0034] I represents a matrix of all 1s, They represent the forward and inverse Fourier transform of the two-dimensional real quaternion in space; T l represents the threshold operator, S is the sampling operator, and its elements are 0 and 1, where 1 represents known and 0 represents missing channels; α is the weighting factor, which is used to control the proportion of original sampling data participating in reconstruction and thus realize anti-aliasing denoising interpolation, 0<α≤1, N iter Indicates the maximum number of iterations.

[0035] In an embodiment of the present invention, inversely transforming the frequency-space domain reconstruction result to the time-space domain includes: performing a one-dimensional real quaternion inverse Fourier transform along the frequency dimension on the frequency-space domain reconstruction result to the time-space domain.

[0036] Another aspect of the present invention provides a three-component seismic data vector anti-aliasing interpolation reconstruction device, comprising:

[0037] Vector union module, used to represent the three-component seismic data as pure quaternions in the time domain, and use pure quaternions to perform vector union of the three-component data;

[0038] A domain transformation module is used to transform the pure quaternion data in the time-space domain into the frequency-space domain to obtain frequency-space domain data, and transform the frequency-space domain data into the frequency-wavenumber domain;

[0039] The anti-aliasing interpolation reconstruction module is used to construct a mask matrix in the frequency-wavenumber domain using a tilt scanning strategy, and perform vector anti-aliasing interpolation reconstruction based on the frequency-space domain data and the mask matrix to obtain the frequency-space domain reconstruction result;

[0040] The domain transformation module is further used to inversely transform the frequency-space domain reconstruction result to the time-space domain to obtain the time domain three-component three-dimensional data anti-aliasing reconstruction result.

[0041] The present invention also provides a computer device, comprising: a memory, a processor and a computer program, wherein the computer program is stored in the memory and configured to be executed by the processor to implement the above-mentioned three-component seismic data vector anti-aliasing interpolation reconstruction method.

[0042] The present invention employs a vector anti-aliasing convex set projection reconstruction technique based on real quaternion Fourier transforms to perform trace densification and interpolation for three-component seismic data with regular missing traces. This effectively solves the problem of vector anti-aliasing reconstruction for three-component seismic data containing both irregular and regular missing traces. Furthermore, the present invention employs an anti-aliasing strategy based on dip scanning, using the maximum of the negative second-order derivative of the dip scanning energy spectrum to identify and determine the dip of the event. This improves the accuracy of identifying the effective wave event compared to using the maximum of the dip scanning energy spectrum to identify and determine the dip of the event.

[0043] Other features and advantages of the embodiments of the present invention will be described in detail in the subsequent detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0045] FIG1A is a flow chart of a method for anti-aliasing interpolation and reconstruction of three-component seismic data vectors provided by an embodiment of the present invention;

[0046] FIG1B is a flow chart of vector anti-aliasing convex set projection interpolation according to a specific embodiment of the present invention;

[0047] FIG2 is a rectangular bordered window function (a) and its Fourier domain wavenumber spectrum (b) in an example of the present invention;

[0048] FIG3 is a Gaussian rimmed window function (a) and its Fourier domain wavenumber spectrum (b) in an example of the present invention;

[0049] Figure 4 shows the normalized wavenumber spectrum of the complete Y component data at 20 Hz (a) and the normalized wavenumber spectrum of the Y component regularly missing data (b);

[0050] FIG5 is a mask matrix (a) established by the single-component anti-aliasing technique for Y-component data and a normalized wavenumber spectrum (b) of the single-component anti-aliasing interpolation result;

[0051] FIG6 is a mask matrix (a) established by the vector anti-aliasing technique for Y-component data and a normalized wavenumber spectrum (b) of the vector anti-aliasing interpolation result;

[0052] FIG7 is a diagram showing the plane wave tilt angle determined by the maximum value of the energy spectrum (a) and the plane wave tilt angle determined by the maximum value of the negative second-order derivative of the energy spectrum (b);

[0053] Figure 8 is a slice display of the original three-component OBN common receiver gather at Crossline = 112, (a) X component, (b) Y component and (c) Z component;

[0054] Figure 9 is an enlarged display of the original three-component OBN common receiver gather within the rectangular area, (a) X component, (b) Y component and (c) Z component;

[0055] Figure 10 is an enlarged display of the three-component data after the regularity is lost in the rectangular area, (a) X component, (b) Y component and (c) Z component;

