Method and device for determining seismic reflection coefficient

Abstract

This specification provides a method and device for determining a seismic reflection coefficient. Based on this method, after constructing a first objective function for the seismic reflection coefficient of a target area based on post-stack seismic data and a seismic wavelet convolution model, a dual approximate function corresponding to the first objective function can be constructed as a second objective function, thereby converting the problem of directly solving the optimal value of the first objective function into a corresponding dual problem, avoiding the direct solution of the first objective function; then, the second objective function is processed by adopting a preset processing method based on semidefinite programming theory to determine the reflection time. This eliminates the need to discretize the sparse domain of the reflection coefficient, effectively avoids the problem of basis mismatch, and thus accurately inverts the reflection coefficient to obtain a higher-precision reflection coefficient, solving the technical problems of large errors and low precision in the determined reflection coefficient in existing methods.

Description

Technical Field

[0001] This specification belongs to the field of geophysical exploration technology, and in particular to a method and device for determining seismic reflection coefficients. Background Art

[0002] In geophysical exploration, when there is little data (such as lack of well logging data), sparse inversion is often performed using post-stack seismic data to obtain the inversion result of the reflection coefficient.

[0003] Based on existing methods, when performing specific sparse inversion, the Fourier basis (DFT basis) is often used as the transformation basis of the reflection coefficient, and the continuous parameter space is simplified into a finite set of grid points by discretization, and corresponding processing is performed. However, in reality, the reflection coefficient is distributed in the continuous parameter space. Therefore, through the above discretization method, no matter how finely the grid points in the grid point set are divided, it is impossible to guarantee that all data signals are located at the center of the grid cell, which will lead to the problem of basis mismatch, affecting the accuracy of the final determined reflection coefficient.

[0004] Currently, no effective solutions have been proposed for the above technical problems. Summary of the Invention

[0005] This specification provides a method and device for determining a seismic reflection coefficient, which does not require discretization of the sparse domain of the reflection coefficient, can effectively avoid the problem of basis mismatch, and can accurately invert to obtain a reflection coefficient with higher precision, solving the technical problems existing in existing methods such as large reflection time error and insufficient sparsity of the determined reflection coefficient, resulting in low precision.

[0006] This specification provides a method for determining a seismic reflection coefficient, including:

[0007] Acquire post-stack seismic data in the target area;

[0008] constructing a first objective function of a seismic reflection coefficient of a target area based on the post-stack seismic data and the seismic wavelet convolution model;

[0009] According to the first objective function, construct a corresponding dual approximate function as the second objective function;

[0010] processing the second objective function by a preset processing method based on semidefinite programming theory to determine the reflection time;

[0011] The seismic reflection coefficient of the target area is determined according to the reflection time.

[0012] In one embodiment, processing the second objective function by a preset processing method based on semidefinite programming theory to determine the reflection time includes:

[0013] Obtain and use the Hermite matrix to transform the second objective function into a function based on semidefinite programming theory as the third objective function;

[0014] The reflection time is determined according to the third objective function.

[0015] In one embodiment, obtaining and utilizing a Hermite matrix to convert the second objective function into a function based on semidefinite programming theory as the third objective function includes constructing the following formula as the third objective function:

[0016] based on

[0017] Among them, Q can be specifically expressed as a Hermite matrix, c can be specifically expressed as a target coefficient, i is the row number of the matrix, j is the column number of the matrix, and n is the size of the matrix.

[0018] In one embodiment, after obtaining and using the Hermite matrix to convert the second objective function into a function based on semidefinite programming theory as the third objective function, the method further includes:

[0019] Determine the noise level based on the post-stack seismic data of the target area;

[0020] Determining a regularization adjustment parameter according to the noise level;

[0021] Constructing a fourth objective function according to the regularization adjustment parameter and the third objective function;

[0022] Correspondingly, the reflection time is determined according to the fourth objective function.

[0023] In one embodiment, constructing a fourth objective function according to the regularization adjustment parameter and the third objective function includes constructing the following formula as the fourth objective function:

[0024]

[0025] based on

[0026] Among them, λ can be specifically expressed as a regularization adjustment parameter.

[0027] In one embodiment, determining the reflection time according to the fourth objective function includes:

[0028] Solving the fourth objective function to determine the target coefficient;

[0029] Calculating intermediate parameters according to the target coefficient and the polynomial of the constraint function;

[0030] The reflection time is determined according to the intermediate parameter.

[0031] In one embodiment, determining the seismic reflection coefficient of the target area according to the reflection time includes:

[0032] The reflection time is substituted into a characterization function of a reflection coefficient based on Fourier transform, and the characterization function is solved using a least squares method to obtain a corresponding reflection amplitude.

[0033] In one embodiment, after determining the seismic reflection coefficient of the target area based on the reflection time, the method further includes:

[0034] According to the seismic reflection coefficient of the target area, seismic exploration of the target area is guided.

[0035] This specification provides a device for determining a seismic reflection coefficient, comprising:

[0036] Acquisition module, used to obtain post-stack seismic data of the target area;

[0037] A first construction module is configured to construct a first objective function of a seismic reflection coefficient of a target area based on the post-stack seismic data and the seismic wavelet convolution model;

[0038] A second construction module is used to construct a corresponding dual approximation function according to the first objective function as a second objective function;

[0039] a processing module, configured to process the second objective function by a preset processing method based on semidefinite programming theory to determine a reflection time;

[0040] The determination module is used to determine the seismic reflection coefficient of the target area according to the reflection time.

