Seismic spherical reflection wave oscillation-slowly-varying kernel decoupling framework-based seabed elastic parameter inversion method, system and device

Abstract

The present application relates to a kind of seabed elastic parameter inversion method, system and device under the oscillation-slowly varying nuclear decoupling framework of seismic spherical reflection wave, belong to geophysical prospecting, acoustic detection field.The method includes the following steps: (1) input observation data and initialize seabed elastic parameter;(2) determine integration interval and decompose integration interval into several sub-intervals;(3) calculate the local integral matrix of oscillation kernel corresponding to the incidence angle of observation data;(4) calculate the local mean vector of slowly varying kernel;(5) calculate the spherical wave reflection coefficient of oscillation-slowly varying nuclear decoupling;(6) decoupled spherical wave reflection coefficient is used to construct objective function and solve.In the process of solving objective function, only need to repeat "step (4) (5)" after updating seabed elastic parameter, without repeating the calculation of oscillation kernel local integral matrix in step (3), avoid the redundant calculation about oscillation kernel integration, improve the calculation efficiency.

Description

Technical Field

[0001] This invention belongs to the field of geophysics, specifically relating to a method, system, and apparatus for inverting seabed elastic parameters under a seismic spherical reflection wave oscillation-gradient core decoupling framework. Background Technology

[0002] Seismic waves reflected from the seabed carry rich information about the elastic parameters of seabed sediments. The seabed reflection coefficient, unaffected by the source wavelet, is an inherent property of the seabed reflection interface, determined by the elastic parameters on both sides of the interface. Therefore, the seabed reflection coefficient is an effective way to indirectly obtain seabed elastic parameters. The seabed plane wave reflection coefficient, due to its simple and efficient calculation process, has been widely used in calculating the relationship between the seabed reflection coefficient and the incident angle. Currently, the calculation method for the seabed reflection coefficient with the incident angle is mainly based on plane wave theory. However, in actual geophysical exploration, seismic waves originate from point sources and form spherical waves. Plane waves are an approximation of spherical waves in the high-frequency, far-field case. This means that plane wave theory cannot accurately describe the seabed spherical wave reflection coefficient in the low-frequency, near-field case, especially at large incident angles, where the plane wave reflection coefficient will produce significant errors. Spherical wave theory can better describe the relationship between the seabed reflection coefficient and the incident angle, but because it requires numerical integration of a rapidly oscillating function, its computational efficiency is significantly lower than that of calculation methods based on plane wave theory. This severely restricts the application of spherical wave theory in related inversion problems. Summary of the Invention

[0003] To address the problem of low calculation efficiency of seabed spherical wave reflection coefficient, this invention provides a method, system, and apparatus for inverting seabed elastic parameters under the framework of seismic spherical reflected wave oscillation-gradient kernel decoupling.

[0004] This invention is achieved through the following technical solution:

[0005] A method for inverting seafloor elastic parameters within a seismic spherical reflection wave oscillation-gradiently varying kernel decoupling framework, the steps of which are as follows:

[0006] Step 1: Obtain observation data Initialize seabed elastic parameters ;

[0007] Step 2: Based on the observation data Determine the integration interval Undetermined parameters And discretize the integration interval into several sub-intervals, using Represents any one of the subintervals ( );

[0008] further, The value of does not need to be strictly calculated; it is only necessary to ensure that the integral outside the interval is much smaller than the integral inside the interval. The union of all subintervals forms the integration interval. The intersection of any two subintervals is an empty set.

[0009] Step 3: Calculate the oscillation kernel integral corresponding to the incident angle of the observed data in all sub-intervals in Step 2, and construct the local integral matrix U of the oscillation kernel;

[0010] Furthermore, the local integral matrix of the oscillating kernel ;in, ... Indicates the angle of incidence corresponding to the observed data. ; Indicates a given angle of incidence Below, sub-interval Internal oscillating nucleus The definite integral value is calculated using the following formula:

[0011] ;

[0012] Step 4: Calculate the local mean vector of the slowly varying kernel; sequentially across all sub-intervals in "Step 2". Internally determined by the current seabed elastic parameters Calculate the plane wave reflection coefficient mean The local mean vector of the slowly varying kernel is obtained. ;

[0013] Furthermore, in the first calculation of the plane wave reflection coefficient At that time, the current seabed elastic parameters Refers to the seabed elastic parameters initialized in the "first step". In subsequent calculations of the plane wave reflection coefficient During the iterative solution process, the current seabed elastic parameters... Refers to the updated seabed elasticity parameters after "step six". .

