Bayesian-based pseudo-random binary sequence transient electromagnetic data reconstruction method

Abstract

The application relates to a Bayesian-based pseudo-random binary sequence transient electromagnetic data reconstruction method, which comprises the following steps: step 1, obtaining transient electromagnetic measured data; step 2, presetting basic parameters and a sampling range of Bayesian sampling; step 3, guiding Bayesian sampling to randomly select period data in the transient electromagnetic measured data through a likelihood function, and generating alternative data based on the period data; step 4, calculating an acceptance ratio of the alternative data, if the acceptance ratio is greater than a preset value, the alternative data is accepted, and the alternative data is set as initial data for the next sampling; otherwise, the alternative data is rejected, and the next sampling is continued; step 5, repeating steps 3-4 until convergence, ending the sampling, and arranging all the alternative data into a data sample set; and step 6, performing reconstruction calculation on the data sample set to obtain reconstructed transient electromagnetic data. The application can reconstruct high-quality transient electromagnetic pseudo-random binary sequence data from actual observation data.

Description

Technical Field

[0001] This invention relates to the field of transient electromagnetic detection technology, and in particular to a Bayesian-based method for reconstructing transient electromagnetic data from pseudo-random binary sequences. Background Technology

[0002] The transient electromagnetic method (TEM) obtains subsurface resistivity information by transmitting an electromagnetic source signal underground and then observing the electromagnetic response signal of the subsurface medium at the surface. In conventional methods, the electromagnetic source signal is a bipolar rectangular wave signal, and the response signal is a pure secondary field signal acquired during the source turn-off period. This method can eliminate the interference of the source signal on the response and extract a stable transient electromagnetic attenuation curve for subsequent information extraction. However, the spectral components of the source signal in this method are singular and cannot be adjusted, making the optimization of the source signal a key focus of research in the transient electromagnetic method in recent years.

[0003] A pseudo-random binary sequence is a signal sequence that satisfies the randomness assumption but can be generated using a feedback shift register. This sequence can be generated deterministically and exhibits excellent autocorrelation and spectral characteristics. In recent years, it has been widely studied and applied as a transmission source in transient electromagnetic detection. In practical detection, optimal detection results can be achieved by using a pseudo-random binary sequence and setting the sequence order and minimum pulse width according to the depth of the target. However, compared to conventional bipolar rectangular waves, the signal of a pseudo-random binary sequence is more susceptible to interference from the source signal, and the reconstruction of the response data is more difficult.

[0004] Conventional methods employ bipolar waveforms, repeating multiple cycles of transmission and observation, followed by signal inverse superposition to eliminate random and non-random interference signals while retaining the useful signal. However, when using a pseudo-random binary sequence as the transmission source, inverse superposition is not feasible; instead, repeated observations followed by averaging are typically used. In this case, only random interference can be eliminated, not non-random interference, making it difficult to obtain a pure response signal that meets the inversion requirements. Therefore, a Bayesian-based method for reconstructing transient electromagnetic data from pseudo-random binary sequences is proposed. Summary of the Invention

[0005] The purpose of this invention is to provide a Bayesian-based method for reconstructing transient electromagnetic data from pseudo-random binary sequences. When a pseudo-random binary sequence is used as the emission source, a high-quality pseudo-random binary sequence response is reconstructed from the observed full waveform response. Utilizing efficient random sampling through Bayesian inversion, the method judges and evaluates the pseudo-random binary sequence signal for each period of the observation, eliminates significant interference in signal observation, assesses the quality of each time channel data, obtains the error statistics parameters for each time channel, and finally reconstructs the transient electromagnetic data for each measurement point.

[0006] To achieve the above objectives, the present invention provides the following solution:

[0007] A Bayesian-based method for reconstructing transient electromagnetic data from pseudo-random binary sequences includes:

[0008] Step 1: Obtain transient electromagnetic measurement data using the transient electromagnetic method;

[0009] Step 2: Preset the basic parameters and sampling range of Bayesian sampling, wherein the basic parameters include the maximum number of iterations, the standard deviation of the proposed distribution, and the initial data for sampling;

[0010] Step 3: Guide the Bayesian sampling by the likelihood function to randomly select periodic data from the transient electromagnetic measured data, and generate candidate data based on the periodic data;

[0011] Step 4: Calculate the acceptance ratio of the candidate data. If the acceptance ratio is greater than a preset value, accept the candidate data and set the candidate data as the initial data for the next sampling; otherwise, reject the candidate data and continue to the next sampling.

