Seismic data interpolation method and system based on mathematical morphology theory

Abstract

The application discloses a seismic data interpolation method and system based on mathematical morphology theory. The selected structural elements and the shot gather waveforms in the selected dip range of the same phase axis are subjected to open operation to obtain a first point set; the selected structural elements and the shot gather waveforms in the selected dip range of the same phase axis are subjected to closed operation to obtain a second point set; the first and second point sets are subjected to amplitude balance calculation according to the amplitude balance principle of the mathematical morphology theory to determine the interpolated seismic data. The sparse sampling seismic data can be encrypted and interpolated, false high-frequency information caused by too large line spacing is avoided, the interpolation result can better reflect the actual geological conditions, the interpolation can be effectively and quickly performed without the need of transformation domain and any prior information or geological model constraint, the interpolation effect is better, the interpolation precision of the sparse sampling data under any complex geological conditions is higher, the required internal memory is lower, and the calculation speed and efficiency are higher.

Description

Technical Field

[0001] This invention relates to the field of oil and gas geophysical exploration engineering technology, and in particular to a seismic data interpolation method and system based on mathematical morphology theory. Background Technology

[0002] In actual seismic exploration field data acquisition, large line spacing and trace spacing are often used to save costs, which leads to insufficient data sampling. Excessive trace spacing can cause spatial aliasing during migration, and the sparsely sampled spectrum will have a smaller amplitude relative to the true signal, affecting the accuracy of seismic migration imaging and failing to meet the requirements for detailed reservoir interpretation and description. Therefore, it is necessary to densify and interpolate sparsely sampled seismic data to improve migration imaging accuracy.

[0003] Currently, there are three main categories of seismic data interpolation methods: transform-based interpolation methods, filtering-based interpolation methods, and partial differential equation-based interpolation methods. Transform-based methods primarily utilize Fourier transforms to obtain the transform domain data of the original seismic data. A prediction operator is then obtained through least-squares inversion, followed by an inverse transform to obtain the interpolated data gather. Filtering-based methods use interpolation filters and data convolution to achieve data interpolation. Wave equation-based interpolation methods leverage Kirchhoff integral and migration operators to fully utilize ground record information; however, for data with dispersion, the interpolation results still contain artifacts. While these methods produce natural interpolated waveforms, they require significant memory and often produce poor interpolation results for seismic data with steep dips or low signal-to-noise ratios. Summary of the Invention

[0004] To address the aforementioned problems, the inventors have developed this invention, which, through specific implementation methods, provides a seismic data interpolation method and system based on mathematical morphology theory.

[0005] In a first aspect, embodiments of the present invention provide a seismic data interpolation method based on mathematical morphology theory, comprising the following steps:

[0006] An opening operation is performed on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element to obtain the first point set;

[0007] A closing operation is performed on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element to obtain the second point set;

[0008] The interpolated seismic data is determined based on the mean amplitude of corresponding points in the first and second point sets.

[0009] Specifically, the seismic data interpolation method based on mathematical morphology further includes the following steps:

[0010] Before determining the first or second point set, a digital test signal is set up, and one-dimensional gray value mathematical morphological erosion and dilation operations are performed on the digital test signal respectively. The waveform changes of the digital test signal before and after the operation are compared to determine the waveform obtained after the opening and closing operations of the digital test signal.

[0011] Specifically, selecting the tilt range of the in-phase axis includes the following steps:

[0012] The slope of the phase axis when the shot-receiver distance angle is at its maximum is determined as the upper limit of the phase axis tilt range parameter.

[0013] Specifically, selecting structural elements includes the following steps:

[0014] The structural element adopts a one-dimensional gray value 3-point format that is symmetric about the geometric center, and the centroid of the structural element coincides with the geometric center.

[0015] Specifically, the opening operation is performed on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element to obtain the first point set, including the following steps:

[0016] The waveform obtained by performing erosion operation on the selected in-phase axis tilt range and the selected structural element is then subjected to dilation operation with the structural element to obtain the first point set.