[0041] This specification provides a server, including a processor and a memory for storing processor-executable instructions, wherein when the processor executes the instructions, it obtains post-stack seismic data of a target area; constructs a first objective function regarding the seismic reflection coefficient of the target area based on the post-stack seismic data and a seismic wavelet convolution model; constructs a corresponding dual approximation function as a second objective function based on the first objective function; processes the second objective function through a preset processing method based on semidefinite programming theory to determine a reflection time; and determines the seismic reflection coefficient of the target area based on the reflection time.

[0042] This specification provides a method and device for determining a seismic reflection coefficient. After constructing a first objective function for the seismic reflection coefficient of a target area based on post-stack seismic data and a seismic wavelet convolution model, a dual approximate function corresponding to the above-mentioned first objective function can be first constructed as a second objective function, thereby converting the problem of directly solving the optimal value of the first objective function into a corresponding dual problem, avoiding the direct solution of the first objective function; and then processing the second objective function by adopting a preset processing method based on semidefinite programming theory to determine the reflection time. In this way, there is no need to discretize the sparse domain of the reflection coefficient, and the problem of basis mismatch can be effectively avoided, so that the reflection coefficient with higher precision can be accurately inverted, solving the technical problems of large error and low precision of the determined reflection coefficient in the existing methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the embodiments of this specification, the following will briefly introduce the drawings required for use in the embodiments. The drawings described below are only some embodiments recorded in this specification. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0044] Figure 1 is a flow chart of a method for determining a seismic reflection coefficient provided by an embodiment of this specification;

[0045] Figure 2 This is a schematic diagram of the structure of a server provided by an embodiment of this specification;

[0046] Figure 3 This is a schematic diagram of the structure of a device for determining a seismic reflection coefficient provided in one embodiment of this specification;

[0047] Figure 4 This is a schematic diagram of an embodiment of a method for determining a seismic reflection coefficient provided in an embodiment of this specification, in a scenario example;

[0048] Figure 5 This is a schematic diagram of an embodiment of a method for determining a seismic reflection coefficient provided in an embodiment of this specification, in a scenario example;

[0049] Figure 6 This is a schematic diagram of an embodiment of a method for determining a seismic reflection coefficient provided in an embodiment of this specification, in a scenario example;

[0050] Figure 7 This is a schematic diagram of an embodiment of a method for determining a seismic reflection coefficient provided in an embodiment of this specification, in a scenario example;

[0051] Figure 8 This is a schematic diagram of an embodiment of a method for determining a seismic reflection coefficient provided in an embodiment of this specification, in a scenario example;

[0052] Figure 9 This is a schematic diagram of an embodiment of a method for determining a seismic reflection coefficient provided in an embodiment of this specification, in a scenario example;

[0053] Figure 10 This is a schematic diagram of an embodiment of a method for determining a seismic reflection coefficient provided in an embodiment of this specification, in a scenario example;

[0054] Figure 11 This is a schematic diagram of an embodiment of a method for determining a seismic reflection coefficient provided in an embodiment of this specification, in a scenario example. DETAILED DESCRIPTION

[0055] To help those skilled in the art better understand the technical solutions in this specification, the following will provide a clear and complete description of the technical solutions in the embodiments of this specification, in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of this specification, not all of them. All other embodiments derived by those skilled in the art based on the embodiments in this specification without creative effort shall fall within the scope of protection of this specification.

[0056] Considering the existing sparse inversion method, when obtaining the reflection coefficient based on the inversion of post-stack seismic data, it is often necessary to use, for example, Fourier as the transformation basis, and adopt a discretization method to simplify the continuous parameter space into a finite set of grid points before performing specific data processing. However, in fact, the reflection coefficient is distributed in the continuous parameter space. Through the above-mentioned discretization method, no matter how finely the grid points in the grid point set are divided, it cannot be guaranteed that all data signals are in the center of the grid unit, which makes it easy to have a basis mismatch problem. The greater the degree of basis mismatch, the greater the error in the inversion result, which in turn affects the accuracy of the final determination of the reflection coefficient.

[0057] It can be seen that based on the existing method, by using a discrete sparse basis (i.e., Fourier basis) to discretize the sparse domain of the reflection coefficient, the problem of basis mismatch cannot be avoided, resulting in the technical problems of large error and low precision of the determined reflection coefficient when the existing method is implemented.

[0058] In order to address the root cause of the above-mentioned problems, this specification considers that in the process of sparse inversion, the method of discretizing the sparse domain of the reflection coefficient using a discrete sparse basis can be abandoned, thereby avoiding the problem of basis mismatch at the source. In contrast, after constructing a first objective function for the seismic reflection coefficient of the target area based on post-stack seismic data and the seismic wavelet convolution model, a dual approximate function corresponding to the above-mentioned first objective function can be first constructed as the second objective function, converting the problem of directly solving the optimal value of the first objective function into the corresponding dual problem, thereby avoiding the direct solution of the first objective function; further, the second objective function is processed by adopting a preset processing method based on semidefinite programming theory to determine the reflection time, so that the sparse domain of the reflection coefficient does not need to be discretized, so that the reflection coefficient with higher precision can be accurately inverted, solving the technical problems of large error and low precision of the determined reflection coefficient in the existing method.

[0059] Based on the above ideas, see Figure 1 As shown, the embodiment of this specification provides a method for determining a seismic reflection coefficient. When the method is implemented, it may include the following contents.

[0060] S101: Acquire post-stack seismic data of the target area.

[0061] S102: Constructing a first objective function of the seismic reflection coefficient of the target area according to the post-stack seismic data and the seismic wavelet convolution model.

[0062] S103: Based on the first objective function, construct a corresponding dual approximate function as the second objective function.

[0063] S104: Processing the second objective function in a preset processing method based on semidefinite programming theory to determine the reflection time.