[0056] Figure 11 is a partial enlarged display of the single-component anti-aliasing convex set projection reconstruction result, (a) X component, (b) Y component and (c) Z component;

[0057] FIG12 is a partial enlarged display of the vector anti-aliasing convex set projection reconstruction result, (a) X component, (b) Y component and (c) Z component. DETAILED DESCRIPTION

[0058] To make the technical solutions and advantages of the embodiments of the present invention more clearly understood, exemplary embodiments of the present invention are further described in detail below with reference to the accompanying drawings. It should be noted that the embodiments described are only a portion of the embodiments of the present invention, and are not an exhaustive list of all embodiments. It should be noted that the embodiments of the present invention and the features thereof may be combined with each other unless they conflict.

[0059] Existing multi-component seismic data reconstruction methods generally lack anti-aliasing mechanisms and are unable to jointly reconstruct multi-component regularly missing trace data. Single-component anti-aliasing reconstruction methods cannot be directly applied to the interpolation reconstruction of multi-component regularly missing data.

[0060] To address the above-mentioned problems, an embodiment of the present invention provides a method for vector anti-aliasing interpolation reconstruction of three-component seismic data, comprising: representing the three-component seismic data as pure quaternions in the time domain, and using the pure quaternions to vector-unite the three-component data; transforming the pure quaternion data in the time-space domain to the frequency-space domain to obtain frequency-space domain data, and transforming the frequency-space domain data to the frequency-wavenumber domain; constructing a mask matrix in the frequency-wavenumber domain using a tilt scanning strategy, and performing vector anti-aliasing interpolation reconstruction based on the frequency-space domain data and the mask matrix to obtain a frequency-space domain reconstruction result; and inversely transforming the frequency-space domain reconstruction result to the time-space domain to obtain a time-domain three-component three-dimensional data anti-aliasing reconstruction result. The present invention is based on the vector anti-aliasing convex set projection reconstruction technology of the real quaternion Fourier transform, and vectorizes and expands the existing single-component anti-aliasing convex set projection method, which can effectively solve the problem of vector anti-aliasing reconstruction of three-component seismic data containing both irregular missing traces and regular missing traces.

[0061] In addition, the present invention is based on an anti-aliasing strategy based on tilt scanning, and uses the maximum value of the negative second-order derivative of the tilt scanning energy spectrum to identify and determine the tilt of the event axis. Compared with using the maximum value of the tilt scanning energy spectrum to identify and determine the tilt of the event axis, the accuracy of identifying the effective wave event axis can be improved; using a Gaussian edged window function to widen and edge the mask matrix can alleviate the Gibbs energy oscillation tailing phenomenon at the edge of the event axis.

[0062] As shown in FIG1A , the anti-aliasing interpolation reconstruction method for three-component seismic data vectors provided by an embodiment of the present invention includes the following steps:

[0063] S110, representing the three-component seismic data as pure quaternions in the time domain, and performing vector union of the three-component data using the pure quaternions;

[0064] S120, transforming the pure quaternion data in the time-space domain into the frequency-space domain to obtain frequency-space domain data;

[0065] S130, transforming the frequency-space domain data into the frequency-wavenumber domain;

[0066] S140, constructing a mask matrix using a tilt scanning strategy in the frequency-wavenumber domain;

[0067] S150, performing vector anti-aliasing interpolation reconstruction based on the frequency-space domain data and the mask matrix to obtain a frequency-space domain reconstruction result;

[0068] S160 , inversely transforming the frequency-space domain reconstruction result into the time-space domain to obtain a time-domain three-component three-dimensional data anti-aliasing reconstruction result.

[0069] In the above step S110 , the three-dimensional three-component seismic data is represented in the time domain as a pure quaternion with a real part of 0, thereby realizing vector union of the three-component data.

[0070] In the above step S120 , a one-dimensional real quaternion Fourier transform is performed on the pure quaternion data along the time variable, and the pure quaternion data is transformed from the time domain to the frequency domain to obtain quaternion frequency-space domain data.

[0071] In the above step S130 , a two-dimensional real quaternion Fourier transform of the spatial dimension is performed on the quaternion frequency-space domain data to obtain the quaternion frequency-wavenumber domain.