[0017] Specifically, the etching operation is performed on the shot gather waveform within the selected phase axis tilt range and the selected structural element, including the following steps:

[0018] Using the selected structuring element, iterate through each point of the shot gather waveform within the selected in-phase axis tilt range. When all waveform points covered by the structuring element have the same gray value as the structuring element, retain the gray value of the shot gather waveform points covered by the structuring element. When there are waveform points covered by a structuring element that have a different gray value than the structuring element, change the gray value of the waveform points covered by the structuring element that have the same gray value as the structuring element to be different from the gray value of the structuring element.

[0019] Specifically, the waveform obtained by performing erosion operations on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element, and then performing dilation operations on the structural element, yields the first point set, including the following steps:

[0020] Using the selected structuring element, the waveforms obtained by erosion operations on the shot gather waveforms within the selected in-phase axis tilt range and the selected structuring element are traversed. The gray values ​​of all waveform points covered by the structuring element are adjusted to be consistent with the gray values ​​of the structuring element, thus obtaining the first point set.

[0021] Specifically, the second point set is obtained by performing a closing operation on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element, including the following steps:

[0022] The waveform obtained by performing dilation operation on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element is then subjected to erosion operation with the structural element to obtain the second point set.

[0023] Specifically, the expansion calculation is performed on the shot gather waveform within the selected phase axis tilt range and the selected structural element, including the following steps:

[0024] Using the selected structuring element, iterate through each point of the shot gather waveform within the selected in-phase axis tilt range, and adjust the gray values ​​of all waveform points covered by the structuring element to be consistent with the gray values ​​of the structuring element.

[0025] Specifically, the second point set is obtained by performing dilation operations on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element, and then performing erosion operations on the structural element. This includes the following steps:

[0026] Using the selected structuring element, traverse the shot gather waveform within the selected in-phase axis tilt range and perform dilation operations on each point of the waveform obtained by the selected structuring element. When all waveform points covered by the structuring element have the same gray value as all points of the structuring element, retain the gray value of the waveform points covered by the structuring element. When there are waveform points covered by the structuring element with inconsistent gray values, change the gray value of the waveform points covered by the structuring element with consistent gray values ​​to be inconsistent with the gray value of the structuring element, and obtain the second point set.

[0027] Secondly, embodiments of the present invention provide a seismic data interpolation system based on mathematical morphology theory, comprising:

[0028] The first point set determination module is used to perform an opening operation on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element to obtain the first point set;

[0029] The second point set determination module is used to perform a closing operation on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element to obtain the second point set;

[0030] The interpolated waveform determination module is used to determine the interpolated seismic data based on the mean amplitude of corresponding points in the first and second point sets.

[0031] Based on the same inventive concept, embodiments of the present invention provide an electronic device, including: a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor executes the computer program to implement the aforementioned seismic data interpolation method based on mathematical morphology theory.

[0032] Based on the same inventive concept, embodiments of the present invention provide a computer storage medium storing computer-executable instructions, which, when executed, implement the aforementioned seismic data interpolation method based on mathematical morphology theory.

[0033] The beneficial effects of the above-described technical solutions provided in the embodiments of the present invention include at least the following:

[0034] It can perform encrypted interpolation on sparsely sampled seismic data, avoiding the introduction of false high-frequency information due to excessive line spacing, making the interpolation results more reflective of the actual geological conditions. Furthermore, it does not require a transform domain or any prior information or geological model constraints, and requires less memory for computation, greatly solving the problem of large memory requirements. It can perform interpolation effectively and quickly, with good interpolation results. It has higher interpolation accuracy for sparsely sampled data under arbitrarily complex geological conditions, and has lower computational memory requirements, resulting in higher computational speed and efficiency.

[0035] Other features and advantages of the invention will be set forth in the following description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings.