[0064] S105: Determine the seismic reflection coefficient of the target area according to the reflection time.

[0065] In one embodiment, the target area may be understood as an area to be seismically explored. The post-stack seismic data of the target area may be seismic data collected from the target area. Specifically, the post-stack seismic data may include seismic records, seismic wavelets, and other data.

[0066] In a specific implementation, the spectrum of the corresponding reflection coefficient (also called the reflection coefficient spectrum) can be obtained by dividing the seismic record spectrum by the seismic wavelet spectrum based on the post-stack seismic data. For example, it can be expressed as y = [R(0) R(1) … R(N-1)] T). Here, N in the reflection coefficient spectrum data (y) can be expressed as the total number of frequency domain sampling points. Furthermore, the corresponding noise level can be estimated based on post-stack seismic data through observation or other methods. For example, whether the noise is strong or weak can be estimated.

[0067] In one embodiment, the seismic convolution model can be understood as a model for producing synthetic seismic records. Based on the seismic convolution model, it is assumed that each seismic record is composed of the convolution of the seismic wavelet and the reflection function of each layer of the underground model.

[0068] In one embodiment, according to the earthquake convolution model, the earthquake record (which can be denoted as s(t)) can be expressed as follows:

[0069] s(t)=w(t)*r(t), (1)

[0070] Among them, w(t) can specifically represent the seismic wavelet, and r(t) can specifically represent the reflection coefficient sequence.

[0071] In the frequency domain, equation (1) can be further expressed as follows:

[0072] S(f)=W(f)×R(f), (2)

[0073] Among them, S(f) can be specifically expressed as the spectrum of the seismic record, W(f) can be specifically expressed as the spectrum of the seismic wavelet, and R(f) can be specifically expressed as the spectrum of the reflection coefficient sequence.

[0074] In one embodiment, when processing based on existing methods, it is generally assumed that the spectrum of the seismic wavelet is known. Then, the spectrum of the seismic record can be divided by the spectrum of the seismic wavelet to obtain the spectrum of the reflection coefficient sequence. Combined with discrete Fourier transform, the following formula for inverting the reflection coefficient in the frequency domain is obtained:

[0075]

[0076] in, Based on the layered medium assumption, the reflection coefficient sequence is sparse. Combining with equation (3), we can see that r is also sparse in the Fourier basis.

[0077] Considering that the reflection coefficient sequence is essentially a continuous-time signal, only when N→∞ can equation (3) accurately express the relationship between the reflection coefficient sequence and its spectrum. In this case, equation (3) can be expressed as:

[0078] R=ψ1θ ψ1∈C N×N (4)

[0079] Here, ψ1 can be specifically expressed as an exact Fourier basis, and θ can be specifically expressed as a true reflection coefficient sequence. However, in actual processing, the value of N cannot be infinitely large, that is, the inversion grid cannot be infinitely small, so basis mismatch is bound to occur. Therefore, equation (3) can be expressed as:

[0080] R=ψ0x ψ0∈C N×N (5)

[0081] Where ψ0 is the DFT basis under conventional discretization, and x is the reflection coefficient sequence reconstructed based on ψ0. In this case, it is impossible to make each reflection position fall precisely on the grid points divided by ψ0. Therefore, the obtained x often contains a large error. Combining equations (4) and (5), we can obtain the following equation:

[0082] x=ψθ, (6)

[0083] in, ψ specifically represents the degree of mismatch between ψ0 and ψ1. If ψ0 = ψ1, then ψ = I, meaning θ = x, and there is no basis mismatch. If ψ0 ≠ ψ1, then let ψ = I + E, where I is the identity matrix and E is the perturbation term.

[0084] Based on the above formula, it can be seen that when all the reflection coefficients are located on the preset grid points, the commonly used seismic inversion method using the principle of compressed sensing can achieve accurate sparse inversion. However, under normal circumstances, the actual position of the reflection coefficient often deviates from the preset grid points, resulting in a basis mismatch problem, which causes the inversion results to be affected by the basis mismatch and have errors.

[0085] In one embodiment, based on the method provided in this specification, the reflection coefficient sequence r can be expressed as follows based on the above-mentioned seismic wavelet convolution model and the layered medium assumption:

[0086]

[0087] Among them, N can be specifically expressed as the number of seismic signal sampling points (time domain sampling points), a j Specifically, it can be expressed as the amplitude of the reflection coefficient at the sampling point numbered j (i.e., the reflection amplitude), t j Specifically, it is represented by the time position of the reflection coefficient at the sampling point numbered j (i.e., the reflection time), and δ can be specifically represented as a pulse function. According to the Fourier transform, equation (7) can be converted into the following form:

[0088]

[0089] Among them, j can be specifically represented as the number of the time domain sampling point, a jSpecifically, it can be expressed as the reflection amplitude of the time domain sampling point numbered j, t j Specifically, it can be expressed as the reflection time of the reflection coefficient at the time domain sampling point numbered j.

[0090] It should be added that, based on the layered medium assumption, the reflection coefficient of the stratum can be considered to be sparse, and the convolution model can be regarded as a sparse representation model of the seismic record, and the sparsity constraint of the reflection coefficient can be used to perform seismic inversion.

[0091] Combined with the above formula, in order to recover a wide-band sparse pulse reflection coefficient sequence from low-frequency seismic records, the spectral data of the reflection coefficient in the post-stack seismic data can be used to establish an optimization solution problem for the reflection coefficient in the sense of minimizing the L1 norm, and the first objective function of the seismic reflection coefficient of the target area can be obtained from the construction.

