A reweighted inverse arc tangent total variation constrained wave impedance inversion method

Abstract

The present application belongs to the field of seismic data processing and oil and gas exploration technology, and proposes a heavy weighted inverse tangent total variation constraint wave impedance inversion method. In view of the problems of false layer phenomenon, insufficient lateral continuity and easy to fall into local optimal solution in wave impedance inversion of traditional L1 norm and Lp quasi-norm constraint method, the method innovatively introduces heavy weighted inverse tangent total variation constraint, and combines with alternating direction multiplier method (ADMM) and Sylvester equation solution, effectively reduces the generation of false layer by dynamically adjusting the weight matrix, significantly improves the lateral continuity and overall accuracy of the inversion result. In addition, the method also has the advantages of high calculation efficiency and strong stability. In oil and gas exploration, the method can provide more accurate and reliable wave impedance model, greatly enhances the identification ability of oil and gas reservoir, is suitable for the field of seismic data processing and oil and gas resource development, and has important practical application value for improving the efficiency and accuracy of oil and gas exploration.

Description

TECHNICAL FIELD

[0001] The present application relates to seismic wave impedance inversion, belongs to the technical field of oil and gas exploration and seismic inversion, and provides a wave impedance inversion method based on reweighted inverse tangent total variation constraint. BACKGROUND

[0002] Seismic wave impedance inversion uses the mathematical and physical relationship between post-stack seismic records and wave impedance to establish a mathematical model, and uses an optimization method to solve the mathematical model to obtain seismic wave impedance from seismic records, and is an important means of oil and gas exploration. Seismic wave impedance inversion based on sparse constraint is an important method of seismic wave impedance inversion. It introduces sparse constraint as prior information into the forward model, and successfully improves the accuracy of the inversion result.

[0003] Seismic wave impedance inversion based on L1 norm constraint is an important method of seismic wave impedance inversion based on sparse constraint. This method uses L1 norm as a constraint term to construct a forward model, and iteratively solves the optimization problem formed by the forward model by using an optimization method, and finally obtains the wave impedance inversion result. Li et al. first introduced anisotropic total variation regularization based on L1 norm into wave impedance inversion, and proved that this method can improve the inversion accuracy. He et al. used weighted L1 norm constraint for single-channel wave impedance inversion, and used the alternating direction multiplier method to solve it, and proved the feasibility of this method in seismic wave impedance inversion. However, L1 norm cannot completely exploit sparsity and cannot reflect the relationship between channels, resulting in false layers in the inversion result and poor lateral continuity, thereby reducing the accuracy. Wu et al. combined fractional difference with ATpV to use fractional anisotropic total variation method to solve the problem of false layers and poor lateral continuity of the inversion result caused by L1 norm, but the inversion method based on Lp quasi-norm will fall into local optimum in the solving process, resulting in poor recovery near the pinch point and thin layer, thereby reducing the inversion accuracy, so an inversion method is needed to overcome the above problems. SUMMARY

[0004] The present application aims to solve the problems of existing seismic wave impedance inversion methods based on L1 norm and Lp quasi-norm constraint, such as false layers in the inversion result, poor lateral continuity, and easy to fall into local optimum, thereby improving the accuracy of wave impedance inversion.

[0005] In order to achieve the above-mentioned purpose, the following technical means are adopted in the present application:

[0006] The present application provides a wave impedance inversion method based on reweighted inverse tangent total variation constraint, comprising the following steps:

[0007] Step 1: Preprocess multi-channel seismic data and obtain an initial model profile of wave impedance, wherein the seismic data includes seismic records, well logging data and horizon information;

[0008] Step 2: calculate the initial log wave impedance according to the initial model profile of wave impedance, initialize the reweighting matrix, and establish the seismic wave impedance forward model based on the reweighting arctangent total variation constraint;

[0009] Step 3: input the initial matrix of Lagrange multiplier term and the initial matrix of its dual term, update the initial log wave impedance, the initial matrix of Lagrange multiplier term and the initial matrix of its dual term by combining the alternating direction multiplier method and the Sylvester equation and the seismic wave impedance forward model constrained by the arctangent total variation, and obtain the updated log wave impedance;

[0010] Step 4: judge whether the values of the initial log wave impedance before and after updating meet the condition, if yes, take the updated log wave impedance, the Lagrange multiplier term and the dual term as the initial values, and go to step 3, otherwise, perform exponential operation on the updated log wave impedance to obtain the inversion result of wave impedance.

[0011] The step 1 in the above scheme comprises the following steps:

[0012] Step 1.1: extract the post-stack seismic record, well logging data and horizon information from multi-channel seismic data, and perform low-pass filtering processing on the well logging data to obtain the initial model profile of the parameter to be inverted, i.e. the initial model profile of wave impedance.

