A tunnel magnetic resonance and transient electromagnetic joint inversion method

Abstract

The present application relates to the technical field of geophysical signal processing and analysis, in particular to a tunnel magnetic resonance and transient electromagnetic joint inversion method, comprising: using a magnetic resonance and transient electromagnetic joint instrument, placing it at a tunnel face for detection, and obtaining observation data of a water-bearing structure in front of the tunnel face; using a Markov chain Monte Carlo algorithm to invert the collected data, obtaining stratum resistivity, water content distribution in front of the tunnel face, and interface position information of each layer, and probability distribution of these inversion parameters; while inverting and interpreting resistivity and water content information in front of the tunnel face, the uncertainty of the inversion result and the result of correlation analysis are given; finally, the resistivity and water content information distribution is given according to probability, which provides early warning guidance for tunnel engineering safety development.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of geophysical signal processing and analysis, in particular to a tunnel magnetic resonance and transient electromagnetic joint inversion method. BACKGROUND

[0002] In the construction process of tunnel engineering, geological disasters such as sudden gushing water and collapse often occur, which not only causes construction delay, but also threatens the safety of construction personnel. As a new geophysical exploration technology, nuclear magnetic resonance detection method has been used to detect water inrush in underground buildings in the past decade. Due to its direct sensitivity to water molecules, non-invasive nuclear magnetic resonance detection technology has important significance in preventing water inrush disasters in tunnels. Previous research results show that this technology has the ability to directly and quantitatively track water in tunnels, so as to effectively prevent tunnel water inrush accidents.

[0003] Correct interpretation of tunnel magnetic resonance data is very important, which determines the correct judgment of the geological conditions in front of the construction personnel. Magnetic resonance inversion is a nonlinear problem, and its solution is usually not unique, that is, for the selection of underground model parameters, there are multiple or infinite parameter models that can match the measured data, and the conventional inversion method can only give a single optimal solution, and cannot obtain the uncertainty and correlation information of the current inversion model parameters, and the formation resistivity information has a great influence on the magnetic resonance forward result. SUMMARY

[0004] The purpose of the present application is to overcome the shortcomings of the prior art and provide a tunnel magnetic resonance and transient electromagnetic joint inversion method, which can interpret the resistivity and water content information in front of the tunnel face while giving the uncertainty and correlation analysis results of the inversion results, and finally give the resistivity and water content information distribution according to the probability, providing early warning guidance for tunnel engineering safety development.

[0005] The purpose of the present application is achieved by the following technical solutions:

[0006] A tunnel magnetic resonance and transient electromagnetic joint inversion method, the method comprising the following steps:

[0007] S1, using a magnetic resonance and transient electromagnetic joint instrument, placing it at the tunnel face for detection, and obtaining observation data of the water-bearing structure in front of the tunnel face;

[0008] S2, using Markov chain Monte Carlo algorithm to invert the collected data, obtaining the formation resistivity, water content distribution and interface position information in front of the tunnel face, and the probability distribution of these inversion parameters.

[0009] Further, the magnetic resonance and transient electromagnetic combined instrument in step S1 adopts an overlapping loop configuration, and a transmitting system outputs a transmitting signal close to the tunnel face, and a receiving system synchronously collects observation signal data.

[0010] Further, the detection range of the tunnel face water-bearing structure in step S1 is 0 to 25 meters in front and back of the tunnel face.

[0011] Further, the Markov chain Monte Carlo algorithm is used to invert the collected data in step S2, including the following specific steps.

[0012] Step 1, prior distribution and initial model:

[0013] In the tunnel magnetic resonance and transient electromagnetic joint inversion, the inversion parameters include water content, resistivity, layer interface and layer number, the prior probability distribution of the water content, resistivity and layer interface is set as the uniform distribution of the corresponding interval, wherein the layer interface position interval is [-25, 25] with the unit of m, the water content interval is [0, 100%], the resistivity interval is [0, 600] with the unit of Ωm, after setting the prior distribution, the initial model is generated from the prior distribution;

[0014] Step 2, select a candidate model:

[0015] The proposal distribution is expressed as:

[0016] ,

[0017] Wherein and represent the current model and the candidate model respectively, and represent the current water content layer interface and the candidate water content layer interface position respectively, and represent the current resistivity layer interface and the candidate resistivity layer interface position respectively, and represent the current water content and the candidate water content respectively, and represent the current resistivity and the candidate resistivity respectively, , , and represent the water content layer interface position, the resistivity layer interface position, the water content and the resistivity respectively, the layer interface proposal distribution satisfies two states:

[0018] Layer interface disturbance: randomly advance a layer interface, and make it randomly disturbed between adjacent two layer interfaces with a probability .

