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

Abstract

The invention relates to a Bayesian-based pseudo-random binary sequence transient electromagnetic data reconstruction method. The method comprises the steps of 1, acquiring transient electromagnetic measured data; step 2, presetting basic parameters and a sampling range of Bayesian sampling; 3, guiding Bayesian sampling through a likelihood function to randomly select periodic data in the transient electromagnetic measured data, and generating alternative data based on the periodic data; step 4, calculating an acceptance proportion of the alternative data, if the acceptance proportion is greater than a preset value, accepting the alternative data, and setting the alternative data as the next sampling initial data; otherwise, rejecting the alternative data, and continuing to carry out the next sampling; 5, repeating the steps 3-4 until convergence, ending sampling, and sorting all alternative data into a data sample set; and step 6, performing reconstruction calculation on the data sample set to obtain reconstructed transient electromagnetic data. According to the method, high-quality transient electromagnetic pseudo-random binary sequence data can be reconstructed from actual observation data.

Description

Technical Field

[0001] The invention relates to the technical field of transient electromagnetic detection, and in particular to a Bayesian-based pseudo-random binary sequence transient electromagnetic data reconstruction method. Background Art

[0002] The transient electromagnetic method obtains underground resistivity information by transmitting an electromagnetic source signal underground and then observing the electromagnetic response signal of the underground medium on 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 collected during the source shutdown 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 component of the source signal of this method is single and cannot be adjusted, making the optimization of the source signal of the transient electromagnetic method one of the research focuses of this method in recent years.

[0003] A pseudo-random binary sequence is a signal sequence that satisfies the randomness assumption but can be generated by a feedback shift register. This sequence can be generated deterministically, and has excellent autocorrelation performance and spectral characteristics. In recent years, it has been introduced as a transmitting source into transient electromagnetic detection and has been widely studied and applied. In actual detection, the best detection effect can be obtained by adopting a pseudo-random binary sequence and setting the sequence order and the narrowest pulse width according to the depth of the detection target. However, compared with conventional bipolar rectangular waves, the signal of the pseudo-random binary sequence is easily interfered by the source signal, and the reconstruction of the response data is more difficult.

[0004] Since the conventional method uses a bipolar waveform, by repeating multiple cycles of emission and observation, and then using the signal reverse superposition method, random and non-random interference signals can be eliminated and useful signals can be retained. However, when a pseudo-random binary sequence is used as the emission source, the reverse superposition method cannot be used. Usually, the method of repeated observation and then superposition and averaging is used. At this time, only random interference in the signal can be eliminated, and non-random interference in the signal cannot be eliminated, making it difficult to obtain a pure response signal that meets the inversion requirements. Therefore, a Bayesian-based pseudo-random binary sequence transient electromagnetic data reconstruction method is proposed. Summary of the invention

[0005] The purpose of the present invention is to provide a Bayesian-based pseudo-random binary sequence transient electromagnetic data reconstruction method, which reconstructs a high-quality pseudo-random binary sequence response from the observed full waveform response when the pseudo-random binary sequence is used as a transmission source; utilizes efficient random sampling of Bayesian inversion to judge and evaluate the pseudo-random binary sequence signal of each cycle of the observation, eliminates major interference in the signal observation, and evaluates the quality of each time channel data obtained, obtains the error statistical parameters of each time channel, and finally reconstructs the transient electromagnetic data of each measuring point.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] The Bayesian-based pseudo-random binary sequence transient electromagnetic data reconstruction method includes:

[0008] Step 1, obtaining transient electromagnetic measured data by transient electromagnetic method;

[0009] Step 2: presetting 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 of the sampling;

[0010] Step 3: guiding the Bayesian sampling to randomly select periodic data from the transient electromagnetic measured data through a likelihood function, and generating 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 with the next sampling.

