Method for establishing surface layer model through shallow seismic data interpolation method based on angle relation

Abstract

The invention discloses a method for establishing a surface layer model through a shallow seismic data interpolation method based on an angle relation, and the method specifically comprises the steps: setting a surface layer point action range, and calculating the inverse distance weighted interpolation of surface layer points in a modeling point range; selecting the action range of the optimal surface layer point, and calculating the angle relation coefficient of the surface layer point; a final interpolation formula can be obtained by combining inverse distance weighted interpolation and an angle relation coefficient formula, the surface layer thickness, speed and bottom boundary data of the surface layer point within the action range of the modeling point are respectively substituted into the formula for interpolation calculation, the surface layer thickness, speed and bottom boundary data of the modeling point can be obtained, and surface layer model establishment of the point is completed; all modeling points are subjected to modeling calculation according to the mode. According to the established model, transition between sample points is more uniform without edges and corners, model achievement transition is also more uniform, a surface layer medium change rule is met, and model mutation is effectively avoided.

Description

Technical Field

[0001] The present invention belongs to the technical field of seismic exploration, and particularly relates to a method for establishing a surface layer model by using a shallow seismic data interpolation method based on angular relationships. Background Art

[0002] For the surface layer modeling of the Ordos Basin, the quality of the spatial interpolation method directly affects the final model form. Therefore, it is particularly important to select a suitable interpolation algorithm. Currently, the interpolation sample range used is circular radiation or triangular grid division, but this will cause over-application or uneven application of surface layer points. As a result, the model established has a "patchy" shape when viewed from the plane and a sudden change in velocity or thickness when viewed from the section.

[0003] Circular radiation interpolation generally refers to a method of using a circular range to enclose surface layer control points of samples for interpolation modeling of model points. Specifically, grid interpolation calculation methods such as pure inverse distance weighted interpolation, average value interpolation, median interpolation, or minimum curvature are used. However, the disadvantage of the circular radiation interpolation method is that it has no screening ability for surface layer points of samples, which easily produces inappropriate interpolation results and reduces the accuracy of the surface layer model.

[0004] Triangular grid interpolation, also known as triangular weighted interpolation, uses three sample points to form a surrounding triangle for the interpolation point. For the value of any interpolated point located within the triangle, the weighted average will be calculated using the values at each vertex of this 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 disadvantages. For example, when the shape of the triangular mesh is relatively slender, the interpolation result is not ideal; the transition between triangular meshes is rigid and not smooth; it is difficult to perform interpolation modeling for modeling points located outside all triangular meshes. Therefore, it is necessary to design a surface layer structure modeling method suitable for the case of complex surface layer structures and uneven distribution of surface layer points to meet the higher accuracy requirements of surface layer modeling and lay a foundation for the "double high" processing in complex surface layer areas. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for establishing a surface layer model by using a shallow seismic data interpolation method based on angular relationships. The transition of the model results is also relatively uniform, conforms to the variation law of the surface layer medium, and effectively avoids model mutations.

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

[0007] Step 1, set the surface layer point scope of action, and calculate the inverse distance weighted interpolation of the surface layer points within the modeling point range;

[0008] Step 2, select the optimal surface layer point scope of action, and calculate the angular relationship coefficient of the surface layer points;

[0009] Step 3: By combining the inverse distance weighted interpolation in Step 1 and the angular relationship coefficient formula in Step 2, the final interpolation formula can be obtained. Substitute the surface layer thickness, velocity, and bottom boundary data of the surface layer points within the scope of the action of the modeling points into the formula for interpolation calculation respectively, and the surface layer thickness, velocity, and bottom boundary data of the modeling points can be obtained, that is, the establishment of the surface layer model of this point is completed; perform the modeling calculation for all modeling points in this way, and finally complete the establishment of the fine surface layer model of the work area.

[0010] The characteristics of the present invention also lie in that

[0011] In Step 1, specifically:

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

[0013] Step 1.2: Calculate the inverse distance weighted interpolation of the surface layer points within the scope of the modeling points as the initial calculation weight of the surface layer points.

