CN116794733A - Tunnel magnetic resonance and transient electromagnetic joint inversion method - Google Patents
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Abstract
The invention relates to the technical research field of geophysical signal processing and analysis, in particular to a tunnel magnetic resonance and transient electromagnetic joint inversion method, which comprises the following steps: using a magnetic resonance and transient electromagnetic combined instrument, placing the instrument at the tunnel face for detection, and obtaining observation data of a water-containing structure in front of the tunnel face; inversion is carried out on the acquired data by using a Markov chain Monte Carlo algorithm to obtain the resistivity of stratum in front of the tunnel face, the water content distribution and the interface position information of each layer and the probability distribution of inversion parameters, uncertainty of inversion results and correlation analysis results are given out while the resistivity and the water content information in front of the tunnel face are inverted and interpreted, and finally the resistivity and the water content information distribution are given out according to probability, so that early warning guidance is provided for tunnel engineering safety development.
Description
Technical Field
The invention relates to the technical research field of geophysical signal processing and analysis, in particular to a tunnel magnetic resonance and transient electromagnetic joint inversion method.
Background
In the construction process of tunnel engineering, geological disasters such as underground water burst and collapse are often faced, and the disasters not only can cause construction delay, but also can cause tunnel collapse to threaten the life safety of constructors. As an emerging geophysical prospecting technique, nuclear magnetic resonance detection methods have been used to detect water gushes in underground structures during the last decade. Because of the direct sensitivity to water molecules, non-invasive nuclear magnetic resonance detection technology is of great importance in preventing water inrush disasters of tunnels. The prior research results show that the technology has the capability of directly and quantitatively tracking the water body in the tunnel, so that the tunnel water burst accident can be effectively prevented.
The correct interpretation of the tunnel magnetic resonance data is important, which determines the correct judgment of the constructor on the forward geological condition. The magnetic resonance inversion is a nonlinear problem, and the solution is usually not unique, namely, for the selection of parameters of an underground model, a plurality of or infinite number of parameter models can be matched with measured data, but the conventional inversion method can only give a single optimal solution, can not obtain uncertainty and correlation information of the parameters of the current inversion model, and the formation resistivity information has great influence on the forward result of the magnetic resonance.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a tunnel magnetic resonance and transient electromagnetic joint inversion method, provides uncertainty of an inversion result and a correlation analysis result while inverting and interpreting resistivity and water content information in front of a tunnel face, and finally provides resistivity and water content information distribution according to probability, thereby providing early warning guidance for tunnel engineering safety development.
The invention aims at realizing the following technical scheme:
a tunnel magnetic resonance and transient electromagnetic joint inversion method, comprising the steps of:
s1, using a magnetic resonance and transient electromagnetic combined instrument, placing the instrument at a tunnel face for detection, and obtaining observation data of a water-containing structure in front of the tunnel face;
s2, inversion is carried out on the acquired data by using a Markov chain Monte Carlo algorithm, and the resistivity, the water content distribution and the interface position information of each layer of the front stratum of the face and the probability distribution of inversion parameters are obtained.
Further, the magnetic resonance and transient electromagnetic combined instrument in the step S1 adopts overlapping loop configuration, a transmitting system outputs a transmitting signal by being abutted against a face, and a receiving system synchronously acquires observation signal data;
further, the detection range of the water-containing structure of the tunnel face in the step S1 is within 0 to 25 meters in front of and behind the face.
