Seismic data interpolation method and system based on mathematical morphology theory

Abstract

The invention discloses a seismic data interpolation method and system based on a mathematical morphology theory. Performing opening operation on the shot gather waveform in the selected event inclination range and the selected structural element to obtain a first point set; performing closed operation on the shot gather waveform in the selected event inclination range and the selected structural element to obtain a second point set; and carrying out amplitude balance calculation on the first point set and the second point set according to a mathematical morphology theory amplitude balance principle, and determining interpolated seismic data. According to the method, encrypted interpolation can be carried out on the sparsely sampled seismic data, false high-frequency information is prevented from being introduced due to an overlarge line distance, the interpolation result can better reflect the actual geological condition, a transform domain is not needed, any prior information or geological model constraint is not needed, interpolation can be effectively and rapidly carried out, the interpolation effect is good, and the method is suitable for large-scale popularization and application. The sparse sampling data interpolation precision under any complex geological condition is higher, the memory required by calculation is lower, and the calculation speed and the calculation efficiency are higher.

Description

Technical Field

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

[0002] In actual field data collection for seismic exploration, large line and trace spacings are often used to save costs, resulting in undersampling. Excessively large trace spacing can lead to spatial aliasing during migration, and the sparsely sampled spectrum can be reduced relative to the true signal amplitude, compromising the accuracy of seismic migration imaging and making it impossible to achieve detailed reservoir interpretation and characterization. Therefore, it is necessary to perform encrypted interpolation on sparsely sampled seismic data to improve migration imaging accuracy.

[0003] Currently, there are three main types of seismic data interpolation methods: transformation-based interpolation methods, filtering-based interpolation methods, and partial differential equation-based interpolation methods. Transformation-based methods are mainly based on Fourier transforms, obtaining the transform domain data of the original seismic data, obtaining the prediction operator through least squares inversion, and then obtaining the interpolated data set through inverse transforms. Filtering-based methods use interpolation filters and data convolution to achieve the purpose of data interpolation. Wave equation-based interpolation methods use Kirchhoff integral operators and migration operators to fully utilize ground recording information, but for data with dispersion, the interpolation results still have artifacts. The above methods interpolate waveforms naturally, but the memory required for calculation is large, and the interpolation effect is often poor for seismic data with steep dip formations and low signal-to-noise ratio. Summary of the Invention

[0004] In order to solve the above problems, the inventors have made the present invention, and through specific implementation methods, provide a seismic data interpolation method and system based on mathematical morphology theory.

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

[0006] Performing an opening operation on the shot gather waveforms of the selected event tilt range and the selected structural elements to obtain the first point set;

[0007] Performing a closing operation on the shot gather waveforms within the selected event tilt range and the selected structural elements to obtain a second point set;

[0008] The interpolated seismic data is determined according to the mean of the amplitudes of the corresponding points of 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, and one-dimensional gray value mathematical morphology corrosion 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 operation and the closing operation of the digital test signal.

[0011] Specifically, selecting the event tilt range includes the following steps:

[0012] The slope of the event axis when the offset angle is the largest is determined as the upper limit of the event axis tilt range.

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

[0014] A one-dimensional gray value three-point format structural element is used that is symmetrical about the geometric center, and the centroid of the structural element coincides with the geometric center.

[0015] Specifically, performing an opening operation on the shot gather waveform within the selected event tilt range and the selected structural element to obtain a first point set includes the following steps:

[0016] The waveform obtained by performing an erosion operation on the shot gather waveform of the selected event tilt range and the selected structural element is then dilated with the structural element to obtain a first point set.

[0017] Specifically, the shot gather waveform within the event tilt range and the selected structural element are subjected to erosion operation, including the following steps:

[0018] With the selected structural element, each point of the shot gather waveform within the selected event tilt range is traversed. When all waveform points covered by the structural element are consistent with the structural element gray value, the gray value of the shot gather waveform points covered by the structural element is retained. When there are waveform points covered by the structural element that are inconsistent with the structural element gray value, the gray value of the waveform points covered by the structural element that are consistent with the structural element gray value is changed to be inconsistent with the structural element gray value.