[0013] The step 2 in the above scheme comprises the following steps:

[0014] Step 2.1: obtain the initial log wave impedance L0 based on the initial model profile of wave impedance and the logarithmic operation formula, and the logarithmic operation formula is:

[0015] L = ln(Z) (1)

[0016] Wherein, Z represents wave impedance, Z0 is the initial wave impedance for solving the initial log wave impedance L0, L represents the log wave impedance matrix, and ln represents the natural logarithm operation.

[0017] Step 2.2: construct the log wave impedance longitudinal difference L v and the log wave impedance transverse difference L x by using the longitudinal difference matrix D y and the transverse difference matrix D x of the difference matrix D, and construct the reweighting arctangent total variation constraint term based on the log wave impedance longitudinal difference L y and the log wave impedance transverse difference L x , and the formula is:

[0018] L y = D​​y L (2)

[0019] L x =LD x (3)

[0020] Vertical difference matrix D y The expression is as follows:

[0021]

[0022] Where m represents the number of sampling points per channel of the logarithmic wave impedance;

[0023] lateral difference matrix D x The expression is as follows:

[0024]

[0025] Where t represents the number of channels in the logarithmic impedance profile;

[0026] The reweighted arctangent total variation constraint term is:

[0027]

[0028] Where 'a' is a given arctangent total variation parameter, determining the sparsity of the arctangent total variation, and L... x (i) represents the transverse differential impedance L x The i-th path number, L y (j) represents the longitudinal differential impedance L of the wavelet. y The j-th path number, where M x With M y The reweighted matrix controls the regularization coefficients for updating the horizontal and vertical difference terms, with an initial value of 1. The update formula is as follows:

[0029]

[0030] ∈ is a constant used to prevent division by zero errors;

[0031] Step 2.3: Based on the given arctangent total variation parameters a, sparse constraint weighting coefficients μ, initial model profile weighting coefficients ω, and convolution matrix W, construct a seismic impedance forward model based on reweighted arctangent total variation constraints:

[0032]

[0033] Among them, ||*|| F Represents the Frobenius norm, matrix is referred to as a set of all log wave impedance L that makes the function J(L) obtain its minimum value, WDL refers to multiplication of the convolution matrix W, the difference matrix D and the log wave impedance matrix L, the meaning of ψ(*) is a reweighted arctangent total variation constraint term, the meaning of S0 is actual seismic data;

[0034] The convolution matrix W is expressed as:

[0035]

[0036] wherein w q represents the qth sampling point of the seismic wavelet, and m represents the sampling point number of the log wave impedance single trace;

[0037] Step 2.4: introducing a Lagrange multiplier term R x , R y and a dual term C x , C y based on the seismic wave impedance forward model to obtain a seismic wave impedance inversion objective function based on a reweighted arctangent total variation constraint:

[0038]

[0039] wherein a represents an arctangent total variation parameter, λ is a dual term weight coefficient, R x (i) represents a Lagrange multiplier term of the ith log wave impedance profile, R y (j) represents a Lagrange multiplier term of the jth sampling point of the log wave impedance single trace, and S0 represents actual seismic records.

[0040] In the above scheme, the step 3 comprises the following steps:

[0041] Step 3.1: taking an initial log wave impedance L0 as an initial model profile L 1 , introducing a Lagrange multiplier term initial matrix and a dual term initial matrix wherein, represents a Lagrange multiplier term of the initialized ith log wave impedance profile, represents a Lagrange multiplier term of the initialized jth sampling point of the log wave impedance single trace, represents a dual term of the initialized ith log wave impedance profile, represents a dual term of the initialized jth sampling point of the log wave impedance single trace;

[0042] Step 3.2: based on step 3.1, using an alternating direction multiplier algorithm and a Sylvester equation solving method to solve the objective function to obtain a wave impedance log L* updating formula and update the wave impedance log L*, the formula is as follows:

[0043]

[0044] where vec denotes a matrix vectorization operator, E n denotes an n x n identity matrix, and T denotes the transpose of a matrix, denotes a Kronecker product, and matrices A, B, and C are expressed as:

[0045]

[0046] where E m-1 denotes an (m-1) x (m-1) identity matrix, and λ is a dual weight coefficient.

[0047] In the above scheme, step 4 is to determine whether the values of the initial log impedance before and after updating satisfy the condition ||L * -L 1 ||2 / ||L * ||2>tol, where tol is a given error term value, if yes, the updated log impedance, Lagrange multiplier term and the dual term are taken as initial values, and step 3 is entered, otherwise, the inversion result Z r of the impedance is obtained by performing an exponential operation based on the updated log impedance, and step 2 is entered.