[0012] Step 5: Repeat steps 3-4 until convergence, end sampling, and organize all candidate data into a data sample set;

[0013] Step 6: Perform reconstruction calculations on the data sample set to obtain the reconstructed transient electromagnetic data.

[0014] Optionally, the average of the data collected during the repeated periods using the transient electromagnetic method is taken as the transient electromagnetic measured data, which is:

[0015]

[0016] In the formula, For transient electromagnetic measured data, d i Let N be the data for the i-th period, and N be the total number of periods.

[0017] Optionally, the sampling range is d down ~d up ,in,

[0018]

[0019] In the formula, For transient electromagnetic measured data, δ d The standard deviation of each time channel data point.

[0020] Optionally, the likelihood function is:

[0021]

[0022] In the formula, d' represents the candidate data for the current iteration step, and d0 represents the data for the current period. For transient electromagnetic measured data, δ d The standard deviation of each time channel data point.

[0023] Optionally, the method for generating candidate data based on the periodic data is as follows:

[0024]

[0025] In the formula, q(·|·) is the proposed distribution value, d is the current data of the iteration step, d' is the candidate data of the current iteration step, and δ c This represents the standard deviation of the proposed distribution.

[0026] Optionally, the method for calculating the acceptance rate of the candidate data is as follows:

[0027]

[0028] In the formula, α is the acceptance ratio, p(·|·) is the likelihood function value, and q(·|·) is the proposed distribution value.

[0029] Optionally, the reconstruction calculation of the data sample set includes:

[0030] The mean of all data samples in the data sample set is calculated as the reconstructed transient electromagnetic data.

[0031] The beneficial effects of this invention are as follows:

[0032] This invention proposes a Bayesian-based method for reconstructing transient electromagnetic data from pseudo-random binary sequences. When a pseudo-random binary sequence is used as the emission source, it reconstructs a high-quality pseudo-random binary sequence response from the observed full waveform response. Utilizing efficient random sampling through Bayesian inversion, it judges and evaluates the pseudo-random binary sequence signal for each period of the observation, eliminating significant interference in signal observation, assessing the quality of each time channel data, obtaining error statistics parameters for each time channel, and ultimately reconstructing the transient electromagnetic data for each measurement point. This invention can reconstruct high-quality transient electromagnetic pseudo-random binary sequence data from actual observation data. Under different signal-to-noise ratios, the extracted data can suppress various types of noise in the signal, obtaining data with better coupling to the source signal. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0034] Figure 1 This is a flowchart of the Bayesian-based pseudo-random binary sequence transient electromagnetic data reconstruction method according to an embodiment of the present invention.

[0035] Figure 2 The pseudo-random binary sequence source signal, original data, and reconstructed data at an offset of 500 meters are provided in this embodiment of the invention.

[0036] Figure 3 The pseudo-random binary sequence source signal, original data, and reconstructed data at an offset of 1000 meters are provided in this embodiment of the invention.

[0037] Figure 4 The pseudo-random binary sequence source signal, original data, and reconstructed data are located at an offset of 2000 meters in this embodiment of the invention. Detailed Implementation

[0038] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0040] Existing methods for reconstructing pseudo-random binary sequence response signals typically involve sampling multiple times, superimposing the data, and then averaging the results. This approach struggles to eliminate non-random interference, limiting signal quality. Therefore, this embodiment provides a Bayesian-based method for reconstructing transient electromagnetic data from pseudo-random binary sequences. This method extracts high-quality data and error statistics from the full waveform signal of a repeatedly observed pseudo-random binary sequence. For example... Figure 1 As shown, it includes the following:

[0041] Step 1: Obtain transient electromagnetic measurement data using the transient electromagnetic method;

[0042] Step 2: Preset the basic parameters and sampling range of Bayesian sampling. The basic parameters include the maximum number of iterations, the standard deviation of the proposed distribution, and the initial data for sampling.