Further, in step S2, inversion is carried out on the acquired data by adopting a Markov chain Monte Carlo algorithm, and the method comprises the following specific steps;
step 1, prior distribution and initial model:
in the tunnel magnetic resonance and transient electromagnetic joint inversion, inversion parameters comprise water content, resistivity, layer interfaces and layer numbers, wherein the water content, the resistivity and the prior probability distribution of the layer interfaces are set to be uniform distribution of corresponding intervals, the position interval of the layer interfaces is [ -25, 25], the unit is m, the water content interval is [0, 100% ], the resistivity interval is [0, 600], the unit is omega m, and after the prior distribution is set, an initial model is generated from the prior distribution;
step 2, selecting candidate models:
the suggested distribution is expressed as:
q(m′|m)＝q(z′|z)q(d′|d)q(w′|z′,w)q(ρ′|d′,ρ)
wherein m and m ' represent the current model and the candidate model, z and z ' represent the current water content layer interface and the candidate water content layer interface position, d and d ' represent the current resistivity layer interface and the candidate resistivity layer interface position, w and w ' represent the current water content and the candidate water content, ρ and ρ ' represent the current resistivity and the candidate resistivity, q (z ' |z), q (d ' |d), q (w ' |z ', w) and q (ρ ' |d ', ρ) represent the water content layer interface position, the resistivity layer interface position, the suggested distribution of the water content and the resistivity, respectively, the suggested distribution of the layer interface satisfies two states:
layer interface perturbation: randomly advancing one layer of interface to randomly disturb the interface between two adjacent layers of interfaces, wherein the probability p=2/3;
the layer interface is unchanged: probability p=1/3;
the water content and resistivity advice distribution is set as a normal distribution with the current water content and resistivity as the average value:
wherein σ is the variance of the normal distribution;
step 3, accepting or rejecting candidate models
When the candidate model is obtained through sampling, whether the candidate model is accepted or not is determined by accepting the probability alpha, wherein the calculation formula of alpha is as follows:
in the middle ofRepresenting the probability ratio of a jump from the candidate model to the current model and the current model to the candidate model, +.>Representing the ratio of the candidate model to the current model likelihood function;
the likelihood function is used for calculating the fitting degree between the model data and the real data, and the likelihood function is defined as multidimensional normal distribution:
wherein N represents the number of observed data, d obs Representing measured data, g (m) representing magnetic resonance and transient electromagnetic combined forward modeling of a given modelC should be d Represents the data covariance matrix, |C d The I represents a matrix corresponding determinant; when the data does not meet the normal distribution, the Laplace distribution is adopted for representation:
finally, generating a random number mu between [0,1], accepting the transition if mu is smaller than the acceptance probability alpha, otherwise rejecting;
and 4, continuously updating and sampling the model according to the steps 1-3 until the iteration times are reached, carrying out probability statistics on all the sampled models, and finally outputting the maximum probability and posterior probability distribution of the model parameters.
Further, the analysis of uncertainty and correlation in the step S3 refers to obtaining an uncertainty and correlation diagram of the interface position of the model resistivity and the resistivity layer and the interface of the model water content and the aquifer according to the inversion result of the Markov chain Monte Carlo, and analyzing the correlation and distribution probability of the resistivity and the water content and the interface position of the corresponding layer.
The beneficial effects are that: the invention uses Markov chain Monte Carlo algorithm to carry out inversion interpretation on tunnel magnetic resonance and transient electromagnetic data, the inversion searches all possible conforming models from the whole world, and inversion result distribution is obtained from the probability. The method can ensure the global optimality of the inversion result, analyze the uncertainty and the correlation of the inversion result, and master the probability distribution of the earth resistivity and the aquifer information in front of the tunnel face. In addition, the joint inversion of magnetic resonance and transient electromagnetic can also effectively improve the accuracy of aquifer information in an inversion result. Therefore, the position of the water-inrush layer is predicted more accurately, the guarantee is provided for the safe construction of the tunnel, and the method has a larger practical application value.
Drawings
FIG. 1 is a schematic diagram of a combined detection mode of tunnel magnetic resonance and transient electromagnetic provided by an embodiment of the invention;
FIG. 2 is a flow chart of inversion by the Markov chain Monte Carlo algorithm provided by an embodiment of the present invention;
fig. 3 is a simulation diagram of a tunnel magnetic resonance noise-containing receiving signal (a) and a transient electromagnetic noise-containing receiving signal (b) provided by an embodiment of the present invention;
FIG. 4 shows a data joint inversion result of a Markov chain Monte Carlo algorithm-based tunnel magnetic resonance (a) and transient electromagnetic (b) according to an embodiment of the present invention;
FIG. 5 is a graph of water content and layer interface position uncertainty and correlation of joint inversion results of a Markov chain Monte Carlo algorithm provided by an embodiment of the present invention;
FIG. 6 is a graph of layer resistivity versus layer interface position uncertainty and correlation for a joint inversion result of a Markov chain Monte Carlo algorithm provided by an embodiment of the present invention;
Detailed Description
The invention is described in further detail below with reference to the attached drawings and examples:
the invention discloses a tunnel magnetic resonance and transient electromagnetic joint inversion method based on a Markov chain Monte Carlo algorithm, which comprises the following steps:
s1, using a magnetic resonance and transient electromagnetic combined instrument, placing the instrument at a tunnel face for detection, and obtaining observation data of a water-containing structure in front of the tunnel face;
s2, inversion is carried out on the acquired data by using a Markov chain Monte Carlo algorithm, and the resistivity, the water content distribution and the interface position information of each layer of the front stratum of the tunnel face and the probability distribution of inversion parameters are obtained;
the inversion result of the Markov chain Monte Carlo algorithm is more accurate relative to a single inversion method of magnetic resonance or transient electromagnetic, and uncertainty and correlation analysis results of the stratum resistivity and resistivity layer interface position in front of the tunnel face and the stratum water content and aquifer interface position can be given out.