[0014] In Step 1.1, the action range is set to 1 km to 3 km.

[0015] In Step 1.2, the calculation formula of the inverse distance weighted interpolation is shown in Equation (1);

[0016]

[0017] In the formula, n is the number of surface layer points within the scope of the modeling points; i is the label of the i-th surface layer point, i = 1, 2,..., n; p is a constant greater than 0, which is the weighted power exponent; (x, y) is the plane coordinate of the modeling point, x is the abscissa, and y is the ordinate; (x i, y i ) is the plane coordinate of the i-th surface layer point, and z i is the value of the i-th point; is the horizontal distance from (x, y) to (x i , y i ).

[0018] In Step 2, specifically:

[0019] Step 2.1: Take the nearest surface layer point as the focus, and find the vertical line between the modeling point and the nearest surface layer point; with this surface layer point as the center, bend the vertical line in the direction opposite to the target point at an angle θ; with the distance between the modeling point and the surface layer point as a reference, repeat the above steps in ascending order until a closed area can be connected by the bent vertical line to form the surface layer point action domain. This closed area is the effective area of the modeling point, the surface layer points within the area are effective surface layer points, and those outside the area are ineffective surface layer points;

[0020] Step 2.2: Calculate the angular relationship coefficient according to the enclosed effective area of the modeling points.

[0021] Set an invalid buffer zone from the bent vertical line towards the center of the invalid area. The control points within the buffer zone are set with angular relationship coefficients according to the angle of entry into the invalid area. The position of the bent vertical line, which is the starting angular relationship coefficient of the invalid area, is 1, and the angular relationship coefficient close to the center of the invalid area is set to 0. Then the range of the angular relationship coefficients of the surface points within the buffer zone is from 1 to 0, so that the weights of the surface points within the buffer zone gradually decrease towards the center position of the invalid area.

[0022] In Step 2.2, the calculation formula of the angular relationship coefficient A is as shown in Equation (2).

[0023]

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

[0025] In Step 3, specifically:

[0026] Step 3.1: Combining the inverse distance weighted interpolation formula in Step 1 and the angular relationship coefficient formula in Step 2, the final interpolation formula can be obtained, as shown in Equation (3).

[0027]

[0028] Where: The angular relationship coefficient of the i-th surface point; α i Is the actual angle of the i-th surface point entering the invalid area, f(x, y): the interpolation result of the modeling point;

[0029] Step 3.2: According to Equation (3), take the surface thickness, velocity, and bottom boundary data of the surface points within the scope of the action area of the modeling point as the z value in the formula for interpolation calculation respectively, and the surface thickness, velocity, and bottom boundary data of the modeling point can be obtained, that is, the establishment of the surface model of this point is completed; all the modeling points in the work area are modeled and calculated in this way, and finally the fine surface model of the work area is completed.

[0030] The beneficial effects of the present invention are that the model established by this method has a more uniform and angular-free transition between sample points, and the model results also have a relatively uniform transition, which conforms to the variation law of the surface medium and effectively avoids model mutations. At the same time, the method of preferentially selecting shallow seismic data inverse distance weighted interpolation samples based on the angular relationship coefficient makes the establishment of the surface model more accurate, and greatly improves the imaging effect of seismic data. Description of the Drawings

[0031] Figure 1 It is a schematic flow chart of the method for establishing a surface layer model by the shallow seismic data interpolation method based on angular relationships;

[0032] Figure 2 It is a schematic diagram of the selection range of modeling points based on angular relationships;

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

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

[0035] Figure 5 It is a schematic diagram of the invalid area buffer;

[0036] Figure 6 It is a schematic diagram of the final effective area of the preferred interpolation sample. Specific implementation manners

[0037] The present invention will be described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0038] The method for establishing a surface layer model by the shallow seismic data interpolation method based on angular relationships of the present invention is specifically implemented according to the following steps:

[0039] Step 1, set the scope of influence of surface layer points, and calculate the inverse distance weighted interpolation of surface layer points within the range of modeling points; specifically:

