Earth pulse electromagnetic response extraction method based on Bayesian method

Abstract

The invention discloses an earth pulse electromagnetic response extraction method based on a Bayesian method. The method comprises the following steps: acquiring transient electromagnetic observation data; and acquiring earth pulse electromagnetic response in the transient electromagnetic observation data by using a Bayesian method. According to the method, the earth impulse response can be extracted from the observed source signal and the response signal, the Bayesian sampling is adopted to replace the deconvolution process, and compared with a conventional method, the method provided by the invention is more stable and higher in anti-noise capability.

Description

Technical Field

[0001] The invention belongs to the technical field of electromagnetic detection, and in particular relates to a method for extracting earth pulse electromagnetic response based on a Bayesian method. Background Art

[0002] Transient electromagnetic method is an artificial source electromagnetic detection method. This method injects electromagnetic signals into the ground and then observes the response of the underground medium to the signal. In this process, it is crucial to extract the pure induction field without the source signal from the observed response. For this reason, a time period when the source is turned off is generally specially designed in the transient electromagnetic source signal, and the attenuation signal of the transient electromagnetic is collected during this time period. However, due to the performance limitations of the actual circuit, the source signal emitted into the ground is often distorted, making the observed attenuation curve not an ideal saving or pulse signal, and it is necessary to further eliminate the influence of the source distortion from the signal.

[0003] At present, there are generally two ways to eliminate the impact of source distortion on the signal. One is to consider the shutdown effect in numerical simulation, and then introduce it into the inversion of transient electromagnetic data to offset the impact of the shutdown effect on the signal. The other is to record the source signal emitted into the ground while observing the transient electromagnetic response, and then use the deconvolution method to eliminate the effect caused by the source distortion and obtain the earth pulse response.

[0004] However, both methods currently have obvious limitations: In idea one, the shutdown time is closely related to the electrical characteristics of the underground medium, so the shutdown time at each observation point is different. How to count and introduce the shutdown time is a very tedious task. In addition, the inversion with the shutdown effect can only eliminate the distortion of the signal caused by the shutdown effect, and the distortion of other source signals will still affect the observed response. In idea two, the deconvolution process is an ill-posed inverse problem and is extremely sensitive to noise. The transient electromagnetic observation signal contains various types of noise interference during observation, making it difficult to obtain a stable earth pulse response signal using the deconvolution method in practice. Therefore, there is an urgent need for a method for extracting the earth pulse electromagnetic response based on the Bayesian method. Summary of the invention

[0005] In order to solve the above technical problems, the present invention proposes a method for extracting the pulse electromagnetic response of the earth based on the Bayesian method. Starting from the idea of ​​deconvolution, the present invention adopts the Bayesian method to solve the ill-posed problem of deconvolution, and extracts the earth pulse response from the recorded source signal and response signal.

[0006] To achieve the above object, the present invention provides a method for extracting ground pulse electromagnetic response based on a Bayesian method, comprising:

[0007] Acquire transient electromagnetic observation data;

[0008] The Bayesian method is used to obtain the earth pulse electromagnetic response in the transient electromagnetic observation data.

[0009] Optionally, the transient electromagnetic observation data includes: a source signal and a response signal.

[0010] Optionally, the response signal is:

[0011] v(r,t)=s(r,t)*g(r,t)+n(r,t)

[0012] Among them, v is the response signal, n is the environmental noise, r is the location of the observation point, t is the time, g is the earth pulse response, and * is the convolution symbol.

[0013] Optionally, using the Bayesian method to obtain the earth pulse electromagnetic response in the transient electromagnetic observation data includes:

[0014] S1. Acquire an earth pulse response based on the transient electromagnetic observation data, and determine an earth pulse response boundary based on the earth pulse response;

[0015] S2. Establishing a priori distribution based on the earth pulse response boundary, and generating candidate samples of the earth pulse response based on the priori distribution;

[0016] S3, calculating the likelihood of the candidate sample, and determining whether the candidate sample is accepted based on the likelihood and the candidate sample;

[0017] S4. Repeat S1-S3 until the target number of times is reached, and the mean of the obtained sample set is the earth pulse electromagnetic response.