[0048] Z f = exp(L*) (16)

[0049] where exp denotes an exponential operator.

[0050] In the above scheme, the steps for updating the Lagrange multiplier term and the dual term are as follows:

[0051] The log impedance horizontal difference 1 and the log impedance vertical difference of L are calculated, and the Lagrange multiplier term is updated according to the alternating direction multiplier method and the soft threshold method, and the calculation formula is as follows:

[0052]

[0053]

[0054] is a constant for preventing division by zero error, and sign denotes a sign function, and the expression is as follows:

[0055]

[0056] Based on the wave impedance logarithm L* and the updated Lagrange multiplier term Updating the dual term according to the alternating direction multiplier method The calculation formula is as follows:

[0057] .

[0058] Because the present application adopts the above technical means, it has the following beneficial effects:

[0059] First, the present application adopts the heavy weighted inverse tangent total variation constraint, combined with the alternating direction multiplier method (ADMM) and the Sylvester equation solution. It solves the technical problem that the sparse constraint based on the L1 norm and the Lp quasi-norm in the existing technology is prone to produce false layers in the seismic wave impedance inversion, and the lateral continuity of the inversion result is poor, resulting in low inversion accuracy. By introducing the heavy weighted inverse tangent total variation constraint, the generation of false layers is effectively reduced, the lateral continuity of the inversion result is improved, and the accuracy of the wave impedance inversion is significantly improved.

[0060] Second, through the combination of the alternating direction multiplier method (ADMM) and the Sylvester equation solution, the technical problem that the existing inversion method is prone to fall into local optimum in the iteration process, resulting in the inability to obtain the global optimal inversion result is solved. The ADMM method can effectively decompose complex optimization problems, combined with the Sylvester equation solution, to ensure that a solution closer to the global optimum can be found in the inversion process, avoiding the trap of local optimum, thereby improving the reliability of the inversion result.

[0061] Third, by initializing the heavy weighted matrix and dynamically updating the weight according to the difference of the logarithmic wave impedance in the iteration process. It solves the technical problem that in the traditional sparse constraint method, the weight is usually fixed and cannot be adaptively adjusted, resulting in inaccurate inversion results. Dynamically updating the heavy weighted matrix enables the constraint term to adaptively adjust and better capture the sparse characteristics of the wave impedance, improving the precision and accuracy of the inversion.

[0062] Fourth, by introducing the Lagrange multiplier term and the dual term, and combining the soft threshold method to update these terms, the problem of difficult optimization of the constraint term in the inversion process is solved, achieving a better balance between regularization and data fitting.

[0063] Fifth, through the preprocessing of multi-channel seismic data and the construction of the initial model, the technical problem that the single-channel inversion method cannot fully utilize the information of multi-channel seismic data, resulting in poor lateral continuity and overall consistency of the inversion result is solved. Through the joint processing of multi-channel seismic data, the correlation between channels can be fully utilized, improving the lateral continuity and overall consistency of the inversion result, thereby improving the comprehensive quality of the inversion.

[0064] In summary, this invention effectively solves the problems of pseudo-layers, poor lateral continuity, and easy getting trapped in local optima in the wave impedance inversion of the prior art by means of reweighted arctangent total variational constraints, alternating direction multiplier method, solving Sylvester equation, dynamically updating the reweighted matrix, and introducing Lagrange multipliers and dual terms. It significantly improves the accuracy and reliability of the inversion results and has important application value. Attached Figure Description

[0065] Figure 1 This is a flowchart of the present invention;

[0066] Figure 2 This is a seismic profile in this invention, representing a post-stack seismic record;

[0067] Figure 3 This is a schematic diagram of the cross-section of the initial multichannel impedance model in this invention;

[0068] Figure 4 This is a schematic diagram of the multichannel impedance inversion results in this invention;

[0069] Figure 5 To extract the seismic single trace near the measured well for single-trace analysis. Detailed Implementation

[0070] The embodiments of the present invention will be described in detail below. Although the present invention will be described and illustrated in conjunction with some specific embodiments, it should be noted that the present invention is not limited to these embodiments. On the contrary, any modifications or equivalent substitutions made to the present invention should be covered within the scope of the claims of the present invention.

[0071] Furthermore, to better illustrate the present invention, numerous specific details are set forth in the following detailed embodiments. Those skilled in the art will understand that the present invention can be practiced without these specific details.

[0072] The following is combined Figures 1-5 The present invention will be described in detail below.