[0040] Step 1.1, set the scope of influence of surface layer points according to regional characteristics, and the scope of influence is set to 1 km to 3 km. All modeling points retrieve the surrounding surface layer points according to this range for subsequent modeling calculations;

[0041] Step 1.2, calculate the inverse distance weighted interpolation of surface layer points within the range of modeling points as the initial calculation weight value of surface layer points, as shown in formula (1);

[0042]

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

[0044] In terms of screening surface points, a relatively high weight share is given to the surface points closer to the modeling points, and a relatively small weight share is given to the surface points farther from the modeling points, so that each modeling point uses an indefinite number of surface points, and each surface point can be used more effectively and "fairly" in space.

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

[0046] Step 2.1: Taking the nearest surface point as the focus, find the vertical line between the modeling point and the nearest surface point; with this surface point as the center, bend the vertical line in the direction opposite to the target point at a small angle θ; taking 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 the bent vertical line to form the surface point scope. This closed area is the effective area of the modeling point, and the surface points within the area are effective surface points, while those outside the area are ineffective surface points.

[0047] Since the surface points closer to the modeling point have the opportunity to invalidate the surface points farther away through the angular relationship, the bent vertical lines are calculated and the closed area is connected in the order from near to far. In this way, the control points farther away that have already been invalidated do not need to be calculated for bending the vertical line, etc., which can improve the operation efficiency.

[0048] Step 2.2: Calculate the angular relationship coefficient according to the closed effective area of the modeling point;

[0049] Since adjacent modeling points may cause different ineffective control points due to a slight angular difference, resulting in a sudden change in the interpolation result. To avoid this situation, an ineffective buffer area is set in the direction from the bent vertical line to the center of the ineffective area. As Figure 5 shown, the control points within the buffer area are set with angular relationship coefficients according to the angles at which they enter the ineffective area. The position of the bent vertical line, that is, the starting angular relationship coefficient of the ineffective area, is 1, and the angular relationship coefficient close to the center of the ineffective area is set to 0. Then the range of the angular relationship coefficients of the surface points within the buffer area is from 1 to 0, so that the weights of the surface points within the buffer area gradually decrease towards the center position of the ineffective area. The calculation formula for the angular relationship coefficient A is shown in Equation (2);

[0050]

[0051] In the formula, A is the angular relationship coefficient; θ1 is the angle entering the completely ineffective area; θ2 is the angle just entering the ineffective area; the area between θ1 and θ2 is the buffer area; α is the actual angle at which the surface point enters the ineffective area.

[0052] Step 3: Establish a surface model using the corrected interpolation formula; specifically:

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

[0054]

[0055] where: The angular relationship coefficient of the i-th surface point; α i is the actual angle at which the i-th surface point enters the invalid area, and f(x, y): the interpolation result of the modeling point.

[0056] Step 3.2, according to Equation (3), using the surface thickness, velocity, and bottom boundary data of the surface points within the scope of the modeling point's action area as the z value in the formula for interpolation calculation, the surface thickness, velocity, and bottom boundary data of the modeling point can be obtained, which completes the establishment of the surface model for this point. All the modeling points in the work area are modeled and calculated in this way, and finally, the fine surface model of the work area is completed.

[0057] Example 1

[0058] See Figure 1 , the method for establishing a surface model by the shallow seismic data interpolation method based on angular relationship in this embodiment includes the following steps:

[0059] Step 1, set the surface point action area and calculate the inverse distance weight for the surface points within the scope of the modeling point;

[0060] As Figure 2 shown, according to the understanding and experience of the surface interpreter on the regional characteristics, set the action range of the surface points. Usually, the action range is set to 1 km to 3 km. All the modeling points search for the surrounding surface points according to this range for subsequent modeling calculations;

[0061] Assume that there are n surface points within the action range of the current modeling point,, and then according to the inverse distance weighted interpolation formula, calculate the distance weight corresponding to each surface point for the modeling point The inverse distance weight is the reciprocal of the distance weight This value is used as the initial calculation weight of the surface point. The inverse distance weighted interpolation formula is as follows;

[0062]

