Method for establishing a surface model based on an angle relationship shallow seismic data interpolation

Abstract

This invention discloses a method for establishing a surface model based on shallow seismic data interpolation using angle relationships. Specifically, it involves: defining the scope of a surface point; calculating the inverse distance weighted interpolation of surface points within the modeling point's scope; selecting the optimal scope of the surface point and calculating the angle relationship coefficients for the surface point; combining the inverse distance weighted interpolation and angle relationship coefficient formulas to obtain the final interpolation formula; and substituting the surface thickness, velocity, and bottom boundary data of the surface points within the modeling point's scope into the formula for interpolation calculation to obtain the surface thickness, velocity, and bottom boundary data for that point, thus completing the surface model establishment for that point. This method is applied to all modeling points. The model established by this invention exhibits more uniform and smooth transitions between sample points, and the model results also show more uniform transitions, conforming to the variation laws of the surface medium and effectively avoiding abrupt model changes.

Description

Technical Field

[0001] This invention belongs to the field of seismic exploration technology, specifically relating to a method for establishing a surface model based on shallow seismic data interpolation using angle relationships. Background Technology

[0002] For surface modeling of the Ordos Basin, the quality of the spatial interpolation method directly affects the final model morphology, so selecting a suitable interpolation algorithm is particularly important. Currently used interpolation sample ranges are circular radial or triangular mesh divisions, but this can lead to over-application or uneven application of surface points. As a result, the model appears "patched" in plan view and shows abrupt changes in velocity or thickness in cross-section.

[0003] Circular radial interpolation generally refers to a method of interpolating model points by delineating control points on the sample surface within a circular range. Specifically, it uses gridded interpolation calculation methods such as pure inverse distance weighted interpolation, mean interpolation, median interpolation, or minimum curvature interpolation. However, the disadvantage of circular radial interpolation is that it has no ability to filter sample surface points, which can easily produce inappropriate interpolation results and reduce the accuracy of the surface model.

[0004] Triangular mesh interpolation, also known as triangle weighted interpolation, uses three sample points to form a triangle enclosing the interpolation point. For any interpolated point located within the triangle, a weighted average is calculated using the values ​​at each vertex of the triangle and the area of ​​the triangle formed by these points to obtain the value of the interpolated point. Although this method is a classic planar interpolation algorithm, it still has some insurmountable drawbacks, such as unsatisfactory interpolation results when the triangular mesh shape is relatively thin and long; abrupt and unsmooth transitions between triangular meshes; and difficulty in interpolating and modeling points falling outside all triangular meshes. Therefore, it is necessary to design a surface structure modeling method suitable for complex surface structures and uneven distribution of surface points to meet the requirements of higher accuracy in surface modeling and lay the foundation for handling "double-high" conditions in complex surface areas. Summary of the Invention

[0005] The purpose of this invention is to provide a method for establishing a surface model based on shallow seismic data interpolation with angular relationships. The model results have a more uniform transition, conform to the variation law of the surface medium, and effectively avoid abrupt changes in the model.

[0006] The technical solution adopted in this invention is a method for establishing a surface model based on shallow seismic data interpolation using angular relationships, specifically implemented according to the following steps:

[0007] Step 1: Define the scope of the surface points and calculate the inverse distance weighted interpolation of the surface points within the modeling point range;

[0008] Step 2: Select the scope of the optimal surface point and calculate the angular relationship coefficient of the surface point;

[0009] Step 3: Combining the inverse distance weighted interpolation from Step 1 and the angle relationship coefficient formula from Step 2, the final interpolation formula can be obtained. Substitute the surface thickness, velocity, and bottom boundary data of the surface points within the scope of the modeling point into the formula for interpolation calculation to obtain the surface thickness, velocity, and bottom boundary data of the modeling point, thus completing the surface model establishment of that point. Perform modeling calculations on all modeling points in this way to finally complete the establishment of the fine surface model of the work area.

[0010] The invention is further characterized in that,

[0011] Step 1 specifically involves:

[0012] Step 1.1: Set the scope of the surface points according to the regional characteristics, and search for surrounding surface points for all modeling points according to this scope for subsequent modeling calculations;

[0013] Step 1.2: Calculate the inverse distance weighted interpolation of the surface points within the modeling point range, and use it as the initial calculation weight of the surface points.

[0014] In step 1.1, the effective range is set to 1km to 3km.