[0073] like Figure 1 As shown, a method for impedance inversion based on reweighted arctangent total variation constrained wave includes the following steps:

[0074] Step 1: Preprocess the multichannel seismic data and obtain the initial model profile of wave impedance. The seismic data includes seismic records, well logging data, and stratigraphic information.

[0075] Step 1.1: Extract post-stack seismic records, well logging data, and stratigraphic information from multichannel seismic data. Perform low-pass filtering on the well logging data to obtain the initial model profile of the parameters to be inverted, i.e., the initial model profile of wave impedance, as shown below.Figure 3 is shown.

[0076] Step 2: Calculate the initial log wave impedance according to the initial model profile of wave impedance, initialize the reweighting matrix, and establish the seismic wave impedance forward model based on the reweighting inverse tangent total variation constraint;

[0077] Step 2.1: Obtain the initial log wave impedance L0 based on the initial model profile of wave impedance and the logarithmic operation formula:

[0078] L = ln(Z) (1)

[0079] Wherein, Z represents wave impedance, Z0 is the initial wave impedance for solving the initial log wave impedance L0, L represents the log wave impedance, and ln represents the natural logarithm operation;

[0080] Step 2.2: Construct the log wave impedance longitudinal difference L y and the log wave impedance transverse difference L x based on the longitudinal difference matrix D y and the transverse difference matrix D x of the difference matrix D, and construct the reweighting inverse tangent total variation constraint term based on the log wave impedance longitudinal difference L y and the log wave impedance transverse difference L x , the formula is:

[0081] L y = D y L (2)

[0082] L x = LD x (3)

[0083] The expression of the longitudinal difference matrix D y is as follows:

[0084]

[0085] Wherein, m represents the sampling point number of the log wave impedance single trace;

[0086] The expression of the transverse difference matrix D x is as follows:

[0087]

[0088] Wherein, t represents the number of traces of the log wave impedance profile;

[0089] The reweighting inverse tangent total variation constraint term is:

[0090]

[0091] where atan denotes the inverse tangent function, a is a given inverse tangent total variation parameter, determines the sparsity degree of the inverse tangent total variation, L x (i) denotes the i-th trace of the lateral difference of the slowness impedance, L x y (j) denotes the j-th trace of the longitudinal difference of the slowness impedance, L y where M x and M y are the reweighting matrices, control the regularization coefficients of the lateral and longitudinal difference terms, and the initial values are 1, and the update formula is as follows:

[0092]

[0093] is a very small constant, the value of is 0.00045, which is used to prevent division by zero error.

[0094] Step 2.3: Based on the given inverse tangent total variation parameter a, the sparsity constraint weight coefficient μ, the weight coefficient ω of the initial model profile and the convolution matrix W, the seismic slowness impedance forward model based on the reweighting inverse tangent total variation constraint is constructed:

[0095]

[0096] where ||*|| F denotes the Frobenius norm, and the matrix F is the set of all pairs of slowness impedances L that make the function J(L) attain its minimum value, and WDL means the multiplication of the convolution matrix W, the difference matrix D and the slowness impedance matrix L.

[0097] The convolution matrix W is expressed as:

[0098]

[0099] where w q denotes the q-th sampling point of the seismic wavelet;

[0100] Step 2.4: Based on the seismic slowness impedance forward model, the Lagrange multiplier terms R x , R y and the dual terms C x , C y are introduced, and the seismic slowness impedance inversion objective function based on the reweighting inverse tangent total variation constraint is obtained:

[0101]

[0102] where λ is the weight coefficient of the dual term, R x (i) denotes the Lagrange multiplier term of the i-th trace of the slowness impedance profile, R y ​​(j) represents the Lagrange multiplier term of the jth sampling point of the log wave impedance single channel.

[0103] Step 3: input the initial matrix of the Lagrange multiplier term and the initial matrix of its dual term, update the initial log wave impedance, the initial matrix of the Lagrange multiplier term and the initial matrix of its dual term by combining the alternating direction multiplier method and the seismic wave impedance forward model of the Sylvester equation and the arctangent total variation constraint, and obtain the updated log wave impedance;

[0104] The specific steps are as follows:

[0105] Step 3.1: take the initial log wave impedance L0 as the initial model profile L 1 , introduce the initial matrix of the Lagrange multiplier term and the initial matrix of its dual term , wherein, represents the Lagrange multiplier term of the initialized i-th log wave impedance profile, represents the Lagrange multiplier term of the jth sampling point of the initialized log wave impedance single channel, represents the dual term of the initialized i-th log wave impedance profile, represents the dual term of the jth sampling point of the initialized log wave impedance single channel.