[0014] Step 5: Calculate the spherical wave reflection coefficient of oscillation-gradiently varying kernel decoupling. ;

[0015] Step 6: Construct the objective function using the spherical wave reflection coefficients decoupled in Step 5 and solve it. In this step, after updating the seabed elastic parameters, the spherical wave reflection coefficients only need to be updated by returning to Step 4 and Step 5 to recalculate the local mean matrix of the slowly varying kernel, without having to repeatedly calculate the local integral matrix of the oscillation kernel.

[0016] This invention also provides a seabed elastic parameter inversion system under the seismic spherical reflection wave oscillation-gradient kernel decoupling framework; the system includes a data input and initialization module, an integral interval discretization module, an oscillation kernel local integral matrix calculation module, a graded kernel local mean vector calculation module, a reflection coefficient calculation module under the decoupling framework, an objective function module, and an output module;

[0017] The data input module and initialization module execute the first step of the method; the integral interval discretization module executes the second step; the oscillation kernel local integral matrix calculation module executes the third step; the slowly varying kernel local mean vector calculation module executes the fourth step; the reflection coefficient calculation module under the decoupling framework executes the fifth step; and the objective function module and output module execute the sixth step. The specific steps are as follows:

[0018] After the data input module and initialization module obtain the observation data and initialize the seabed elastic parameters, they first determine the integration interval, and then the integration interval discretization module discretizes the integration interval. All sub-intervals obtained after discretization by the integration interval discretization module are simultaneously fed into the oscillation kernel local integration matrix calculation module and the gradually varying kernel local mean vector calculation module. In the oscillation kernel local integration matrix calculation module, the local integration values ​​of all sub-intervals corresponding to the incident angle of the observation data are calculated, and the oscillation kernel local integration matrix is ​​constructed. In the gradually varying kernel local mean vector calculation module, the sub-intervals input by the integration interval discretization module and the current seabed are used. The elastic parameters are calculated using the local mean vector of the gradually varying kernel. The local mean vector of the gradually varying kernel and the local integral matrix of the oscillating kernel are input into the reflection coefficient calculation module under the decoupled framework to obtain the spherical wave reflection coefficient of the oscillation-gradually varying kernel decoupled system. The obtained spherical wave reflection coefficient is input into the objective function module. The objective function module determines whether the spherical wave reflection system is optimal. If so, the output module outputs the current seabed elastic parameter value as the result. If not, the seabed elastic parameters are updated, the local mean vector of the gradually varying kernel is recalculated, and the spherical wave reflection coefficient is updated. This process is repeated until the optimal spherical wave reflection coefficient is obtained and the result is output.

[0019] The present invention also provides a seabed elastic parameter inversion device under the seismic spherical reflection wave oscillation-gradient core decoupling framework, wherein the device is equipped with the above-mentioned inversion system and performs the above-mentioned calculation method.

[0020] The advantages of this invention compared to existing technologies are as follows: This invention decouples the oscillating and slowly varying parts of the integrand in the integral expression of the seabed spherical wave reflection coefficient, rewriting the original integral expression as the product of the local integral matrix of the oscillating kernel and the local mean vector of the slowly varying kernel. This establishes a method for inverting seabed elastic parameters within the decoupled framework of the oscillating and slowly varying kernels. The inversion process within the decoupled framework updates the spherical wave reflection coefficient by iteratively calculating the local mean vector of the slowly varying kernel. Figure 1(shaded area), without having to repeatedly calculate the local integral matrix of the oscillation kernel, avoids a large amount of redundant calculations and greatly improves computational efficiency. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the inversion method under the decoupling framework;

[0022] Figure 2 This is a diagram of observation data from an example; A represents low-velocity seabed data, and B represents high-velocity seabed data.

[0023] Figure 3 Here is a diagram of the local integral matrix of the oscillating kernel; A is the natural logarithm of the modulus, B is the natural logarithm of the absolute value of the real part, and C is the natural logarithm of the absolute value of the imaginary part.