[0015] In step 1.2, the calculation formula for inverse distance weighted interpolation is shown in equation (1);

[0016]

[0017] In the formula, n is the number of surface points within the modeling point range; i is the label of the i-th surface point, i = 1, 2, ..., n; p is a constant greater than 0, representing the weighted exponent; (x, y) are the planar coordinates of the modeling point, where x is the abscissa and y is the ordinate; (x i, y i Let z be the planar coordinates of the i-th surface point. i Let i be the value of the i-th point; From (x,y) to (x i ,y i ) horizontal distance.

[0018] Step 2 specifically involves:

[0019] Step 2.1: Using the nearest surface point as the focus, find the perpendicular line between the modeling point and the nearest surface point; using this surface point as the center, bend the perpendicular line at an angle θ in the opposite direction to the target point; using the distance between the modeling point and the surface point as a reference, repeat the above steps in ascending order until a closed region can be connected by the bent perpendicular line, forming the scope of the surface point. This closed region is the effective region of the modeling point. Surface points within the region are effective surface points, and those outside the region are invalid surface points.

[0020] Step 2.2: Calculate the angle relationship coefficients based on the effective area of ​​the closed modeling points;

[0021] An invalid buffer zone is set from the bent vertical line toward the center of the invalid region. The control points in the buffer zone are set with angle relationship coefficients according to the angle of entry into the invalid region. The angle relationship coefficient at the position of the bent vertical line, i.e. the starting point of the invalid region, is 1, and the angle relationship coefficient near the center of the invalid region is set to 0. The range of the angle relationship coefficient of the surface points in the buffer zone is from 1 to 0, so that the weight of the surface points in the buffer zone gradually decreases toward the center of the invalid region.

[0022] In step 2.2, the formula for calculating the angular relationship coefficient A is shown in equation (2);

[0023]

[0024] In the formula, A is the angle relationship coefficient; θ1 is the angle of entering the completely invalid region; θ2 is the angle of just entering the invalid region; there is a buffer zone between θ1 and θ2; and α is the actual angle of the surface point entering the invalid region.

[0025] Step 3 specifically involves:

[0026] Step 3.1, combining the inverse distance weighted interpolation formula of Step 1 and the angle relationship coefficient formula of Step 2, the final interpolation formula can be obtained, as shown in Equation (3);

[0027]

[0028] in: Angular relationship coefficient of the i-th surface point; α i f(x,y) represents the actual angle at which the i-th surface point enters the invalid region; f(x,y) represents the interpolation result of the modeling point.

[0029] Step 3.2: According to formula (3), the surface thickness, velocity and bottom boundary data of the surface points within the scope of the modeling point are used as z values ​​in the formula for interpolation calculation. The surface thickness, velocity and bottom boundary data of the modeling point can be obtained, and the surface model of the point is established. All modeling points in the work area are modeled and calculated in this way, and the fine surface model of the work area is finally established.

[0030] The beneficial effects of this invention are that the model established by this method has a more uniform and smooth transition between sample points, and the transition of model results is also more uniform, conforming to the variation law of the surface medium, and effectively avoiding abrupt changes in the model. At the same time, the method of selecting shallow seismic data inverse distance weighted interpolation samples based on angle relationship coefficients improves the accuracy of surface model establishment, greatly enhancing the effect of seismic data imaging. Attached Figure Description

[0031] Figure 1 This is a flowchart illustrating the method for establishing a surface model based on shallow seismic data interpolation using angle relationships.

[0032] Figure 2 This is a schematic diagram illustrating the range of modeling points selected based on angular relationships;

[0033] Figure 3 This is a schematic diagram of the vertical line between the modeling point and the nearest surface point;

[0034] Figure 4 It is a schematic diagram of a bent vertical line;

[0035] Figure 5 This is a schematic diagram of the invalid region buffer.

[0036] Figure 6 This is a schematic diagram of the final effective region of the preferred interpolation sample. Detailed Implementation

[0037] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0038] The present invention provides a method for establishing a surface model based on shallow seismic data interpolation using angular relationships, which is implemented according to the following steps:

[0039] Step 1: Define the scope of the surface points and calculate the inverse distance weighted interpolation of the surface points within the modeling point range; specifically:

[0040] Step 1.1: Set the effective range of surface points according to regional characteristics. The effective range is set to 1km to 3km. All modeling points retrieve surrounding surface points according to this range for subsequent modeling calculations.