[0036] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0037] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0038] Figure 1 This is a flowchart of the seismic data interpolation method based on mathematical morphology theory in an embodiment of the present invention;

[0039] Figure 2 This is a schematic diagram of structural elements in an embodiment of the present invention;

[0040] Figure 3 This is a flowchart of the encryption interpolation method for sparsely sampled seismic data in an embodiment of the present invention;

[0041] Figure 4 This is a diagram of the heterogeneous isotropic BP1994 model in an embodiment of the present invention;

[0042] Figure 5 This is the original seismic record diagram in an embodiment of the present invention;

[0043] Figure 6 This is a seismic record image with a sampling interval of 200m in an embodiment of the present invention;

[0044] Figure 7 This is a seismic record image obtained by encryption and interpolation of sparsely sampled seismic records in an embodiment of the present invention;

[0045] Figure 8 This is a comparison diagram of extraction channels in an embodiment of the present invention;

[0046] Figure 9 This is a 200m seismic record image with sparse sampling and noise in an embodiment of the present invention;

[0047] Figure 10 For the purposes of this embodiment of the invention Figure 9 Seismic record graph after encryption and interpolation of seismic records;

[0048] Figure 11 This is a schematic diagram of the structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0049] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0050] To address the problems existing in the prior art, embodiments of the present invention provide a seismic data interpolation method, system, electronic device, and computer storage medium based on mathematical morphology theory.

[0051] This invention provides a seismic data interpolation method based on mathematical morphology theory, the process of which is as follows: Figure 1 As shown, it includes the following steps:

[0052] Step S1: Perform an opening operation on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element to obtain the first point set.

[0053] In some specific embodiments, the seismic data interpolation method based on mathematical morphology further includes the following steps:

[0054] Before determining the first or second point set, a digital test signal is set up. One-dimensional gray-value mathematical morphological erosion and dilation operations are performed on the digital test signal, and the waveform changes before and after the operations are compared to determine the waveforms obtained after opening and closing operations. The interpolation effect of the seismic data is verified based on the interpolation effect of the digital test signal. In some specific embodiments, the in-phase axis tilt range is selected, including the following steps: the slope of the in-phase axis at the maximum shot-receiver offset angle is determined as the upper limit of the in-phase axis tilt range parameter. That is, based on the analysis of the in-phase axis tilt range from the shot gather records, the slope of the in-phase axis at the maximum shot-receiver offset angle is generally taken as the upper limit of the tilt range parameter. A shot gather refers to a single shot gather, and a gather refers to a collection of multiple seismic trace data.

[0055] In some specific embodiments, selecting a structural element includes the following steps: employing a one-dimensional gray-value 3-point format structural element symmetric about the geometric center, with the centroid of the structural element coinciding with the geometric center. Specifically, structural elements of different formats can interpolate and reconstruct missing points smaller than the structural element size. When densifying sparsely sampled seismic data, a 3-point format structural element is generally used, which can successfully reconstruct missing points. Specifically, in this method, the structural element is designed as an operator with its centroid located at the center, such as... Figure 2 As shown, the first row is a schematic diagram of two-dimensional structural elements. From left to right, they are two-dimensional structural elements in 5-point, 9-point, 13-point, and 25-point formats, respectively. The light-colored rectangle in the middle represents the centroid of this structural element. This method uses one-dimensional grayscale structural elements. Figure 2 The second row shows the structuring element formats degenerated from two-dimensional to one-dimensional. The two on the left are two-dimensional 5-point and 9-point formats degenerated into one-dimensional 3-point formats, and the two on the right are two-dimensional 13-point and 25-point formats degenerated into one-dimensional 5-point formats. Structuring elements are symmetric about their geometric center. The values ​​of the three points in a structuring element (such as a 3-point format) participate in calculations, and the result is placed at the centroid. In morphology, structuring elements are also called kernels or structural operators, and can be rectangular, elliptical, cross-shaped, etc., used to overlay on the target image and perform logical operations with the corresponding overlaid points of the target image. In this embodiment, [the following is selected] Figure 2 The first graphic on the left in the second row serves as the structural element.

