Seabed elastic parameter inversion method, system and device under seismic spherical reflection wave oscillation-slow change nuclear decoupling framework

Abstract

The invention relates to a seabed elastic parameter inversion method, system and device under an earthquake spherical reflection wave oscillation-gradual change nuclear decoupling framework, and belongs to the field of geophysical detection and acoustic detection. The method comprises the following steps: (1) inputting observation data and initializing seabed elastic parameters; (2) determining an integral interval and decomposing the integral interval into a plurality of sub-intervals; (3) calculating an oscillation nuclear local integral matrix corresponding to the incident angle of the observation data; (4) calculating a slowly-varying kernel local mean vector; (5) calculating a spherical wave reflection coefficient of oscillation-gradual change kernel decoupling; and (6) constructing a target function by using the decoupled spherical wave reflection coefficient, and solving the target function. In the objective function solving process, only the steps (4) and (5) need to be repeatedly executed after the seabed elastic parameters are updated, the oscillation nuclear local integral matrix in the step (3) does not need to be repeatedly calculated, redundant calculation about oscillation nuclear integration is avoided, and the calculation efficiency is improved.

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: 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: 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 Represents any one of the subintervals ( ); 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.

[0005] Third step: Calculate the oscillatory kernel integral corresponding to the observation data incident angle in all sub-intervals in the second step, and construct the oscillatory kernel local integral matrix U; Further, the oscillatory kernel local integral matrix ; wherein, … denotes the incident angle corresponding to the observation data, ; denotes the given incident angle , the definite integral value of the oscillatory kernel in the sub-interval , and the specific calculation formula is: ; Fourth step: Calculate the slowly varying kernel local mean vector; in all sub-intervals of the second step, calculate the mean value of the plane wave reflection coefficient from the current seabed elastic parameters , and obtain the slowly varying kernel local mean vector ; Further, when calculating the plane wave reflection coefficient for the first time, the current seabed elastic parameters refer to the seabed elastic parameters initialized in the first step; when calculating the plane wave reflection coefficient , the current seabed elastic parameters refer to the seabed elastic parameters updated in the sixth step in the solving iteration.

[0006] Fifth step: Calculate the spherical wave reflection coefficient decoupled from the oscillatory-slowly varying kernel ; Sixth step: Use the spherical wave reflection coefficient decoupled in the fifth step to construct the objective function and solve it; in the solving iteration, after updating the seabed elastic parameters, only the spherical wave reflection coefficient needs to be updated by returning to the fourth step and the fifth step to recalculate the slowly varying kernel local mean matrix, without repeating the calculation of the oscillatory kernel local integral matrix.

[0007] The application also provides a seabed elastic parameter inversion system under the oscillatory-slowly varying kernel decoupling framework of seismic spherical reflection wave; the system comprises a data input and initialization module, an integral interval discretization module, an oscillatory kernel local integral matrix calculation module, a slowly varying kernel local mean vector calculation module, a reflection coefficient calculation module under the decoupling framework, an objective function module, and an output module. ​The data input module and the initialization module run the first step of the method, the integral interval discretization module runs the second step of the method, the oscillation kernel local integral matrix calculation module runs the third step of the method, the slowly-varying kernel local mean vector calculation module runs the fourth step of the method, the reflection coefficient calculation module under the decoupling framework runs the fifth step of the method, and the objective function module and the output module run the sixth step of the method. After the data input module and the initialization module obtain the observation data and initialize the seabed elastic parameters, firstly, the integral interval is determined, and the integral interval is discretized by the integral interval discretization module, all subintervals obtained after the integral interval discretization module is discretized enter the oscillation kernel local integral matrix calculation module and the slowly-varying kernel local mean vector calculation module at the same time; the local integral values of all subintervals corresponding to the observation data incidence angle are calculated in the oscillation kernel local integral matrix calculation module, and the oscillation kernel local integral matrix is constructed; the subintervals input by the integral interval discretization module and the current seabed elastic parameters are used to calculate the slowly-varying kernel local mean vector in the slowly-varying kernel local mean vector calculation module; the slowly-varying kernel local mean vector and the oscillation kernel local integral matrix are input into the reflection coefficient calculation module under the decoupling framework to obtain the spherical wave reflection coefficient of the oscillation-slowly-varying kernel decoupling; the obtained spherical wave reflection coefficient is input into the objective function module; whether the spherical wave reflection coefficient is optimal is judged in the objective function module, if yes, the current seabed elastic parameter value is output as a result by the output module; if not, the seabed elastic parameters are updated, the slowly-varying kernel local mean vector is recalculated, and then the spherical wave reflection coefficient is updated, and the cycle is continued until the optimal spherical wave reflection coefficient is obtained and the result is output.

[0008] The application further provides a seabed elastic parameter inversion device under a seismic spherical reflection wave oscillation-slowly-varying kernel decoupling framework.