[0019] Specifically, the waveform obtained by performing an erosion operation on the shot gather waveform of the selected event tilt range and the selected structuring element is subjected to an expansion operation on the structuring element to obtain a first point set, including the following steps:

[0020] The waveform obtained by performing an erosion operation on the shot gather waveform within the selected event tilt range and the selected structuring element using the selected structuring element is then adjusted to have the same gray value as the structuring element for all waveform points covered by the structuring element, thereby obtaining a first point set.

[0021] Specifically, performing a closing operation on the shot gather waveform within the selected event tilt range and the selected structural element to obtain a second point set includes the following steps:

[0022] The waveform obtained by dilating the shot gather waveform of the selected event tilt range and the selected structural element is eroded with the structural element to obtain a second point set.

[0023] Specifically, the shot gather waveform within the selected event tilt range and the selected structural element are subjected to dilation operation, including the following steps:

[0024] With the selected structural element, each point of the shot gather waveform within the selected event tilt range is traversed, and the gray values ​​of all waveform points covered by the structural element are adjusted to be consistent with the gray value of the structural element.

[0025] Specifically, the waveform obtained by dilating the shot gather waveform of the selected event tilt range and the selected structural element is eroded with the structural element to obtain the second point set, which includes the following steps:

[0026] The second point set is obtained by traversing the shot gather waveform of the selected event tilt range and the selected structuring element and performing dilation operation on each point of the waveform. When the gray values ​​of all waveform points covered by the structuring element are consistent with those of all points of the structuring element, the gray values ​​of the waveform points covered by the structuring element are retained. When there are waveform points covered by the structuring element with gray values ​​inconsistent with those of the structuring element, the gray values ​​of the waveform points covered by the structuring element with gray values ​​consistent with those of the structuring element are changed to be inconsistent with those of the structuring element.

[0027] In a second aspect, an embodiment of the present invention provides a seismic data interpolation system based on mathematical morphology theory, comprising:

[0028] A first point set determination module is used to perform an opening operation on the shot gather waveform of the selected event tilt range and the selected structural element to obtain a first point set;

[0029] The second point set determination module is used to perform a closing operation on the shot gather waveform of the selected event 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 according to the average of the amplitudes of the corresponding points of the first and second point sets.

[0031] Based on the same inventive concept, an embodiment of the present invention provides an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, the aforementioned seismic data interpolation method based on mathematical morphology theory is implemented.

[0032] Based on the same inventive concept, an embodiment of the present invention provides a computer storage medium, wherein the computer storage medium stores computer executable instructions, and when the computer executable instructions are executed, the aforementioned seismic data interpolation method based on mathematical morphology theory is implemented.

[0033] The beneficial effects of the above technical solutions provided by the embodiments of the present invention include at least:

[0034] It can perform encrypted interpolation on sparsely sampled seismic data, avoiding the introduction of false high-frequency information due to excessive line spacing, so that the interpolation results can better reflect the actual geological conditions. It does not require a transformation domain, nor does it require any prior information or geological model constraints. The memory required for calculation is small, which greatly solves the problem of large memory required for calculation. It can interpolate effectively and quickly, with good interpolation effect. It has higher interpolation accuracy for sparsely sampled data under any complex geological conditions, and the memory required for calculation is low, with higher calculation speed and efficiency.

[0035] Other features and advantages of the present invention will be described in the following description or understood through implementation of the present invention. The purpose and other advantages of the present invention can be realized and obtained through the structures particularly pointed out in the written description, claims, and drawings.