[0056] In some specific embodiments, an opening operation is performed on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element to obtain a first point set. This includes the following steps: performing an erosion operation on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element, and then performing an expansion operation on the structural element to obtain the first point set.

[0057] In some specific embodiments, the erosion operation is performed on the shot gather waveform within the selected phase axis tilt range and the selected structural element, including the following steps: using the selected structural element, traverse each point of the shot gather waveform within the selected phase axis tilt range; when all waveform points covered by the structural element are consistent with the gray value of the structural element, retain the gray value of the shot gather waveform points covered by the structural element; when there are waveform points covered by a structural element that are inconsistent with the gray value of the structural element, change the gray value of the waveform points covered by the structural element that are consistent with the gray value of the structural element to be inconsistent with the gray value of the structural element.

[0058] Specifically, the expression for the erosion operation is as follows:

[0059]

[0060] The expression for the expansion operation is:

[0061]

[0062] Where Θ is the erosion operator, This is the dilation operator. Sets A and B are the target dataset (i.e., image data, such as the shot gather waveform in the example above) and the point set corresponding to the selected structuring element, respectively. t These are the points in set A that participate in the calculation. The points in set A are time series, where t represents time, and its value range is the recording time of the seismic data. k is the number of data points delineated by the structure operator (i.e., the structure element) B when it moves on set A. In this method, only a 3-point format structure element (such as...) is needed. Figure 2 As shown in the first figure on the left in the second row, the range of values ​​for k is [1, 3]. It is a set of delineated data points.

[0063] In some specific embodiments, the waveform obtained by performing erosion operations on the shot gather waveform within the selected phase axis tilt range and the selected structural element, and then performing dilation operations on the structural element to obtain a first point set, includes the following steps: using the selected structural element, traversing the shot gather waveform within the selected phase axis tilt range and the waveform obtained by performing erosion operations on the selected structural element, adjusting the gray values ​​of all waveform points covered by the structural element to be consistent with the gray values ​​of the structural element, thus obtaining the first point set. The above process can be represented as follows: AE is the first point set.

[0064] Step S2: Perform a closing operation on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element to obtain the second point set.

[0065] In some specific embodiments, a closing operation is performed on the shot gather waveform within a selected in-phase axis tilt range and a selected structural element to obtain a second point set. This includes the following steps: performing an expansion operation on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element, and then performing an erosion operation on the structural element to obtain the second point set. The above process can be represented as follows: AD stands for the second point set.

[0066] In some specific embodiments, the expansion operation is performed on the shot gather waveform within the selected phase axis tilt range and the selected structural element, including the following steps: using the selected structural element, traversing each point of the shot gather waveform within the selected phase axis tilt range, and adjusting the gray values ​​of all waveform points covered by the structural element to be consistent with the gray values ​​of the structural element.

[0067] In some specific embodiments, the waveform obtained by performing dilation operation on the shot gather waveform within the selected phase axis tilt range and the selected structural element is then subjected to erosion operation with the structural element to obtain a second point set. This includes the following steps: using the selected structural element, traversing each point of the waveform obtained by performing dilation operation on the shot gather waveform within the selected phase axis tilt range and the selected structural element; when all waveform points covered by the structural element have the same gray value as all points of the structural element, retaining the gray value of the waveform points covered by the structural element; when there are waveform points covered by a structural element with a gray value inconsistent with the gray value of the structural element, changing the gray value of the waveform points covered by the structural element with the same gray value as the structural element to be inconsistent with the gray value of the structural element, thus obtaining the second point set.

[0068] Step S3: Determine the interpolated seismic data based on the mean amplitude of corresponding points in the first and second point sets. For example, the above process can be represented as follows:

[0069] x j and t i Let A(t) represent the x-coordinate and y-coordinate of the image corresponding to the seismic data, respectively. The x-coordinate represents the offset, and the y-coordinate represents the recording time of the seismic data. The range of values ​​for i is the recording time of the seismic data, and the range of values ​​for j is the range of the x-coordinate of the seismic data. i x j () represents the interpolated seismic data, which includes the coordinates of the points to be interpolated.