[0009] Compared with the prior art, the application has the beneficial effects that: the application decouples the oscillation and slowly-varying parts in the integral function of the seabed spherical wave reflection coefficient integral expression, writes the original integral expression as the product of the oscillation kernel local integral matrix and the slowly-varying kernel local mean vector, and further establishes the seabed elastic parameter inversion method under the oscillation-slowly-varying kernel decoupling framework. The inversion process under the decoupling framework updates the spherical wave reflection coefficient by iteratively calculating the slowly-varying kernel local mean vector, without repeatedly calculating the oscillation kernel local integral matrix, avoids a large amount of redundant calculation, and greatly improves the calculation efficiency. Figure 1 The shadow part), without repeatedly calculating the oscillation kernel local integral matrix, avoids a large amount of redundant calculation, and greatly improves the calculation efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0010] Figure 1 It is a flowchart of the inversion method under the decoupling framework. Figure 2Figure for observation data of example; A is low-velocity seabed data, and B is high-velocity seabed data; Figure 3 Figure for local integral matrix of oscillatory kernel; A is natural logarithm of modulus, B is natural logarithm of absolute value of real part, and C is natural logarithm of absolute value of imaginary part; Figure 4 Figure for local mean vector of slowly varying kernel; A is modulus, B is real part, and C is imaginary part; Figure 5 Figure for comparison of reflection coefficient with respect to incident angle; the solid line in A represents the reflection coefficient obtained by the present application, the circle point represents the exact value obtained by formula (1), and B is the difference between the reflection coefficient of the present application and the exact value; Figure 6 Figure for convergence curve; A is P-wave velocity, B is S-wave velocity, C is density, D is P-wave velocity difference, E is S-wave velocity difference, and F is density difference; Figure 7 Figure for data fitting; A is low-velocity seabed condition, B is high-velocity seabed condition, C is the difference between two forward results of A condition, and D is the difference between two forward results of B condition. DETAILED DESCRIPTION

[0011] The technical solutions of the present application will be described in detail below with reference to the drawings. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by a person skilled in the art without creative labor fall within the protection scope of the present application.

[0012] The seabed elastic parameter inversion method under the oscillatory-slowly varying kernel decoupling framework of the seismic spherical reflection wave of the present application, as shown in Figure 1 , mainly has the following principles.

[0013] The spherical wave reflection coefficient can be calculated by the following formula (1) In formula (1), is the wave number of the seismic wave, e is a natural constant, is the plane wave reflection coefficient, is the horizontal distance between the source and the receiving point, represents the wave field propagation distance, and are the distances from the source and the receiving point to the reflection interface respectively, J0 represents the first-order zero Bessel function, is the integral variable representing the incident angle. The exact spherical wave reflection coefficient can be obtained by formula (1) However, the theoretical calculation directly using the formula is low in efficiency. The present application writes the integral function in formula (1) as the product of an oscillation kernel and a slowly-varying kernel according to the oscillation of the integral function with the integral variable and the variable determining the function. and the slowly-varying kernel . Therefore, the reflection coefficient of the seabed spherical wave can be equivalently written as: (2) Obviously, in the above formula, . Further, the oscillation kernel and the slowly-varying kernel of formula (2) are decoupled in a local sub-interval. The integral of the product of the oscillation kernel and the slowly-varying kernel is written in the form of the product of the integral of the oscillation kernel and the average of the slowly-varying kernel in the local sub-interval. Finally, the integral results of all the sub-intervals are accumulated to obtain the final result (i.e. the expression given in step five). The local integral of the oscillation kernel is only related to the frequency of the seismic wave and the parameters of the observation system, and the local average of the slowly-varying kernel is only determined by the elastic parameters of the seabed. This makes it only necessary to recalculate the local average of the slowly-varying kernel when updating the elastic parameters of the seabed in the inversion process, without the need to recalculate the local integral of the oscillation kernel, greatly reducing the calculation amount of the spherical wave inversion. The innovation points of the present application are embodied in two aspects: one is to decouple the integral expression of the spherical wave reflection coefficient into the product of the local integral matrix of the oscillation kernel and the local average vector of the slowly-varying kernel in a local sub-interval; the other is to update only the local average vector of the slowly-varying kernel in the inversion process under the above oscillation-slowly-varying kernel decoupling framework, avoiding the repeated calculation of the oscillation kernel part and improving the calculation efficiency.

[0014] The seabed elastic parameter inversion method under the oscillation-slowly-varying kernel decoupling framework of the seismic spherical reflection wave proposed by the present application has the specific algorithm process as shown in Figure 1 , and specifically comprises the following steps: First step: obtaining observation data , initializing the elastic parameters of the seabed .

[0015] This embodiment takes single reflection point data under two conditions of low-velocity seabed and high-velocity seabed as examples to describe the technical solution. The observation data are shown in Figure 2 , wherein A is the low-velocity seabed data, B is the high-velocity seabed data; the minimum incidence angle of the data is 1°, the maximum incidence angle is 65°, and the incidence angles are distributed at equal intervals of 1°. The frequencies of the data shown in the figure are all 100 Hz, the distances of the source and the receiving point from the reflection interface are both 50 m (i.e. ), and can be calculated according to the geometric relationship of the incidence angles shown in the figure. The elastic parameters of the seabed under the two seabed conditions are both initialized as .

[0016] Second step: determining the integral interval according to the observation data ​ Undetermined parameters And discretize the integration interval into several sub-intervals, using Represents any one of the subintervals ( ); 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.

[0017] This embodiment takes The integral is set to 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.

[0018] 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. ; 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: .

[0019] 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.

[0020] Step 4: Calculate the local mean vector of the slowly varying kernel; 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.

[0021] 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".

[0022] Step 5: Calculate the spherical wave reflection coefficient of oscillation-gradiently varying kernel decoupling. .

[0023] 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.

[0024] Step 6: Construct the objective function using the spherical wave reflection coefficients decoupled in Step 5 and solve for it.

[0025] 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: ; 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.

[0026] 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).

[0027] 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.

[0028] Table 1. Calculation Time (Unit: seconds) .

[0029] Example 2 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; 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.

[0030] 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 in all sub-intervals in Step 2, and construct the local integral matrix U of the oscillation kernel; 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 third step, the local integral matrix of the oscillation 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: Where k is the wave number of the seismic wave, and D represents the wave field propagation distance. e It is a natural constant.

4. 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. .

5. 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 the decoupling framework, an objective function module, and an output module. 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.

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

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