[0036] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

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

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

[0040] Figure 3 This is a flow chart of a method for encrypting and interpolating sparsely sampled seismic data according to 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 earthquake record diagram in the embodiment of the present invention;

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

[0044] Figure 7 This is a seismic record diagram obtained by performing encrypted interpolation on sparsely sampled seismic records in an embodiment of the present invention;

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

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

[0047] Figure 10 In the embodiment of the present invention, Figure 9 Seismic record map after encrypted difference of seismic records;

[0048] Figure 11 Schematic diagram of the structure of an electronic device in an embodiment of the present invention. DETAILED DESCRIPTION

[0049] Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0050] In order to solve 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] The embodiment of the present invention provides a seismic data interpolation method based on mathematical morphology theory, the process of which is as follows: Figure 1 As shown, the following steps are included:

[0052] Step S1: performing an opening operation on the shot gather waveform of the selected event tilt range and the selected structural element to obtain a 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, 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, and the waveforms obtained after the opening and closing operations of the digital test signal are determined. The interpolation effect of the digital test signal is verified based on the interpolation effect of the digital test signal. In some specific embodiments, the phase axis tilt range is selected, including the following steps: the slope of the phase axis when the shot offset angle is maximum is determined as the parameter upper limit of the phase axis tilt range. That is, the phase axis tilt range is analyzed based on the shot gather record, and the slope of the phase axis when the shot offset angle is maximum is generally taken as the parameter upper limit of the tilt range. 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: using a one-dimensional gray value 3-point format structural element that is symmetrical about the geometric center, and the center of gravity of the structural element coincides with the geometric center. Specifically, structural elements of different formats can interpolate and reconstruct missing points that are smaller than the size of the structural element. When encrypting sparsely sampled seismic data, a 3-point format structural element is generally used, which can successfully reconstruct missing points. Specifically, the structural element in this method is designed as an operator with the center of gravity at the center, such as Figure 2 As shown in the figure, the first row is a schematic diagram of a two-dimensional structure element. From left to right, there are two-dimensional 5-point, 9-point, 13-point and 25-point structure elements. The light-colored rectangle in the middle is the center of gravity of the structure element. In this method, a one-dimensional gray value structure element is used. Figure 2 The second row is the structuring element format degenerated from two dimensions to one dimension. The two on the left are the one-dimensional 3-point format degenerated from two-dimensional 5-point and 9-point, and the two on the right are the one-dimensional 5-point format degenerated from two-dimensional 13-point and 25-point. The structuring element is symmetrical about the geometric center. The values ​​of the three points in the structuring element (such as the 3-point format) are involved in the operation, and the result after the operation is placed at the center of gravity. In morphology, the structuring element is also called a kernel, or a structural operator, which can be a rectangle, ellipse, cross, etc., and is used to cover the target image and perform logical operations with the corresponding points of the covered target image. In this embodiment, select Figure 2 The first shape on the left in the second row serves as a structural element.

[0056] In some specific embodiments, an opening operation is performed on the shot gather waveform of the selected event tilt range and the selected structural element to obtain a first point set, which includes the following steps: a waveform obtained by performing an erosion operation on the shot gather waveform of the selected event tilt range and the selected structural element, and a dilation operation on the structural element to obtain the first point set.

[0057] In some specific embodiments, a shot gather waveform within a selected event tilt range and a selected structural element are subjected to an erosion operation, comprising the following steps: using the selected structural element, traversing each point of the shot gather waveform within the selected event tilt range; when all waveform points covered by the structural element are consistent with the gray value of the structural element, retaining the gray value of the shot gather waveform points covered by the structural element; when there are waveform points covered by the structural element that are inconsistent with the gray value of the structural element, changing 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 of the corrosion operation is

[0059]

[0060] The expression of the expansion operation is

[0061]

[0062] where Θ is the erosion operator, is the expansion operator, and sets A and B are the target data set (i.e., image data, such as the shot waveform in the above example) and the point set corresponding to the selected structural element, respectively. t is the point in set A that participates in the operation. The points in set A are time series. t represents time, and its value range is the recording time of the seismic data. k is the number of data points that the structural operator (that is, the structural element) B demarcates when it moves on set A. In this method, only the structural element of the 3-point format (such as Figure 2 As shown in the first figure on the left of the second row), the value range of k is [1,3]. is the set of circled data points.

