A Wave Impedance Inversion Method Based on Improved Bayesian Algorithm

Abstract

This application belongs to the field of geophysical exploration technology, and specifically discloses a wave impedance inversion method based on an improved Bayesian algorithm, including: obtaining the prestack seismic record and well log wave impedance data of the target area; performing time-depth conversion on the well log wave impedance data to obtain the actual wave impedance model and the low-frequency wave impedance model; introducing a randomly perturbed signal processed by Kalman filtering into the low-frequency wave impedance model to construct an initial wave impedance model; performing inversion based on the initial wave impedance model; sampling the inversion result using the posterior distribution sampling method to obtain an accepted initial wave impedance model; repeating the above steps to obtain a large number of posterior distribution samples; generating an inversion wave impedance profile based on the posterior distribution samples, and discussing and evaluating the inversion result. The inversion of this application has high precision, can obtain an inversion wave impedance profile with relatively high precision, and has good application prospects in improving inversion resolution and uncertainty analysis.

Description

Technical Field

[0001] This application relates to the field of geophysical exploration technology, and specifically relates to a wave impedance inversion method based on an improved Bayesian algorithm. Background Art

[0002] The Bayesian algorithm is an inversion method based on the principles of probability and statistics. It updates the prior probability according to the observed data and finally obtains the distribution of the posterior data through iteration. This method uses the likelihood function composed of prior information and observed data to form a constraint condition, integrates the forward calculation and the posterior distribution sampling method, infers the posterior probability distribution of the model parameters, and extracts statistical parameters for uncertainty analysis. The Bayesian formula can generally be expressed as:

[0003] ,

[0004] where, X represents the model parameters; D represents the observed data; represents the prior probability distribution of the model X , which is determined by prior information; represents the total probability model, which represents the occurrence probability of the observed data D ; represents the likelihood function, which represents the probability of obtaining the observed data X when the model D is known; represents the posterior probability, which represents the probability of the model parameters D appearing under the joint constraints of prior information and observed data when the observed data X is known.

[0005] In actual inversion, since is independent of the model parameters and only plays a role of regularization in inversion, it can be regarded as the normalization constant 1 / h , so that the sum of the integrals of the probability values over the entire region remains 1. In summary, the above formula can be rewritten as:

[0006] ,

[0007] According to the above formula, the prior distribution can be optimized and iterated through prior information and observed data, and finally the posterior distribution can be obtained by solving, which is also the basic principle of the Bayesian inversion method.

[0008] However, the traditional Bayesian wave impedance inversion method has problems such as excessive random noise components in the inversion initial model and insufficient constraint ability of the likelihood function in actual seismic data inversion, which affect the inversion effect.

[0009] Therefore, it is urgent to improve the Bayesian algorithm, use the improved Bayesian algorithm to improve the seismic data inversion effect, and conduct uncertainty analysis on it to evaluate the quality of the seismic data inversion results. Summary of the Invention

[0010] In view of this, the present application proposes a wave impedance inversion method based on an improved Bayesian algorithm, which can smoothly analyze and process seismic data and logging data, and finally obtain the true underground wave impedance information through Bayesian wave impedance inversion of various data.

[0011] In a first aspect, an embodiment of the present application provides a wave impedance inversion method based on an improved Bayesian algorithm, including:

[0012] S01, obtaining the pre-stack seismic record and logging wave impedance data of the target area;

[0013] S02, performing time-depth conversion on the logging wave impedance data to obtain an actual wave impedance model; obtaining a low-frequency wave impedance model corresponding to the target area based on the actual wave impedance model;

[0014] S03, introducing a randomly perturbed signal processed by Kalman filtering into the low-frequency wave impedance model to construct an initial wave impedance model;

[0015] S04, based on the initial wave impedance model, generating a prior probability distribution and a likelihood function for inversion to obtain a posterior distribution sample;

[0016] S05, using a posterior distribution sampling method to sample the posterior distribution sample to obtain an acceptable posterior distribution sample;

[0017] S06, repeating steps S03 - S05 until a large number of posterior distribution samples are obtained;

[0018] S07, extracting the posterior mean solution or the maximum a posteriori probability solution from the posterior distribution samples, generating an inversion wave impedance profile, and performing uncertainty analysis using the posterior standard deviation to discuss and evaluate the inversion results.