[0106] Step 3.2: based on step 3.1, use the alternating direction multiplier algorithm and the Sylvester equation solution method to solve the objective function to obtain the wave impedance log L* update formula and update the wave impedance log L*, the formula is as follows:

[0107]

[0108] Wherein, vec represents the matrix vectorization operator, E n represents an n*n unit matrix, T represents the transpose of the matrix, represents the Kronecker product, and the expressions of the matrices A, B and C are as follows:

[0109]

[0110] Wherein, E m-1 represents an (m-1)×(m-1) unit matrix.

[0111] Step 4: judge whether the values of the initial log wave impedance before and after updating meet the conditions, if yes, take the updated log wave impedance, the Lagrange multiplier term and the dual term as the initial values, and go to step 3, otherwise, perform exponential operation on the updated log wave impedance to obtain the inversion result of the wave impedance, as shown in Figure 4 .

[0112] The step 4 is to judge whether the values before and after the initial log wave impedance update satisfy the condition ||L * 1 ||2 / ||L * ||2>tol, wherein tol is a given error term value, if yes, the updated log wave impedance, Lagrange multiplier term and the dual term are taken as initial values, and step 3 is turned to, otherwise, the inversion result Z r of the wave impedance is obtained by performing exponential operation based on the updated log wave impedance.

[0113] Z r =exp(L * ) (16)

[0114] Wherein, exp represents an exponential operator.

[0115] The Lagrange multiplier term and the dual term are updated as follows:

[0116] The log wave impedance transverse difference 1 and the log wave impedance longitudinal difference of L are calculated, and the Lagrange multiplier term is updated according to the alternating direction multiplier method and the soft threshold method, and the calculation formula is as follows:

[0117]

[0118] ∈ is a very small constant, used to prevent division by zero error, and sign represents a sign function, and the expression is as follows:

[0119]

[0120] The wave impedance log L* and the updated Lagrange multiplier term are used to update the dual term according to the alternating direction multiplier algorithm, and the calculation formula is as follows:

[0121] .

[0122] The application also provides a seismic wave impedance inversion system based on log total variation sparse constraint, comprising:

[0123] A preprocessing module: pre-processes multi-channel seismic data and obtains an initial model profile of wave impedance, wherein the seismic data comprises seismic records, logging data and horizon information;

[0124] ​Seismic wave impedance forward model establishment module: Calculate the initial logarithmic wave impedance based on the initial model profile of wave impedance, initialize the reweighting matrix, and establish a seismic wave impedance forward model based on the reweighted arctangent total variation constraint.

[0125] Update module: Input the initial matrix of Lagrange multipliers and its dual initial matrix, and combine the alternating direction multiplier method with the Sylvester equation and the seismic impedance forward model with reweighted arctangent total variational constraints to update the initial logarithmic impedance, the initial matrix of Lagrange multipliers and its dual initial matrix, and obtain the updated logarithmic impedance.

[0126] Judgment Module: Determines whether the initial logarithmic wave impedance values ​​before and after the update meet the conditions. If so, it updates the logarithmic wave impedance and Lagrange multipliers. and dual terms As the initial value, proceed to step 3; otherwise, perform an exponential operation based on the updated logarithmic wave impedance to obtain the inversion result of the wave impedance.

[0127] Furthermore, the specific implementation steps of the preprocessing module are as follows:

[0128] Step 1.1: Extract post-stack seismic records, well logging data, and stratigraphic information from multichannel seismic data. Perform low-pass filtering on the well logging data to obtain the initial model profile of the parameters to be inverted, i.e., the initial model profile of wave impedance, as shown below. Figure 3 As shown.

[0129] Furthermore, the specific implementation steps of the seismic wave impedance forward model establishment module are as follows:

[0130] Step 2.1: Based on the initial model profile of the wave impedance and the logarithmic operation formula, obtain the initial logarithmic wave impedance L0. The logarithmic operation formula is as follows:

[0131] L=ln(Z) (1)

[0132] Where Z represents wave impedance, Z0 is the initial wave impedance for solving the initial logarithmic wave impedance L0, L represents the logarithmic wave impedance, and ln represents the natural logarithm operation.