[0043] Step 3: Guide Bayesian sampling using the likelihood function to randomly select periodic data from the transient electromagnetic measured data, and generate candidate data based on the periodic data;

[0044] Step 4: Calculate the acceptance rate of candidate data. If the acceptance rate is greater than the preset value, accept the candidate data and set it as the initial data for the next sampling. Otherwise, reject the candidate data and continue to the next sampling.

[0045] Step 5: Repeat steps 3-4 until convergence, end sampling, and organize all candidate data into a data sample set;

[0046] Step 6: Perform reconstruction calculations on the data sample set to obtain the reconstructed transient electromagnetic data.

[0047] Specifically, the Bayesian-based method for reconstructing transient electromagnetic data from pseudo-random binary sequences proposed in this embodiment reconstructs high-quality pseudo-random binary sequence responses from the observed full waveform response when the pseudo-random binary sequence is used as the emission source. It utilizes efficient random sampling through Bayesian inversion to judge and evaluate the pseudo-random binary sequence signal for each period of observation, eliminating significant interference in signal observation, assessing the quality of each time channel data, obtaining error statistics parameters for each time channel, and finally reconstructing the transient electromagnetic data for each measurement point. This invention can reconstruct high-quality transient electromagnetic pseudo-random binary sequence data from actual observation data. Under different signal-to-noise ratios, the extracted data can suppress various types of noise in the signal, obtaining data with better coupling to the source signal.

[0048] Furthermore, step 1 involves obtaining transient electromagnetic measurement data using the transient electromagnetic method, specifically including:

[0049] In this embodiment, the average value of the data collected during the repeated periods using the transient electromagnetic method is taken as the transient electromagnetic measured data. The transient electromagnetic measured data is as follows:

[0050]

[0051] In the formula, For transient electromagnetic measured data, d i Let N be the data for the i-th period, and N be the total number of periods.

[0052] Furthermore, in step 2, the basic parameters and sampling range of Bayesian sampling are preset. The basic parameters include the maximum number of iterations, the standard deviation of the proposed distribution, and the initial data for sampling.

[0053] In this embodiment, the maximum number of iterations is set to 1,000,000, and the standard deviation of the suggested distribution is [value missing]. The initial data for sampling is

[0054] The boundaries of the sampling range are generated based on the data mean and standard deviation, and are denoted as d. down ~d up ,in,

[0055]

[0056] In the formula, δ d The standard deviation for each time channel data is expressed as:

[0057]

[0058] Furthermore, in step 3, Bayesian sampling guided by the likelihood function is used to randomly select periodic data from the transient electromagnetic measurement data, and candidate data is generated based on the periodic data. Specifically, this includes:

[0059] The likelihood function is used to evaluate the difference between the obtained transient electromagnetic data and the true transient electromagnetic data, thereby guiding the Bayesian sampling method. Constructing the likelihood function is a crucial step in Bayesian sampling and serves as a bridge connecting Bayesian methods with practical problems.

[0060] The likelihood function constructed in this embodiment is:

[0061]

[0062] In the formula, d' represents the candidate data for the current iteration step, d0 represents the data for the current period, d represents the transient electromagnetic measured data, and δ... d The standard deviation of each time channel data point.

[0063] The transient electromagnetic method samples data periodically and repeatedly, randomly selecting data from one period with equal probability; and from the sampling range, candidate data d' is generated using the following Gaussian distribution.

[0064]

[0065] In the formula, d represents the current data of the iteration step, and δ c It is the standard deviation of the suggested distribution.

[0066] Furthermore, in step 4, the acceptance ratio of the candidate data is calculated. If the acceptance ratio is greater than a preset value, the candidate data is accepted and set as the initial data for the next sampling; otherwise, the candidate data is rejected and the next sampling is carried out.

[0067] Specifically, by calculating the likelihood function value and the proposed distribution value, the acceptance ratio α is then calculated as follows:

[0068]

[0069] Generate a random number b between (0, 1]. If α > b, accept the data sample and set it as the current iteration step for the next sampling; otherwise, reject the data sample and continue with the next sampling.

[0070] Furthermore, in step 5, steps 3-4 are repeated until convergence, at which point the sampling ends, and all candidate data are organized into a data sample set.

[0071] Furthermore, in step 6, the data sample set is reconstructed to obtain the reconstructed transient electromagnetic data. Specifically, the mean of all data samples in the data sample set is calculated as the reconstructed transient electromagnetic data.