[0019] In a possible implementation manner, after obtaining the pre-stack seismic record and logging wave impedance data of the target area, a normal distribution test is performed on the logging wave impedance data to ensure that the data points are basically near the normal distribution reference line.

[0020] In a possible implementation manner, the performing time-depth conversion on the logging wave impedance data to obtain an actual wave impedance model is specifically: establishing a connection between the depth domain and the time domain, converting the logging wave impedance data in the depth domain to the time domain to obtain the wave impedance information in the time domain, and obtaining the actual wave impedance model. The calculation formula is:

[0021] ,

[0022] Among them, represents time; represents depth; represents the velocity information in the depth domain.

[0023] In a possible implementation manner, step S03 is specifically: generating a random perturbation, performing Kalman filtering on the random perturbation, storing the filtered value, and after completing the filtering process, obtaining the filtered perturbation. Then the initial wave impedance model is:

[0024] ,

[0025] Among them, represents the initial wave impedance model; represents the low-frequency wave impedance model; is a constant; represents the variance of the actual wave impedance model, represents the filtered perturbation.

[0026] In a possible implementation manner, the performing Kalman filtering on the random perturbation is specifically:

[0027] Step S321, establishing a state equation and an observation equation;

[0028] The state equation is:

[0029] ,

[0030] Among them, represents the state of the random perturbation data at time; represents the state transition matrix; represents the state of the random perturbation data at time; represents the control input matrix; represents the control input at time; represents the process noise at time;

[0031] The observation equation can be expressed as:

[0032] ,

[0033] Among them, represents the observation data at time, represents the observation matrix, represents the observation noise at time;

[0034] Step S322: Predict the current state and update the uncertainty of the state. The calculation formula is:

[0035] ,

[0036] ,

[0037] where, represents the predicted state at time represents the filtered disturbance at time represents the predicted covariance matrix at time represents the covariance of the process noise; represents the covariance matrix at time represents the transpose matrix of the state transition matrix ;

[0038] Step S323: Update the prediction result to obtain the filtered disturbance. The calculation formula is:

[0039] ,

[0040] ,

[0041] ,

[0042] where, represents the Kalman coefficient; represents the transpose matrix of the observation matrix ; represents the covariance of the observation noise; represents the control input at time represents the filtered disturbance at time represents the covariance matrix at time represents the identity matrix.

[0043] In a possible implementation, the likelihood function is:

[0044] ,

[0045] where, represents the likelihood function, represents the adjustment parameter, represents the observed data, represents the forward model data, represents the noise weighting operator, represents a matrix of the transposed matrix;

[0046] can be expressed as:

[0047] ,

[0048] wherein, represents extracting the elements in to create a diagonal matrix, represents the filtered perturbation.

[0049] In a possible implementation, calculate the energy difference corresponding to the initial wave impedance model parameters before and after iteration ;

[0050] If , then the posterior distribution sample is an acceptable posterior distribution sample;

[0051] If , then generate a first random number between 0 and 1 using a random function, and determine the initial acceptance rate whether it is greater than the first random number. If the initial acceptance rate is greater than the first random number, then the posterior distribution sample is an acceptable posterior distribution sample; if the initial acceptance rate is less than the first random number, then generate a second random number between 0 and 1 using the random function again, and determine the re - acceptance rate whether it is greater than the second random number. If the re - acceptance rate is greater than the second random number, then the posterior distribution sample is an acceptable posterior distribution sample. If the re - acceptance rate is less than the second random number, then the posterior distribution sample is an unacceptable posterior distribution sample;

[0052] Store the accepted posterior distribution samples and discard the unacceptable posterior distribution samples.

[0053] In a possible implementation, the calculation formula for the energy difference is:

[0054] ,

[0055] wherein, represents the energy after the th iteration of the initial wave impedance model; represents the energy after the th iteration of the initial wave impedance model, and the calculation formula is:

[0056]

[0057] Among them, represents a constant; represents the observed data; represents the forward modeling data after the th iteration of the model; represents the noise weighting operator; represents the matrix <> transpose matrix.

[0058] In a possible implementation manner, the initial acceptance rate is:

[0059] ,

[0060] Among them, is a constant;

[0061] The re-acceptance rate is:

[0062] ,

[0063] Among them, is a constant; represents the Pearson correlation coefficient between the synthetic seismic record and the actual seismic record.