[0092] In one embodiment, the first objective function for the seismic reflection coefficient of the target area is constructed based on the post-stack seismic data and the seismic wavelet convolution model. In a specific implementation, the first objective function can be constructed according to the following formula:

[0093] min||x||1 based on y=Fx (9)

[0094] Among them, x can be expressed as the amplitude data of the reflection coefficient, which can be specifically expressed as x=[a0 a1 … a N-1 ] T , y can be expressed as the spectrum data of the reflection coefficient, specifically y = [R(0) R(1) … R(N-1)] T , T represents transpose, F can be specifically expressed as the Fourier transform matrix, and ||.||1 can be specifically expressed as solving the norm.

[0095] In one embodiment, when specifically processing the above-mentioned first objective function, considering that solving the first objective function in a norm with an absolute value operator is a highly nonlinear convex optimization problem, the above-mentioned optimal value problem of solving the first objective function can be first converted into a corresponding dual problem. Specifically, the corresponding dual approximate function (or dual approximate equation) can be constructed as the second objective function based on the first objective function. Then, by processing the above-mentioned second objective function, the dual problem is processed to obtain the required data results, avoiding the direct solution of the first objective function, thereby avoiding the derivation of the absolute value operator, reducing the error of the solution process, and more efficiently obtaining a more accurate solution result.

[0096] In one embodiment, based on the first objective function, a corresponding dual approximation function is constructed as the second objective function. In specific implementation, the second objective function can be constructed according to the following formula:

[0097] max Re<y,c> , based on ||F * c|| ∞ ≤1 (10)

[0098] Among them, c can be specifically expressed as a target coefficient, which can be a target coefficient vector, Re<y,c> Specifically, it can be expressed as the calculation of the real part after the inner product of the complex vector. F can be specifically expressed as the Fourier matrix, * represents conjugate, ||F * c|| ∞ ≤1 is the constraint condition. The inner product of the above complex vector can be expressed as:

[0099] The above constraint function can be expressed as:

[0100]

[0101] Among them, k can be specifically expressed as the number of the frequency domain sampling point, f c Specifically, it can be expressed as high cutoff frequency.

[0102] The above processing is based on the consideration that the l-norm in equation (9) contains an absolute value operator and cannot usually be directly differentiated. It is also noted that the problem of solving the l-norm minimization problem in equation (9) can be regarded as a highly nonlinear optimization problem, and therefore can be solved using semidefinite programming theory. If it is to be solved using semidefinite programming theory, it is necessary to first transition to its dual function. Through the above processing, the original problem of solving the l-norm minimum value of x in the first objective function can be converted into solving the maximum value problem in the dual approximate function (i.e., equation (10)).

[0103] In one embodiment, in the process of processing the above-mentioned second objective function, in order to avoid the basis mismatch problem caused by using a discrete sparse basis (for example, a Fourier basis, etc.) to discretize the sparse domain of the reflection coefficient, a preset processing method based on semidefinite programming theory can be selected to process the second objective function to determine the reflection time, thereby avoiding errors caused by the basis mismatch problem during the processing process.

[0104] In one embodiment, a problem of finding the minimum (maximum) value of a linear function of a set of variables that may be subject to linear inequalities, linear symmetric matrix inequalities, and semidefinite constraints may be referred to as a semidefinite programming problem.

[0105] In one embodiment, the above-mentioned processing of the second objective function by a preset processing method based on semidefinite programming theory to determine the reflection time may include the following steps during specific implementation:

[0106] S1: Obtain and use the Hermite matrix to convert the second objective function into a function based on semidefinite programming theory as the third objective function;

[0107] S2: Determine the reflection time according to the third objective function.

[0108] In one embodiment, based on the semidefinite programming theory, when solving the second objective function (10), the following theorem (Candès and Fernandez-Granda, 2014) is often used: a trigonometric polynomial With 1 as the boundary, There is only one Hermite matrix The following relations are satisfied:

[0109]

[0110] Among them, since the semi-positive constraint is equivalent to Q-cc * ≥0, so the following formula exists:

[0111] z * Qz≥|c * z| 2 (13)

[0112] Among them, Z* can be specifically expressed as the conjugate transpose of Z.

[0113] Based on the above theorem, let z k =e i2πkt , where t can be expressed as the reflection time. From formula (12), the following relationship can be obtained:

[0114] z * Qz=1,|c * z| 2 =|(F * c)(t)| 2 (14)

[0115] Therefore, the following constraints can be obtained:

[0116] 1≥|(F * c)(t)| 2 (15)

[0117] The above constraints show that F * c is uniformly bounded. Therefore, we can introduce and utilize the Hermite matrix to transform the second objective function into a function based on semidefinite programming theory, obtaining the third objective function. Furthermore, the dual problem regarding the second objective function can be further transformed into a semidefinite programming problem regarding the third objective function.

[0118] In one embodiment, the above-mentioned acquisition and use of the Hermite matrix to convert the second objective function into a function based on semidefinite programming theory as the third objective function may include: constructing the following formula as the third objective function:

[0119] based on

[0120] Where Q is the Hermite matrix, c is the target coefficient, i is the row number of the matrix, j is the column number of the matrix, and n is the size of the matrix.

[0121] In one embodiment, the third objective function may be solved to obtain a corresponding target coefficient; and then the corresponding reflection time may be calculated based on the target coefficient.

[0122] In one embodiment, in order to be able to further more accurately determine the reflection time, a regularization adjustment parameter regarding sparsity can be introduced to adaptively adjust the third objective function to obtain a fourth objective function that is more in line with the actual sparsity of the reflection coefficient of the target area. The fourth objective function can then be used to replace the third objective function to obtain a reflection time with relatively higher accuracy, thereby further reducing errors.