[0070] In a specific embodiment, such as Figure 3 As shown, the specific process of the method for densifying and interpolating sparsely sampled seismic data includes:

[0071] (1) Select the inclination range of the phase axis. Analyze the inclination range of the phase axis based on the shot gather record. Generally, the slope of the inclination axis when the angle with the shot receiver distance is the largest is taken as the upper limit of the inclination range parameter.

[0072] (2) Select the length of the structuring element. Structuring elements of different formats can interpolate and reconstruct missing points smaller than the structuring element size. When decrypting sparsely sampled seismic data, a 3-point format structuring element is generally used, which can successfully reconstruct missing points.

[0073] (3) Test signal. Set an arbitrary digital signal (with a certain frequency), and put the signal into the basic operations of one-dimensional gray value mathematical morphology erosion and dilation. Compare the changes in the signal waveform before and after the operation to determine the basic opening and closing operations.

[0074] (4) Based on the basic operations of morphological erosion and dilation, using interpolation formulas

[0075] The interpolated seismic data is obtained. Due to the significant differences in the waveforms of seismic records obtained from different geological models, and the varying inclination ranges of the in-phase axes between adjacent traces, the same parameter cannot be used to process seismic records from all geological models. It is necessary to analyze the morphology of different seismic records and make targeted adjustments to establish corresponding interpolation formulas.

[0076] The following is an analysis of the heterogeneous isotropic elastic geological model BP1994 (e.g.) Figure 4 This is an example of densifying sparsely sampled seismic gathers obtained through forward modeling. BP1994 is a publicly available heterogeneous isotropic elastic geological model.

[0077] Original earthquake records such as Figure 5 As shown, Figure 5 The above figure (a) shows the seismic records corresponding to the x-component of the seismic data. Figure 5 Figure (b) below shows the seismic records corresponding to the z-component of the seismic data. The vertical axis represents the recording time, and the horizontal axis represents the offset. The maximum recording time for the seismic data is 6000 ms, and the offset ranges from 0 to 1260 m, corresponding to A(t). i x j In the equation, i ∈ [1, 6000], j ∈ [0, 1260]. The x-component and z-component are the seismic wave components received in the x-axis and z-axis directions, respectively.

[0078] Figure 6 These are seismic records with a sampling interval of 200m. Figure 6 The left figure (a) shows the seismic records corresponding to the x-component of the seismic data. Figure 6 The right figure (b) shows the seismic record corresponding to the z-component of the seismic data.

[0079] Figure 7 This is a seismic record map after densification and interpolation of sparsely sampled seismic records. Figure 7 The above figure (a) shows the seismic records corresponding to the x-component of the seismic data. Figure 7 Figure (b) below shows the seismic record corresponding to the z-component of the seismic data. It can be seen that the waveform of the encrypted seismic data is consistent with that of the original data. The trace comparison results show that, except for the direct wave, the amplitude and phase of the encrypted reflected wave waveform are basically consistent with the original record, which has a good interpolation effect.

[0080] Figure 8 The diagram shows the comparison of traces extracted from the original seismic record and the 200th trace of the x-component of the encrypted interpolated seismic record using this method. The horizontal axis represents the recording time, and the vertical axis represents the amplitude. Figure 8 In the interpolated data, the trajectories of the original data and the interpolated data basically overlap, indicating that the interpolation effect is good and the data characteristics of the original data are well preserved.

[0081] Figure 9 This is a 200m seismic record image with sparse sampling and noise. Figure 9 The left figure (a) shows the seismic records corresponding to the x-component of the seismic data. Figure 9 The right figure (b) shows the seismic record corresponding to the z-component of the seismic data.