[0024] Figure 4 This is a local mean vector diagram of a slowly varying kernel; A is the magnitude, B is the real part, and C is the imaginary part.

[0025] Figure 5 The graph shows the relationship between the reflection coefficient and the incident angle. In A, the solid line represents the reflection coefficient obtained by the present invention, and the dots represent the accurate value obtained by equation (1). B is the difference between the reflection coefficient of the present invention and the accurate value.

[0026] Figure 6 This is a convergence curve diagram; A represents P-wave velocity, B represents S-wave velocity, C represents density, D represents the difference in P-wave velocity, E represents the difference in S-wave velocity, and F represents the difference in density.

[0027] Figure 7 The data fitting diagram shows that A represents the low-sound seabed condition, B represents the high-sound seabed condition, C represents the difference between the two forward modeling results for condition A, and D represents the difference between the two forward modeling results for condition B. Detailed Implementation

[0028] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings. It is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0029] This invention relates to a method for inverting seabed elastic parameters within a seismic spherical reflection wave oscillation-gradiently varying kernel decoupling framework, such as... Figure 1 As shown, its main principle is as follows.

[0030] The spherical wave reflection coefficient can be calculated using the following formula.

[0031] (1)

[0032] In equation (1), The wave number of the seismic wave. e It is a natural constant. The plane wave reflection coefficient, The horizontal distance between the seismic source and the receiving point. Indicates the propagation distance of the wave field. and , , respectively, are the distances from the source and receiver to the reflecting interface, and J0 represents the zeroth-order Bessel function of the first kind. Let the incident angle be the integral variable. The accurate spherical wave reflection coefficient can be obtained from equation (1). However, directly using this formula for theoretical calculations is inefficient. Based on the oscillation of the integrand with the integral variable and its determining variables in formula (1), this invention writes the integrand as an oscillating kernel. With slow-changing nuclei Product. Therefore, the reflection coefficient of spherical waves on the seabed can be equivalently written as:

[0033] (2)

[0034] Obviously, in the above formula Furthermore, the oscillating kernel and the slowly varying kernel in equation (2) are decoupled within a local sub-interval. The integral of the product of the oscillating kernel and the slowly varying kernel is written in the form of the product of the oscillating kernel integral and the mean of the slowly varying kernel within the local sub-interval. Finally, the integral results of all sub-intervals are summed to obtain the final result with solution (i.e., the expression given in step five). The local integral of the oscillating kernel is only related to the seismic wave frequency and the observation system parameters, while the local mean of the slowly varying kernel is only determined by the seabed elastic parameters. This makes it possible to update the seabed elastic parameters during the inversion process only to recalculate the local mean of the slowly varying kernel, without having to recalculate the local integral of the oscillating kernel, which greatly reduces the computational workload of spherical wave inversion. The innovation of this invention is reflected in two aspects: first, the integral expression of the spherical wave reflection coefficient is decoupled into the product of the local integral matrix of the oscillating kernel and the local mean vector of the slowly varying kernel within the local sub-interval; second, the inversion process under the above oscillating-slowly varying kernel decoupling framework only updates the local mean vector of the slowly varying kernel, avoiding the repeated calculation of the oscillating kernel part and improving the computational efficiency.

[0035] The proposed method for inverting seabed elastic parameters within the seismic spherical reflection wave oscillation-gradient kernel decoupling framework is described in the following algorithm flow: Figure 1 As shown, the specific steps include:

[0036] Step 1: Obtain observation data Initialize seabed elastic parameters .

[0037] This embodiment uses single-reflection point data under both low-speed and high-speed sound seabed conditions as examples to describe the technical solution. The observation data is as follows: Figure 2 As shown, A represents low-velocity seabed data, and B represents high-velocity seabed data; the minimum incident angle of the data is 1°, and the maximum incident angle is 65°, distributed at 1° intervals. The frequency of all data shown is 100Hz, and the distance from the source and receiver to the reflecting interface is 50m (i.e.,...). ), and The incident angle shown in the figure can be calculated based on geometric relationships. The seabed elastic parameters for both seabed conditions are initialized to... .