[0123] In one embodiment, after obtaining and utilizing the Hermite matrix to convert the second objective function into a function based on semidefinite programming theory as the third objective function, the specific implementation of the method may further include the following: determining the noise level based on the post-stack seismic data of the target area; determining a regularization adjustment parameter based on the noise level; constructing a fourth objective function based on the regularization adjustment parameter and the third objective function; and correspondingly, determining the reflection time based on the fourth objective function.

[0124] In specific implementation, the above noise level can be estimated through observation and other methods based on the post-stack seismic data of the target area.

[0125] In one embodiment, the above-mentioned regularization adjustment parameter is determined based on the noise level. When specifically implemented, it may include: when it is determined that the value of the noise level is large, the value of the regularization adjustment parameter can be set to a relatively large value to suppress redundant reflections and avoid false reflections caused by noise in the inversion result; when it is determined that the value of the noise level is small, the value of the regularization adjustment parameter can be set to a relatively small value to better retain the reflection coefficients of each layer, so as to obtain a fourth objective function that is more accurate and has a better effect than the third objective function.

[0126] In one embodiment, the fourth objective function is constructed based on the regularization adjustment parameter and the third objective function. In a specific implementation, the fourth objective function may include constructing the following formula as the fourth objective function:

[0127]

[0128] based on

[0129] Among them, λ can be specifically expressed as a regularization adjustment parameter.

[0130] Furthermore, the corresponding reflection time can be determined more accurately by using the fourth objective function instead of the third objective function used previously.

[0131] In one embodiment, the above-mentioned determination of the reflection time based on the fourth objective function may include the following contents during specific implementation: solving the fourth objective function to determine the target coefficient; calculating the intermediate parameter (which can be denoted as z) based on the target coefficient and the polynomial of the constraint function; and determining the reflection time based on the intermediate parameter.

[0132] In one embodiment, during implementation, the cvx package in Matlab can be used to solve the third or fourth objective function to calculate the target coefficient c. Of course, the above-mentioned methods for solving the third or fourth objective function are merely illustrative. During implementation, other suitable methods can be flexibly employed to solve for the target coefficient c, depending on the specific circumstances and accuracy requirements.

[0133] In one embodiment, when calculating the intermediate parameters, the target coefficient c obtained above can be first substituted into the polynomial of the constraint function shown below:

[0134]

[0135] Wherein, z can be specifically expressed as the intermediate parameter to be determined, and the polynomial of the above constraint function can be specifically obtained by transforming the equation (15), and the subscript n is equal to 2f c +1 (equivalent to the number of frequency sampling points, where f c is high cutoff frequency), in - Indicates conjugation.

[0136] Furthermore, the above equation (18) is solved to obtain the root value z of the trigonometric polynomial as the intermediate parameter. Since the modulus of z is 1, only the roots on the unit circle need to be considered.

[0137] Furthermore, the corresponding reflection time can be calculated according to the intermediate parameter z.

[0138] Substitute the above reflection time into equation (8) (which can be expressed as a characterization function of the reflection coefficient based on Fourier transform), that is, The equation (8) is solved to determine the corresponding reflection amplitude, thereby determining the required reflection coefficient.

[0139] In one embodiment, when solving equation (8) with the reflection time substituted in, the least squares method can be used to solve the problem, thereby more efficiently solving the corresponding reflection amplitude. Of course, the least squares method listed above is only an illustrative example. During implementation, other suitable solution processing methods can also be used to solve the reflection amplitude based on specific circumstances and accuracy requirements. This specification does not limit this.

[0140] In one embodiment, the above-mentioned determination of the seismic reflection coefficient of the target area based on the reflection time may include the following contents during specific implementation: substituting the reflection time into the characterization function of the reflection coefficient based on Fourier transform, and using the least squares method to solve the characterization function to obtain the corresponding reflection amplitude.

[0141] In one embodiment, after determining the seismic reflection coefficient of the target area according to the reflection time, the method may further include the following when implemented: guiding seismic exploration of the target area according to the seismic reflection coefficient of the target area.

[0142] In one embodiment, during the various stages of exploration and development of a target area, especially in the early stages of seismic exploration, available data is often relatively limited. For example, well logging data for the target area may not yet be available. In this case, the methods described herein can be used to process the acquired post-stack seismic data to obtain reflection coefficients with high accuracy, low error, and good resolution. These reflection coefficients can then be used to conduct preliminary seismic exploration of the target area, obtaining preliminary seismic exploration results. These preliminary seismic exploration results can then be used as a reference to guide further, more in-depth seismic exploration.

[0143] As can be seen from the above, the method for determining the seismic reflection coefficient provided in the embodiment of this specification, after constructing the first objective function of the seismic reflection coefficient of the target area based on the post-stack seismic data and the seismic wavelet convolution model, can first construct a dual approximate function corresponding to the above-mentioned first objective function as the second objective function, thereby converting the problem of directly solving the optimal value of the first objective function into the corresponding dual problem, avoiding the direct solution of the first objective function; then, the second objective function is processed by adopting a preset processing method based on the semidefinite programming theory to determine the reflection time, so that there is no need to discretize the sparse domain of the reflection coefficient, and the problem of basis mismatch can be effectively avoided, so that the reflection coefficient with higher precision can be accurately inverted, which solves the technical problems of large reflection time error and insufficient sparsity of the determined reflection coefficient in the existing method, resulting in low precision.

[0144] An embodiment of this specification also provides a server, including a processor and a memory for storing processor executable instructions. When the processor is implemented, it can perform the following steps according to the instructions: obtain post-stack seismic data of the target area; construct a first objective function about the seismic reflection coefficient of the target area based on the post-stack seismic data and the seismic wavelet convolution model; construct a corresponding dual approximation function as a second objective function based on the first objective function; process the second objective function through a preset processing method based on semidefinite programming theory to determine the reflection time; and determine the seismic reflection coefficient of the target area based on the reflection time.