[0082] To verify the noise resistance of the method, we added Gaussian white noise to the sparsely sampled seismic data. We can see that the deep reflection energy of the coefficient sampled seismic records after adding noise is very weak, and the shape of the shallow reflection phase axis is not clear. Figure 10 To Figure 9 Seismic record graph after encryption and interpolation of seismic records. Figure 10 The left figure (a) shows the seismic records corresponding to the x-component of the seismic data. Figure 10 The right figure (b) shows the seismic record corresponding to the z-component of the seismic data. Figure 10 For the encrypted noisy record, compare Figure 5 The original seismic record without noise shows the basic shape of the shallow reflection wave phase axis, verifying the effectiveness of this method in encrypting sparsely sampled seismic data under high noise conditions.

[0083] In the above method of this embodiment, the sparsely sampled seismic data can be encrypted and interpolated, avoiding the introduction of false high-frequency information due to excessive line spacing. This makes the interpolation results more reflective of the actual geological conditions. Furthermore, it does not require a transform domain or any prior information or geological model constraints, and the memory required for computation is small, which greatly solves the problem of large memory requirements. It can perform interpolation effectively and quickly, with good interpolation results. It has higher interpolation accuracy for sparsely sampled data under any complex geological conditions, and the memory required for computation is low, resulting in higher computation speed and efficiency.

[0084] Those skilled in the art can change the above order without departing from the scope of protection of this disclosure.

[0085] Another embodiment of the present invention provides a seismic data interpolation system based on mathematical morphology theory, comprising:

[0086] The first point set determination module is used to perform an opening operation on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element to obtain the first point set;

[0087] The second point set determination module is used to perform a closing operation on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element to obtain the second point set;

[0088] The interpolated waveform determination module is used to determine the interpolated seismic data based on the mean amplitude of corresponding points in the first and second point sets.

[0089] Regarding the system in the above embodiments, the specific ways in which each module performs operations have been described in detail in the embodiments related to the method, and will not be elaborated here.

[0090] In this embodiment, encrypted interpolation can be performed on sparsely sampled seismic data, avoiding the introduction of false high-frequency information due to excessive line spacing. This makes the interpolation results more reflective of the actual geological conditions. Furthermore, it does not require a transform domain or any prior information or geological model constraints, and the computational memory required is small, which greatly solves the problem of large computational memory requirements. It can perform interpolation effectively and quickly, with good interpolation results. It has higher interpolation accuracy for sparsely sampled data under any complex geological conditions, and the computational memory required is low, resulting in higher computational speed and efficiency.

[0091] Based on the same inventive concept, embodiments of the present invention provide an electronic device, the structure of which is as follows: Figure 11 As shown, it includes: a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements the aforementioned seismic data interpolation method based on mathematical morphology theory.

[0092] Based on the same inventive concept, embodiments of the present invention provide a computer storage medium storing computer-executable instructions, which, when executed, implement the aforementioned seismic data interpolation method based on mathematical morphology theory.

[0093] Any modifications, additions, and equivalent substitutions made within the scope of the principles of this invention shall still fall within the patent coverage of this invention.

Claims

1. A seismic data interpolation method based on mathematical morphology theory, characterized in that, Includes the following steps: The process involves performing an opening operation on the shot gather waveform within the selected phase axis tilt range and the selected structural element to obtain the first point set. This includes the following steps: performing an erosion operation on the shot gather waveform within the selected phase axis tilt range and the selected structural element, and then performing a dilation operation on the structural element to obtain the first point set. Selecting the phase axis tilt range involves the following steps: determining the slope of the phase axis at the maximum shot-receiver distance angle as the upper limit of the phase axis tilt range. Selecting the structural element involves the following steps: using a one-dimensional gray-value 3-point format structural element that is symmetric about the geometric center, with the centroid of the structural element coinciding with the geometric center. The second point set is obtained by performing a closing operation on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element, including the following steps: performing an expansion operation on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element, and then performing an erosion operation on the structural element to obtain the second point set. The interpolated seismic data is determined based on the mean amplitude of corresponding points in the first and second point sets.