[0072] In step S140, a tilt scanning strategy is used in the frequency-wavenumber domain. Starting from zero wavenumber, linear scans are performed along different tilt angles. The energy spectra and negative second-order derivatives of the energy spectra corresponding to the different tilt angles are calculated. The mask matrix corresponding to each frequency slice is calculated using the maximum points of the negative second-order derivatives of the energy spectra. The mask matrix is ​​widened and edged using a Gaussian window function to obtain an updated mask matrix.

[0073] In the above step S150, the frequency slice data in the frequency-space domain data is reconstructed using a vector convex set projection iterative algorithm, and the mask matrix corresponding to the frequency slice is placed into the iterative reconstruction expression in each iteration to achieve vector anti-aliasing interpolation reconstruction.

[0074] In the above step S160, the frequency-space domain reconstruction result is subjected to one-dimensional real quaternion inverse Fourier transform along the frequency dimension to the time-space domain to obtain the time domain three-component three-dimensional data anti-aliasing interpolation reconstruction result.

[0075] Referring to FIG1B , in one embodiment, vector anti-aliasing channel encryption interpolation is performed on sparsely sampled data collected from three-component three-dimensional common shot point domain gathers and common reception point domain gathers. Taking the three-component sparsely sampled data in the common reception point domain as an example, anti-aliasing reconstruction includes the following steps:

[0076] (1) Set DX obs (t,x,y),DY obs (t,x,y) and DZ obs (t, x, y) represent the sparse sampling data corresponding to the three components of the common receiving point domain X, Y, and Z collected by OBN exploration. The three-component data are represented by vector joint using real quaternion, which is recorded as a pure quaternion Q with a real part of 0. obs (t,x,y), Q obs (t,x,y)=DX obs (t,x,y)i+DY obs (t,x,y)j+DZ obs (t,x,y)k;

[0077] (2) Quaternion Q obs (t,x,y) implements the one-dimensional real quaternion Fourier transform along the time variable t, and converts Q obs (t,x,y) is transformed from the time domain to the quaternion frequency domain, denoted as

[0078] (3) Yes Implement the two-dimensional real quaternion Fourier transform on the variables x and y along the spatial dimension, and The transformation from the quaternion frequency-space domain to the quaternion frequency-wavenumber domain is recorded as

[0079] (4) In the quaternion frequency-wavenumber domain, rays are emitted from zero wavenumber along different inclination slopes p x and p y Perform linear scanning and calculate the energy spectrum E(p x ,p y ) and its negative second-order derivative E"(p x ,p y ), where E(p x ,p y ) and E"(p x ,p y ) are calculated as follows:

[0080] Among them, p x and p y is the quaternion ω-k x -k y The slope of the linear ray in the domain, ω n 、k x and k y is the normalized frequency and wave number, satisfying 0<ω n <0.5,-0.5<k x <0.5,-0.5<k y <0.5, ω represents the frequency, n represents the frequency slice number, N ω Indicates the number of frequency slices, Represents the Fourier spectrum coefficient value of the quaternion observation data in the frequency-wavenumber domain, Represents the floor operator.

[0081] (5) Take the negative second-order derivative of the energy spectrum E"(p x ,p y ) to generate each frequency slice ω n The corresponding mask matrix M(ω n ,k x ,k y ). In this matrix, the values ​​of the elements corresponding to the inclination angles of the first L maximum energy values ​​are all 1, and the rest of the elements are 0. Calculate M(ω n ,k x ,k y ) is:

[0082] In order to alleviate the Gibbs energy oscillation tailing phenomenon in the anti-aliasing interpolation result caused by the widening of the mask matrix by the rectangular window function, the spatial two-dimensional Gaussian function G(x,y) is used as the window function to widen the mask matrix M(ω n ,kx ,k y ) is widened and edged, and the expression of G(x,y) is:

[0083] x∈[0,2N x ],y∈[0,2N y ];

[0084] The expression of the rimmed window function W(x,y) is:

[0085] Among them, N x 、N y Respectively represent the edge length of the Gaussian window function in the x and y directions, L x 、L y Respectively represent the length of the central part of the window function in the x and y directions, h x and h y It is a constant in the Gaussian function. The larger its value is, the smaller the slope of the window edge is and the smoother the slope of the window edge is.