[0133] Step 2.2: Using the vertical difference matrix D y Horizontal difference matrix D x Constructing the longitudinal differential L-axis of logarithmic wave impedance y And logarithmic wave impedance transverse differential L x And based on the logarithmic wave impedance longitudinal differential L y And logarithmic wave impedance transverse differential L x Construct the reweighted arctangent total variation constraint term, as shown in the formula:

[0134] Ly =D y L (2)

[0135] L x =LD x (3)

[0136] Vertical difference matrix D y The expression is as follows:

[0137]

[0138] Where m represents the number of sampling points per channel of the logarithmic wave impedance;

[0139] lateral difference matrix D x The expression is as follows:

[0140]

[0141] Where t represents the number of channels in the logarithmic impedance profile;

[0142] The reweighted arctangent total variation constraint term is:

[0143]

[0144] Where atan represents the arctangent function, a is a given arctangent total variation parameter that determines the sparsity of the arctangent total variation, and L... x (i) represents the transverse differential impedance L x The i-th path number, L y (j) represents the longitudinal differential impedance L of the wavelet. y The j-th path number, where M x With M y The reweighted matrix controls the regularization coefficients for updating the horizontal and vertical difference terms, with an initial value of 1. The update formula is as follows:

[0145]

[0146] ∈ is a very small constant used to prevent division by zero errors.

[0147] Step 2.3: Based on the given arctangent total variation parameters a, sparse constraint weighting coefficients μ, initial model profile weighting coefficients α, and convolution matrix W, construct a seismic impedance forward model based on reweighted arctangent total variation constraints:

[0148]

[0149] Among them, ||*|| F Represents the Frobenius norm, matrix is referred to as a set of all pairs of log wave impedance L that makes the function J(L) take its minimum value, WDL refers to multiplication of the convolution matrix W, the difference matrix D and the log wave impedance matrix L;

[0150] The convolution matrix W is expressed as:

[0151]

[0152] where w q represents the qth sampling point of the seismic wavelet;

[0153] Step 2.4: Introducing Lagrange multiplier term R x , R y and dual term C x , C y based on the seismic wave impedance forward model to obtain a seismic wave impedance inversion objective function based on reweighted arctangent total variation constraint:

[0154]

[0155] where λ is a dual term weight coefficient, R x (i) represents the Lagrange multiplier term of the i-th log wave impedance profile, R y (j) represents the Lagrange multiplier term of the jth sampling point of the log wave impedance single channel.

[0156] Further, the specific implementation steps of the updating module are:

[0157] Step 3.1: Taking the initial log wave impedance L0 as the initial model profile L 1 , introducing the Lagrange multiplier term initial matrix and its dual term initial matrix wherein, represents the Lagrange multiplier term of the i-th log wave impedance profile after initialization, represents the Lagrange multiplier term of the jth sampling point of the log wave impedance single channel after initialization, represents the dual term of the i-th log wave impedance profile after initialization, represents the dual term of the jth sampling point of the log wave impedance single channel after initialization;

[0158] Step 3.2: Based on step 3.1, the log wave impedance L* update formula is obtained by using the alternating direction multiplier algorithm and the Sylvester equation solving method to solve the objective function and updating the log wave impedance L*, the formula is as follows:

[0159]

[0160] wherein, vec represents a matrix vectorization operator, En Let T denote an n×n identity matrix, and let T denote the transpose of the matrix. The expression for the Kronecker product, matrices A, B, and C, is as follows:

[0161]

[0162] Among them, E m-1 This represents an identity matrix of size (m-1)×(m-1).

[0163] Judgment Module: Determines whether the initial logarithmic wave impedance values ​​before and after the update meet the conditions. If so, it updates the logarithmic wave impedance and Lagrange multipliers. and dual terms As the initial value, proceed to step 3; otherwise, perform an exponential operation based on the updated logarithmic wave impedance to obtain the inversion result of the wave impedance, such as... Figure 4 As shown.

[0164] Determine whether the initial logarithmic impedance values ​​before and after the update satisfy the condition ||L * -L 1 ||2 / ||L * ||2>tol, where tol is a given error term value. If so, the updated logarithmic wave impedance and Lagrange multipliers will be updated. and dual terms As the initial value, proceed to step 3; otherwise, perform an exponential operation based on the updated logarithmic wave impedance to obtain the wave impedance inversion result Z. r :

[0165] Z r =exp(L*) (16)

[0166] Here, exp represents the exponentiation operator.

[0167] Lagrange multiplier terms and dual terms The update steps are as follows:

[0168] Calculate L 1 logarithmic wave impedance transverse differential Logarithmic wave impedance longitudinal differential The Lagrange multipliers are updated based on the alternating direction multiplier method and the soft thresholding method. The calculation formula is as follows:

[0169]

[0170] ∈ is a very small constant used to prevent division by zero errors, and sign represents the sign function, expressed as:

[0171]

[0172] Based on the logarithm of wave impedance L* and the updated Lagrange multipliers Update the dual term according to the alternating direction multiplier algorithm. The calculation formula is as follows:

[0173] .