[0064] S In a possible implementation manner, the Pearson correlation coefficient between the synthetic seismic record and the actual seismic record

[0065] ,

[0066] Among them, represents the data length of the synthetic seismic record; represents the forward modeling data of the model; represents the observed data.

[0067] Compared with the prior art, the present application has achieved the following remarkable technical effects.

[0068] (1) The present application performs Kalman filtering on the random perturbation components in the initial inversion wave impedance model. Compared with the prior art that simply attenuates the signals in a specific frequency range by using Butterworth filtering or Chebyshev filtering, the present application uses Kalman filtering based on Bayesian theory, combines observation and prediction, filters the signals, reduces the interference of random perturbation components to a certain extent, and constructs an initial impedance model that contains more effective information, making the constructed initial impedance model closer to the actual wave impedance model.

[0069] (2) Compared with the likelihood function in the traditional method that only considers the forward modeling data of the model and the actual seismic records Regarding the numerical relationship therebetween, the present application considers the influence of weighted error in the likelihood function and introduces a noise weighting operator so that the likelihood function can fully reflect the relationship between the data and the model.

[0070] (3) In the traditional Bayesian inversion method, when sampling the posterior distribution, the MH MCMC sampling is often used. The present application expands on this basis. When sampling the posterior distribution, a two-time acceptance-rejection strategy is introduced, thereby increasing the search range of the algorithm, achieving a more comprehensive exploration of the global probability space of the model parameters, and improving the accuracy of inversion. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0072] Figure 1 is a schematic flowchart of a wave impedance inversion method based on an improved Bayesian algorithm provided by an embodiment of the present application;

[0073] Figure 2 is the actual prestack seismic data provided by an embodiment of the present application;

[0074] Figure 3 is a schematic diagram of the normal distribution test of well logging wave impedance data provided by an embodiment of the present application;

[0075] Figure 4 is a schematic diagram of a low-frequency wave impedance model provided by an embodiment of the present application;

[0076] Figure 5 is an inversion wave impedance profile generated from the posterior mean solution provided by an embodiment of the present invention;

[0077] Figure 6 is an analysis curve of the uncertainty of the inversion result of the well-side trace provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0078] In order to better understand the technical solutions of the present application, the embodiments of the present application will be described in detail below with reference to the drawings.

[0079] It should be clear that the described embodiments are only some embodiments of the present application, rather than all embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present application without creative efforts belong to the scope of protection of the present application.

[0080] The terms used in the embodiments of the present application are for the purpose of describing specific embodiments only and are not intended to limit the present application. The singular forms "a", "the", and "said" used in the embodiments of the present application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.

[0081] It should be understood that the term "and / or" used herein is merely a description of the associated relationship of the associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist simultaneously, and B exists alone. In addition, the character " / " herein generally represents an "or" relationship between the associated objects before and after.

[0082] See Figure 1 , which is a schematic flow chart of a wave impedance inversion method based on an improved Bayesian algorithm provided by an embodiment of the present application. As Figure 1 shown, it mainly includes the following steps.

[0083] Step S01: Obtain the pre-stack seismic record and well logging wave impedance data of the target area, and perform a normal distribution test on the well logging wave impedance data to ensure that the data points are basically near the normal distribution reference line.

[0084] Preferably, the pre-stack seismic record and well logging wave impedance data of the target area are obtained through seismic exploration and well logging work.

[0085] It should be particularly noted that ensuring that the data points are basically near the normal distribution reference line is to verify the rationality and feasibility of applying the Bayesian algorithm to the target area.

[0086] See Figure 2 , which is the actual pre-stack seismic data provided by an embodiment of the present application. As Figure 2 shown, the part within the red dashed box is the inversion target area. The longitudinal time is from 1660 to 1960 ms, the time sampling interval is 4 ms, the number of samples per trace is 76, the trace interval is 25 m, and there are 31 traces in total. Among them, the trace adjacent to the well is the 1573rd trace; through spectral analysis, it can be known that the main frequency of this pre-stack seismic record is 33 Hz, and a Ricker wavelet with a main frequency of 33 Hz is selected in the inversion to generate a synthetic seismic record. See Figure 3 , which is a schematic diagram of the normal distribution test for the well logging wave impedance data provided by an embodiment of the present application. As Figure 3 shown, using time-depth conversion, the well logging wave impedance data in the depth domain is converted to the time domain and a normal distribution test is performed. It can be seen that except for a very few discrete points, the data is basically near the standard normal distribution curve ( Figure 3The red dashed line), that is, the method in this application is applicable to this target area.