[0063] In the formula, n is the number of surface points within the scope of the modeling point; i is the label of the i-th surface point, i = 1, 2,..., n; p is a constant greater than 0, called the weighted power exponent; (x, y) is the plane coordinate of the modeling point, x is the abscissa, and y is the ordinate; (x i , y i ) is the plane coordinate of the i-th surface point, zi is the value of the i-th point (the value for interpolation); is the horizontal distance from (x, y) to (x i , y i );

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

[0065] First, enclose the effective area of the modeling points according to the angular relationship between the modeling points and the surface points. The process is as follows: taking the nearest surface point as the focus, find the vertical line between the modeling point and the nearest surface point, as Figure 3 shown; taking this surface point as the center, bend the vertical line in the direction opposite to the target point at a small angle θ, as Figure 4 shown; taking 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 the bent vertical line to form the surface point scope. This closed area is the effective area of the modeling points. The surface points within the area are effective surface points, and those outside the area are ineffective surface points, as Figure 6 shown. Then, calculate the angular relationship coefficient according to this closed effective area of the modeling points;

[0066] Since adjacent modeling points may cause different ineffective control points due to a slight angular difference, resulting in a sudden change in the interpolation result. To avoid this situation, set an ineffective buffer area from the bent vertical line towards the center of the ineffective area, as Figure 5 shown. The control points within the buffer area are set with angular relationship coefficients according to the angle of entering the ineffective area. The angular relationship coefficient at the position of the bent vertical line, which is the starting angle of the ineffective area, is 1, and the angular relationship coefficient close to the center of the ineffective area is set to 0. Then, the range of the angular relationship coefficient of the surface points within the buffer area is from 1 to 0, so that the weight of the surface points within the buffer area gradually decreases towards the center position of the ineffective area. The calculation formula of the angular relationship coefficient A is as follows;

[0067]

[0068] In the formula, A is the angular relationship coefficient; θ1 is the angle of entering the completely ineffective area; θ2 is the angle of just entering the ineffective area; the area between θ1 and θ2 is the buffer area; α is the actual angle of the surface point entering the ineffective area.

[0069] Each surface point calculates the angular relationship coefficient A according to its angle with the modeling point for subsequent modeling calculations.

[0070] Step 3: Establish a surface model using the corrected interpolation formula;

[0071] Combining the inverse distance weighted interpolation formula in Step 1 and the angular relationship coefficient formula in Step 2, the final interpolation formula can be obtained as follows;

[0072]

[0073] Where: The angular relationship coefficient of the i-th surface point; α i Is the actual angle at which the i-th surface point enters the invalid area, f(x, y): the interpolation result of the modeling point.

[0074] According to the final formula, taking the surface thickness, velocity, and bottom boundary data of the surface points within the scope of the modeling point as the z value in the formula respectively, and substituting them into the formula for interpolation calculation, the surface thickness, velocity, and bottom boundary data of the modeling point can be obtained, that is, the establishment of the surface model of this point is completed. Modeling calculations are carried out for all modeling points in the work area in this way, and finally the fine surface model of the work area is completed.

[0075] In this embodiment, in terms of screening surface points, a higher weight share is given to the surface points closer to the modeling point, and a smaller weight share is given to the surface points farther from the modeling point, so that each modeling point uses an indefinite number of surface points, which can more effectively "fairly" use each surface point in terms of spatial distance. Then, combined with the angular relationship between the modeling point and the surface points, the surface point scope of action is optimized, so that the control "strength" of each surface point during interpolation modeling of the modeling point is more reasonable, and finally a surface model that conforms to the regional characteristics and surface settlement law is established.

[0076] Embodiment 2

[0077] Corresponding to the method in Embodiment 1, the present invention embodiment optimizes the 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 scope of the modeling point; i is the label of the i-th surface point, i = 1, 2,..., n; p is a constant greater than 0, called the weighted power exponent; (x, y) is the planar coordinate of the modeling point, x is the abscissa, and y is the ordinate; (x i , y i ) is the planar coordinate of the i-th surface point, z i Is the value of the i-th point (the value used for interpolation); Is the horizontal distance from (x, y) to (x i , y i );

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

[0082] When p = 0, the weight is equal to 1. Substituting it into the inverse distance interpolation formula, it is found that the formula becomes the average value formula, losing the function of using distance to control the control intensity of surface points.