2. The method as described in claim 1, characterized in that, The seismic data interpolation method based on mathematical morphology further includes the following steps: Before determining the first or second point set, a digital test signal is set up, and one-dimensional gray value mathematical morphological erosion and dilation operations are performed on the digital test signal respectively. The waveform changes of the digital test signal before and after the operation are compared to determine the waveform obtained after the opening and closing operations of the digital test signal.

3. The method as described in claim 1, characterized in that, The etching operation is performed on the selected shot gather waveform within the tilt range of the phase axis and the selected structural element, including the following steps: Using the selected structuring element, iterate through each point of the shot gather waveform within the selected in-phase axis tilt range. When all waveform points covered by the structuring element have the same gray value as the structuring element, retain the gray value of the shot gather waveform points covered by the structuring element. When there are waveform points covered by a structuring element that have a different gray value than the structuring element, change the gray value of the waveform points covered by the structuring element that have the same gray value as the structuring element to be different from the gray value of the structuring element.

4. The method as described in claim 1, characterized in that, The waveform obtained by performing erosion operation on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element is then subjected to dilation operation with the structural element to obtain the first point set, including the following steps: Using the selected structuring element, the waveforms obtained by erosion operations on the shot gather waveforms within the selected in-phase axis tilt range and the selected structuring element are traversed. The gray values ​​of all waveform points covered by the structuring element are adjusted to be consistent with the gray values ​​of the structuring element, thus obtaining the first point set.

5. The method as described in claim 1, characterized in that, The expansion calculation is performed on the shot gather waveform within the selected phase axis tilt range and the selected structural element, including the following steps: Using the selected structuring element, iterate through each point of the shot gather waveform within the selected in-phase axis tilt range, and adjust the gray values ​​of all waveform points covered by the structuring element to be consistent with the gray values ​​of the structuring element.

6. The method as described in claim 1, characterized in that, The second point set is obtained by performing dilation operations on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element, and then performing erosion operations on the structural element. This includes the following steps: Using the selected structuring element, traverse the shot gather waveform within the selected in-phase axis tilt range and perform dilation operations on each point of the waveform obtained by the selected structuring element. When all waveform points covered by the structuring element have the same gray value as all points of the structuring element, retain the gray value of the waveform points covered by the structuring element. When there are waveform points covered by the structuring element with inconsistent gray values, change the gray value of the waveform points covered by the structuring element with consistent gray values ​​to be inconsistent with the gray value of the structuring element, and obtain the second point set.

7. A seismic data interpolation system based on mathematical morphology theory, characterized in that, include: The first point set determination module is used to perform an opening operation on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element to obtain the first point set. This includes the following steps: performing an erosion operation on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element, and then performing a dilation operation on the structural element to obtain the first point set. Selecting the in-phase axis tilt range includes the following steps: determining the slope of the in-phase axis when the shot-receiver distance angle is at its maximum as the upper limit of the in-phase axis tilt range parameter. Selecting the structural element includes the following steps: using a one-dimensional gray-value 3-point format structural element that is symmetric about the geometric center, with the centroid of the structural element coinciding with the geometric center. The second point set determination module is used to perform a closing operation on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element to obtain the second point set. The module includes the following steps: performing an expansion operation on the shot gather waveform within the selected in-phase axis tilt range and the selected structural element, and then performing an erosion operation on the structural element to obtain the second point set. The interpolated waveform determination module is used to determine the interpolated seismic data based on the mean amplitude of corresponding points in the first and second point sets.

8. An electronic device, characterized in that, include: A memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor, when executing the computer program, implements the seismic data interpolation method based on mathematical morphology theory as described in any one of claims 1 to 6.

9. A computer storage medium, characterized in that, The computer storage medium stores computer-executable instructions, which, when executed, implement the seismic data interpolation method based on mathematical morphology theory as described in any one of claims 1 to 6.

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