[0087] Step S02: Perform time-depth conversion on the logging wave impedance data to obtain an actual wave impedance model; perform horizon interpolation, extrapolation, and smoothing on the wave impedance information corresponding to the time series in the actual wave impedance model, and integrate relevant information such as the position and morphology of the seismic reflection events in the prestack seismic record to obtain a low-frequency wave impedance model corresponding to the target area. See Figure 4 , which is a schematic diagram of the low-frequency wave impedance model provided by the embodiment of this application, as Figure 4 shown, the amplitude information in the prestack seismic record has been converted into wave impedance information. This model conforms to the basic trend of the prestack seismic record and contains the necessary information in the logging wave impedance data.

[0088] The performing of time-depth conversion on the logging wave impedance data to obtain an actual wave impedance model is specifically as follows: Establish a connection between the depth domain and the time domain, convert the logging wave impedance data in the depth domain to the time domain to obtain wave impedance information in the time domain, and obtain the actual wave impedance model. The calculation formula is:

[0089] ,

[0090] wherein, represents time; represents depth; represents the velocity information in the depth domain, which can be obtained through logging data or using empirical formulas, represents taking the reciprocal.

[0091] Step S03: Introduce a randomly perturbed signal that has been processed by Kalman filtering into the low-frequency wave impedance model to construct an initial wave impedance model. Specifically:

[0092] Step S31: Generate a random perturbation , , wherein, represents the number of data points of the random perturbation. Taking a model composed of 120 data points as an example, it can be expressed as: .

[0093] Step S32: Perform Kalman filtering on the random perturbation to obtain a filtered perturbation , then the initial wave impedance model is expressed as:

[0094] ,

[0095] wherein, represents the initial wave impedance model; Represents the low-frequency wave impedance model; Is a constant; Represents the variance of the actual wave impedance model, Represents the filtered perturbation.

[0096] Specifically, perform Kalman filtering on the said random perturbation, specifically:

[0097] Step S321, establish the state equation and the observation equation.

[0098] The said state equation is:

[0099] ,

[0100] Among them, Represents the random perturbation Data at Moment state; Represents the state transition matrix; Represents the random perturbation Data at Moment state; Represents the control input matrix; Represents Moment control input; Represents Moment process noise, which follows a normal distribution with an expectation of 0 and a covariance of Normal distribution.

[0101] The said observation equation can be expressed as:

[0102] ,

[0103] Among them, Represents Moment observation data, Represents the observation matrix, Represents Moment observation noise, which follows a normal distribution with an expectation of 0 and a covariance of Normal distribution.

[0104] Step S322, predict the current state and update the uncertainty of the state.

[0105] The calculation formula is:

[0106] ,

[0107] ,

[0108] Among them, Represents Moment predicted state; express The filtered disturbance at time ; express The forecast covariance matrix at time t; represents the covariance of process noise; express The covariance matrix at time t, Represents the state transition matrix The transposed matrix of .

[0109] Step S323: Update the prediction result and obtain the filtered disturbance The calculation formula is:

[0110] ,

[0111] ,

[0112] ,

[0113] in, represents the Kalman coefficient; Represents the observation matrix The transposed matrix of represents the covariance of the observation noise; express Control input at each moment; express The filtered disturbance at time ; express The covariance matrix of the time instant; Represents the identity matrix.

[0114] In the above process, the values of various parameters can be set specifically according to actual problems.

[0115] Step S04: Based on the initial wave impedance model, generate a prior probability distribution and a likelihood function to perform inversion to obtain a posterior distribution sample.

[0116] During inversion, the likelihood function is improved by introducing a noise weighting operator so that it can fully and accurately reflect the relationship between the data and the model. The calculation formula of the likelihood function is:

[0117] ,

[0118] in, represents the likelihood function, represents the adjustment parameter, represents the observation data, represents the model forward data, represents the noise weighting operator, Denote the matrix as the transposed matrix of.