[0041] Step 1.2: Calculate the inverse distance weighted interpolation of the surface points within the modeling point range as the initial calculation weight of the surface points, as shown in Equation (1);

[0042]

[0043] In the formula, n is the number of surface points within the modeling point range; i is the label of the i-th surface point, i = 1, 2, ..., n; p is a constant greater than 0, called the weighted exponent; (x, y) are the planar coordinates of the modeling point, x is the abscissa, and y is the ordinate; (x i ,y i Let z be the planar coordinates of the i-th surface point. i Let i be the value of the i-th point; From (x,y) to (x i ,y i ) horizontal distance;

[0044] In selecting surface points, surface points closer to the modeling point are given a higher weight share, while surface points farther from the modeling point are given a lower weight share. This allows each modeling point to use an indefinite number of surface points, making it more effective to use each surface point "fairly" in space.

[0045] Step 2: Select the scope of the optimal surface point and calculate the angular relationship coefficient of the surface point; specifically:

[0046] Step 2.1: Using the nearest surface point as the focus, find the perpendicular line between the modeling point and the nearest surface point; using this surface point as the center, bend the perpendicular line at a small angle θ in the opposite direction to the target point; using the distance between the modeling point and the surface point as a reference, repeat the above steps in ascending order until a closed region can be connected by the bent perpendicular line, forming the scope of the surface point. This closed region is the effective region of the modeling point, and surface points within the region are valid surface points, while those outside the region are invalid surface points.

[0047] Since surface points closer to the modeling point can invalidate distant surface points through angular relationships, the bending vertical lines are calculated and connected to the closed area in order of distance from nearest to farthest. In this way, control points that have been invalidated and are far away do not need to be calculated by bending vertical lines, which can improve the calculation efficiency.

[0048] Step 2.2: Calculate the angle relationship coefficients based on the effective area of ​​the closed modeling points;

[0049] Because adjacent modeling points may have slightly different invalid control points due to slight angle differences, causing abrupt changes in the interpolation results, an invalid buffer is set from the curved vertical line towards the center of the invalid region to avoid this situation. Figure 5 As shown, the angle relationship coefficients of the control points in the buffer are set according to the angle of entry into the invalid region. The angle relationship coefficient at the position of the bent vertical line, i.e., the starting angle relationship coefficient of the invalid region, is 1, and the angle relationship coefficient near the center of the invalid region is set to 0. Then the range of the angle relationship coefficient of the surface points in the buffer is from 1 to 0, so that the weight of the surface points in the buffer gradually decreases towards the center of the invalid region. The calculation formula of the angle relationship coefficient A is shown in equation (2).

[0050]

[0051] In the formula, A is the angle relationship coefficient; θ1 is the angle of entering the completely invalid region; θ2 is the angle of just entering the invalid region; there is a buffer zone between θ1 and θ2; and α is the actual angle of the surface point entering the invalid region.

[0052] Step 3: Build the surface model using the modified interpolation formula; specifically:

[0053] Step 3.1, combining the inverse distance weighted interpolation formula of Step 1 and the angle relationship coefficient formula of Step 2, the final interpolation formula can be obtained, as shown in Equation (3);

[0054]

[0055] in: Angular relationship coefficient of the i-th surface point; α i f(x,y) represents the actual angle at which the i-th surface point enters the invalid region, and f(x,y) represents the interpolation result of the modeling point.

[0056] Step 3.2: According to formula (3), the surface thickness, velocity, and bottom boundary data of the surface points within the scope of the modeling point are used as z-values ​​in the formula for interpolation calculation. This yields the surface thickness, velocity, and bottom boundary data of the modeling point, thus completing the surface model establishment for that point. All modeling points within the work area are modeled and calculated in this manner to ultimately complete the establishment of the detailed surface model of the work area.

[0057] Example 1

[0058] See Figure 1 The method for establishing a surface model based on shallow seismic data interpolation according to angular relationships in this embodiment includes the following steps:

[0059] Step 1: Define the scope of the surface points and calculate the inverse distance weights for the surface points within the modeling point range;

[0060] like Figure 2 As shown, based on the surface interpreters' understanding and experience of regional characteristics, the scope of the surface points is set, usually 1km to 3km. All modeling points search for surrounding surface points according to this scope for subsequent modeling calculations.