[0019] Layer interface invariable: probability ;

[0020] The water content, resistivity suggested distribution is set as a normal distribution with the current water content, resistivity as the mean value:

[0021] , ,

[0022] wherein is the variance of the normal distribution;

[0023] Step 3, accept or reject the candidate model,

[0024] When the candidate model is sampled, whether to accept the candidate model is determined by the acceptance probability , and the calculation formula is:

[0025] ,

[0026] In the formula, represents the probability ratio of jumping from the candidate model to the current model and jumping from the current model to the candidate model, represents the ratio of the likelihood function of the candidate model to the current model;

[0027] wherein, the likelihood function is used to calculate the fitting degree between the model data and the real data, and the likelihood function is defined as a multi-dimensional normal distribution:

[0028] ,

[0029] wherein, represents the number of observation data, represents the measured data, represents the joint forward response of magnetic resonance and transient electromagnetic method of the given model, represents the data covariance matrix, represents the determinant of the matrix; when the data does not satisfy the normal distribution, the Laplace distribution is used to represent:

[0030] ,

[0031] Finally, a random number between 0 and 1 is generated , if is less than the acceptance probability , the transition is accepted, otherwise it is rejected;

[0032] Step 4, constantly update the model and sample according to steps 1-3 until the number of iterations is reached, and the probability statistics of all sampled models are performed, and finally the maximum probability and posterior probability distribution of the model parameters are output.

[0033] ​Further, the analysis of the uncertainty and correlation in step S3 refers to obtaining the uncertainty and correlation diagrams of the model resistivity and the resistivity layer interface position and the model water content and the water content layer interface according to the Markov chain Monte Carlo inversion result, and analyzing the correlation and distribution probability of the resistivity, water content and their corresponding layer interface positions.

[0034] Beneficial effects: the Markov chain Monte Carlo algorithm is used to perform inversion interpretation on the tunnel magnetic resonance and transient electromagnetic data, the inversion searches all possible models from the global, and the inversion result distribution is obtained from probability. The method can guarantee the global optimality of the inversion result, and can perform uncertainty and correlation analysis on the inversion result, and master the probability distribution of the ground resistivity and water-bearing layer information in front of the tunnel face. In addition, the joint inversion of magnetic resonance and transient electromagnetic can effectively improve the accuracy of the water-bearing layer information in the inversion result. Therefore, the position of the water inrush layer can be more accurately predicted, the safety construction of the tunnel is ensured, and the method has great practical application value. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 A tunnel magnetic resonance and transient electromagnetic joint detection method provided for an embodiment of the present application is shown in the figure;

[0036] Figure 2 A flowchart of the Markov chain Monte Carlo algorithm for inversion provided for an embodiment of the present application is shown in the figure;

[0037] Figure 3 A tunnel magnetic resonance noise-containing received signal (a) and a transient electromagnetic noise-containing received signal (b) simulation diagram provided for an embodiment of the present application is shown in the figure;

[0038] Figure 4 A Markov chain Monte Carlo algorithm-based tunnel magnetic resonance (a) and transient electromagnetic (b) data joint inversion result provided for an embodiment of the present application is shown in the figure;

[0039] Figure 5 A Markov chain Monte Carlo algorithm-based joint inversion result water content and layer interface position uncertainty and correlation diagram provided for an embodiment of the present application is shown in the figure. DETAILED DESCRIPTION

[0040] The present application will be further described in detail below in combination with the drawings and embodiments:

[0041] The present application is a tunnel magnetic resonance and transient electromagnetic joint inversion method based on the Markov chain Monte Carlo algorithm, and the method comprises the following steps:

[0042] S1, using a magnetic resonance and transient electromagnetic combination instrument, placing the instrument at the tunnel face for detection, and obtaining observation data of water-bearing structures in front of the tunnel face;

[0043] S2, using Markov chain Monte Carlo algorithm to invert the collected data to obtain the stratum resistivity, water content distribution and interface position information in front of the tunnel face, and the probability distribution of these inversion parameters;

[0044] The inversion result of the Markov chain Monte Carlo algorithm is more accurate than the single inversion method of magnetic resonance or transient electromagnetic method, and can give the uncertainty and correlation analysis result of the stratum resistivity in front of the tunnel face, the resistivity layer interface position, and the stratum water content and water content layer interface position.