[0119] It can be expressed as:

[0120] ,

[0121] where, denotes extracting the elements in to create a diagonal matrix, denotes the filtered perturbation.

[0122] Step S05, sample the posterior distribution samples using the posterior distribution sampling method to obtain acceptable posterior distribution samples. Specifically:

[0123] Step S51, when performing Bayesian inversion, define the energy after the th iteration of the initial wave impedance model as:

[0124] ,

[0125] where, denotes a constant; denotes the observed data; denotes the forward modeling data after the th iteration of the model; denotes the noise weighting operator; denotes the matrix as the transposed matrix of.

[0126] Denote the energy difference corresponding to the initial wave impedance model before and after iteration as , It can be expressed as:

[0127] ,

[0128] where, denotes the energy after the th iteration of the initial wave impedance model.

[0129] If , it indicates that the energy of the initial wave impedance model decreases after modification, then the posterior distribution sample is an acceptable posterior distribution sample;

[0130] If , then generate a first random number between 0 and 1 using a random function, and judge whether the initial acceptance rate is greater than the first random number. If the initial acceptance rate is greater than the first random number, then the posterior distribution sample is an acceptable posterior distribution sample; if the initial acceptance rate If it is less than the first random number, a second random number between 0 and 1 is generated again using a random function, and the re-acceptance rate is judged. Whether it is greater than the second random number. If the re-acceptance rate is greater than the second random number, the posterior distribution sample is an acceptable posterior distribution sample. If the re-acceptance rate is less than the second random number, the posterior distribution sample is an unacceptable posterior distribution sample.

[0131] Furthermore, in the initial acceptance-rejection strategy, the initial acceptance rate is:

[0132] ,

[0133] where is a constant;

[0134] Furthermore, in the secondary acceptance-rejection strategy, the re-acceptance rate is:

[0135] ,

[0136] where is a constant; represents the Pearson correlation coefficient between the synthetic seismic record and the prestack seismic record.

[0137] Furthermore, the formula for calculating the Pearson correlation coefficient between the synthetic seismic record and the prestack seismic record is:

[0138] ,

[0139] where represents the data length of the synthetic seismic record; represents the forward modeling data of the model, that is, the synthetic seismic record; represents the prestack seismic record, that is, the observed data.

[0140] The synthetic seismic record is generated by convolving the reflection coefficient obtained from the posterior distribution sample with the Ricker wavelet, and can be expressed as:

[0141] ,

[0142] where represents the forward modeling data of the model, that is, the synthetic seismic record; represents the data length of the synthetic seismic record; represents the Ricker wavelet; represents the data length of the Ricker wavelet; represents the reflection coefficient obtained from the posterior distribution sample; represents the data length of the reflection coefficient.

[0143] Ricker wavelet The expression in the time domain is:

[0144] ,

[0145] Ricker wavelet The expression in the frequency domain is:

[0146] ,

[0147] in, represents the time variable of the wavelet; represents the frequency variable of the wavelet; It indicates the dominant frequency of the Ricker wavelet and can be set or modified as appropriate based on the dominant frequency of the pre-stack record and other information.

[0148] Preferably, the Ricker wavelet in this embodiment is a Ricker wavelet with a main frequency of 33 Hz.

[0149] In step 52, the accepted posterior distribution samples are stored, and unacceptable posterior distribution samples are discarded.

[0150] Step S06: repeat steps S03-S05 until a large number of posterior distribution samples are obtained.

[0151] Step S07: extract the posterior mean solution or the maximum posterior probability solution from the posterior distribution samples, generate the inverted wave impedance profile, and use the posterior standard deviation to perform uncertainty analysis, and discuss and evaluate the inversion results.

[0152] In this embodiment, the posterior mean solution is extracted from the posterior distribution sample, and the variation trend between the posterior mean solution and the actual wave impedance model is observed to be the same, and their degree of agreement is compared. It is also observed whether the actual wave impedance model is basically within the 99% confidence interval of the posterior distribution sample. The 99% confidence interval is Within the range, Posterior standard deviation.