[0061] Assuming there are n surface points within the range of the current modeling point, the distance weight of the modeling point corresponding to each surface point is calculated using the inverse distance weighted interpolation formula. The inverse distance weight is the reciprocal of the distance weight. This value serves as the initial calculation weight for the surface points. The inverse distance weighted interpolation formula is as follows;

[0062]

[0063] In the formula, n is the number of surface points within the modeling point range; i is the label of the i-th surface point, i = 1, 2, ..., n; p is a constant greater than 0, called the weighted exponent; (x, y) are the planar coordinates of the modeling point, x is the abscissa, and y is the ordinate; (x i ,y i Let z be the planar coordinates of the i-th surface point.i This is the value at the i-th point (the value used for interpolation); From (x,y) to (x i ,y i ) horizontal distance;

[0064] Step 2: Select the optimal scope of the surface point and calculate the angular relationship coefficient of the surface point:

[0065] First, the effective area of ​​the modeling point is demarcated based on the angular relationship between the modeling point and the surface point. The process involves finding the perpendicular line between the modeling point and the nearest surface point, using the nearest surface point as the focal point. Figure 3 As shown; using this surface point as the center, bend the vertical line at a small angle θ in the opposite direction to the target point, as follows. Figure 4 As shown; using the distance between the modeling point and the surface point as a reference, repeat the above steps in ascending order until a closed region can be connected by a bent vertical line, forming the scope of the surface point. This closed region is the effective region of the modeling point; surface points within the region are valid surface points, and those outside the region are invalid surface points. Figure 6 As shown, the angular relationship coefficients are then calculated based on the effective area of ​​this closed modeling point.

[0066] Because adjacent modeling points may have slightly different invalid control points due to slight angle differences, causing abrupt changes in the interpolation results, an invalid buffer is set from the curved vertical line towards the center of the invalid region to avoid this situation. Figure 5 As shown, the angle relationship coefficients of the control points within the buffer are set according to the angle at which they enter the invalid region. The angle relationship coefficient at the position of the vertical bend, i.e., the starting point of the invalid region, is 1, and the angle relationship coefficient near the center of the invalid region is set to 0. Therefore, the range of the angle relationship coefficients for the surface points within the buffer is from 1 to 0, causing the weight of the surface points within the buffer to gradually decrease towards the center of the invalid region. The formula for calculating the angle relationship coefficient A is shown below.

[0067]

[0068] In the formula, A is the angle relationship coefficient; θ1 is the angle of entering the completely invalid region; θ2 is the angle of just entering the invalid region; there is a buffer zone between θ1 and θ2; and α is the actual angle of the surface point entering the invalid region.

[0069] Each surface point has an angular relationship coefficient A calculated based on its angle with the modeling point, which is used for subsequent modeling calculations.

[0070] Step 3: Use the modified interpolation formula to build the surface model;

[0071] Combining the inverse distance weighted interpolation formula from step 1 and the angle relationship coefficient formula from step 2, the final interpolation formula can be obtained, as shown below;

[0072]

[0073] in: Angular relationship coefficient of the i-th surface point; α i f(x,y) represents the actual angle at which the i-th surface point enters the invalid region, and f(x,y) represents the interpolation result of the modeling point.

[0074] According to the final formula, the surface thickness, velocity, and bottom boundary data of the surface points within the modeling point's domain are used as the z-values ​​in the formula. These values ​​are then substituted into the formula for interpolation calculations to obtain the surface thickness, velocity, and bottom boundary data of the modeling point, thus completing the surface model establishment for that point. All modeling points within the work area are modeled and calculated in this way, ultimately completing the establishment of a detailed surface model for the work area.

[0075] In this embodiment, when selecting surface points, surface points closer to the modeling point are given a higher weight share, while surface points farther from the modeling point are given a lower weight share. This allows each modeling point to use a variable number of surface points, enabling a more effective and "fair" use of each surface point in terms of spatial distance. Furthermore, by combining the angular relationship between the modeling point and the surface points, the scope of the surface points is optimized, making the control "strength" of each surface point during interpolation modeling more reasonable. Ultimately, a surface model that conforms to regional characteristics and surface subsidence patterns is established.

[0076] Example 2

[0077] Corresponding to the method in Embodiment 1, the present invention preferably uses a constant p in the inverse distance weight.

[0078] The inverse distance weighted interpolation formula in step 1 is as follows:

[0079]

[0080] In the formula, n is the number of surface points within the modeling point range; i is the label of the i-th surface point, i = 1, 2, ..., n; p is a constant greater than 0, called the weighted exponent; (x, y) are the planar coordinates of the modeling point, x is the abscissa, and y is the ordinate; (x i ,y i Let z be the planar coordinates of the i-th surface point. i This is the value at the i-th point (the value used for interpolation); From (x,y) to (x i ,y i ) horizontal distance;

[0081] The inverse distance weight of each surface point is: The constant p in the weighting is set to 0, 1, 2, 3... respectively for weighting calculation.