[0045] As shown in Figure 1 In step S1, the magnetic resonance and transient electromagnetic combined instrument is placed at the tunnel face for detection to obtain and record the magnetic resonance and transient electromagnetic observation data at the tunnel face, wherein the magnetic resonance and transient electromagnetic combined instrument is a small-sized magnetic resonance and transient electromagnetic combined detection system suitable for tunnel detection, adopts an overlapping loop configuration, and the transmitting system outputs a transmitting signal by abutting against the tunnel face, and the receiving system synchronously collects observation signal data;

[0046] In the embodiment of the application, the tunnel model is set as a model of 25 meters in front of and behind the tunnel face, and there is a low-resistance water-bearing structure between 5 meters and 20 meters in front of the tunnel face, corresponding to a water content of 70% and a resistivity of 20 Ωm, and the remaining strata are relatively high-resistance, with a resistivity of 130 Ωm from 0 meters to 5 meters and a resistivity of 200 Ωm from 20 meters to 25 meters. The above-mentioned magnetic resonance and transient electromagnetic combined system is used to detect the tunnel, with a transmitting side length of 6 meters, 5 turns, a transmitting current of 10 A, and random noise of 10 nV is added, and the model forward observation signal is as shown in Figure 3 ;

[0047] The collected data is inverted and explained by using the Markov chain Monte Carlo algorithm, and the algorithm flowchart is as shown in Figure 2 , including the following specific steps:

[0048] Prior distribution and initial model:

[0049] In the tunnel magnetic resonance and transient electromagnetic combined inversion, the inversion parameters include water content, resistivity and their layer interface and number. The prior probability distribution of the water content, resistivity and their layer interface is set as a uniform distribution in the corresponding interval, wherein the layer interface position interval is [-25, 25] with the unit of m, the water content interval is [0, 100%], and the resistivity interval is [0, 600] with the unit of Ωm. After setting the prior distribution, the initial model is generated from the prior distribution.

[0050] Selecting a candidate model:

[0051] The selection of candidate model depends on proposal distribution. According to the no aftereffect of Markov chain, the generation of candidate model is only related to current model and has nothing to do with previous model parameters. The proposal distribution can be expressed as:

[0052] ,

[0053] Wherein and represent the current model and candidate model respectively, and represent the current water content layer interface and candidate water content layer interface position respectively, and represent the current resistivity layer interface and candidate resistivity layer interface position respectively, and represent the current water content and candidate water content respectively, and represent the current resistivity and candidate resistivity respectively. , , and represent the proposal distribution of water content layer interface position, resistivity layer interface position, water content and resistivity respectively. The layer interface proposal distribution satisfies two states:

[0054] Layer interface disturbance: randomly advance a layer interface, make it randomly disturbed between adjacent two layer interfaces, with probability .

[0055] Layer interface invariable: with probability .

[0056] The water content and resistivity proposal distribution is set to normal distribution with current water content and resistivity as mean value:

[0057] , ,

[0058] Wherein is the variance of normal distribution, which affects the step length of sampling to some extent.

[0059] Accept or reject the candidate model,

[0060] When the candidate model is obtained by sampling, the next step of Markov chain Monte Carlo algorithm is to decide whether to accept the candidate model by acceptance probability , The calculation formula is:

[0061] ,

[0062] In the formula, The probability ratio of jumping from the candidate model to the current model and jumping from the current model to the candidate model, The ratio of the candidate model to the current model likelihood function.

[0063] The Markov Chain Monte Carlo algorithm likelihood function is used to calculate the fitting degree between the model data and the real data. In the field of geophysical exploration, the data noise obeys the Gaussian distribution, and is independent of each other with each inversion parameter. The likelihood function is defined as a multi-dimensional normal distribution:

[0064] ,

[0065] Wherein, The number of observation data, The measured data, The given model of the magnetic resonance and transient electromagnetic joint forward response, The data covariance matrix, The matrix corresponding determinant. When the data does not satisfy the normal distribution, the Laplace distribution is used to represent:

[0066] ,

[0067] Finally generate a random number between [0, 1] If is less than the acceptance probability , the transition is accepted, otherwise rejected. According to the above method, the model is updated and sampled continuously until the iteration number is reached to terminate the algorithm.