[0038] Step 2: Based on the observation data Determine the integration interval Undetermined parameters And discretize the integration interval into several sub-intervals, using Represents any one of the subintervals ( );

[0039] As a specific implementation method: the integration interval Decompose into several sub-intervals, using Represents any one of the subintervals ( The subintervals can be decomposed into equal or non-equal intervals; the smaller the interval, the higher the calculation accuracy. exist The data decays rapidly, and the higher the frequency of data d, the faster the decay. The value of only needs to ensure that the integral outside the interval is much smaller than that inside the interval when the frequency is lowest.

[0040] This embodiment takes The value is 1, and the integration interval is decomposed into 5600 subintervals, i.e. Sub-interval index and Figure 3 , Figure 4 The horizontal axis corresponds to the horizontal axis.

[0041] Step 3: Calculate the oscillation kernel integral corresponding to the incident angle of the observed data within all sub-intervals of Step 2, and construct the local integral matrix of the oscillation kernel. ;

[0042] As a preferred implementation, the oscillation kernel local integral matrix .in, ... Indicates the angle of incidence corresponding to the observed data. . Indicates a subinterval under a given incident angle. Internal oscillating nucleus The definite integral value is calculated using the following formula:

[0043] .

[0044] The local integral matrix of the oscillation kernel calculated based on the relevant parameters of the input data in "Step One" in this embodiment is as follows: Figure 3 As shown in the figure. The vertical axis represents the angle of incidence. ... and Figure 2 The input data shown corresponds to incident angles of 1°, 2°, ..., 65° (n=65); the horizontal axis represents the sub-interval number and the sub-interval number in "Step Two". correspond.

[0045] Step 4: Calculate the local mean vector of the slowly varying kernel;

[0046] In all sub-intervals of "Step Two" sequentially Internally determined by the current seabed elastic parameter value Calculate the plane wave reflection coefficient mean The local mean vector of the slowly varying kernel is obtained. . In subinterval Within a certain range, it can be considered a constant. In this embodiment, the mean value within the interval is represented by the function value at the midpoint of the sub-interval, i.e. In this embodiment, the locally mean vector of the slowly varying kernel is obtained as follows: Figure 4 As shown.

[0047] It is important to note that the gradually varying core is determined by the seabed elastic parameters. Because the local mean vector of the gradually varying core is constantly updated and changing during the inversion process, Figure 4 The seabed elastic parameters corresponding to the locally mean vector of the slowly varying core shown are the initial values ​​set in "Step 1".

[0048] Step 5: Calculate the spherical wave reflection coefficient of oscillation-gradiently varying kernel decoupling. .

[0049] As a specific implementation method, such as Figure 5 As shown, the spherical wave reflection coefficient calculated by the oscillation-gradiently varying core decoupling method in this embodiment is represented by a solid line, while the seabed reflection coefficient calculated by the precise seabed reflection coefficient formula (1) is represented by dots. It can be seen that the two are basically consistent, which indicates that the oscillation-gradiently varying core decoupling method for calculating the spherical wave reflection coefficient proposed in this embodiment is effective. Figure 5 The seabed elastic parameters used and Figure 4 Same. At the same time, It is independent of the seabed elastic parameters, only This is related to seabed elastic parameters, which is the key to improving the efficiency of seabed elastic parameter inversion in the next step.

[0050] Step 6: Construct the objective function using the spherical wave reflection coefficients decoupled in Step 5 and solve for it.

[0051] The solution process only requires updating the local average vector of the slowly varying kernel; there is no need to repeatedly calculate the local integral matrix of the oscillating kernel (see the process below). Figure 1 (Shaded area). This embodiment uses the least squares objective function. The gradient of the objective function with respect to the seabed elastic parameters under the oscillating-gradient kernel decoupling framework can be written as:

[0052] ;

[0053] in, Let be the gradient operator, d be the observed data, and U be the local integral matrix of the oscillation kernel. Local mean vector of a slowly varying kernel.