[0063] In some specific embodiments, the waveform obtained by performing an erosion operation on the shot gather waveform within the selected event tilt range and the selected structuring element is then dilated with the structuring element to obtain a first point set, which includes the following steps: using the selected structuring element to traverse the waveform obtained by performing an erosion operation on the shot gather waveform within the selected event tilt range and the selected structuring element, and adjusting the gray values ​​of all waveform points covered by the structuring element to be consistent with the gray value of the structuring element to obtain the first point set. The above process can be expressed as AE is the first point set.

[0064] Step S2: Perform a closing operation on the shot gather waveforms of the selected event tilt range and the selected structural element, to obtain a second point set.

[0065] In some specific embodiments, a closing operation is performed on the shot gather waveform within the selected event tilt range and the selected structuring element to obtain a second point set, which includes the following steps: performing an erosion operation on the waveform obtained by performing an expansion operation on the shot gather waveform within the selected event tilt range and the selected structuring element, and obtaining the second point set. The above process can be expressed as AD is the second point set.

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

[0067] In some specific embodiments, a waveform obtained by performing a dilation operation on a shot gather waveform of a selected event tilt range and a selected structural element is subjected to an erosion operation on the structural element to obtain a second point set, comprising the following steps: using the selected structural element to traverse each point of the waveform obtained by performing a dilation operation on the shot gather waveform of the selected event tilt range and the selected structural element, when the gray values ​​of all waveform points covered by the structural element are consistent with the gray values ​​of all points of the structural element, retaining the gray values ​​of the waveform points covered by the structural element, and when there are waveform points covered by the structural element that are inconsistent with the gray values ​​of the structural element, changing the gray values ​​of the waveform points covered by the structural element that are consistent with the gray values ​​of the structural element to be inconsistent with the gray values ​​of the structural element, to obtain the second point set.

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

[0069] x j and t i They represent the horizontal and vertical coordinates of the image corresponding to the seismic data, respectively. The horizontal coordinate represents the offset distance, and the vertical coordinate represents the recording time of the seismic data. The value range of i is the recording time of the seismic data, and the value range of j is the horizontal coordinate range of the seismic data. A(t i , x j ) represents the interpolated seismic data, which includes the coordinates of the points to be interpolated.

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

[0071] (1) Select the event tilt range. Analyze the event tilt range based on the shot gather records. Generally, the slope of the event at the maximum angle with the offset is taken as the upper limit of the tilt range parameter.

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

[0073] (3) Test signal. Set any digital signal (with a certain frequency) and subject the signal to the one-dimensional gray value mathematical morphology corrosion and dilation basic operations. 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 corrosion and expansion, the interpolation formula is used

[0075] Obtain interpolated seismic data. Because seismic waveforms obtained from different geological models vary significantly, and the tilt ranges of the event axes between adjacent traces are different, the same parameters 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 the corresponding interpolation formula.

[0076] The following is an analysis of the heterogeneous isotropic elastic geological model BP1994 (such as Figure 4 BP1994 is a publicly available heterogeneous isotropic elastic geological model.

[0077] The original earthquake records are as follows Figure 5 As shown, Figure 5 The figure (a) above is the earthquake record corresponding to the x component of the earthquake data. Figure 5 The figure below (b) is the seismic record corresponding to the z component of the seismic data. The ordinate represents the recording time and the abscissa represents the offset. The maximum recording time of the seismic data is 6000ms, and the offset range is 0-1260m. The corresponding A(t i , x j ), where i∈[1,6000] and j∈[0,1260]. The x component and z component are the components of the seismic wave received in the x-axis direction and the z-axis direction, respectively.

[0078] Figure 6 It is a seismic record with a sampling interval of 200m. Figure 6 The left figure (a) is the earthquake record corresponding to the x component of the earthquake data. Figure 6 The right figure (b) is the seismic record corresponding to the z component of the seismic data.