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

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

[0014] Optionally, the data of repeated cycles in the process of collecting using the transient electromagnetic method is averaged as the transient electromagnetic measured data, and the transient electromagnetic measured data is:

[0015]

[0016] In the formula, is the transient electromagnetic measured data, d i is the data of the i-th cycle, and N is the total number of cycles.

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

[0018]

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

[0020] Optionally, the likelihood function is:

[0021]

[0022] In the formula, d' is the candidate data of the current iteration step, d0 is the data of the current cycle, is the transient electromagnetic measured data, δ d is the standard deviation of the data for each time channel.

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

[0024]

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

[0026] Optionally, the method for calculating the acceptance ratio of the candidate data is:

[0027]

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

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

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

[0031] The beneficial effects of the present invention are:

[0032] The Bayesian-based pseudo-random binary sequence transient electromagnetic data reconstruction method proposed in the present invention reconstructs a high-quality pseudo-random binary sequence response from the observed full waveform response when the pseudo-random binary sequence is used as the emission source; utilizes efficient random sampling of Bayesian inversion to judge and evaluate the pseudo-random binary sequence signal of each observed period, eliminates major interference in signal observation, and evaluates the quality of each time channel data obtained, obtains the error statistical parameters of each time channel, and finally reconstructs the transient electromagnetic data of each measuring point; the present invention can reconstruct high-quality transient electromagnetic pseudo-random binary sequence data from actual observed data, and under different data signal-to-noise ratios, the extracted data can suppress various types of noise in the signal and obtain data that is better coupled with the source signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, 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 invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0034] Figure 1 This is a flow chart of a 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 in an embodiment of the present invention;

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

[0037] Figure 4 These are the pseudo-random binary sequence source signal, original data, and reconstructed data at an offset of 2000 meters in an embodiment of the present invention. DETAILED DESCRIPTION

[0038] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0039] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0040] The reconstruction of existing pseudo-random binary sequence response signals generally involves multiple sampling and superposition and then taking the average value, which makes it difficult to eliminate non-random interference in the signal and limits the signal quality. Therefore, this embodiment provides a Bayesian-based pseudo-random binary sequence transient electromagnetic data reconstruction method to extract high-quality data and error statistical parameters from the pseudo-random binary sequence full waveform signal that has been repeatedly observed. Figure 1 As shown, including the following:

[0041] Step 1, obtaining transient electromagnetic measured data by transient electromagnetic method;

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

[0043] Step 3: randomly selecting periodic data from the transient electromagnetic measured data by guiding Bayesian sampling through a likelihood function, and generating candidate data based on the periodic data;

[0044] 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 it as the initial data for the next sampling. Otherwise, reject the candidate data and continue with the next sampling.

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

[0046] Step 6: Reconstruct the data sample set to obtain reconstructed transient electromagnetic data.

[0047] Specifically, the Bayesian-based pseudo-random binary sequence transient electromagnetic data reconstruction method proposed in this embodiment reconstructs a high-quality pseudo-random binary sequence response from the observed full waveform response when the pseudo-random binary sequence is used as the emission source; utilizes efficient random sampling of Bayesian inversion to judge and evaluate the pseudo-random binary sequence signal of each observed period, eliminates major interference in the signal observation, and evaluates the quality of each time channel data obtained, obtains the error statistical parameters of each time channel, and finally reconstructs the transient electromagnetic data of each measuring point; the present invention can reconstruct high-quality transient electromagnetic pseudo-random binary sequence data from actual observed data, and under different data signal-to-noise ratios, the extracted data can suppress various types of noise in the signal and obtain data that is better coupled with the source signal.

[0048] Furthermore, in step 1, the transient electromagnetic measured data is obtained by the transient electromagnetic method, specifically including:

[0049] In this embodiment, the data of repeated cycles in the transient electromagnetic method acquisition process are averaged as the transient electromagnetic measured data. The transient electromagnetic measured data is:

[0050]

[0051] In the formula, is the transient electromagnetic measured data, d i is the data of the i-th cycle, and N is the total number of cycles.