[0174] In summary, a seismic impedance inversion method based on reweighted arctangent total variational constraints is proposed for the impedance inversion of multi-channel seismic profiles (two-dimensional seismic data obtained from seismic data), such as... Figures 2-5 As shown, the horizontal axis represents the number of seismic traces (Distance / Trace), and the vertical axis represents the number of sampling points (Depth / Sampling point). The inversion results of the acoustic impedance profile better conform to the trend of the seismic record compared to the initial model, proving the correctness of the method. Meanwhile, Figure 4 The inversion results have very good continuity, such as Figure 5 As shown, True Model represents the theoretical model, Initial Model represents the initial model, and Inversion Results represent the inversion results. The inversion results are very close to the true wave impedance and do not cause pseudo-layer phenomena, further proving the correctness of the method. This invention replaces the L1 norm in the L1 norm sparse constraint with a reweighted arctangent total variational sparse constraint, and proposes a wave impedance inversion method based on the reweighted arctangent total variational constraint by combining the alternating direction multiplier method. The initial model is updated by the inversion method described above, and the optimal inversion result is output through repeated iterations. This invention solves the problems of pseudo-layers, poor lateral continuity, and easy getting trapped in local optima caused by the existing seismic wave impedance inversion methods based on L1 norm and Lp pseudo-norm constraints, thereby improving the accuracy of wave impedance inversion.

[0175] The above are merely representative embodiments among the many specific applications of this invention, and do not constitute any limitation on the scope of protection of this invention. All technical solutions formed by transformation or equivalent substitution fall within the scope of protection of this invention.

Claims

1. A method for impedance inversion based on reweighted arctangent total variational constraint wave impedance, characterized in that, Includes the following steps: Step 1: Preprocess the multichannel seismic data and obtain the initial model profile of wave impedance. The seismic data includes seismic records, well logging data, and stratigraphic information. Step 2: Calculate the initial logarithmic wave impedance based on the initial model profile of the wave impedance, initialize the reweighting matrix, and establish a forward model of seismic wave impedance based on the reweighted arctangent total variation constraint. The reweighted arctangent total variation constraint term is: This indicates the number of sampling points per channel of the logarithmic impedance. This indicates the number of channels in the logarithmic impedance profile. Represents logarithmic wave impedance. For a given total variation parameter of the arctangent, determine the sparsity of the total variation of the arctangent. Represents the transverse differential of logarithmic wave impedance The Tao number, Represents the longitudinal differential of logarithmic wave impedance The Tao number, and The reweighted matrix controls the regularization coefficients for updating the horizontal and vertical difference terms, with an initial value of 1. The update formula is as follows: It is a constant used to prevent division by zero errors; Seismic impedance inversion objective function based on reweighted arctangent total variation constraint: Given the initial logarithmic wave impedance, For convolution matrix, Difference matrix The vertical difference matrix, Difference matrix Horizontal difference matrix The meaning is the reweighted arctangent total variation constraint term. These are the sparse constraint weight coefficients. These are the weighting coefficients for the initial model profile. and This represents the dual term of the logarithmic wave impedance. These are the weight coefficients for the dual terms. Indicates the first Lagrange multipliers of the logarithmic wave impedance profile, The first channel of the logarithmic wave impedance represents the first channel of the logarithmic wave impedance. Lagrange multipliers at each sampling point Represents actual earthquake records; Step 3: Input the initial matrix of the Lagrange multipliers and its dual initial matrix, and update the initial logarithmic wave impedance, the initial matrix of the Lagrange multipliers and its dual initial matrix by combining the alternating direction multiplier method and the seismic wave impedance forward model with the Sylvester equation and the arctangent total variation constraint, so as to obtain the updated logarithmic wave impedance. Step 4: Determine whether the values ​​of the initial logarithmic wave impedance before and after the update meet the conditions. If so, update the logarithmic wave impedance and Lagrange multipliers. , and dual terms , As the initial value, proceed to step 3; otherwise, perform an exponential operation based on the updated logarithmic wave impedance to obtain the inversion result of the wave impedance.

2. The method for impedance inversion based on reweighted arctangent total variation constrained wave impedance according to claim 1, characterized in that: Step 1 includes the following steps: Step 1.1: Extract post-stack seismic records, well logging data, and stratigraphic information from multichannel seismic data, and perform low-pass filtering on the well logging data to obtain the initial model profile of the parameters to be inverted, i.e., the initial model profile of wave impedance.