[0086] Apply W(x,y) to the mask matrix M(ω n ,k x ,k y ), so that it widens and edges the range containing 1 elements, and the updated mask matrix is ​​recorded as Its expression is:

[0087] (6) Yes Each frequency slice data of the positive and negative frequency parts is reconstructed using a vector convex set projection iterative algorithm based on real quaternion Fourier transform, and the mask matrix Abbreviated as And insert the vector convex set projection iterative reconstruction expression to suppress spatial aliasing and realize anti-alias channel encryption interpolation. The expression of vector anti-alias convex set projection iterative interpolation is:

[0088] in, represents the reconstruction result of the lth iteration,

[0089] is the quaternion Q obs (t,x,y) is the result of Fourier transform of one-dimensional real quaternion along the time dimension, Q obs (t,x,y)=DX obs (t,x,y)i+DY obs (t,x,y)j+DZ obs (t,x,y)k;

[0090] I represents a matrix of all 1s, They represent the forward and inverse Fourier transforms of two-dimensional real quaternions in space respectively;

[0091] T l Represents the threshold operator, which includes linear, exponential and data-driven models to choose from;

[0092] S is a sampling operator, whose elements are 0 and 1, where 1 indicates that the channel is known and 0 indicates that the channel is missing;

[0093] α is a weighting factor, which is used to control the proportion of original sampling data participating in reconstruction and thus realize anti-aliasing denoising interpolation, 0<α≤1, N iter Indicates the maximum number of iterations.

[0094] (7) Anti-aliasing reconstruction results The frequency variable ω in the vector is transformed into a one-dimensional real quaternion Fourier transform to obtain the vector anti-aliasing interpolation result Q in the time domain. recon (t,x,y), Q recon (t,x,y)=DX recon (t,x,y)i+DY recon (t,x,y)j+DZ recon (t,x,y)k;

[0095] From the above, we can get the anti-aliasing interpolation reconstruction result DX corresponding to the X, Y, and Z components recon (t,x,y),DY recon (t,x,y),DZ recon (t,x,y), complete the final reconstruction.

[0096] This invention uses a vector anti-aliasing convex set projection reconstruction technique based on real quaternion Fourier transforms to perform channel densification and interpolation for three-component seismic data with regularly missing traces. First, a tilt-sweep strategy is used in the vector reconstruction technique to construct a mask matrix to suppress spatial aliasing, enabling anti-aliasing and channel densification for the vector reconstruction technique. This addresses the problem that current vector reconstruction techniques for three-component seismic data, which lack an anti-aliasing mechanism, cannot achieve channel densification and interpolation for three-component sparsely sampled data. Second, during the tilt sweep, the maximum of the negative second-order derivative of the energy spectrum is used to identify and determine the dip of the event. Compared to methods that directly use the maximum of the energy spectrum to determine the dip of the event, the present invention provides a more accurate estimate of the dip. Third, a Gaussian-shaped bordering window function is used to widen and border the mask matrix. Compared to current techniques that use rectangular-shaped bordering windows to widen and border the mask matrix, the present invention can effectively mitigate and suppress the energy oscillation tailing phenomenon that occurs at the edges of the event in the reconstruction results, resulting in a more accurate vector-reconstructed seismic wavefield. In addition, the model and actual tests show that compared with the single-component anti-aliasing convex set projection reconstruction technology, the quaternion-based vector convex set projection reconstruction technology of the present invention has a higher reconstructed signal-to-noise ratio in the anti-aliasing interpolation of three-component seismic data and has more advantages in protecting weak effective wave phase axes.

[0097] The following lists examples of the three-component seismic data vector anti-aliasing interpolation reconstruction method of the present invention in specific application scenarios to demonstrate its effect.

[0098] Example 1: Synthesize a two-dimensional Gaussian edged window function and a rectangular edged window function for spectrum analysis comparison;

[0099] Figure 2(a) shows the rectangular bordered window function currently used in single-component data anti-aliasing interpolation;

[0100] Figure 2(b) shows the spatial two-dimensional Fourier transform wavenumber spectrum of the rectangular rimmed window function;

[0101] FIG3( a ) is a Gaussian rimmed window function designed by the present invention;

[0102] Figure 3(b) shows the spatial two-dimensional Fourier transform wavenumber spectrum of the Gaussian edge window function;

[0103] It can be seen from Figure 2(b) that the rectangular window function has an obvious energy oscillation continuation phenomenon around the central zero wavenumber, while in Figure 3(b), the energy oscillation continuation phenomenon around the central zero wavenumber of the wavenumber spectrum corresponding to the Gaussian window function of the present invention is effectively alleviated and suppressed.