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

[0053] In this example, the maximum number of iterations is set to 1,000,000 and the standard deviation of the recommended distribution is The initial data of the sampling is

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

[0055]

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

[0057]

[0058] Furthermore, in step 3, the likelihood function is used to guide Bayesian sampling to randomly select periodic data from the transient electromagnetic measured data, and candidate data is generated based on the periodic data, specifically including:

[0059] The likelihood function is used to evaluate the difference between the acquired transient electromagnetic data and the real transient electromagnetic data, thus guiding the Bayesian sampling method. The construction of the likelihood function is a key link in Bayesian sampling and a bridge between the Bayesian method and practical problems.

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

[0061]

[0062] In the formula, d' is the candidate data of the current iteration step, d0 is the data of the current cycle, d is the transient electromagnetic measured data, δ d is the standard deviation of the data for each time channel.

[0063] The transient electromagnetic method sampling is repeated periodically, and the data of one cycle is randomly selected with equal probability; and the candidate data d' is generated from the sampling range using the following Gaussian distribution.

[0064]

[0065] In the formula, d is the current data of the iteration step, δ c is the standard deviation of the proposed 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 continued;

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

[0068]

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

[0070] Furthermore, in step 5, steps 3 and 4 are repeated until convergence, the sampling is terminated, and all candidate data are organized into a data sample set.

[0071] Furthermore, in step 6, reconstruction calculation is performed on the data sample set to obtain 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 measured data at different offset distances to demonstrate the difference between the reconstructed response and the response obtained by the conventional method (superposition and averaging).

[0073] like Figure 2 , Figure 3 , Figure 4 As shown in the figure, by comparing the pseudo-random binary sequence source signal and the original data at offsets of 500 meters, 1000 meters and 2000 meters, it can be seen that due to external electromagnetic interference, even in the case of a high signal-to-noise ratio, the coupling between the observed original data and the source signal is weak and cannot be directly used for subsequent inversion. In conventional methods, the superposition averaging method is often used to obtain data, but the processing results show that although the superposition averaging method can restore a certain trend of the source signal, it is still difficult to extract valid data, and a special denoising process needs to be further designed to improve the signal-to-noise ratio.

[0074] In contrast, the methods proposed in this embodiment can extract good pseudo-random binary sequence transient electromagnetic data. The extracted data is closely coupled with the emitted source signal, and the quality of the reconstructed data is much better than the reconstruction result of the conventional method, and can be directly used for subsequent data inversion work, especially when the offset distance is small. When the offset distance is large, this method can still reconstruct data that is well coupled with the source signal. At this time, it is difficult for conventional methods to recover usable data.

[0075] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A Bayesian pseudo-random binary sequence transient electromagnetic data reconstruction method, characterized in that: include: Step 1, obtaining transient electromagnetic measured data by transient electromagnetic method; Step 2: presetting 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 of the sampling; Step 3: guiding the Bayesian sampling to randomly select periodic data from the transient electromagnetic measured data through a likelihood function, and generating 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, 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 and 4 until convergence, end sampling, and organize all candidate data into a data sample set; Step 6: Perform reconstruction calculation on the data sample set to obtain reconstructed transient electromagnetic data.

2. The Bayesian pseudo-random binary sequence transient electromagnetic data reconstruction method according to claim 1 is characterized in that: The data of repeated cycles in the transient electromagnetic method acquisition process are averaged as the transient electromagnetic measured data, and the transient electromagnetic measured data is: In the formula, is the transient electromagnetic measured data, d i is the data of the i-th cycle, and N is the total number of cycles.

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

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

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

6. The Bayesian pseudo-random binary sequence transient electromagnetic data reconstruction method according to claim 5 is characterized in that: The method for calculating the acceptance ratio of the candidate data is: Where α is the acceptance ratio, p(·|·) is the likelihood function value, and q(·|·) is the proposed distribution value.

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

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