3. The method for impedance inversion based on reweighted arctangent total variation constrained wave impedance according to claim 1, characterized in that: Step 2 includes the following steps: Step 2.1: Obtain the initial logarithmic wave impedance based on the initial model profile and logarithmic calculation formula of the wave impedance. The formula for logarithmic operations is: in, Indicates wave impedance, To solve for the initial logarithmic wave impedance The initial wave impedance, Represents the logarithmic wave impedance matrix. Represents the natural logarithm operation; Step 2.2: Using the difference matrix Longitudinal difference matrix Horizontal difference matrix Constructing a logarithmic wave impedance longitudinal differential And logarithmic wave impedance transverse differential And based on logarithmic wave impedance longitudinal differential And logarithmic wave impedance transverse differential Construct the reweighted arctangent total variation constraint term, as shown in the formula: Vertical difference matrix The expression is as follows: in, This indicates the number of sampling points per channel of the logarithmic impedance; lateral difference matrix The expression is as follows: in, This indicates the number of channels in the logarithmic impedance profile. The reweighted arctangent total variation constraint term is: in, For a given total variation parameter of the arctangent, determine the sparsity of the total variation of the arctangent. Represents the transverse differential of logarithmic wave impedance The Tao number, Represents the longitudinal differential of logarithmic wave impedance The The number of paths is among them, and The reweighted matrix controls the regularization coefficients for updating the horizontal and vertical difference terms, with an initial value of 1. The update formula is as follows: It is a constant used to prevent division by zero errors; Step 2.3: Based on the given arctangent total variation parameters Sparse constraint weight coefficients Weighting coefficients of the initial model profile and convolution matrix Construct a forward model of seismic wave impedance based on reweighted arctangent total variational constraints: in, Represents the Frobenius norm, matrix , This refers to making the function All logarithmic wave impedances that achieve their minimum value The set of WDLs, where WDL refers to convolutional matrices. Difference matrix Logarithmic wave impedance matrix Multiply, The meaning is the reweighted arctangent total variation constraint term. The meaning is actual earthquake data; Convolution matrix Represented as: in, This represents the q-th sampling point of the seismic wavelet. This indicates the number of sampling points per channel of the logarithmic impedance; Step 2.4: Introduce Lagrange multipliers based on the seismic wave impedance forward model. , and dual terms , The seismic wave impedance inversion objective function based on the reweighted arctangent total variation constraint is obtained as follows: in Represents the total variational parameter of the arctangent. These are the weight coefficients for the dual terms. Indicates the first Lagrange multipliers of the logarithmic wave impedance profile, The first channel of the logarithmic wave impedance represents the first channel of the logarithmic wave impedance. Lagrange multipliers at each sampling point This represents the actual earthquake record.

4. The method for impedance inversion based on reweighted arctangent total variation constrained wave impedance according to claim 3, characterized in that: Step 3 includes the following steps: Step 3.1: Set the initial logarithmic wave impedance As the initial model profile Introducing the initial matrix of Lagrange multipliers and its dual initial matrix ,in, Represents the first after initialization Lagrange multipliers of the logarithmic wave impedance profile, This represents the first channel of the initialized logarithmic wave impedance. Lagrange multipliers at each sampling point Represents the first after initialization The dual term of the logarithmic wave impedance profile, This represents the first channel of the initialized logarithmic wave impedance. The dual terms of each sampling point; Step 3.2: Based on Step 3.1, the objective function is solved using the alternating direction multiplier algorithm and the Sylvester equation solution method to obtain the logarithm of the wave impedance. Update the formula and update the logarithm of the wave impedance. The formula is as follows: in, Represents matrix vectorization operators. Indicates size is identity matrix Represents the transpose of a matrix. Represents the Kronecker product, a matrix , , The expression is: in, Indicates size is identity matrix These are the weight coefficients for the dual terms.

5. The method for impedance inversion based on reweighted arctangent total variation constrained wave impedance according to claim 4, characterized in that: Step 4 involves determining whether the values ​​of the initial logarithmic wave impedance before and after the update meet the conditions. ,in, Given the error term value, if so, the updated logarithmic wave impedance and Lagrange multipliers will be... , and dual terms , As the initial value, proceed to step 3; otherwise, perform an exponential operation based on the updated logarithmic wave impedance to obtain the inversion result of the wave impedance. : in, This represents the exponentiation operator.

6. The method for impedance inversion based on reweighted arctangent total variation constrained wave impedance according to claim 5, characterized in that: Lagrange multiplier terms , and dual terms , The update steps are as follows: calculate logarithmic wave impedance transverse differential Logarithmic wave impedance longitudinal differential The Lagrange multipliers are updated based on the alternating direction multiplier method and the soft thresholding method. , The calculation formula is as follows: `sign` is a constant used to prevent division by zero errors. `sign` represents the sign function, and its expression is: Based on the logarithm of wave impedance and the updated Lagrange multiplier terms , Update the dual terms according to the alternating direction multiplier algorithm. , The calculation formula is as follows: 。

Images