[0018] Optionally, the earth impulse response boundary is:

[0019] g up (r,t)=0.5g0(r,t).

[0020] g down (r,t)=2g0(r,t).

[0021] Where g0 is the earth pulse response, g up (r, t) is the upper boundary of the earth pulse response, g down (r, t) is the lower boundary of the earth impulse response.

[0022] Optionally, the alternative samples are:

[0023]

[0024] Among them, q(g|g′) is the recommended distribution for generating candidate samples, g is the sample of the current earth impulse response, g′ is the generated earth impulse response sample, δ g Parameters generated for the control samples.

[0025] Optionally, using a likelihood function, the likelihood of the candidate sample is calculated;

[0026] The likelihood function is:

[0027]

[0028] in, is the likelihood function, δ v is the standard deviation of the earth pulse response obtained by deconvolution, v is the response signal observed at the measuring point, and v' is the response signal obtained by the alternative earth pulse response sample.

[0029] Optionally, determining whether the candidate sample is accepted includes:

[0030] Using the acceptance ratio, determining whether the candidate sample is accepted;

[0031] The calculation method of the receiving ratio is:

[0032]

[0033] Among them, α(d′|d) is the acceptance scale factor, is the likelihood function value of the alternative sample, is the likelihood function value of the current sample, q(g|g′) is the recommended distribution value of the alternative sample, and q(g′|g) is the recommended distribution value of the current sample.

[0034] Compared with the prior art, the present invention has the following advantages and technical effects:

[0035] The present invention proposes a new method for extracting the earth pulse response. The method can extract the earth pulse response from the observed source signal and the response signal for subsequent inversion to extract resistivity information. By adopting Bayesian sampling instead of the deconvolution process, the method proposed by the present invention is more stable and has stronger noise resistance than conventional methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0037] Figure 1 This is a flow chart of a method for extracting the pulsed electromagnetic response of the earth based on the Bayesian method according to an embodiment of the present invention;

[0038] Figure 2 The method of the embodiment of the present invention can obtain a stable and smooth earth impulse response diagram at different offset distances;

[0039] Figure 3 The earth impulse response diagram extracted by the deconvolution method at different offset distances according to the embodiment of the present invention;

[0040] Figure 4 This is a diagram showing the effect of extracting the earth pulse response according to an embodiment of the present invention. Figure 4 (a) is the extraction result of the earth pulse response under 2.5% noise level and the added noise. Figure 4 (b) is the extraction result of the earth pulse response under 5% noise level and the added noise. Figure 4 (c) is the extraction result of the earth pulse response under 10% noise level and the added noise. Figure 4 (d) is the extracted result of the earth impulse response and the added noise at a 20% noise level. DETAILED DESCRIPTION

[0041] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0042] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0043] The present invention relates to response extraction of transient electromagnetic method. Transient electromagnetic method is an important means to obtain underground electrical information and is widely used in detection in the fields of resources, environment and engineering. This method transmits an electromagnetic source signal to the underground, and after the source is turned off, collects the response signal generated by electromagnetic induction of the underground medium. The signal collected in this way is a pure induction signal that does not contain any source signal, and is generally regarded as an ideal step signal or pulse signal in subsequent processing and inversion. However, in practice, since the transient electromagnetic emission source contains a shutoff effect, the signal emitted to the underground is often not an ideal step signal, resulting in errors in data and processing interpretation. The present invention mainly aims at the actually observed transient electromagnetic signal, eliminates the influence of source distortion on the signal, and extracts the ideal earth pulse response.

[0044] The present invention proposes a method for extracting the pulse electromagnetic response of the earth based on the Bayesian method. Figure 1 As shown, the specific steps include:

[0045] Acquire transient electromagnetic observation data;

[0046] The Bayesian method is used to obtain the pulse electromagnetic response of the earth in transient electromagnetic observation data.

[0047] Furthermore, the transient electromagnetic observation data includes: source signal and response signal.

[0048] Furthermore, the response signal is:

[0049] v(r,t)=s(r,t)*g(r,t)+n(r,t)

[0050] Among them, v is the response signal, n is the environmental noise, r is the location of the observation point, t is the time, g is the earth pulse response, and * is the convolution symbol.