[0082] When p = 0, the weight is equal to 1. Substituting this into the inverse distance interpolation formula, we find that the formula becomes an average value formula, thus losing the ability to control the intensity of the surface points using distance.

[0083] When p = 1, the weight is equal to The obtained weights are not suitable in space. As the distance from the modeling point increases, the weights decrease linearly, which will eventually lead to unsuitable model interpolation results.

[0084] When p = 2, the weight is equal to The resulting weights decay exponentially with increasing distance from the modeling point, which is more in line with natural laws.

[0085] When p = 3, the weight is equal to The weights obtained decrease rapidly as the distance from the modeling point increases. This can cause surface points that are close to the modeling point to have an excessive influence, resulting in modeling and interpolation results that do not conform to natural laws.

[0086] Based on the above findings, a constant p = 2 is ultimately chosen, and the inverse distance interpolation formula becomes:

[0087]

[0088] The inverse distance weight of each surface point is:

[0089] Step 2: Select the optimal scope of the surface point and calculate the angular relationship coefficient of the surface point:

[0090] First, the effective region of the modeling point is delineated based on the angular relationship between the modeling point and the surface point. The process is as follows: using the nearest surface point as the focal point, find the perpendicular line between the modeling point and the nearest surface point. Using this surface point as the center, bend the perpendicular line in the opposite direction of the target point at a small angle θ. Using the distance between the modeling point and the surface point as a reference, repeat the above steps in ascending order until a closed region can be formed by connecting the bent perpendicular lines, creating the surface point's scope. This closed region is the effective region of the modeling point; surface points within this region are valid surface points, and those outside the region are invalid surface points. Then, based on this closed effective region of the modeling point, calculate the angular relationship coefficient.

[0091] Because adjacent modeling points may have different invalid control points due to angle differences, causing abrupt changes in the interpolation results, an invalid buffer is set from the bent vertical line towards the center of the invalid region to avoid this situation. The control points within the buffer have angle relationship coefficients set according to the angle at which they enter the invalid region. The angle relationship coefficient at the starting point of the invalid region (the position of the bent vertical line) is 1, and the coefficient near the center of the invalid region is set to 0. Therefore, the range of the angle relationship coefficient for surface points within the buffer is from 1 to 0, gradually reducing the weight of surface points towards the center of the invalid region. The formula for calculating the angle relationship coefficient A is shown below.

[0092]

[0093] In the formula, A is the angle relationship coefficient; θ1 is the angle of entering the completely invalid region; θ2 is the angle of just entering the invalid region; there is a buffer zone between θ1 and θ2; and α is the actual angle of the surface point entering the invalid region.

[0094] Each surface point has an angular relationship coefficient A calculated based on its angle with the modeling point, which is used for subsequent modeling calculations.

[0095] Step 3: Use the modified interpolation formula to build the surface model;

[0096] Combining the inverse distance weighted interpolation formula from step 1 and the angle relationship coefficient formula from step 2, the final interpolation formula can be obtained, as shown below;

[0097]

[0098] in: Angular relationship coefficient of the i-th surface point; α i f(x,y) represents the actual angle at which the i-th surface point enters the invalid region, and f(x,y) represents the interpolation result of the modeling point.

[0099] According to the final formula, the surface thickness, velocity, and bottom boundary data of the surface points within the modeling point's domain are used as the z-values ​​in the formula. These are then substituted into the formula for interpolation calculations to obtain the surface thickness, velocity, and bottom boundary data of the modeling point, thus completing the surface model establishment for that point. All modeling points within the work area are modeled and calculated in this way, ultimately completing the establishment of a detailed surface model for the work area.

[0100] In this embodiment, the constant p of the inverse distance weight in the interpolation formula is preferred. When p = 2, the change of the inverse distance weight with distance is closer to the exponential decay law of e. This successfully realizes the characteristic that the surface points closer to the modeling point have a strong effect on the modeling point, while the surface points farther away play a small control role. This makes the spatial morphological changes of the final surface model result more natural and more in line with the surface medium settlement law.

[0101] Example 3

[0102] Corresponding to the method in Embodiment 2, this embodiment of the invention provides a method for selecting a reasonable effective area, invalid area and buffer zone of surface points in angular relationships.