[0068] The tunnel model inversion result is shown in Figure 4 It can be concluded that the water content corresponding to the maximum probability in the inversion result and the position information of the layer interface are basically consistent with the set model. All accepted models fluctuate around the set model. Further according to the Markov Chain Monte Carlo inversion result, the uncertainty and correlation of the model water-bearing layer interface position and the model water content are obtained, as shown in Figure 5 .

[0069] According to the Markov Chain Monte Carlo inversion result, the information of the water content and the position of the layer interface can be accurately judged, and their uncertainty and correlation can also be obtained. Therefore, the Markov Chain Monte Carlo inversion algorithm can relatively comprehensively invert the tunnel magnetic resonance and transient electromagnetic data, and more accurately give the position of the water-bearing layer, providing protection for the safety construction of the tunnel project.

Claims

1. A tunnel magnetoresistive and transient electromagnetic joint inversion method, characterized in that, The method comprises the following steps: S1, using a magnetic resonance and transient electromagnetic combination instrument, placed at the tunnel face, to detect and obtain observation data of water-bearing structures in front of the tunnel face; S2, using the Markov chain Monte Carlo algorithm to invert the collected data to obtain the resistivity, water content distribution and interface position information of each layer in front of the tunnel face, and the probability distribution of these inversion parameters; The Markov chain Monte Carlo algorithm is used to invert the collected data in step S2, comprising the following specific steps; Step 1, prior distribution and initial model: In the joint inversion of tunnel magnetic resonance and transient electromagnetic method, the inversion parameters include water content, resistivity, layer interface and layer number, the prior probability distribution of water content, resistivity and layer interface is set as a uniform distribution in the corresponding interval, wherein the layer interface position interval is [-25, 25] with unit m, the water content interval is [0, 100%], the resistivity interval is [0, 600] with unit Ωm, after setting the prior distribution, the initial model is generated from the prior distribution; Step 2, select candidate model: The proposal distribution is expressed as: ， wherein and respectively denote the current model and the candidate model, and respectively denote the current water cut layer interface and the candidate water cut layer interface position, and respectively denote the current resistivity layer interface and the candidate resistivity layer interface position, and respectively denote the current water cut and the candidate water cut, and respectively denote the current resistivity and the candidate resistivity, , , and respectively denote the suggested distribution of water cut layer interface position, resistivity layer interface position, water cut and resistivity, the layer interface suggested distribution satisfies two states: Layer interface disturbance: randomly advance a layer interface, make it randomly disturbed between adjacent two layer interfaces, probability ; Layer interface invariant: probability ; The water content and resistivity proposal distribution is set as a normal distribution with the current water content and resistivity as the mean value: ， ， wherein is the variance of the normal distribution; Step 3, accept or reject candidate model When a candidate model is sampled, whether to accept the candidate model is decided by an acceptance probability The calculation formula of the acceptance probability is as follows: The calculation formula of the acceptance probability is as follows: ， wherein denotes the ratio of the probability of jumping from the candidate model to the current model and vice versa, denotes the ratio of the candidate model to the current model likelihood function; Wherein, the likelihood function is used to calculate the fitting degree between model data and real data, and the likelihood function is defined as a multi-dimensional normal distribution: ， wherein, denotes the number of observation data, denotes the measured data, denotes the joint forward response of magnetic resonance and transient electromagnetic method for a given model, denotes the data covariance matrix, denotes the determinant of a matrix; when the data does not satisfy the normal distribution, the Laplace distribution is used to represent: ， Finally generate a random number between 0 and 1 If is less than the acceptance probability then accept the transition, otherwise reject it; Step 4, continuously update the model and sample according to steps 1-3 until the iteration number is reached, and the probability statistics of all sampled models are performed, and finally the maximum probability and posterior probability distribution of the model parameters are output.

2. The joint inversion method of tunnel magnetic resonance and transient electromagnetic according to claim 1, characterized in that, The magnetic resonance and transient electromagnetic combination instrument in step S1 adopts an overlapping loop configuration, and the transmitting system outputs transmitting signals by abutting against the tunnel face, and the receiving system synchronously collects observation signal data.

3. The joint inversion method of tunnel magnetic resonance and transient electromagnetic according to claim 1, characterized in that, The detection range of the water-bearing structure of the tunnel face in step S1 is within 0 to 25 meters in front and back of the tunnel face.

4. The method of claim 1, wherein, It also includes S3, obtaining the uncertainty and correlation diagram of model resistivity and resistivity layer interface position and model water content and water-bearing layer interface according to the Markov chain Monte Carlo inversion result, and analyzing the correlation and distribution probability of resistivity, water content and their corresponding layer interface position.

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