Wave impedance inversion method based on improved Bayesian algorithm

Abstract

The invention belongs to the technical field of geophysical exploration, and particularly discloses a wave impedance inversion method based on an improved Bayesian algorithm, and the method comprises the steps: obtaining a pre-stack seismic record and logging wave impedance data of a target region; performing time-depth conversion on the logging wave impedance data to obtain an actual wave impedance model and a low-frequency wave impedance model; introducing random disturbance processed by Kalman filtering into the low-frequency wave impedance model, and constructing an initial wave impedance model; performing inversion based on the initial wave impedance model; sampling an inversion result by using a posterior distribution sampling mode to obtain a received initial wave impedance model; repeating the steps to obtain a large number of posteriori distribution samples; and generating an inversion wave impedance profile based on the posterior distribution sample, and discussing and evaluating an inversion result. According to the method, the inversion precision is high, the inversion wave impedance profile with relatively high precision can be obtained, and the method has a good application prospect in the aspects of improving the 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 probability and statistics principles. 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, fuses 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: , wherein, 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 occurrence of the model parameters D under the joint constraints of prior information and observed data when the observed data X is known.

[0003] In actual inversion, since has nothing to do with 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: , 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.

[0004] However, the traditional Bayesian wave impedance inversion method has problems such as too much random noise component in the inversion initial model and insufficient constraint ability of the likelihood function in actual seismic data inversion, which affects the inversion effect. Therefore, it is urgent to improve the Bayesian algorithm, use the improved Bayesian algorithm to improve the seismic data inversion effect, and perform uncertainty analysis on it to evaluate the quality of the seismic data inversion result. Summary of the Invention

[0005] In view of this, the present application proposes a wave impedance inversion method based on an improved Bayesian algorithm to smoothly analyze and process seismic data and well logging data. By performing Bayesian wave impedance inversion on various data, the true underground wave impedance information is finally obtained.

[0006] In a first aspect, an embodiment of the present application provides a wave impedance inversion method based on an improved Bayesian algorithm, including: S01, obtaining the pre-stack seismic record and well logging wave impedance data of the target area; S02, performing time-depth conversion on the well 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; S03, introducing a randomly perturbed value processed by Kalman filtering into the low-frequency wave impedance model to construct an initial wave impedance model; S04, performing inversion based on the initial wave impedance model by generating a prior probability distribution and a likelihood function to obtain a posterior distribution sample; S05, sampling the posterior distribution sample using a posterior distribution sampling method 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 inversion wave impedance profile, and performing uncertainty analysis using the posterior standard deviation to discuss and evaluate the inversion results.

[0007] In a possible implementation, after obtaining the pre-stack seismic record and well logging wave impedance data of the target area, a normal distribution test is performed on the well logging wave impedance data to ensure that the data points are basically near the normal distribution reference line.

[0008] In a possible implementation, the performing time-depth conversion on the well 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 well 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: , where, represents time; represents depth; represents the velocity information in the depth domain.

[0009] In a possible implementation, step S03 is specifically as follows: Generate a random perturbation, perform Kalman filtering on the random perturbation, store the filtered value, and after completing the filtering process, obtain the filtered perturbation. Then the initial wave impedance model is: ,

[0010] where, 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.

[0011] In a possible implementation, the performing Kalman filtering on the random perturbation is specifically as follows: Step S321, establish the state equation and the observation equation; The state equation is: , where, 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 The observation equation can be expressed as: , where, represents the observation data at represents the observation matrix, represents the observation noise at Step S322, predict the current state and update the uncertainty of the state. The calculation formula is: , , where, represents the predicted state at represents the filtered perturbation at represents the predicted covariance matrix at Represents the covariance of the process noise; Represents The covariance matrix at time Represents the state transition matrix The transpose matrix of; Step S323, update the prediction result to obtain the filtered perturbation, and the calculation formula is: , , , where Represents the Kalman coefficient; Represents the observation matrix The transpose matrix of; Represents the covariance of the observation noise; Represents The control input at time Represents The filtered perturbation at time Represents The covariance matrix at time Represents the identity matrix.

[0012] In a possible implementation, the likelihood function is: , where Represents the likelihood function, Represents the adjustment parameter, Represents the observed data, Represents the forward model data, Represents the noise weighting operator, Represents the matrix The transpose matrix of; Can be expressed as: , where Represents extracting The elements in to create a diagonal matrix, Represents the filtered perturbation.