[0103] In step 2, during the process of closing the effective area of ​​the modeling point based on the angular relationship between the modeling point and the surface point, the vertical line between the modeling point and the nearest surface point is calculated using the nearest surface point as the focus. Using this surface point as the center, the vertical line is bent at a small angle θ in the opposite direction to the target point. Using the distance between the modeling point and the surface point as a reference, the above steps are repeated in ascending order until a closed area can be connected by the bent vertical line, forming the scope of the surface point. This closed area is the effective area of ​​the modeling point, and the surface points within the area are valid surface points, while those outside the area are invalid surface points.

[0104] Assuming the modeling point is located 180° from the surface point, we experiment with different values ​​of θ to observe the effects on the closed effective region.

[0105] When θ = 0°, Figure 4 The effective region is 90° to 270°, and the ineffective region is 270° to 90°. When a closed region is formed, the surface points are connected at approximately right angles, and no ineffective regions are formed. Figure 6 The morphology in the model causes other surface points that are slightly farther apart from two valid surface points to be excluded, which does not conform to the actual law.

[0106] When θ = 20°, Figure 4 The effective region is 70° to 290°, with an effective range of 220°. The ineffective region is 290° to 70°, with an ineffective range of 140°. When these regions are connected to form a closed area, they will form something like... Figure 6 The morphology in the model allows other surface points that are slightly farther apart from two effective surface points to also play a controlling role, which is more in line with actual laws.

[0107] When θ = 40°, Figure 4 The effective range is 50° to 310°, reaching 260°, while the ineffective range is 310° to 50°, with an ineffective range of only 100°. The effective range is too large, and the ineffective range is too small. When these areas form a closed region, compared to... Figure 6 In this process, an excessively distant effective zone is generated between two effective points, forming a sea urchin-like shape. This means that other surface points that are too far apart from the two effective surface points also play a controlling role, which is not in line with the actual laws.

[0108] Experimental calculations show that when θ ranges from 10° to 30°, the effective and ineffective ranges are relatively reasonable.

[0109] In addition, since surface points closer to the modeling point can invalidate distant surface points through angular relationships, the bending vertical lines are calculated and connected to the closed area in order of distance from near to far. In this way, the invalidated distant control points do not need to be calculated for bending vertical lines, which can improve the calculation efficiency.

[0110] Then, based on the effective area of ​​this closed modeling point, the angle relationship coefficient is calculated. Since adjacent modeling points may have slightly different angles, resulting in different invalid control points and abrupt changes in the interpolation results, an invalid buffer zone is set from the bent vertical line towards the center of the invalid area to avoid this situation. The angle relationship coefficients of the control points within the buffer zone are set according to the angle at which they enter the invalid area. The angle relationship coefficient at the position of the bent vertical line, i.e., the starting point of the invalid area, is 1, and the angle relationship coefficient near the center of the invalid area is set to 0. Therefore, the range of the angle relationship coefficients for the surface points within the buffer zone is from 1 to 0, gradually reducing the weight of the surface points towards the center of the invalid area. The formula for calculating the angle relationship coefficient A is shown below.

[0111]

[0112] In the formula, A is the angle relationship coefficient; θ1 is the angle of entering the completely invalid region; θ2 is the angle of just entering the invalid region; there is a buffer zone between θ1 and θ2; and α is the actual angle of the surface point entering the invalid region.

[0113] For the reasonable range test of the effective and ineffective regions, the reasonable range of θ2 is 10° to 30°; combined with the reasonable range of θ2, the reasonable range of θ1 can be determined:

[0114] First, it should be assumed that there should be a difference of 20° to 40° between θ1 and θ2; otherwise, the buffer will be too small or too large, thus losing its function. Therefore, the reasonable range of θ1 should be between 30° and 70°, keeping the size of the buffer between 20° and 40°.

[0115] Each surface point has an angular relationship coefficient A calculated based on its angle with the modeling point, which is used for subsequent modeling calculations.

[0116] Step 3: Use the modified interpolation formula to build the surface model;

[0117] Combining the inverse distance weighted interpolation formula from step 1 and the angle relationship coefficient formula from step 2, the final interpolation formula can be obtained, as shown below;

[0118]

[0119] in: Angular relationship coefficient of the i-th surface point; α if(x,y) represents the actual angle at which the i-th surface point enters the invalid region, and f(x,y) represents the interpolation result of the modeling point.