[0079] Figure 7 This is the seismic record map after encrypted interpolation of sparsely sampled seismic records. Figure 7 The figure (a) above is the earthquake record corresponding to the x component of the earthquake data. Figure 7 Figure (b) below shows the seismic record corresponding to the z component of the seismic data. The encrypted seismic data has the same waveform as the original data. The comparison of the extracted traces shows that, with the exception of the direct wave, the amplitude and phase of the encrypted reflected wave waveforms are essentially consistent with the original records, demonstrating excellent interpolation results.

[0080] Figure 8 This is a comparison chart of extracted tracks. Taking the original seismic record and the 200th track of the x component of the encrypted interpolated seismic record using this method as an example, the horizontal axis is the recording time and the vertical axis is the amplitude. Figure 8 In the figure, the trajectories of the original data and the interpolated data basically coincide with each other, which shows 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 with sparse sampling and noise. Figure 9 The left figure (a) is the earthquake record corresponding to the x component of the earthquake data. Figure 9 The right figure (b) is the seismic record corresponding to the z component of the seismic data.

[0082] In order to verify the noise resistance of the method, we added Gaussian white noise to the sparsely sampled seismic data. It can be seen that the deep reflection energy of the coefficient sampling seismic records after adding noise is very weak, and the shallow reflection phase axis morphology is not clear. Figure 10 For Figure 9 Seismic record map after encrypted difference of seismic records, Figure 10 The left figure (a) is the earthquake record corresponding to the x component of the earthquake data. Figure 10 The right figure (b) is the seismic record corresponding to the z component of the seismic data. Figure 10 For the encrypted noisy record, compare Figure 5 The noise-free original seismic records show the basic form of the shallow reflection wave phase axis, which verifies the effectiveness of this method in encrypting sparsely sampled seismic data under high noise conditions.

[0083] In the above method of this embodiment, sparsely sampled seismic data can be encrypted and interpolated, avoiding the introduction of false high-frequency information due to excessive line spacing, so that the interpolation results can better reflect the actual geological conditions, and no transformation domain is required, nor any prior information or geological model constraints are required. The memory required for calculation is small, which greatly solves the problem of large memory required for calculation. Interpolation can be performed effectively and quickly, with good interpolation effect. The interpolation accuracy of sparsely sampled data under any complex geological conditions is higher, and the memory required for calculation is low, with higher calculation speed and efficiency.

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

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

[0086] A first point set determination module is used to perform an opening operation on the shot gather waveform of the selected event tilt range and the selected structural element to obtain a first point set;

[0087] The second point set determination module is used to perform a closing operation on the shot gather waveform of the selected event 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 according to the average of the amplitudes of the corresponding points of the first and second point sets.

[0089] Regarding the system in the above embodiment, the specific manner in which each module performs operations has been described in detail in the embodiment of 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, so that the interpolation results can better reflect the actual geological conditions. No transformation domain is required, and no prior information or geological model constraints are required. The memory required for calculation is small, which greatly solves the problem of large memory required for calculation. Interpolation can be performed effectively and quickly, with good interpolation effect. The interpolation accuracy of sparsely sampled data under any complex geological conditions is higher, and the memory required for calculation is low, with higher calculation speed and efficiency.

[0091] Based on the same inventive concept, an embodiment of the present invention provides 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, the above-mentioned seismic data interpolation method based on mathematical morphology theory is implemented.

[0092] Based on the same inventive concept, an embodiment of the present invention provides a computer storage medium, wherein the computer storage medium stores computer executable instructions, and when the computer executable instructions are executed, the aforementioned seismic data interpolation method based on mathematical morphology theory is implemented.

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

Claims

1. A seismic data interpolation method based on mathematical morphology theory, characterized in that: The following steps are involved: Performing an opening operation on the shot gather waveforms of the selected event tilt range and the selected structural elements to obtain the first point set; Performing a closing operation on the shot gather waveforms within the selected event tilt range and the selected structural elements to obtain a second point set; The interpolated seismic data is determined according to the mean of the amplitudes of the corresponding points of the first and second point sets.