[0153] See also Figure 5 , which is the inversion wave impedance profile generated by the posterior mean solution provided by the embodiment of the present invention, such as Figure 5 As shown in the figure, the combined logging wave impedance curve is plotted near the well bypass. It can be seen that the trend between it and the well bypass wave impedance inversion result is basically the same. The inverted wave impedance profile is consistent with the logging wave impedance curve characteristics, with high resolution, and the inverted wave impedance profile shows good continuity and consistency in the horizontal direction. Therefore, it can be seen that the result is reasonable and reliable. In this embodiment, uncertainty analysis can be used to discuss and evaluate the inversion results, so as to better understand the quality of the inversion results. Figure 6, which is the uncertainty analysis curve of the inversion result of the well-side trace provided by the embodiment of the present invention. As Figure 6 shown, the inversion result of the 1573rd trace is generally less different from the well-log wave impedance curve as a whole. The fitting degree is high at the arrow-marked place, and the trends are consistent. Moreover, the values of most of the well-log wave impedance curves fall within 99% of the inversion result (i.e., within the interval, where is the posterior standard deviation). Thus, it can be determined that the inversion result is reasonable and reliable.

[0154] The present invention proposes a wave impedance inversion technology based on an improved Bayesian algorithm, which is an important method for analyzing and processing seismic data and well-log data. However, the constraint ability of the traditional Bayesian inversion algorithm is limited, which affects the inversion result to a certain extent. The present invention aims to further improve the inversion accuracy and improves the Bayesian wave impedance inversion algorithm. The main improvement points include: performing Kalman filtering on the random perturbation component in the initial inversion wave impedance model to make the constructed initial impedance closer to the actual wave impedance model; introducing a noise weighting operator in the likelihood function to strengthen the inversion constraint; expanding on the basis of the MH MCMC sampling in the traditional method, and introducing a two-time acceptance-rejection strategy when sampling the posterior distribution data, which expands the search space of the solution to a certain extent. To verify the effect, the algorithm is applied to actual seismic data, and an inversion wave impedance profile with high accuracy is obtained, revealing its good prospects in improving inversion resolution and uncertainty analysis.

[0155] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An impedance inversion method based on an improved Bayesian algorithm, characterized in that, Including: S01, obtaining the pre-stack seismic records and well log impedance data of the target area; S02, performing time-depth conversion on the well log impedance data to obtain the actual impedance model; obtaining the low-frequency impedance model corresponding to the target area based on the actual impedance model and the pre-stack seismic records; S03, introducing a randomly perturbed value processed by Kalman filtering into the low-frequency impedance model to construct an initial impedance model; S04, based on the initial impedance model, generating a prior probability distribution and a likelihood function for inversion to obtain a posterior distribution sample; the likelihood function is: p(D|X) ∝ exp[p_adjust(d obs -d syn ) T ·W·(d obs -d syn ))] Among them, p(D|X) represents the likelihood function, p_adjust represents the adjustment parameter, and d obs represents the observed data, and d syn represents the forward modeling data of the model. W represents the noise weighting operator, and (d obs -d syn ) T represents the transposed matrix of the matrix (d obs -d syn ); W can be expressed as: where diag means to extract the elements in to create a diagonal matrix, and filtered_disturbance means the filtered disturbance; S05, using the posterior distribution sampling method to sample the posterior distribution sample to obtain an acceptable posterior distribution sample; S06, repeating steps S03 - S05 until a large number of posterior distribution samples are obtained; S07, extracting the posterior mean solution or the maximum a posteriori probability solution from the posterior distribution samples, generating an inverted impedance profile, and performing uncertainty analysis using the posterior standard deviation to discuss and evaluate the inversion results.

2. The wave impedance inversion method based on an improved Bayesian algorithm according to claim 1, characterized in that After obtaining the pre-stack seismic records and well log impedance data of the target area, perform a normal distribution test on the well log impedance data to ensure that the data points are basically near the normal distribution reference line.

3. A wave impedance inversion method based on an improved Bayesian algorithm according to claim 1, characterized in that The performing time-depth conversion on the well log impedance data to obtain the actual impedance model is specifically: establishing a connection between the depth domain and the time domain, converting the well log impedance data in the depth domain to the time domain to obtain the impedance information in the time domain, and obtaining the actual impedance model. The calculation formula is: Where, T(y) represents time; y represents depth; V(y) represents the velocity information in the depth domain.