[0054] To facilitate the demonstration of the calculation process and comparison of the differences between the two inversion methods, this embodiment normalizes the maximum component of the gradient during the inversion process, while scaling other components proportionally, with a step size set to 0.25; the number of iterations is standardized to 1200. Figure 6 As shown in A, B, and C, the black dashed line represents the inversion driven by the exact equation (spherical wave reflection coefficient calculation formula (1)), and the green solid line represents the inversion under the decoupling framework of this invention. The larger convergent values ​​in A, B, and C are obtained from hypersonic seabed data, and the smaller convergent values ​​are obtained from hyposonic seabed data. Figure 6 In the figure, D, E, and F represent the differences between the two inversion methods corresponding to A, B, and C, where the black dashed line represents the hypersonic seabed and the green solid line represents the hyposonic seabed (the green and black blocky shapes in the figure are actually generated by curve oscillations). Clearly, the method proposed in this invention is basically consistent with the inversion results driven by the exact equation. There are slight differences in the intermediate calculation process, but these have little impact on the final result. The forward modeling data corresponding to the inversion results of the two methods fit the observation data very well. Figure 7 In the diagram, A and B represent observation data (red dots), the solid green line represents the forward modeling results of this invention, and the dashed black line (which largely overlaps with the solid green line) represents the forward modeling results of the exact equation-driven method. Furthermore, the forward modeling data from the two methods are largely consistent with each other, with very small differences. Figure 7 (C and D in the text).

[0055] Table 1 shows the computation time of the exact equation-driven inversion and the decoupled inversion of this invention in the MATLAB R2023b environment. The time to the left of the slash " / " represents the time taken by the Intel(R) Core(TM) i9-10980XE CPU to complete the inversion process, and the time to the right of the slash " / " represents the time taken by the Hygon C86-3G (OPN:3350) CPU to complete the inversion process. The calculation of the local integral matrix of the oscillating core in the table was completed in parallel by 18 cores on the Intel CPU and in parallel by 8 cores on the Hygon CPU; other calculations were not parallelized. Although the absolute time taken by different computing platforms may vary, the computation time of the decoupled inversion proposed in this invention is significantly less than that of the exact equation-driven inversion.

[0056] Table 1. Calculation Time (Unit: seconds)

[0057] .

[0058] Example 2

[0059] This embodiment provides a seabed elastic parameter inversion system under the decoupling framework of seismic spherical reflection wave oscillation-gradient kernel; the system includes a data input and initialization module, an integral interval discretization module, an oscillation kernel local integral matrix calculation module, a graded kernel local mean vector calculation module, a reflection coefficient calculation module under the decoupling framework, an objective function module, and an output module;

[0060] After the data input module and initialization module obtain the observation data and initialize the seabed elastic parameters, they first determine the integration interval, and then the integration interval discretization module discretizes the integration interval. All sub-intervals obtained after discretization by the integration interval discretization module are simultaneously entered into the oscillation kernel local integration matrix calculation module and the gradually varying kernel local mean vector calculation module. In the oscillation kernel local integration matrix calculation module, the local integration values ​​of all sub-intervals corresponding to the incident angle of the observation data are calculated, and the oscillation kernel local integration matrix is ​​constructed. In the gradually varying kernel local mean vector calculation module, the sub-intervals input by the integration interval discretization module and the current seabed elastic parameters are used. The local mean vector of the gradually varying kernel is calculated. The local mean vector of the gradually varying kernel and the local integral matrix of the oscillating kernel are input into the reflection coefficient calculation module under the decoupling framework to obtain the spherical wave reflection coefficient of the oscillation-gradually varying kernel decoupling. The obtained spherical wave reflection coefficient is input into the objective function module. The objective function module determines whether the spherical wave reflection coefficient is optimal. If it is, the output module outputs the current seabed elastic parameter value as the result. If not, the seabed elastic parameter is updated, the local mean vector of the gradually varying kernel is recalculated, and the spherical wave reflection coefficient is updated. This process is repeated until the optimal spherical wave reflection coefficient is obtained and the current seabed elastic parameter is output.

[0061] A device for inverting seabed elastic parameters under the seismic spherical reflection wave oscillation-gradient core decoupling framework, wherein the device is equipped with the above-mentioned inversion system and executes the inversion method described in Example 1.