2. The method according to claim 1, wherein 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, and one-dimensional gray value mathematical morphology corrosion 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 operation and the closing operation of the digital test signal.

3. The method according to claim 1, wherein Selecting the event tilt range includes the following steps: The slope of the event axis when the offset angle is the largest is determined as the upper limit of the event axis tilt range.

4. The method according to claim 1, wherein Selecting structural elements includes the following steps: A one-dimensional gray value three-point format structural element is used that is symmetrical about the geometric center, and the centroid of the structural element coincides with the geometric center.

5. The method according to claim 1, wherein An opening operation is performed on the shot gather waveform of the selected event tilt range and the selected structural element to obtain a first point set, including the following steps: The waveform obtained by performing an erosion operation on the shot gather waveform of the selected event tilt range and the selected structural element is then dilated with the structural element to obtain a first point set.

6. The method according to claim 5, wherein The shot gather waveform of the selected event tilt range and the selected structural element are eroded, including the following steps: With the selected structural element, each point of the shot gather waveform within the selected event tilt range is traversed. When all waveform points covered by the structural element are consistent with the structural element gray value, the gray value of the shot gather waveform points covered by the structural element is retained. When there are waveform points covered by the structural element that are inconsistent with the structural element gray value, the gray value of the waveform points covered by the structural element that are consistent with the structural element gray value is changed to be inconsistent with the structural element gray value.

7. The method according to claim 5, wherein The waveform obtained by performing an erosion operation on the shot gather waveform of the selected event tilt range and the selected structural element is then dilated with the structural element to obtain a first point set, including the following steps: The waveform obtained by performing an erosion operation on the shot gather waveform within the selected event tilt range and the selected structuring element using the selected structuring element is then adjusted to have the same gray value as the structuring element for all waveform points covered by the structuring element, thereby obtaining a first point set.

8. The method according to claim 1, wherein Performing a closing operation on the shot gather waveforms within the selected event tilt range and the selected structural elements to obtain a second point set includes the following steps: The waveform obtained by dilating the shot gather waveform of the selected event tilt range and the selected structural element is eroded with the structural element to obtain a second point set.

9. The method according to claim 8, wherein The dilation operation is performed on the shot gather waveform of the selected event tilt range and the selected structural element, including the following steps: With the selected structural element, each point of the shot gather waveform within the selected event tilt range is traversed, and the gray values ​​of all waveform points covered by the structural element are adjusted to be consistent with the gray value of the structural element.

10. The method according to claim 8, wherein The waveform obtained by dilating the shot gather waveform of the selected event tilt range and the selected structural element is eroded with the structural element to obtain a second point set, including the following steps: The second point set is obtained by traversing the shot gather waveform of the selected event tilt range and the selected structuring element and performing dilation operation on each point of the waveform. When the gray values ​​of all waveform points covered by the structuring element are consistent with those of all points of the structuring element, the gray values ​​of the waveform points covered by the structuring element are retained. When there are waveform points covered by the structuring element with gray values ​​inconsistent with those of the structuring element, the gray values ​​of the waveform points covered by the structuring element with gray values ​​consistent with those of the structuring element are changed to be inconsistent with those of the structuring element.

11. A seismic data interpolation system based on mathematical morphology theory, characterized in that: include: A first point set determination module is used to perform an opening operation on the shot gather waveform of the selected event tilt range and the selected structural element to obtain a first point set; The second point set determination module is used to perform a closing operation on the shot gather waveform of the selected event tilt range and the selected structural element to obtain the second point set; The interpolated waveform determination module is used to determine the interpolated seismic data according to the average of the amplitudes of the corresponding points of the first and second point sets.

12. 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 when the processor executes the computer program, the seismic data interpolation method based on mathematical morphology theory as described in any one of claims 1 to 10 is implemented.

13. 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 10.

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