4. A wave impedance inversion method based on an improved Bayesian algorithm according to claim 1, characterized in that Step S03 is specifically: generating a random perturbation, performing Kalman filtering on the random perturbation, storing the filtered value. After completing the filtering process, obtaining the filtered perturbation filtered_disturbance, then the initial impedance model is: Where, c2 represents the initial impedance model; b represents the low-frequency impedance model; β2 is a constant; var(a) represents the variance of the actual impedance model, and filtered_disturbance represents the filtered perturbation.

5. The wave impedance inversion method based on the improved Bayesian algorithm according to claim 4, characterized in that The performing Kalman filtering on the random perturbation is specifically: Step S321, establishing a state equation and an observation equation; The state equation is: x i = Ax i-1 + Bu i-1 + w i-1 where, x i represents the state of the random disturbance data at time i; A represents the state transition matrix; x i-1 represents the state of the random disturbance data at time i - 1; B represents the control input matrix; u i-1 represents the control input at time i - 1; w i-1 represents the process noise at time i - 1; The observation equation can be expressed as: z i = Hx i + v i where Z i represents the observation data at time i, H represents the observation matrix, and v i represents the observation noise at time i; Step S322, predicting the current state and updating the uncertainty of the state. The calculation formula is: Among them, represents the predicted state at time i; represents the filtered disturbance at time i-1; represents the predicted covariance matrix at time i; Q represents the covariance of the process noise; P i-1 represents the covariance matrix at time i-1, A T represents the transpose matrix of the state transition matrix A; Step S323, updating the prediction result to obtain the filtered perturbation filtered_disturbance. The calculation formula is: Among them, C k represents the Kalman coefficient; H T represents the transpose matrix of the observation matrix H; R represents the covariance of the observation noise; u i represents the control input at the i-th moment; represents the filtered_disturbance at the i-th moment; P i represents the covariance matrix at the i-th moment; I represents the identity matrix.

6. A wave impedance inversion method based on an improved Bayesian algorithm according to claim 1, characterized in that, Calculate the energy difference ΔE corresponding to the initial impedance model parameters before and after iteration; If ΔE ≤ 0, then the posterior distribution sample is an acceptable posterior distribution sample; If ΔE > 0, then generate a first random number between 0 and 1 using a random function, and determine whether the initial acceptance rate ρ(ΔE) is greater than the first random number. If the initial acceptance rate ρ(ΔE) is greater than the first random number, then the posterior distribution sample is an acceptable posterior distribution sample; If the initial acceptance rate ρ(ΔE) is less than the first random number, then a second random number between 0 and 1 is generated again using a random function to determine whether the re-acceptance rate ρ(r d ) is greater than the second random number. If the re-acceptance rate ρ(r d ) is greater than the second random number, then the posterior distribution sample is an acceptable posterior distribution sample. If the re-acceptance rate ρ(r d ) is less than the second random number, then the posterior distribution sample is an unacceptable posterior distribution sample; r d represents the Pearson correlation coefficient between the synthetic seismic record and the actual seismic record; Store the accepted posterior distribution samples and discard the unacceptable posterior distribution samples.

7. A wave impedance inversion method based on an improved Bayesian algorithm according to claim 6, characterized in that The calculation formula for the energy difference ΔE is as follows: ΔE = E(k + 1) - E(k) where E(k + 1) represents the energy after the (k + 1)-th iteration of the initial wave impedance model; E(k) represents the energy after the k-th iteration of the initial wave impedance model, and the calculation formula is: Among them, represents a constant; d obs represents the observed data; d syn (k) represents the forward modeling data after the k-th iteration of the model; W represents the noise weighting operator; (d obs -d syn (k)) T represents the matrix (d obs -d syn (k))'s transpose matrix.

8. A wave impedance inversion method based on an improved Bayesian algorithm according to claim 6, characterized in that, The initial acceptance rate is: ρ(ΔE) = exp(μΔE) where μ is a constant; The re-acceptance rate is: Among them, is a constant; r d represents the Pearson correlation coefficient between the synthetic seismic record and the actual seismic record.

9. The wave impedance inversion method based on an improved Bayesian algorithm according to claim 8, characterized in that Pearson correlation coefficient r between the synthetic seismogram and the actual seismogram d The calculation formula is as follows: Where N represents the data length of the synthetic seismic record; d syn represents the forward modeling data of the model; d obs represents the observed data.

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