In step S1, as shown in fig. 1, a magnetic resonance and transient electromagnetic combined instrument is placed at a tunnel face for detection, and magnetic resonance and transient electromagnetic observation data of the tunnel face are acquired, where the magnetic resonance and transient electromagnetic combined instrument is a small magnetic resonance and transient electromagnetic combined detection system suitable for tunnel detection, and an overlapping loop configuration is adopted, a transmitting system outputs a transmitting signal against the tunnel face, and a receiving system synchronously acquires the observation signal data;
in the embodiment of the invention, the tunnel model is set as the model of 25 meters in front of and behind the tunnel face, a low-resistance water-containing structure exists between 5 meters and 20 meters in front of the tunnel face, the corresponding water content is 70%, the resistivity is 20 omega m, the rest stratum is relatively high-resistance, the resistivity is 130 omega m between 0 meters and 5 meters, and the resistivity is 200 omega m between 20 meters and 25 meters. The tunnel is detected by using the magnetic resonance and transient electromagnetic combined system with the emission side length of 6 meters and the number of turns of 5 turns, the emission current of 10A, random noise with the average value of 10nV is added, and a model forward observation signal is shown in figure 3;
the acquired data is inverted and interpreted by adopting a Markov chain Monte Carlo algorithm, and an algorithm flow chart is shown in fig. 2, and comprises the following specific steps:
(1) a priori distribution and initial model:
in the tunnel magnetic resonance and transient electromagnetic joint inversion, inversion parameters include water content, resistivity, and their layer interfaces and layers. The water content, the resistivity and the prior probability distribution of the layer interfaces are set to be uniform distribution of the corresponding intervals, wherein the interval of the layer interface positions is [ -25, 25], the unit is m, the interval of the water content is [0, 100% ], the interval of the resistivity is [0, 600], and the unit is omega m. After setting the prior distribution, an initial model is generated from the prior distribution.
(2) Selecting candidate models:
the selection of candidate models depends on the suggested distribution. Based on the ineffectiveness of the Markov chain, the generation of candidate models is only related to the current model, and the suggested distribution can be expressed as follows, regardless of the previous model parameters:
q(m′|m)＝q(z′|z)q(d′|d)q(w′|z′,w)q(ρ′|d′,ρ)
wherein m and m ' represent the current model and the candidate model, z and z ' represent the current water content layer interface and the candidate water content layer interface position, d and d ' represent the current resistivity layer interface and the candidate resistivity layer interface position, w and w ' represent the current water content and the candidate water content, and ρ ' represent the current resistivity and the candidate resistivity, respectively. q (z '|z), q (d' |d), q (w '|z', w), and q (ρ '|d', ρ) represent suggested distributions of water content layer interface location, resistivity layer interface location, water content, and resistivity, respectively. The layer interface suggestion distribution satisfies two states:
layer interface perturbation: one layer of interface is randomly advanced, so that the interface is randomly disturbed between two adjacent layers of interfaces, and the probability p=2/3.
The layer interface is unchanged: probability p=1/3.
The water content and resistivity advice distribution is set as a normal distribution with the current water content and resistivity as the average value:
where σ is the variance of the normal distribution, affecting the step size of the sampling to some extent.
(3) Accepting or rejecting candidate models
When a candidate model is obtained through sampling, the next step of the Markov chain Monte Carlo algorithm is to determine whether to accept the candidate model or not through accepting the probability alpha, wherein the calculation formula of alpha is as follows:
in the middle ofRepresenting the probability ratio of a jump from the candidate model to the current model and the current model to the candidate model, +.>Representing the ratio of candidate models to the current model likelihood function.