[0145] In order to complete the above instructions more accurately, refer to Figure 2 As shown, the embodiment of this specification also provides another specific server, wherein the server includes a network communication port 201, a processor 202 and a memory 203, and the above structures are connected through internal cables so that each structure can perform specific data interaction.

[0146] The network communication port 201 can be used to obtain post-stack seismic data of a target area.

[0147] The processor 202 can be specifically used to construct a first objective function regarding the seismic reflection coefficient of the target area based on the post-stack seismic data and the seismic wavelet convolution model; construct a corresponding dual approximation function based on the first objective function as the second objective function; process the second objective function through a preset processing method based on semidefinite programming theory to determine the reflection time; and determine the seismic reflection coefficient of the target area based on the reflection time.

[0148] The memory 203 may be specifically used to store corresponding instruction programs.

[0149] In this embodiment, the network communication port 201 can be a virtual port that is bound to different communication protocols, thereby being capable of sending or receiving different data. For example, the network communication port can be a port responsible for web data communication, a port responsible for FTP data communication, or a port responsible for email data communication. Furthermore, the network communication port can also be a physical communication interface or communication chip. For example, it can be a wireless mobile network communication chip, such as GSM or CDMA; it can also be a Wi-Fi chip; or it can be a Bluetooth chip.

[0150] In this embodiment, the processor 202 may be implemented in any suitable manner. For example, the processor may take the form of a microprocessor or a processor and a computer-readable medium storing computer-readable program code (e.g., software or firmware) executable by the (micro)processor, a logic gate, a switch, an application-specific integrated circuit (ASIC), a programmable logic controller, an embedded microcontroller, etc. This specification is not intended to limit this.

[0151] In this embodiment, the memory 203 may include multiple levels. In a digital system, anything that can store binary data can be a memory. In an integrated circuit, a circuit with a storage function that has no physical form is also called a memory, such as RAM, FIFO, etc. In a system, a storage device with a physical form is also called a memory, such as a memory stick, TF card, etc.

[0152] An embodiment of this specification also provides a computer storage medium based on the above-mentioned method for determining the seismic reflection coefficient, wherein the computer storage medium stores computer program instructions, which, when executed, implement the following: obtaining post-stack seismic data of the target area; constructing a first objective function regarding the seismic reflection coefficient of the target area based on the post-stack seismic data and the seismic wavelet convolution model; constructing a corresponding dual approximate function as a second objective function based on the first objective function; processing the second objective function by a preset processing method based on semidefinite programming theory to determine the reflection time; and determining the seismic reflection coefficient of the target area based on the reflection time.

[0153] In this embodiment, the storage medium includes, but is not limited to, random access memory (RAM), read-only memory (ROM), cache, hard disk drive (HDD), or memory card. The memory can be used to store computer program instructions. The network communication unit can be an interface configured in accordance with the standards specified by the communication protocol for network connection communication.

[0154] In this embodiment, the functions and effects specifically implemented by the program instructions stored in the computer storage medium can be explained in comparison with other implementations and will not be repeated here.

[0155] See Figure 3 As shown, at the software level, the embodiments of this specification also provide a device for determining a seismic reflection coefficient, which may specifically include the following structural modules.

[0156] The acquisition module 301 may be used to obtain post-stack seismic data of a target area;

[0157] The first construction module 302 may be specifically configured to construct a first objective function of the seismic reflection coefficient of the target area based on the post-stack seismic data and the seismic wavelet convolution model;

[0158] The second construction module 303 may be specifically configured to construct a corresponding dual approximation function according to the first objective function as the second objective function;

[0159] The processing module 304 may be specifically configured to process the second objective function using a preset processing method based on semidefinite programming theory to determine the reflection time;

[0160] The determination module 305 may be specifically configured to determine a seismic reflection coefficient of a target area according to the reflection time.

[0161] In one embodiment, the processing module 304 may specifically include the following structural units:

[0162] The conversion unit can be specifically used to obtain and use the Hermite matrix to convert the second objective function into a function based on semidefinite programming theory as the third objective function;

[0163] The determining unit may be specifically configured to determine the reflection time according to the third objective function.

[0164] In one embodiment, when the processing module 304 is implemented, the following formula can be constructed as the third objective function:

[0165] based on

[0166] Where Q is the Hermite matrix, c is the target coefficient, i is the row number of the matrix, j is the column number of the matrix, and n is the size of the matrix.

[0167] In one embodiment, after obtaining and utilizing a Hermite matrix to convert the second objective function into a function based on semidefinite programming theory as the third objective function, the processing module 304 is further configured to determine a noise level based on post-stack seismic data of the target area; determine a regularization adjustment parameter based on the noise level; and construct a fourth objective function based on the regularization adjustment parameter and the third objective function. Accordingly, the determination module 305 may be configured to determine a reflection time based on the fourth objective function.

[0168] In one embodiment, the processing module 304 may further construct the following formula as a fourth objective function:

[0169]

[0170] based on

[0171] Among them, λ is the regularization adjustment parameter.

[0172] In one embodiment, when the determination module 305 is implemented, it can be used to solve the fourth objective function to determine the target coefficient; calculate the intermediate parameters based on the target coefficient and the polynomial of the constraint function; and determine the reflection time based on the intermediate parameters.

[0173] In one embodiment, when the above-mentioned determination module 305 determines the seismic reflection coefficient of the target area based on the reflection time, it can substitute the reflection time into the characterization function of the reflection coefficient based on Fourier transform, and use the least squares method to solve the characterization function to obtain the corresponding reflection amplitude, thereby determining the seismic reflection coefficient of the target area.