[0104] Example 2: Synthesizing three-dimensional, three-component plane wave model data for vector anti-aliasing channel encryption and interpolation experiments. Three-component plane wave data of 501 × 51 × 51 was synthesized. Then, every other channel was deleted in both the inline and crossline directions to create sparsely sampled data with a deletion rate of 75%. Channel encryption and interpolation were then performed using the single-component anti-aliasing convex set projection technique and the vector anti-aliasing convex set projection technique of the present invention. Finally, the reconstructed data was subtracted from the original data to obtain the reconstructed error data.

[0105] Comparing the results of single-component anti-aliasing reconstruction with those of vector anti-aliasing reconstruction shows that both techniques can effectively reconstruct regularly missing traces, restoring spatial continuity of the events. However, the error profile of single-component anti-aliasing reconstruction shows strong residual energy of the effective signal, and clear traces of continued oscillation of the event edge energy. In particular, the missing traces of the weak effective wave events in the Y component data are almost completely unrecovered, and the residual error is large. In contrast, the error profile of vector anti-aliasing interpolation shows weak residual energy of the effective wave signal, a cleaner error profile, weak continued oscillation of the event edge energy, and better recovery of the weak effective wave events in the Y component.

[0106] Figure 4(a) shows the normalized wavenumber spectrum of the original complete data of the Y component at the main frequency of 20 Hz, and Figure 4(b) shows the normalized wavenumber spectrum of the regular missing data of the Y component;

[0107] Figure 5(a) shows the mask matrix created by the current single-component anti-aliasing technology using the tilt scanning strategy and the rectangular edge window function. It can be seen from the figure that the three plane waves with different slopes only generate two rectangular blocks, missing one rectangular block. Figure 5(b) shows the normalized wavenumber spectrum of the Y-component anti-aliasing interpolation result after using the mask matrix to suppress spatial aliasing.

[0108] FIG6(a) shows a mask matrix established using the tilt scanning strategy and Gaussian-edge window function of the present invention. It can be seen from the figure that three plane waves with different slopes precisely correspond to three Gaussian-edge rectangular blocks. FIG6(b) shows the normalized wavenumber spectrum of the Y-component anti-aliasing interpolation result after suppressing spatial aliasing using the mask matrix established by the present invention.

[0109] 7(a) shows the plane wave dip angle determined directly using the first three maxima of the energy spectrum. It can be seen from the figure that the dip angle slope p x =2.0 and p y = 3.0 is omitted, which will result in incomplete suppression of spatial aliasing by the generated mask matrix. FIG7( b ) shows the plane wave dips determined using the first three maxima of the negative second-order derivative of the energy spectrum of the present invention. It can be seen that the technology of the present invention can accurately identify the dip positions corresponding to the three plane waves.

[0110] In order to further demonstrate the reconstruction effect of the technology of the present invention, the reconstruction signal-to-noise ratio SNR is defined as:

[0111] D recon Denotes the anti-aliasing interpolation result, D true Represents the original true complete data. The reconstructed signal-to-noise ratios (SNRs) of the three components of the single-component anti-aliasing convex set projection are 11.94dB, 10.48dB, and 12.09dB, respectively. The reconstructed SNRs of the present invention are 12.33dB, 11.83dB, and 12.34dB, respectively. It can be seen that the vector anti-aliasing convex set projection reconstruction technique is also superior to the single-component anti-aliasing convex set projection reconstruction technique.

[0112] Example 3: The technology of the present invention is applied to the anti-aliasing interpolation processing of the 3C-3D OBN common receiving point data set in a certain block. The X, Y, and Z component data sizes of this OBN node are all 2001×319×320, and the original real data slice is shown in Figure 8. Then, the three-component data is thinned out in both the inline and crossline directions to form three-component sparse sampling data with both regular missing channels and a small number of irregular missing channels, with a data missing rate of 78%. Next, the sparse sampling data is subjected to channel encryption interpolation using the single-component anti-aliasing interpolation technology and the vector anti-aliasing interpolation technology of the present invention. In order to more clearly demonstrate the reconstruction effect, the data within the black rectangular area in Figure 8 is selected for enlarged display. Figure 9 shows the original real complete data of the three components. Figure 10 shows the sparse sampling data after regular missing channels. Figure 11 shows the reconstruction results of the single-component anti-aliasing convex set projection interpolation technology. Figure 12 shows the reconstruction results of the vector anti-aliasing interpolation technology of the present invention. By comparing the reconstruction results of Figures 11 and 12, it can be seen that the event axes of the reconstruction results of the present invention are continuous and clear, the wave group characteristics are obvious, and the spatial structure characteristics of the event axes match the original real data of Figure 9 well. However, there are more noise spots in the single-component anti-aliasing reconstruction results, the wave group characteristics of the event axes are not obvious, and the matching degree with the original real data is also poor, which once again verifies the advanced nature and superiority of the technology of the present invention.