[0072] This embodiment uses transient electromagnetic measurement data at different offsets to demonstrate the difference between the reconstructed response and the response obtained by conventional methods (superposition and averaging).

[0073] like Figure 2 , Figure 3 , Figure 4 As shown, comparing the pseudo-random binary sequence source signals and the original data at offsets of 500 meters, 1000 meters, and 2000 meters reveals that, due to external electromagnetic interference, even with a high signal-to-noise ratio, the coupling between the observed original data and the source signal is weak, making it unsuitable for direct use in subsequent inversion. Conventional methods often employ superposition and averaging to obtain the data; however, the results show that while superposition and averaging can recover some trend of the source signal, it is still difficult to extract effective data. Further design of a dedicated denoising process is needed to improve the signal-to-noise ratio.

[0074] In contrast, the methods proposed in this embodiment are all able to extract excellent pseudo-random binary sequence transient electromagnetic data. The extracted data is closely coupled to the emitted source signal, and the quality of the reconstructed data is far superior to that of conventional methods. Furthermore, it can be directly used for subsequent data inversion, especially when the offset is small. When the offset is large, this method can still reconstruct data that is well coupled to the source signal; in such cases, conventional methods struggle to recover usable data.

[0075] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A Bayesian-based method for reconstructing transient electromagnetic data from pseudo-random binary sequences, characterized in that, include: Step 1: Obtain transient electromagnetic measurement data using the transient electromagnetic method; Step 2: Preset the basic parameters and sampling range of Bayesian sampling, wherein the basic parameters include the maximum number of iterations, the standard deviation of the proposed distribution, and the initial data for sampling; Step 3: Guide the Bayesian sampling by the likelihood function to randomly select periodic data from the transient electromagnetic measured data, and generate candidate data based on the periodic data; Step 4: Calculate the acceptance ratio of the candidate data. If the acceptance ratio is greater than a preset value, then accept the candidate data and set the candidate data as the initial data for the next sampling. Otherwise, reject the candidate data and proceed to the next sampling. Step 5: Repeat steps 3-4 until convergence, end sampling, and organize all candidate data into a data sample set; Step 6: Perform reconstruction calculations on the data sample set to obtain the reconstructed transient electromagnetic data.

2. The Bayesian-based method for reconstructing transient electromagnetic data of pseudo-random binary sequences according to claim 1, characterized in that, The average value of the data collected during the repeated periods using the transient electromagnetic method is taken as the transient electromagnetic measured data. The transient electromagnetic measured data is as follows: In the formula, For transient electromagnetic measured data, d i Let N be the data for the i-th period, and N be the total number of periods.

3. The Bayesian-based method for reconstructing transient electromagnetic data of pseudo-random binary sequences according to claim 1, characterized in that, The sampling range is d down ~d up ,in, In the formula, For transient electromagnetic measured data, δ d The standard deviation of each time channel data point.

4. The Bayesian-based method for reconstructing transient electromagnetic data of pseudo-random binary sequences according to claim 1, characterized in that, The likelihood function is: In the formula, d' represents the candidate data for the current iteration step, and d0 represents the data for the current period. For transient electromagnetic measured data, δ d The standard deviation of each time channel data point.

5. The Bayesian-based method for reconstructing transient electromagnetic data of pseudo-random binary sequences according to claim 4, characterized in that, The method for generating candidate data based on the aforementioned periodic data is as follows: In the formula, q(·|·) is the proposed distribution value, d is the current data of the iteration step, d' is the candidate data of the current iteration step, and δ c This represents the standard deviation of the proposed distribution.

6. The Bayesian-based method for reconstructing transient electromagnetic data of pseudo-random binary sequences according to claim 5, characterized in that, The method for calculating the acceptance rate of the candidate data is as follows: In the formula, α is the acceptance ratio, p(·|·) is the likelihood function value, and q(·|·) is the proposed distribution value.

7. The Bayesian-based method for reconstructing transient electromagnetic data of pseudo-random binary sequences according to claim 1, characterized in that, The reconstruction calculation of the data sample set includes: The mean of all data samples in the data sample set is calculated as the reconstructed transient electromagnetic data.

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