[0174] In one embodiment, the above-mentioned device may further include an exploration module, which, when implemented, may be used to perform preliminary seismic exploration of the target area based on the seismic reflection coefficient of the target area.

[0175] It should be noted that the units, devices or modules described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions. For the convenience of description, the above devices are described in terms of functions and are divided into various modules and described separately. Of course, when implementing this specification, the functions of each module can be implemented in the same or multiple software and / or hardware, or the module that implements the same function can be implemented by a combination of multiple sub-modules or sub-units. The device embodiments described above are merely schematic. For example, the division of the units is only a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0176] As can be seen from the above, the device for determining the seismic reflection coefficient provided in the embodiments of this specification does not need to discretize the sparse domain of the reflection coefficient, can effectively avoid the problem of basis mismatch, and thus can accurately invert to obtain a reflection coefficient with higher precision, solving the technical problems of large error and low precision in the determined reflection coefficient existing in the existing methods.

[0177] In a specific scenario example, the method for determining the seismic reflection coefficient provided in this specification can be used to perform an inversion test.

[0178] Typically, the basic idea for performing the above-mentioned inversion is to find the minimum value of the L1 norm of the reflection coefficient. For this nonlinear optimization problem, algorithms such as basis pursuit and matching pursuit, commonly used in sparse inversion, typically transform the problem into a linear programming problem for solution. The method for determining seismic reflection coefficients provided in this specification allows for the application of semidefinite programming theory to the field of seismic sparse inversion. When solving the sparse constraint problem of L1 norm minimization, the corresponding semidefinite programming problem is solved to avoid discretization of the sparse domain, thereby resolving the basis mismatch problem in sparse reflection coefficient inversion and obtaining more accurate inversion results.

[0179] For detailed processing procedures, please refer to Figure 4 The specific implementation may include the following process steps:

[0180] S1: establishing a reflection coefficient inversion objective equation (i.e., a first objective function) based on original data (e.g., post-stack seismic data) and a seismic wavelet convolution matrix (e.g., a seismic wavelet convolution model);

[0181] S2: List the dual equation and the corresponding approximate equation (i.e., the second objective function) according to the objective equation;

[0182] S3: Use the cvx program to solve the dual approximate equation (i.e., obtain the target coefficients);

[0183] S4: Calculate the solution of the polynomial of the reflection coefficient according to the solution of the equation to be solved, and obtain the reflection coefficient time (recorded as reflection time);

[0184] S5: Construct an accurate Fourier matrix based on the desired reflection time and use the least squares method to calculate the reflection coefficient amplitude.

[0185] In this scenario example, when implementing, you can select two-dimensional layered models (see Figure 5 As shown), and the actual 3D data volume of size 201*201*251 (see Figure 9 As shown in Figure 2, this method is used to perform reflection coefficient inversion test. Figure 5 The two-dimensional layered model in the above example can specifically adopt a two-dimensional sparse reflection coefficient model with a wedge-shaped structure, and make the reflection coefficient randomly distributed. Figure 5 、 Figure 6 、 Figure 7 、 Figure 8 The CDP (Common Depth Point) in the diagram represents a CDP gather, that is, the corresponding recording tracks with a common depth reflection point constitute a common depth point (or common reflection point) gather.

[0186] in, Figure 6 The two-dimensional seismic records shown in can be understood as Figure 5 Synthetic seismic records obtained by convolving the 2D layered model in with a 30 Hz Ricker wavelet and adding 10% random noise.

[0187] In order to better compare the difference between this method and the existing method, we can first use the existing method to use the basis pursuit algorithm to Figure 5 The corresponding results can be obtained by inverting the two-dimensional layered model in Figure 7 shown.

[0188] At the same time, in the use of this method, according to the above process steps, through the semi-definite programming method Figure 5 The corresponding results can be obtained by inverting the two-dimensional layered model in Figure 8 shown.

[0189] Figure 9 The actual post-stack seismic data of a certain area are displayed. Figure 10 The seismic wavelet used in the inversion is shown. Figure 11 Specifically demonstrated the use of semidefinite programming method to invert Figure 9 The results are obtained from the post-stack seismic data in .

[0190] By comparison Figure 7 and Figure 8 From the presented content, we can see that although the inversion results obtained by the basis pursuit algorithm also show the stratigraphic framework of the original model, the results based on the semidefinite programming theory can obtain clearer reflection times and more accurate amplitudes, and maintain good lateral continuity and strong noise resistance.

[0191] according to Figure 11 The three-dimensional data inversion results shown can be seen: Figure 9 Thin layers that cannot be identified in the image can also be clearly shown in the image. Figure 11 The high-resolution profile shown effectively improves the resolution of the inversion. It can be seen that based on the method provided in this specification, the reflection coefficient profile obtained by semidefinite programming inversion is continuous, can reflect more stratigraphic information, and preserves the stratigraphic framework of the original seismic profile.

[0192] Through the above scenario examples, it is verified that the method for determining the seismic reflection coefficient provided in this specification does not require discretization of the sparse domain of the reflection coefficient, can effectively avoid the problem of basis mismatch, and thus can accurately invert to obtain a reflection coefficient with higher precision, solving the technical problems of large error and low precision in the determined reflection coefficient in the existing methods.