[0120] According to the final formula, the surface thickness, velocity, and bottom boundary data of the surface points within the modeling point's scope are used as z-values ​​in the formula for interpolation calculations. This yields the surface thickness, velocity, and bottom boundary data for the modeling point, thus completing the surface model establishment for that point. All modeling points within the work area are modeled and calculated in this manner, ultimately completing the establishment of a detailed surface model for the work area.

[0121] This embodiment provides a method for selecting reasonable effective areas, invalid areas, and buffer zones for surface points in angular relationships, ensuring that each surface point plays its proper role in the modeling process. Furthermore, it calculates bent vertical lines and connects closed regions in order of increasing distance, excluding invalidated, distant control points from calculations such as bent vertical lines, significantly improving computational efficiency. Ultimately, this efficiently and quickly establishes a more realistic and reliable surface model.

[0122] Example 4

[0123] Corresponding to the method in Embodiment 3, this embodiment of the invention provides an interpolation scheme for establishing surface models in different regions using the final interpolation formula.

[0124] In step 3, combining the inverse distance weighted interpolation formula from step 1 and the angle relationship coefficient formula from step 2, the final interpolation formula is as follows;

[0125]

[0126] in: Angular relationship coefficient of the i-th surface point; α i f(x,y) represents the actual angle at which the i-th surface point enters the invalid region, and f(x,y) represents the interpolation result of the modeling point.

[0127] According to the final formula, the surface thickness, velocity, and bottom boundary data of the surface points within the scope of the modeling point are substituted into the formula as z values ​​for interpolation calculation. This yields the surface thickness, velocity, and bottom boundary data of the modeling point, thus completing the establishment of the surface model for that point.

[0128] The surface velocity can be directly calculated using the final interpolation formula, but the model relationship between the surface thickness and the bottom boundary of the model should be:

[0129] B = EH

[0130] In the formula, B is the bottom boundary of the model, E is the measured upper surface layer, and H is the surface layer thickness.

[0131] The surface thickness obtained from the interpolation formula at the same modeling point often fails to satisfy the model relationship formula with the model bottom boundary, resulting in model distortion. Therefore, an interpolation scheme should be adopted based on the characteristics of the surface medium in the region.

[0132] For example, in plains areas, the bottom interface of the model should be flat. Therefore, the bottom boundary data of the model at the surface points should be substituted into the final model interpolation formula to obtain the bottom boundary of the model at the modeling points. The model thickness of the modeling points is obtained through the model relationship, i.e., H = EB.

[0133] In mountainous areas, the bottom boundary of the model usually follows the undulation of the ground surface. Therefore, the model thickness data of the surface points should be substituted into the final model interpolation formula to obtain the model thickness of the modeling points. The bottom boundary of the modeling points is obtained through the model relationship, i.e., B = EH.

[0134] Based on the above rules, a model coefficient m is introduced as the modeling coefficient, ranging from 0 to 1. Using the final model interpolation formula, the model thickness h and model bottom boundary data of the surface points are substituted into the formula to obtain the model thickness h and model bottom boundary b of the modeling points. The formula for calculating the final model thickness H of the modeling points can then be written as:

[0135] H = h·m + (Eb)·(1-m)

[0136] The bottom boundary of the model is B = EH.

[0137] When m = 0, H = Eb, B = EH = b, which is equivalent to only interpolating to calculate the bottom boundary of the model. The model thickness is obtained through the model relationship formula, which conforms to the model rules of plain areas.

[0138] When m = 1, H = h, B = EH, which is equivalent to only interpolating to calculate the model thickness. The bottom boundary of the model is obtained through the model relationship formula, which conforms to the model rules of mountainous areas.

[0139] Each region can take a value for m within the range of 0 to 1 according to its regional characteristics, thus obtaining a surface model that conforms to the regional characteristics.

[0140] All modeling points within the work area are modeled and calculated in this way, ultimately completing the establishment of a detailed surface model of the work area.

[0141] This embodiment provides an interpolation scheme for establishing surface models for different regions using the final interpolation formula. The introduced model coefficient m ensures that the modeling and interpolation results conform to the surface medium characteristics of various regions, fully leveraging the advantages of the modeling method of this invention. Ultimately, a surface model that conforms to regional characteristics, has a realistic and reliable morphological structure, and meets the requirements for surface medium application research is established.