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

[0084] When p = 2, the weight is equal to The obtained weights are basically similar to the exponential decay as the distance from the modeling point increases, which is more in line with the natural law.

[0085] When p = 3, the weight is equal to The obtained weights will decrease rapidly as the distance from the modeling point increases, which will cause the surface points near the modeling point to have too much influence, resulting in the modeling interpolation result not conforming to the natural law.

[0086] Based on the above findings, finally select the constant p = 2, then the inverse distance interpolation formula becomes:

[0087]

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

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

[0090] First, enclose the effective area of the modeling point according to the angular relationship between the modeling point and the surface points. The process is as follows: Taking the nearest surface point as the focus, find the vertical line between the modeling point and the nearest surface point. Taking this surface point as the center, bend the vertical line in the opposite direction of the target point at a small angle θ. Taking 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 the bent vertical lines to form the surface point scope. This closed area is the effective area of the modeling point. The surface points within the area are effective surface points, and those outside the area are ineffective surface points. Then, calculate the angular relationship coefficient according to this closed effective area of the modeling point;

[0091] Since adjacent modeling points may have different invalid control points due to angular differences, resulting in mutations in the interpolation results, to avoid this situation, an invalid buffer is set from the bent vertical line towards the center of the invalid area. The control points within the buffer are set with angular relationship coefficients according to the angles at which they enter the invalid area. The angular relationship coefficient at the position of the bent vertical line, which is the starting angle of the invalid area, is 1, and the angular relationship coefficient close to the center of the invalid area is set to 0. Then, the range of the angular relationship coefficients of the surface points within the buffer is from 1 to 0, causing the weight values of the surface points within the buffer to gradually decrease towards the center position of the invalid area. The calculation formula for the angular relationship coefficient A is as follows;

[0092]

[0093] In the formula, A is the angular relationship coefficient; θ1 is the angle of entry into the completely invalid area; θ2 is the angle of just entering the invalid area; the area between θ1 and θ2 is the buffer; α is the actual angle at which the surface point enters the invalid area.

[0094] For each surface point, the angular relationship coefficient A is calculated based on its angle with the modeling point for subsequent modeling calculations.

[0095] Step 3, establish the surface model using the corrected interpolation formula;

[0096] Combining the inverse distance weighted interpolation formula in Step 1 and the angular relationship coefficient formula in Step 2, the final interpolation formula can be obtained as follows;

[0097]

[0098] Where: The angular relationship coefficient of the i-th surface point; α i Is the actual angle at which the i-th surface point enters the invalid area, f(x, y): the interpolation result of the modeling point.

[0099] According to the final formula, taking the surface thickness, velocity, and bottom boundary data of the surface points within the scope of the action area of the modeling point as the z value in the formula respectively and substituting them for interpolation calculation, the surface thickness, velocity, and bottom boundary data of the modeling point can be obtained, thus completing the establishment of the surface model at this point. All the modeling points in the work area are modeled and calculated in this way, and finally, the fine surface model of the work area is completed.

[0100] In this embodiment, the constant p of the inverse distance weight in the interpolation formula is preferably selected. When p = 2, the change of the inverse distance weight with distance is closer to the e-exponential decay law, successfully realizing the characteristic that the surface points close to the modeling point have a strong influence on the modeling point, and the surface points far away play a small control role, making the morphological change of the final surface model result more natural in space and more in line with the surface medium settlement law.

[0101] Example 3

[0102] Corresponding to the method in Example 2, the present invention provides a method for selecting reasonable ranges of the effective area, ineffective area, and buffer area of surface points in the angular relationship.