[0051] Specifically, in order to extract the earth pulse response from the observed data, it is necessary to use a deconvolution method to recover the earth pulse response from equation (1). However, the deconvolution process is an ill-posed inverse problem and is easily interfered by noise. The present invention uses a Bayesian method to solve the earth pulse response in equation (1).

[0052] Furthermore, using the Bayesian method, the ground pulse electromagnetic response in the transient electromagnetic observation data is obtained, including:

[0053] S1. Obtaining the earth pulse response based on transient electromagnetic observation data, and determining the earth pulse response boundary based on the earth pulse response;

[0054] S2, generating candidate samples of the earth pulse response based on the earth pulse response boundary;

[0055] S3, calculating the likelihood of the candidate sample, and determining whether the candidate sample is accepted based on the likelihood and the candidate sample;

[0056] S4. Repeat S1-S3 until the target number of times is reached, and the mean of the sample set obtained is the earth pulse electromagnetic response.

[0057] Furthermore, the earth impulse response boundary is:

[0058] g up (r,t)=0.5g0(r,t).

[0059] g down (r,t)=2g0(r,t).

[0060] Where g0 is the earth pulse response, g up (r, t) is the upper boundary of the earth pulse response, g down (r, t) is the lower boundary of the earth impulse response.

[0061] Specifically, the deconvolution method is generally used to obtain a preliminary estimate of the earth pulse response g0 from the data. At this time, the range of the earth pulse response candidate samples is [g down ,g up ].

[0062] Furthermore, the alternative samples are:

[0063]

[0064] Among them, q(g|g′) is the recommended distribution for generating candidate samples, g is the sample of the current earth impulse response, g′ is the generated earth impulse response sample, δ g Parameters generated for the control samples.

[0065] Specifically, the present invention proposes to use the following Gaussian distribution to randomly generate candidate earth impulse response samples.

[0066] Furthermore, the likelihood function is:

[0067]

[0068] in, is the likelihood function, δ v is the standard deviation of the earth pulse response obtained by deconvolution, v is the response signal observed at the measuring point, and v' is the response signal obtained by the alternative earth pulse response sample.

[0069] Specifically, v' is calculated as follows:

[0070] v'(r,t)=s(r,t)*g'(r,t).

[0071] Further, determining whether the candidate sample is accepted includes:

[0072] Use the acceptance ratio to determine whether the alternative samples are accepted;

[0073] The calculation method of receiving ratio is:

[0074]

[0075] Among them, α(d′|d) is the acceptance scale factor, is the likelihood function value of the alternative sample, is the likelihood function value of the current sample, q(g|g′) is the recommended distribution value of the alternative sample, and q(g′|g) is the recommended distribution value of the current sample.

[0076] Specifically, a random number b between (0, 1] is generated, and when α>b, the response sample is accepted and set as the current response sample for the next sampling. If it is not accepted, the sample is rejected and the next sampling is continued.

[0077] The present invention proposes a new method for extracting the pulse response of the earth. The method can extract the pulse response of the earth from the observed source signal and the response signal, and is used for subsequent inversion to extract resistivity information. By adopting Bayesian sampling to replace the deconvolution process, the method proposed by the present invention is more stable than the conventional method and has stronger noise resistance. Among them, deconvolution is a typical ill-posed inverse problem, which is sensitive to noise during numerical solution and is extremely unstable. The present invention adopts the idea of ​​Bayesian random sampling, uses the convolution of the generated sample and the emission source waveform to obtain data close to the actual full waveform response, and establishes a Bayesian sampling process and an earth pulse response estimation method. The process only includes the convolution process, avoiding ill-posed deconvolution.

[0078] First, the method proposed in the present invention can extract a stable earth pulse response under different offset distances. Here, the offset distance refers to the distance between the transmitting source and the receiving point. Since the signal-to-noise ratio of transient electromagnetic method data is positively correlated with the offset distance, the size of the offset distance can also reflect the adaptability of the method under different noise levels. The method of the present invention can obtain a stable and smooth earth pulse response under different offset distances. Figure 2 As shown in , the extraction results are less affected by noise. Figure 3 As shown in the figure, the conventional method is interfered by noise, the extracted response is extremely unstable, and the larger the offset distance, the greater the uncertainty of the earth pulse response.