Claims

1. A method for inverting seabed elastic parameters within a seismic spherical reflection wave oscillation-gradiently varying kernel decoupling framework, characterized in that, The steps of the method are as follows: Step 1: Obtain observation data Initialize seabed elastic parameters ; Step 2: Based on the observation data Determine the integration interval Undetermined parameters And discretize the integration interval into several sub-intervals, using To represent any one of the subintervals, ; Step 3: Calculate the oscillation kernel integral corresponding to the incident angle of the observed data within all sub-intervals of Step 2, and construct the oscillation kernel local integration matrix U; oscillation kernel local integration matrix ;in, ... Indicates the angle of incidence corresponding to the observed data. ; Indicates a given angle of incidence Below, sub-interval Internal oscillating nucleus The definite integral value is calculated using the following formula: , where k is the wave number of the seismic wave, D represents the wave field propagation distance, and e is the natural constant; Step 4: Calculate the local mean vector of the slowly varying kernel; sequentially across all sub-intervals in step 2. Internally determined by the current seabed elastic parameters Calculate the plane wave reflection coefficient mean Obtain the local mean vector of the slowly varying kernel ; Step 5: Calculate the spherical wave reflection coefficient of oscillation-gradiently varying kernel decoupling. ; Step 6: Construct the objective function using the spherical wave reflection coefficients decoupled in Step 5 and solve it. In this step, after updating the seabed elastic parameters, the spherical wave reflection coefficients only need to be updated by returning to Step 4 and Step 5 to recalculate the local mean matrix of the slowly varying kernel, without having to repeatedly calculate the local integral matrix of the oscillation kernel.

2. The method according to claim 1, characterized in that, In the second step, The value of does not need to be strictly calculated; it is only necessary to ensure that the integral outside the interval is much smaller than the integral inside the interval; the union of all subintervals forms the integration interval. The intersection of any two subintervals is an empty set.

3. The method according to claim 1, characterized in that, In the fourth step, the plane wave reflection coefficient is calculated for the first time. At that time, the current seabed elastic parameters Refers to the seabed elastic parameters initialized in the first step. In subsequent calculations of the plane wave reflection coefficient During the iterative solution process, the current seabed elastic parameters... Refers to the updated seabed elasticity parameters in step six. .

4. A system for inverting seabed elastic parameters within a seismic spherical reflection wave oscillation-gradiently varying kernel decoupling framework, characterized in that, The system includes a data input and initialization module, an integral interval discretization module, an oscillation kernel local integral matrix calculation module, a slowly varying kernel local mean vector calculation module, a reflection coefficient calculation module under a decoupling framework, an objective function module, and an output module; the system runs the inversion method described in claim 1, specifically as follows: The data input and initialization module is used to obtain observation data. Initialize seabed elastic parameters ; The integral interval discretization module is used to determine the integral interval based on the observed data. Determine the integration interval Undetermined parameters And discretize the integration interval into several sub-intervals, using To represent any one of the subintervals, ; The oscillation kernel local integral matrix calculation module is used to calculate the oscillation kernel integral corresponding to the incident angle of the observed data in all sub-intervals of the integration interval discretization module, and to construct the oscillation kernel local integral matrix. ; The local mean vector calculation module for the slowly varying kernel is used to calculate the local mean vector of the slowly varying kernel; sequentially in all sub-intervals of the integral interval discretization module. Internally determined by the current seabed elastic parameters Calculate the plane wave reflection coefficient mean Obtain the local mean vector of the slowly varying kernel ; The reflection coefficient calculation module within the decoupling framework is used to calculate the reflection coefficient of spherical waves in the oscillating-gradiently varying kernel decoupling configuration. ; The objective function module and the output module are used to construct and solve the objective function using the decoupled spherical wave reflection coefficients in the reflection coefficient calculation module under the decoupling framework. In the solution iteration, after updating the seabed elastic parameters, it is only necessary to recalculate the local mean matrix of the gradually varying kernel by returning to the local mean vector calculation module of the gradually varying kernel and the reflection coefficient calculation module under the decoupling framework to update the spherical wave reflection coefficient, without having to repeatedly calculate the local integral matrix of the oscillation kernel.

5. A device for inverting seabed elastic parameters within a seismic spherical reflection wave oscillation-gradiently varying kernel decoupling framework, characterized in that, The device is equipped with the inversion system of claim 4 and performs the inversion method of any one of claims 1-3.

Images