[0193] Although this specification provides the method operation steps as described in the embodiments or flow charts, more or fewer operation steps may be included based on conventional or non-creative means. The order of steps listed in the embodiments is only one way of executing the order of many steps and does not represent the only execution order. When the device or client product in practice is executed, it can be executed in sequence or in parallel according to the method shown in the embodiments or the drawings (for example, a parallel processor or a multi-threaded processing environment, or even a distributed data processing environment). The term "comprise", "include" or any other variant thereof is intended to cover non-exclusive inclusion, so that the process, method, product or device including a series of elements includes not only those elements, but also includes other elements that are not explicitly listed, or also includes elements inherent to such process, method, product or device. In the absence of more restrictions, it is not excluded that there are other identical or equivalent elements in the process, method, product or device including the elements. Words such as first and second are used to represent names and do not represent any particular order.

[0194] Those skilled in the art will also appreciate that, in addition to implementing the controller in pure computer-readable program code, it is entirely possible to implement the same functionality by logically programming the method steps in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, embedded microcontrollers, and the like. Therefore, such a controller can be considered a hardware component, and the devices included therein for implementing various functions can also be considered structures within the hardware component. Alternatively, the devices for implementing various functions can be considered both software modules implementing the method and structures within the hardware component.

[0195] This specification may be described in the general context of computer-executable instructions, such as program modules, executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, classes, and the like that perform specific tasks or implement specific abstract data types. This specification may also be practiced in distributed computing environments where tasks are performed by remote processing devices connected through a communications network. In a distributed computing environment, program modules may be located in both local and remote computer storage media, including storage devices.

[0196] Through the description of the above embodiments, it can be seen that those skilled in the art can clearly understand that this specification can be implemented by means of software plus the necessary general hardware platform. Based on this understanding, the technical solution of this specification can essentially be embodied in the form of a software product. This computer software product can be stored in a storage medium such as ROM / RAM, a magnetic disk, an optical disk, etc., and includes a number of instructions for enabling a computer device (which can be a personal computer, a mobile terminal, a server, or a network device, etc.) to execute the methods described in various embodiments or certain parts of the embodiments of this specification.

[0197] The various embodiments in this specification are described in a progressive manner. References to the common or similar parts of the various embodiments are sufficient. Each embodiment focuses on the differences from the other embodiments. This specification can be used in a variety of general-purpose or specialized computer system environments or configurations. For example, personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable electronic devices, network PCs, minicomputers, mainframe computers, and distributed computing environments that include any of the above systems or devices.

[0198] Although the present specification has been described through embodiments, those skilled in the art will appreciate that there are many modifications and variations to the present specification without departing from the spirit of the present specification. It is intended that the appended claims include these modifications and variations without departing from the spirit of the present specification.

Claims

1. A method for determining a seismic reflection coefficient, characterized in that: include: Acquire post-stack seismic data in the target area; constructing a first objective function of a seismic reflection coefficient of a target area based on the post-stack seismic data and the seismic wavelet convolution model; According to the first objective function, construct a corresponding dual approximate function as the second objective function; Processing the second objective function using a preset processing method based on semidefinite programming theory to determine a reflection time, including: obtaining and using a Hermite matrix to convert the second objective function into a function based on semidefinite programming theory as a third objective function; determining a noise level based on post-stack seismic data of a target area; determining a regularization adjustment parameter based on the noise level; constructing a fourth objective function based on the regularization adjustment parameter and the third objective function; and determining the reflection time based on the fourth objective function; The seismic reflection coefficient of the target area is determined according to the reflection time.

2. The method according to claim 1, characterized in that Obtain and use the Hermite matrix to convert the second objective function into a function based on semidefinite programming theory as the third objective function, including: constructing the following formula as the third objective function: based on Where Q is the Hermite matrix, c is the target coefficient, i is the row number of the matrix, j is the column number of the matrix, and n is the size of the matrix.

3. The method according to claim 1, characterized in that Constructing a fourth objective function according to the regularization adjustment parameter and the third objective function includes: constructing the following formula as the fourth objective function: based on Among them, λ is the regularization adjustment parameter.

4. The method according to claim 3, characterized in that Determining the reflection time according to the fourth objective function includes: Solving the fourth objective function to determine the target coefficient; Calculating intermediate parameters according to the target coefficient and the polynomial of the constraint function; The reflection time is determined according to the intermediate parameter.

5. The method according to claim 1, wherein Determining the seismic reflection coefficient of the target area based on the reflection time includes: The reflection time is substituted into a characterization function of a reflection coefficient based on Fourier transform, and the characterization function is solved using a least squares method to obtain a corresponding reflection amplitude.

6. The method according to claim 1, characterized in that After determining the seismic reflection coefficient of the target area according to the reflection time, the method further includes: According to the seismic reflection coefficient of the target area, seismic exploration of the target area is guided.

7. A device for determining seismic reflection coefficient, characterized in that: include: Acquisition module, used to obtain post-stack seismic data of the target area; A first construction module is configured to construct a first objective function of a seismic reflection coefficient of a target area based on the post-stack seismic data and the seismic wavelet convolution model; A second construction module is used to construct a corresponding dual approximation function according to the first objective function as a second objective function; a processing module, configured to process the second objective function by a preset processing method based on semidefinite programming theory to determine a reflection time; a determination module, configured to determine a seismic reflection coefficient of a target area according to the reflection time; The processing module is specifically configured to: obtain and utilize a Hermite matrix to convert the second objective function into a function based on semidefinite programming theory as a third objective function; determine a noise level based on post-stack seismic data of a target area; A regularization adjustment parameter is determined according to the noise level; a fourth objective function is constructed according to the regularization adjustment parameter and the third objective function; and a reflection time is determined according to the fourth objective function.

8. A server, characterized in that: The method comprises a processor and a memory for storing processor-executable instructions, wherein the processor implements the steps of the method according to any one of claims 1 to 6 when executing the instructions.

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