[0103] In step 2, during the process of enclosing the effective area of the modeling points according to the angular relationship between the modeling points and the surface points, taking the nearest surface point as the focus, find the vertical line between the modeling point and the nearest surface point; with this surface point as the center, bend the vertical line in the opposite direction of the target point at a small angle θ; taking 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 the bent vertical line to form the surface point action area. This closed area is the effective area of the modeling points, the surface points within the area are effective surface points, and those outside the area are ineffective surface points.

[0104] Assume that the modeling point is at the 180° position of the surface point, and test different values of θ for the effect of enclosing the effective area:

[0105] When θ = 0°, in Figure 4 the effective area is from 90° to 270°, and the ineffective area is from 270° to 90°. When connecting into a closed area, the surface points are basically connected at right angles, and it will not form the shape as in Figure 6 where other surface points that are slightly farther apart between two effective surface points are excluded, which does not conform to the actual law.

[0106] When θ = 20°, in Figure 4 the effective area is from 70° to 290°, and the effective range reaches 220°. The ineffective area is from 290° to 70°, and the ineffective range reaches 140°. When connecting into a closed area, it will form the shape as in Figure 6 so that other surface points that are slightly farther apart between two effective surface points may also play a controlling role, which is more in line with the actual law.

[0107] When θ = 40°, in Figure 4 the effective area is from 50° to 310°, and the effective range reaches 260°. The ineffective area is from 310° to 50°, and the ineffective range is only 100°. The effective range is too large and the ineffective range is too small. When connecting into a closed area, compared with Figure 6 in it, there will be an overly large effective area between two effective points, and the entire effective area is in the shape of a sea urchin, so that other surface points that are too far apart between two effective surface points also play a controlling role, which is not more in line with the actual law.

[0108] Through experimental measurement, when the range of θ is from 10° to 30°, the obtained ranges of the effective area and the ineffective area are relatively reasonable.

[0109] In addition, since the surface points close to the modeling points can invalidate the surface points far away through the angular relationship, the bent vertical lines are calculated and the closed area is connected in the order of distance from near to far. In this way, the far-away control points that have been invalidated do not need to be calculated for bent vertical lines, etc., which can improve the operation efficiency.

[0110] Then, according to this closed valid area of modeling points, the angular relationship coefficient is calculated. Since adjacent modeling points may cause different invalid control points due to a slight angular difference, resulting in a mutation in the interpolation result. To avoid this situation, an invalid buffer is set from the bent vertical line towards the center of the invalid area. The control points within the buffer are set with angular relationship coefficients according to the angle of entry into the invalid area. The angular relationship coefficient at the position of the bent vertical line, which is the starting angle of the invalid area, is 1, and the angular relationship coefficient close to the center of the invalid area is set to 0. Then, the range of the angular relationship coefficients of the surface points within the buffer is from 1 to 0, so that the weights of the surface points within the buffer gradually decrease towards the center position of the invalid area. The calculation formula for the angular relationship coefficient A is as follows:

[0111]

[0112] In the formula, A is the angular relationship coefficient; θ1 is the angle of entry into the completely invalid area; θ2 is the angle of just entering the invalid area; the area between θ1 and θ2 is the buffer; α is the actual angle of the surface point entering the invalid area.

[0113] Through experiments on the reasonable ranges of the valid area and the invalid area, at this time, the reasonable range of θ2 is between 10° and 30°; combined with the reasonable range of θ2, the reasonable range of θ1 can be tested:

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

[0115] Each surface point calculates the angular relationship coefficient A according to its angle with the modeling point for subsequent modeling calculations.

[0116] Step 3, establish the surface model using the modified interpolation formula;

[0117] Combining the inverse distance weighted interpolation formula in Step 1 and the angular relationship coefficient formula in Step 2, the final interpolation formula can be obtained as follows:

[0118]

[0119] Among them: The angular relationship coefficient of the i-th surface point; α iis the actual angle for the i-th surface point to enter the invalid area, and f(x, y) is the interpolation result of the modeling point.

[0120] According to the final formula, substitute the surface layer thickness, velocity, and bottom boundary data of the surface points within the scope of the modeling point's influence into the formula as the z value respectively, and perform interpolation calculations to obtain the surface layer thickness, velocity, and bottom boundary data of the modeling point, thus completing the establishment of the surface layer model for this point. Model all the modeling points in the work area in this way, and finally complete the establishment of the fine surface layer model for the work area.