[0113] An embodiment of the present invention also provides a three-component seismic data vector anti-aliasing interpolation reconstruction device, comprising: a vector union module, a domain transformation module, and an anti-aliasing interpolation reconstruction module. The vector union module is used to represent the three-component seismic data in the time domain as a pure quaternion, and use the pure quaternion to vector-unite the three-component data. The domain transformation module is used to transform the pure quaternion data in the time-space domain to the frequency-space domain to obtain frequency-space domain data, and transform the frequency-space domain data to the frequency-wavenumber domain. The anti-aliasing interpolation reconstruction module is used to construct a mask matrix in the frequency-wavenumber domain using an inclination scanning strategy, perform vector anti-aliasing interpolation reconstruction based on the frequency-space domain data and the mask matrix, and obtain a frequency-space domain reconstruction result. The domain transformation module is also used to inversely transform the frequency-space domain reconstruction result to the time-space domain to obtain a time domain three-component three-dimensional data anti-aliasing reconstruction result.

[0114] In one embodiment, the vector union module represents the three-dimensional, three-component seismic data in the time domain as pure quaternions with a real part of zero, thereby achieving vector union of the three-component data. The domain transformation module performs a one-dimensional real quaternion forward Fourier transform on the pure quaternion data along the time variable, transforming the pure quaternion data from the time domain to the frequency domain to obtain quaternion frequency-space domain data. The quaternion frequency-space domain data is then subjected to a two-dimensional real quaternion forward Fourier transform of the spatial dimension to obtain quaternion data in the frequency-wavenumber domain.

[0115] In one embodiment, the anti-aliasing interpolation reconstruction module utilizes an angle scanning strategy in the frequency-wavenumber domain. Starting from zero wavenumber, linear scans are performed along different angles to calculate the energy spectrum and the negative second-order derivative of the energy spectrum corresponding to the different angles. The mask matrix corresponding to each frequency slice is calculated using the maximum point of the negative second-order derivative of the energy spectrum. Furthermore, a Gaussian window function is used to widen and edge the mask matrix to obtain an updated mask matrix. Vector anti-aliasing interpolation reconstruction is performed based on the frequency-space domain data and the updated mask matrix to obtain a frequency-space domain reconstruction result.

[0116] The three-component seismic data vector anti-aliasing interpolation reconstruction device corresponds to the above-mentioned three-component seismic data vector anti-aliasing interpolation reconstruction method, and specific details can be understood by referring to the above-mentioned method embodiment.

[0117] An embodiment of the present invention further provides a computer device, comprising: a memory and a processor, wherein the memory stores a computer program, and the processor is configured to execute the computer program to implement the above-mentioned three-component seismic data vector anti-aliasing interpolation reconstruction method.

[0118] An embodiment of the present invention further provides a computer program product, comprising a computer program, which implements the above-mentioned three-component seismic data vector anti-aliasing interpolation reconstruction method when executed by a processor.

[0119] An embodiment of the present invention further provides a machine-readable storage medium having computer program instructions stored thereon. When the computer program instructions are executed by a processor, the above-mentioned three-component seismic data vector anti-aliasing interpolation reconstruction method is implemented.

[0120] It will be understood by those skilled in the art that the embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present invention may be implemented in various computer languages, for example, the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0121] The present invention is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device produce a device for implementing the functions specified in one or more processes in the flowchart and / or one or more boxes in the block diagram.

[0122] These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce a product including an instruction device that implements the functions specified in one or more processes in the flowchart and / or one or more boxes in the block diagram.

[0123] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one or more processes in the flowchart and / or one or more boxes in the block diagram.

[0124] Although preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they are aware of the basic inventive concepts. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the invention. Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the invention. Thus, the present invention is intended to include such changes and modifications as fall within the scope of the claims and their equivalents.