[0013] In a possible implementation, calculate the energy difference corresponding to the initial wave impedance model parameters before and after iteration ; If , then the posterior distribution sample is an acceptable posterior distribution sample; If , then generate a first random number between 0 and 1 using a random function, and judge 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 a second random number between 0 and 1 is generated again using a random function, and it is judged whether the re-acceptance rate 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; The accepted posterior distribution samples are stored, and the unacceptable posterior distribution samples are discarded.

[0014] In a possible implementation, the energy difference The calculation formula is: , where 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:

[0015] where 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 transpose matrix of the matrix .

[0016] In a possible implementation, the initial acceptance rate is: , where is a constant; The re-acceptance rate is: , where is a constant; represents the Pearson correlation coefficient between the synthetic seismic record and the actual seismic record.

[0017] In a possible implementation, the Pearson correlation coefficient between the synthetic seismic record and the actual seismic record The calculation formula is: , Among them, represents the data length of the synthetic seismogram; represents the forward modeling data of the model; represents the observed data.

[0018] Compared with the prior art, the present application has achieved the following remarkable technical effects.

[0019] (1) In the present application, the Kalman filtering process is performed on the random perturbation components in the initial inversion wave impedance model. Compared with the prior art where Butterworth filtering or Chebyshev filtering is only used to simply attenuate the signals within a specific frequency range, the present application uses Kalman filtering based on Bayesian theory, combines observation and prediction, and filters the signals. While reducing the interference of random perturbation components to a certain extent, the constructed initial impedance model contains more effective information, making the constructed initial impedance model closer to the actual wave impedance model.

[0020] (2) Compared with the likelihood function in the traditional method that only considers the numerical relationship between the forward modeling data of the model and the actual seismic record , the present application considers the influence of weighted error in the likelihood function and introduces the noise weighting operator , enabling the likelihood function to fully reflect the relationship between the data and the model.

[0021] (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

[0022] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0023] Figure 1 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; Figure 2 is the actual prestack seismic data provided by an embodiment of the present application; Figure 3Schematic diagram of normal distribution test for logging wave impedance data provided by an embodiment of the present application; Figure 4 Schematic diagram of low-frequency wave impedance model provided by an embodiment of the present application; Figure 5 Inversion wave impedance profile generated by posterior mean solution provided by an embodiment of the present invention; Figure 6 Analysis curve of uncertainty of inversion result of well-side trace provided by an embodiment of the present invention. Detailed implementation manners

[0024] To better understand the technical solution of the present application, the embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0025] It should be clear that the described embodiments are only a part of the embodiments of the present application, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts shall fall within the scope of protection of the present application.

[0026] The terms used in the embodiments of the present application are only for the purpose of describing specific embodiments, and are not intended to limit the present application. The singular forms of "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.

[0027] It should be understood that the term " / and / " used herein is only a description of the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B may 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.

[0028] See Figure 1 , which is a schematic flowchart 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.

[0029] Step S01: Obtain the prestack seismic record and logging wave impedance data of the target area, and perform a normal distribution test on the logging wave impedance data to ensure that the data points are basically near the normal distribution reference line.

[0030] Preferably, the prestack seismic record and logging wave impedance data of the target area are obtained through seismic exploration and logging work.

[0031] 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.

[0032] See Figure 2 , which is the actual prestack seismic data provided by the embodiment of the present application. As Figure 2 shown, the part within the red dashed line frame is the inversion target area. The longitudinal time is from 1660 to 1960 ms, the time sampling interval is 4 ms, the number of sampling points 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 spectrum analysis, it can be known that the main frequency of this prestack seismic record is 33 Hz. In the inversion, a Ricker wavelet with a main frequency of 33 Hz is selected to generate a synthetic seismic record. See Figure 3 , which is a schematic diagram of the normal distribution test of the well logging wave impedance data provided by the 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 carried out. It can be seen that except for a very small number of discrete points, the data is basically located near the standard normal distribution curve ( Figure 3 the red dashed line in), that is, the method in the present application is applicable to this target area.

[0033] Step S02: Perform time-depth conversion on the well logging wave impedance data to obtain an actual wave impedance model; perform horizon interpolation, extrapolation and smoothing processing on the wave impedance information corresponding to the time series in the actual wave impedance model, and comprehensively consider relevant information such as the position and shape of the event axis 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 the present 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 well logging wave impedance data.

[0034] The performing time-depth conversion on the well 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 well logging wave impedance data in the depth domain to the time domain, obtaining the wave impedance information in the time domain, and obtaining the actual wave impedance model. The calculation formula is: , where, represents time; represents depth; represents the velocity information in the depth domain, which can be obtained through well logging data or using empirical formulas, represents taking the reciprocal of .