[0079] In order to further demonstrate the adaptability of the proposed method under different noise levels, noise is further added to the observed data, and then the earth pulse is extracted. The results are shown in Figure 4 shown. Figure 4 (a)-(d) are the extraction results of the earth pulse response under different noise levels, where the upper figure is the extracted earth pulse response and the lower figure is the added noise. When the added noise level is low, the method of the present invention can still extract a stable earth pulse response. As the noise level increases, the extracted earth pulse response gradually becomes unstable, but the overall result is still better than the extraction result of the deconvolution method without adding any noise.

[0080] In addition, the results of the present invention can still obtain a clear peak value of the earth pulse response when the noise level is very large. Since the peak value and peak time are important parameters for resistivity extraction, the method proposed by the present invention can obtain more useful information from the data, thereby further optimizing the detection effect of transient electromagnetic.

[0081] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A method for extracting ground pulse electromagnetic response based on Bayesian method, characterized in that: include: Acquire transient electromagnetic observation data; The Bayesian method is used to obtain the earth pulse electromagnetic response in the transient electromagnetic observation data.

2. The method for extracting the ground pulse electromagnetic response based on the Bayesian method according to claim 1 is characterized in that: The transient electromagnetic observation data includes: a source signal and a response signal.

3. The method for extracting the ground pulse electromagnetic response based on the Bayesian method according to claim 2 is characterized in that: The response signal is: v(r,t)=s(r,t)*g(r,t)+n(r,t) Among them, v is the response signal, n is the environmental noise, r is the location of the observation point, t is the time, g is the earth pulse response, and * is the convolution symbol.

4. The method for extracting the ground pulse electromagnetic response based on the Bayesian method according to claim 3 is characterized in that: Using the Bayesian method, obtaining the earth pulse electromagnetic response in the transient electromagnetic observation data includes: S1. Acquire an earth pulse response based on the transient electromagnetic observation data, and determine an earth pulse response boundary based on the earth pulse response; S2. Establishing a priori distribution based on the earth pulse response boundary, and generating candidate samples of the earth pulse response based on the priori distribution; S3, calculating the likelihood of the candidate sample, and determining whether the candidate sample is accepted based on the likelihood and the candidate sample; S4. Repeat S1-S3 until the target number of times is reached, and the mean of the obtained sample set is the earth pulse electromagnetic response.

5. The method for extracting the ground pulse electromagnetic response based on the Bayesian method according to claim 4 is characterized in that: The earth impulse response boundary is: g up (r,t)=0.5g0(r,t). g down (r,t)=2g0(r,t). Where g0 is the earth pulse response, g up (r, t) is the upper boundary of the earth pulse response, g down (r, t) is the lower boundary of the earth impulse response.

6. The method for extracting the ground pulse electromagnetic response based on the Bayesian method according to claim 4 is characterized in that: The alternative samples are: Among them, gp(g|g′) is the proposed distribution for generating candidate samples, g is the sample of the current earth impulse response, g′ is the generated earth impulse response sample, δ g Parameters generated for the control samples.

7. The method for extracting the ground pulse electromagnetic response based on the Bayesian method according to claim 4 is characterized in that: Calculating the likelihood of the candidate sample using a likelihood function; The likelihood function is: Among them, l(g′|v) is the likelihood function, δ v is the standard deviation of the earth pulse response obtained by deconvolution, v is the response signal observed at the measuring point, and v' is the response signal obtained by the alternative earth pulse response sample.

8. The method for extracting the ground pulse electromagnetic response based on the Bayesian method according to claim 4 is characterized in that: Determining whether the candidate sample is accepted includes: Using the acceptance ratio, determining whether the candidate sample is accepted; The calculation method of the acceptance ratio is: Among them, α(d′|d) is the acceptance scale factor, l(v|g′) is the likelihood function value of the alternative sample, l(g′|v) is the likelihood function value of the current sample, q(g|g′) is the recommended distribution value of the alternative sample, and q(g′|g) is the recommended distribution value of the current sample.

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