Claims

1. A three-component seismic data vector anti-aliasing interpolation reconstruction method, characterized in that, Including: Representing three-component seismic data as pure quaternions in the time domain and using pure quaternions to perform vector combination on the three-component data; Transforming the pure quaternion data in the time-space domain to the frequency-space domain to obtain frequency-space domain data; Transforming the frequency-space domain data to the frequency-wavenumber domain; Constructing a mask matrix in the frequency-wavenumber domain using a dip scanning strategy; Performing vector anti-aliasing interpolation reconstruction based on the frequency-space domain data and the mask matrix to obtain a frequency-space domain reconstruction result; Inverse-transforming the frequency-space domain reconstruction result to the time-space domain to obtain an anti-aliasing reconstruction result of three-component three-dimensional data in the time domain.

2. The three-component seismic data vector anti-aliasing interpolation reconstruction method according to claim 1, wherein The transformation of the pure quaternion data in the time-space domain to the frequency-space domain includes: Performing a one-dimensional real quaternion Fourier forward transform on the pure quaternion data along the time variable to transform the pure quaternion data from the time domain to the frequency domain, obtaining quaternion frequency-space domain data.

3. The three-component seismic data vector anti-aliasing interpolation reconstruction method according to claim 2, characterized in that The transformation of the frequency-space domain data to the frequency-wavenumber domain includes: Performing a two-dimensional real quaternion Fourier forward transform on the quaternion frequency-space domain data in the spatial dimension to obtain a quaternion frequency-wavenumber domain.

4. The three-component seismic data vector anti-aliasing interpolation reconstruction method according to claim 1, wherein, The construction of the mask matrix in the frequency-wavenumber domain using a dip scanning strategy includes: In the frequency-wavenumber domain, using a dip scanning strategy, starting from zero wavenumber, linearly scanning along different dips, and calculating the energy spectrum corresponding to different dips and the negative second derivative of the energy spectrum; Calculating the mask matrix corresponding to each frequency slice using the maximum points of the negative second derivative of the energy spectrum.

5. The three-component seismic data vector anti-aliasing interpolation reconstruction method according to claim 4, wherein The expression of the energy spectrum is as follows: The expression for the negative second derivative of the energy spectrum is as follows: where p x and p y are the slopes of linear rays in the quaternion ω-k x -k y domain, ω n , k x and k y are the normalized frequency and wavenumber, satisfying 0 < ω n < 0.5, -0.5 < k x < 0.5, -0.5 < k y < 0.5, ω represents the frequency, n represents the frequency slice number, and N ω represents the frequency slice quantity Denotes the Fourier spectral coefficient value of the frequency-wavenumber domain quaternion observation data, Denoting the floor operator.

6. The three-component seismic data vector anti-aliasing interpolation reconstruction method according to claim 4, wherein The construction of the mask matrix in the frequency-wavenumber domain using a dip scanning strategy further includes: Using a Gaussian window function to broaden and edge the mask matrix to obtain an updated mask matrix.

7. The three-component seismic data vector anti-aliasing interpolation reconstruction method according to claim 6, characterized in that The calculation of the mask matrix corresponding to each frequency slice using the maximum points of the negative second derivative of the energy spectrum includes: Generate the dip slope corresponding to the first L maximum values of the negative second derivative of the energy spectrum for each frequency slice ω n The corresponding mask matrix M(ω n ,k x ,k y ); The element values at the dip angles corresponding to the first L maximum energy values in the mask matrix are all 1, and the remaining elements are 0. The expression for calculating the mask matrix is: Among them, a two-dimensional spatial Gaussian function is used as a window function to broaden and edge the range of elements with value 1 in the mask matrix. The expression of the two-dimensional spatial Gaussian function G(x, y) is as follows: The expression of the bordered window function W(x, y) is as follows: Among them, N x and N y respectively represent the edge lengths of the Gaussian window function in the x and y directions, L x and L y respectively represent the lengths of the central part of the window function in the x and y directions, h x and h y are constants in the Gaussian function; Apply W(x, y) to the mask matrix M(ω n , k x , k y ), so as to broaden and trim the range containing the element 1. The updated mask matrix is denoted as Its expression is:

8. The three-component seismic data vector anti-aliasing interpolation reconstruction method according to claim 4, wherein The vector anti-aliasing interpolation reconstruction based on the frequency-space domain data and the mask matrix includes: Using the vector convex set projection iterative algorithm to reconstruct the frequency slice data in the frequency-space domain, and placing the mask matrix corresponding to the frequency slice into the iterative reconstruction expression at each iteration; To achieve vector anti-aliasing interpolation reconstruction.