[0035] Step S03: Introduce a randomly perturbed signal processed by Kalman filtering into the low-frequency wave impedance model to construct an initial wave impedance model. Specifically: Step S31, generate random perturbations , , where represents the number of data points of the random perturbation. Taking a model composed of 120 data points as an example, can be expressed as: .

[0036] Step S32, perform Kalman filtering on the random perturbation to obtain the filtered perturbation , then the initial wave impedance model is expressed as: ,

[0037] where 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.

[0038] Specifically, performing Kalman filtering on the random perturbation is specifically: Step S321, establish the state equation and the observation equation.

[0039] The state equation is: , where 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 attime, which follows a normal distribution with an expectation of 0 and a covariance of

[0040] The observation equation can be expressed as: , where represents the observation data at time, represents the observation matrix, represents the observation noise attime, which follows a normal distribution with an expectation of 0 and a covariance of

[0041] Step S322: Predict the current state and update the uncertainty of the state.

[0042] The calculation formula is: , , 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 transposed matrix of the state transition matrix Step S323: Update the prediction result to obtain the filtered disturbance . The calculation formula is: , , , where, represents the Kalman coefficient; represents the transposed matrix of the observation matrix ; represents the covariance of the observation noise; represents the control input at represents the filtered disturbance at ; represents the covariance matrix at represents the identity matrix.

[0043] In the above process, the numerical values of each parameter can be specifically set according to the actual problem.

[0044] Step S04: Based on the initial wave impedance model, generate the prior probability distribution and the likelihood function for inversion to obtain a posterior distribution sample.

[0045] During inversion, the likelihood function is improved by introducing a noise weighting operator to enable it to fully and accurately reflect the relationship between the data and the model. The calculation formula of the likelihood function is: , Among them, represents the likelihood function, represents the adjustment parameter, represents the observed data, represents the forward modeling data of the model, represents the noise weighting operator, represents a matrix the transpose matrix of can be expressed as: , wherein, represents extracting the elements in to create a diagonal matrix,

[0046] Step S05, sampling the posterior distribution samples using the posterior distribution sampling method to obtain acceptable posterior distribution samples. Specifically: Step S51, when performing Bayesian inversion, define the energy after the -th iteration of the initial wave impedance model as: , wherein, 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 a matrix the transpose matrix of

[0047] Denote the energy difference corresponding to the initial wave impedance model before and after iteration as , which can be expressed as: , wherein, represents the energy after the -th iteration of the initial wave impedance model. 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; 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, then a second random number between 0 and 1 is generated again using the 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, 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.

[0048] Furthermore, in the initial acceptance-rejection strategy, the initial acceptance rate is: , where is a constant; Furthermore, in the secondary acceptance-rejection strategy, the re-acceptance rate is: , where is a constant; represents the Pearson correlation coefficient between the synthetic seismic record and the prestack seismic record.

[0049] Furthermore, the formula for calculating the Pearson correlation coefficient between the synthetic seismic record and the prestack seismic record is: , 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.

[0050] 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: , 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.

[0051] The Ricker wavelet The expression in the time domain is: , The Ricker wavelet The expression in the frequency domain is: , wherein, represents the time variable of the wavelet; represents the frequency variable of the wavelet; represents the main frequency of the Ricker wavelet, which can be set and modified as appropriate according to information such as the main frequency of the pre-stack record.

[0052] Preferably, the Ricker wavelet in this embodiment is a Ricker wavelet with a main frequency of 33 Hz.

[0053] Step 52, store the accepted posterior distribution samples and discard the unacceptable posterior distribution samples.

[0054] Step S06, repeat steps S03 - S05 until a large number of posterior distribution samples are obtained.

[0055] Step S07, extract the posterior mean solution or the maximum a posteriori probability solution from the posterior distribution samples, generate an inverted impedance profile, and perform uncertainty analysis using the posterior standard deviation to discuss and evaluate the inversion results.

[0056] In this embodiment, extract the posterior mean solution from the posterior distribution samples, observe whether the change trend between the posterior mean solution and the actual impedance model is the same, compare their degree of coincidence, and observe whether the actual impedance model is basically within the 99% confidence interval of the posterior distribution samples. The 99% confidence interval is within the interval, where is the interval, where is the posterior standard deviation.