[0121] In this embodiment, a method for selecting the reasonable ranges of the effective area, invalid area, and buffer area of the surface points in the angle relationship is provided, which can enable each surface point to play its reasonable role that it should play in the modeling process. Calculate the bending vertical lines and connect the closed areas in the order from near to far, so that the control points that are far away and have been invalid do not participate in the calculations such as the bending vertical lines, which can greatly improve the operation efficiency. Finally, a more realistic and reliable surface layer model is established efficiently and quickly.

[0122] Embodiment 4

[0123] Corresponding to the method in Embodiment 3, the present invention provides an interpolation scheme for establishing a surface layer model using the final interpolation formula in different regions.

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

[0125]

[0126] Where: The angle relationship coefficient of the i-th surface point; α i is the actual angle for the i-th surface point to enter the invalid area, and f(x, y) is the interpolation result of the modeling point.

[0127] According to the final formula, substitute the surface layer thickness, velocity, and bottom boundary data of the surface points within the scope of the modeling point's influence into the formula as the z value respectively, and perform interpolation calculations to obtain the surface layer thickness, velocity, and bottom boundary data of the modeling point, thus completing the establishment of the surface layer model for this point.

[0128] Among them, the surface layer velocity can be directly calculated and obtained through the final interpolation formula, but the model relationship between the surface layer thickness and the model bottom boundary should be:

[0129] B = E - H

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

[0131] The surface layer thickness and the model bottom boundary obtained from the same modeling point through the interpolation formula are difficult to satisfy the model relationship formula, resulting in model distortion. Therefore, an interpolation scheme should be adopted according to the characteristics of the surface layer medium in the region.

[0132] For example, in the plain area, the model bottom interface should be flat. Then, the model bottom boundary data of the surface layer points should be substituted into the final model interpolation formula to obtain the model bottom boundary of the modeling point. The model thickness of the modeling point is obtained through the model relationship, that is, H = E - B;

[0133] In the mountainous area, the model bottom interface usually fluctuates with the surface. Then, the model thickness data of the surface layer points should be substituted into the final model interpolation formula to obtain the model thickness of the modeling point. The model bottom boundary of the modeling point is obtained through the model relationship, that is, B = E - H;

[0134] According to the above rules, a model coefficient m is introduced as the modeling coefficient, and its range is from 0 to 1. Substitute the model thickness and model bottom boundary data of the surface layer points into the final model interpolation formula respectively to obtain the model thickness h and model bottom boundary b of the modeling point. Then, the formula for calculating the final model thickness H of the modeling point can be recorded as:

[0135] H = h·m + (E - b)·(1 - m)

[0136] The model bottom boundary B = E - H.

[0137] When m = 0, H = E - b, B = E - H = b, which is equivalent to only interpolating and calculating the model bottom boundary, and the model thickness is obtained through the model relationship formula, conforming to the model law of the plain area;

[0138] When m = 1, H = h, B = E - H, which is equivalent to only interpolating and calculating the model thickness, and the model bottom boundary is obtained through the model relationship formula, conforming to the model law of the mountainous area;

[0139] Each region can assign a value to m within the range of 0 to 1 according to the regional characteristics, and then a surface layer model that conforms to the regional characteristics can be obtained.

[0140] Model all the modeling points in the work area in this way for modeling calculation, and finally complete the establishment of the fine surface layer model of the work area.

[0141] In this embodiment, an interpolation scheme for establishing a surface layer model using the final interpolation formula in different regions is provided. The introduced model coefficient m can make the modeling interpolation result conform to the surface layer medium characteristics of various regions, and give full play to the advantages of the modeling method of the present invention. Finally, a surface layer model that conforms to the regional characteristics, has a true and reliable morphological structure, and meets the application research of the surface layer medium is established.