9. The three-component seismic data vector anti-aliasing interpolation reconstruction method according to claim 8, wherein The use of the vector convex set projection iterative algorithm to reconstruct the frequency slice data in the frequency-space domain, and placing the mask matrix corresponding to the frequency slice into the iterative reconstruction expression at each iteration to achieve vector anti-aliasing interpolation reconstruction includes: For each frequency slice data of the positive and negative frequency parts of the frequency-space domain data, use the vector convex set projection iterative algorithm based on the real quaternion Fourier transform for reconstruction, and the mask matrix Briefly denoted as Placing it into the vector convex set projection iterative reconstruction expression to suppress spatial aliasing and achieve anti-aliasing channel encryption interpolation; Among them, the expression of the vector anti-aliasing convex set projection iterative interpolation is as follows: Indicates the reconstruction result of the l-th iteration, Is the quaternion Q obs (t, x, y) is the result of performing a one-dimensional real quaternion Fourier forward transform along the time dimension; I represents a matrix of all 1s, Respectively representing the two-dimensional real quaternion Fourier forward transform and inverse transform in the spatial dimension; T l represents a threshold operator, and S is a sampling operator with elements 0 and 1, where 1 indicates known and 0 indicates missing traces; α is a weighting factor used to control the proportion of the original sampled data participating in the reconstruction so as to achieve anti-aliasing denoising interpolation, where 0 < α ≤ 1, and N iter represents the maximum number of iterations.

10. The three-component seismic data vector anti-aliasing interpolation reconstruction method according to claim 1, characterized in that The inverse transformation of the frequency-space domain reconstruction result to the time-space domain includes: Performing a one-dimensional real quaternion Fourier inverse transform on the frequency-space domain reconstruction result along the frequency dimension to the time-space domain.

11. A three-component seismic data vector anti-aliasing interpolation reconstruction device, characterized in that, Including: A vector combination module for representing three-component seismic data as pure quaternions in the time domain and using pure quaternions to perform vector combination on the three-component data; A domain transformation module, configured to transform the pure quaternion data in the time - space domain to the frequency - space domain to obtain frequency - space domain data, and transform the frequency - space domain data to the frequency - wavenumber domain; An anti - aliasing interpolation reconstruction module, configured to construct a mask matrix in the frequency - wavenumber domain by using a dip scanning strategy, and perform vector anti - aliasing interpolation reconstruction based on the frequency - space domain data and the mask matrix to obtain a frequency - space domain reconstruction result; The domain transformation module is further configured to inverse - transform the frequency - space domain reconstruction result to the time - space domain to obtain an anti - aliasing reconstruction result of three - component three - dimensional data in the time domain.

12. The three-component seismic data vector anti-aliasing interpolation reconstruction device according to claim 11, wherein Specifically, the domain transformation module is configured to perform a one - dimensional real - quaternion Fourier forward transform on the pure quaternion data along the time variable, transform the pure quaternion data from the time domain to the frequency domain to obtain quaternion frequency - space domain data; and perform a two - dimensional real - quaternion Fourier forward transform on the quaternion frequency - space domain data in the spatial dimension to obtain the quaternion frequency - wavenumber domain.

13. The three-component seismic data vector anti-aliasing interpolation reconstruction device according to claim 11, characterized in that Specifically, the anti - aliasing interpolation reconstruction module is configured to use a dip scanning strategy in the frequency - wavenumber domain, starting from zero wavenumber, linearly scan along different dips, calculate the energy spectrum corresponding to different dips and the negative second derivative of the energy spectrum, calculate the mask matrix corresponding to each frequency slice by using the maximum point of the negative second derivative of the energy spectrum, and perform vector anti - aliasing interpolation reconstruction based on the frequency - space domain data and the mask matrix to obtain a frequency - space domain reconstruction result.

14. A computer device, characterized in that, Comprising: A memory storing a computer program; A processor, configured to execute the computer program to implement the three - component seismic data vector anti - aliasing interpolation reconstruction method according to any one of claims 1 - 10.

15. A computer program product, comprising a computer program, characterized in that, The computer program, when executed by the processor, implements the three - component seismic data vector anti - aliasing interpolation reconstruction method according to any one of claims 1 - 10.

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