[0057] See Figure 5 , the inverted impedance profile generated by the posterior mean solution provided by the embodiment of the present invention. As shown in Figure 5 , by combining with the logging impedance curve and plotting it near the wellbore trace, it can be seen that the trend between it and the wellbore trace impedance inversion result is basically the same. The inverted impedance profile is consistent with the characteristics of the logging impedance curve, has a high resolution, and shows good continuity and consistency in the horizontal direction. Thus, it can be known that this result is reasonable and credible. In this embodiment, through uncertainty analysis, the inversion results can be discussed and evaluated, so as to better understand the quality of the inversion results. See Figure 6 , the uncertainty analysis curve of the wellbore trace inversion result provided by the embodiment of the present invention. As shown in Figure 6 , the inversion result of the 1573rd trace is generally less different from the overall logging impedance curve. The arrow indicates a high degree of fitting and the same trend, and most of the values of the logging impedance curve fall within 99% of the inversion result (i.e., within the interval, where is the interval, where is The posterior standard deviation), from which it can be determined that the inversion result is reasonable and reliable.

[0058] 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 logging data. However, the constraint ability of the traditional Bayesian inversion algorithm is limited, which has a certain impact on 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.

[0059] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; 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 described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the various 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 record 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; S03, introducing a randomly perturbed signal processed by Kalman filtering into the low-frequency impedance model to construct an initial impedance model; S04, generating a prior probability distribution and a likelihood function based on the initial impedance model for inversion to obtain a posterior distribution sample; S05, sampling the posterior distribution sample using a posterior distribution sampling method 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 the improved Bayesian algorithm according to claim 1, wherein, After obtaining the pre-stack seismic record 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 time-depth conversion of 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: ， Among them, represents time; represents depth; represents 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 as follows: generate a random perturbation, perform Kalman filtering on the random perturbation, store the filtered value, and after completing the filtering process, obtain the filtered perturbation , then the initial wave impedance model is: ， 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.

5. A wave impedance inversion method based on an improved Bayesian algorithm according to claim 4, characterized in that The Kalman filtering process for the random perturbation is specifically: Step S321, establishing a state equation and an observation equation; The state equation is: ， Among them, represents the random perturbation The state of the data at time; represents the state transition matrix; represents the random perturbation The state of the data at time; represents the control input matrix; represents The control input at time; represents The process noise at time; The observation equation can be expressed as: ， Among them, represents the observed data at the moment, represents the observation matrix, represents the observation noise at the moment; 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 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 ; Step S323, update the prediction result to obtain the filtered perturbation , and the calculation formula is: ， ， ， Among them, represents the Kalman coefficient; represents the observation matrix of the transposed 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.

6. The wave impedance inversion method based on the improved Bayesian algorithm according to claim 1, wherein The likelihood function is: ， Among them, represents the likelihood function, represents the adjustment parameter, represents the observed data, represents the forward modeling data of the model, represents the noise weighting operator, represents the matrix is the transpose matrix of; It can be expressed as: ， Among them, represents extraction of the elements in to create a diagonal matrix, represents the filtered perturbation.

7. A wave impedance inversion method based on an improved Bayesian algorithm according to claim 1, characterized in that, Calculate the energy difference corresponding to the initial wave impedance model parameters before and after iteration ; If , then the posterior distribution sample is an acceptable posterior distribution sample; If , a first random number between 0 and 1 is generated using a random function, and it is determined whether the initial acceptance rate is greater than the first random number. If the initial acceptance rate is greater than the first random number, the posterior distribution sample is an acceptable posterior distribution sample; if the initial acceptance rate is less than the first random number, a second random number between 0 and 1 is generated again using the random function, and it is determined whether the re - acceptance rate 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; Store the accepted posterior distribution samples and discard the unacceptable posterior distribution samples.

8. The wave impedance inversion method based on an improved Bayesian algorithm according to claim 7, characterized in that Energy difference The calculation formula is as follows: ， Among them, 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 its calculation formula is: ， Among them, represents a constant; represents observed data; represents the forward modeling data after the -th iteration of the model; represents a noise weighting operator; represents the transpose matrix of the matrix ​ 9. A wave impedance inversion method based on an improved Bayesian algorithm according to claim 7, characterized in that The initial acceptance rate is: ， wherein, is a constant; The re-acceptance rate is: ， Among them, is a constant; represents the Pearson correlation coefficient between the synthetic seismic record and the actual seismic record.

10. A wave impedance inversion method based on an improved Bayesian algorithm according to claim 9, characterized in that, Pearson correlation coefficient between synthetic seismogram and actual seismogram The calculation formula is as follows: ， Among them, represents the data length of the synthetic seismogram; represents the forward modeling data of the model; represents the observed data.

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