Claims

1. A method for establishing a surface model by using a shallow seismic data interpolation method based on angular relationships, characterized in that, The implementation is carried out specifically according to the following steps: Step 1: Set the scope of surface points, and calculate the inverse distance weighted interpolation of surface points within the range of modeling points; Step 2: Select the scope of the optimal surface points, and calculate the angular relationship coefficient of surface points; Step 3: Combining the inverse distance weighted interpolation in Step 1 and the angular relationship coefficient formula in Step 2, the final interpolation formula can be obtained. Substitute the surface thickness, velocity, and bottom boundary data of surface points within the scope of the modeling point action range into the formula for interpolation calculation respectively, and the surface thickness, velocity, and bottom boundary data of the modeling point can be obtained, that is, the establishment of the surface model of this point is completed; Model all modeling points in this way for calculation, and finally complete the establishment of the fine surface model of the work area.

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

3. The method for establishing a surface model by using the shallow seismic data interpolation method based on angular relationship as claimed in claim 2, wherein, In Step 1.1, the action range is set to 1 km to 3 km.

4. The method for establishing a surface model by using the shallow seismic data interpolation method based on angular relationships according to claim 2, wherein In Step 1.2, the calculation formula of the inverse distance weighted interpolation is shown in Equation (1); In the formula, n is the number of surface points within the range of modeling points; i is the label of the i-th surface point, where i = 1, 2, …, n; p is a constant greater than 0 and is the weighted power exponent; (x, y) are the planar coordinates of the modeling point, x is the abscissa, and y is the ordinate; (x i, y i ) are the planar coordinates of the i-th surface point, and z i is the value of the i-th point; is the horizontal distance from (x, y) to (x i , y i ).

5. The method for establishing a surface model by using the shallow seismic data interpolation method based on angular relationship according to claim 4, wherein, In Step 2, specifically: Step 2.1: Take the nearest surface point as the focus, and find the vertical line between the modeling point and the nearest surface point; With this surface point as the center, bend the vertical line in the opposite direction of the target point at an angle θ; Taking 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 the bent vertical line to form the scope of surface point action. This closed area is the effective area of the modeling point, and the surface points within the area are effective surface points, and those outside the area are invalid surface points; Step 2.2: Calculate the angular relationship coefficient according to the closed effective area of the modeling point; Set an invalid buffer zone from the bent vertical line to the center direction of the invalid area. The control points within the buffer zone are set with angular relationship coefficients according to the angle of entering the invalid area. The position of the bent vertical line, that is, the starting angular relationship coefficient of the invalid area, is 1, and the angular relationship coefficient close to the center of the invalid area is set to 0. Then the range of the angular relationship coefficients of the surface points within the buffer zone is from 1 to 0, so that the weight values of the surface points within the buffer zone gradually decrease towards the center position of the invalid area.

6. The method for establishing a surface model by using the shallow seismic data interpolation method based on angular relationships as claimed in claim 5, wherein, In Step 2.2, the calculation formula of the angular relationship coefficient A is shown in Equation (2); In the formula, A is the angular relationship coefficient; θ1 is the angle of entering the completely invalid area; θ2 is the angle of just entering the invalid area; The area between θ1 and θ2 is the buffer zone; α is the actual angle of the surface point entering the invalid area.

7. The method for establishing a surface model by using the shallow seismic data interpolation method based on angular relationship according to claim 6, characterized in that In Step 3, specifically: Step 3.1: Combining the inverse distance weighted interpolation formula in Step 1 and the angular relationship coefficient formula in Step 2, the final interpolation formula can be obtained, as shown in Equation (3); Wherein: The angular relationship coefficient of the i-th surface point; α i is the actual angle at which the i-th surface point enters the invalid area, f(x, y): the interpolation result of the modeling point; Step 3.2, according to formula (3), take the surface layer thickness, velocity, and bottom boundary data of the surface layer points within the scope of the modeling point action area as the z values in the formula respectively for interpolation calculation, and the surface layer thickness, velocity, and bottom boundary data of the modeling point can be obtained, that is, the establishment of the surface layer model of this point is completed; all the modeling points in the work area are modeled and calculated in this way, and finally the establishment of the fine surface layer model of the work area is completed.

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