Claims

1. A method for establishing a surface model based on shallow seismic data interpolation using angular relationships, characterized in that, The specific steps are as follows: Step 1: Define the scope of the surface points and calculate the inverse distance weighted interpolation of the surface points within the modeling point range; Step 2: Select the scope of the optimal surface point and calculate the angular relationship coefficient of the surface point; Specifically: Step 2.1: Using the nearest surface point as the focus, find the perpendicular line between the modeling point and the nearest surface point; using this surface point as the center, bend the perpendicular line in the opposite direction of the modeling point at an angle θ. Using the distance between the modeling point and the surface point as a reference, repeat the above steps in ascending order until a closed area can be connected by a curved vertical line, forming the scope of the surface point. This closed area is the effective area of ​​the modeling point. Surface points within the area are valid surface points, and those outside the area are invalid surface points. Step 2.2: Calculate the angle relationship coefficients based on the effective area of ​​the closed modeling points; An invalid buffer zone is set from the bent vertical line toward the center of the invalid region. The control points in the buffer zone are set with angle relationship coefficients according to the angle of entry into the invalid region. The angle relationship coefficient at the position of the bent vertical line, i.e. the starting point of the invalid region, is 1, and the angle relationship coefficient near the center of the invalid region is set to 0. The range of the angle relationship coefficient of the surface points in the buffer zone is from 1 to 0, so that the weight of the surface points in the buffer zone gradually decreases toward the center of the invalid region. The formula for calculating the angular relationship coefficient A is shown in equation (2); （2）； In the formula, A is the angular relationship coefficient; θ 1 represents the angle at which the region enters a completely invalid region; θ 2 represents the angle at which the region just enters the invalid region; θ 1 and θ The space between 2 is a buffer zone; α This represents the actual angle at which a surface point enters the invalid region. Step 3: Combining the inverse distance weighted interpolation from Step 1 and the angle relationship coefficient formula from Step 2, the final interpolation formula is obtained. Substituting the surface thickness, velocity, and bottom boundary data of the surface points within the modeling point's domain into the formula for interpolation calculation, the surface thickness, velocity, and bottom boundary data of the modeling point can be obtained, thus completing the surface model establishment for that point. All modeling points are modeled and calculated in this way to finally complete the establishment of a detailed surface model for the work area; specifically: Step 3.1, combining the inverse distance weighted interpolation formula of Step 1 and the angle relationship coefficient formula of Step 2, the final interpolation formula can be obtained, as shown in Equation (3); （3）； in: , No. i Angular relationship coefficients of surface points; α i For the first i The actual angle at which a surface point enters the invalid region. Interpolation results of modeling points; In the formula, n This represents the number of surface points within the modeling point range; i For the first i The label of each surface point i =1,2,..., n ; p It is a constant greater than 0, and is the weighted exponent; For the planar coordinates of the modeling points, x The x-axis is... y The vertical axis is used as the coordinate. For the first i The planar coordinates of a surface point For the first i The value of each point; for( x , y )arrive( x i , y i ) horizontal distance; Step 3.2: According to formula (3), the surface thickness, velocity and bottom boundary data of the surface points within the scope of the modeling point are used as z values ​​in the formula for interpolation calculation. The surface thickness, velocity and bottom boundary data of the modeling point can be obtained, and the surface model of the point is completed. All modeling points in the work area are modeled and calculated in this way, and the fine surface model of the work area is finally completed.

2. The method for establishing a surface model based on shallow seismic data interpolation according to claim 1, characterized in that, In step 1, specifically: Step 1.1: Set the scope of the surface points according to the regional characteristics, and search for surrounding surface points for all modeling points according to this scope for subsequent modeling calculations; Step 1.2: Calculate the inverse distance weighted interpolation of surface points within the modeling point range. , which serves as the initial calculation weight for the surface points.

3. The method for establishing a surface model based on shallow seismic data interpolation according to claim 2, characterized in that, In step 1.1, the effective range is set to 1km~3km.

4. The method for establishing a surface model based on shallow seismic data interpolation according to claim 2, characterized in that, In step 1.2, the calculation formula for inverse distance weighted interpolation is shown in equation (1); （1）； In the formula, n This represents the number of surface points within the modeling point range; i For the first i The label of each surface point i =1,2,..., n ; p It is a constant greater than 0, and is the weighted exponent; For the planar coordinates of the modeling points, x The x-axis is... y The vertical axis is used as the coordinate. For the first i The planar coordinates of a surface point For the first i The value of each point; for( x , y )arrive( x i , y i (Horizontal distance).

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