The Markov chain Monte Carlo algorithm likelihood function is used to calculate the degree of fit between the model data and the real data. In the field of geophysical prospecting, data noise follows a gaussian distribution and is independent of inversion parameters. The likelihood function is defined as a multidimensional normal distribution:
wherein N represents the number of observed data, d obs Representing measured data, g (m) representing magnetic resonance and transient electromagnetic combined forward response of a given model, C d Represents the data covariance matrix, |C d The i represents the matrix corresponding determinant. When the data does not meet the normal distribution, the Laplace distribution is adopted for representation:
finally, a random number μ is generated between [0,1], and if μ is less than the acceptance probability α, the transition is accepted, otherwise rejected. And continuously updating the model and sampling according to the method until the iteration number terminates the algorithm.
The inversion result of the tunnel model is shown in fig. 4, the water content corresponding to the maximum probability in the inversion result and the position information of a layer interface thereof can be obtained to be basically consistent with the set model, all the accepted models fluctuate near the set model, and uncertainty and correlation between the position of the water-bearing layer interface of the model and the water content of the model are further obtained according to the inversion result of the Markov chain Monte Carlo, as shown in fig. 5; obtaining uncertainty and correlation of the interface position of the model resistivity layer and the model resistivity, as shown in fig. 6;
according to the Markov chain Monte Carlo inversion result, the information of the water content of the stratum and the position of the layer interface of the stratum can be accurately judged, and the uncertainty and the correlation of the water content and the position of the layer interface can be obtained. Therefore, the Markov chain Monte Carlo inversion algorithm can carry out relatively comprehensive inversion interpretation on tunnel magnetic resonance and transient electromagnetic data, more accurately give out the position of the aquifer, and provide guarantee for tunnel engineering safety construction.
Claims (5)
1. A tunnel magnetic resonance and transient electromagnetic joint inversion method, which is characterized by comprising the following steps:
s1, using a magnetic resonance and transient electromagnetic combined instrument, placing the instrument at a tunnel face for detection, and obtaining observation data of a water-containing structure in front of the tunnel face;
s2, inversion is carried out on the acquired data by using a Markov chain Monte Carlo algorithm, and the resistivity, the water content distribution and the interface position information of each layer of the front stratum of the face and the probability distribution of inversion parameters are obtained.
2. The tunnel magnetic resonance and transient electromagnetic joint inversion method according to claim 1, wherein the magnetic resonance and transient electromagnetic joint instrument in the step S1 adopts an overlapping loop configuration, a transmitting system outputs a transmitting signal by being abutted against a face, and a receiving system synchronously acquires observation signal data.
3. The tunnel magnetic resonance and transient electromagnetic joint inversion method of claim 1, wherein the detection range of the tunnel face water-containing structure in step S1 is within 0 to 25 meters in front of and behind the face.
4. The tunnel magnetic resonance and transient electromagnetic joint inversion method according to claim 1, wherein the inversion of the acquired data in step S2 by using a markov chain monte carlo algorithm comprises the following specific steps;
step 1, prior distribution and initial model:
in the tunnel magnetic resonance and transient electromagnetic joint inversion, inversion parameters comprise water content, resistivity, layer interfaces and layer numbers, wherein the water content, the resistivity and the prior probability distribution of the layer interfaces are set to be uniform distribution of corresponding intervals, the position interval of the layer interfaces is [ -25, 25], the unit is m, the water content interval is [0, 100% ], the resistivity interval is [0, 600], the unit is omega m, and after the prior distribution is set, an initial model is generated from the prior distribution;
step 2, selecting candidate models:
the suggested distribution is expressed as:
q(m′|m)＝q(z′|z)q(d′|d)q(w′|z′,w)q(ρ′|d′,ρ)
wherein m and m ' represent the current model and the candidate model, z and z ' represent the current water content layer interface and the candidate water content layer interface position, d and d ' represent the current resistivity layer interface and the candidate resistivity layer interface position, w and w ' represent the current water content and the candidate water content, ρ and ρ ' represent the current resistivity and the candidate resistivity, q (z ' |z), q (d ' |d), q (w ' |z ', w) and q (ρ ' |d ', ρ) represent the water content layer interface position, the resistivity layer interface position, the suggested distribution of the water content and the resistivity, respectively, the suggested distribution of the layer interface satisfies two states:
layer interface perturbation: randomly advancing one layer of interface to randomly disturb the interface between two adjacent layers of interfaces, wherein the probability p=2/3;
the layer interface is unchanged: probability p=1/3;
the water content and resistivity advice distribution is set as a normal distribution with the current water content and resistivity as the average value:
wherein σ is the variance of the normal distribution;
step 3, accepting or rejecting candidate models
When the candidate model is obtained through sampling, whether the candidate model is accepted or not is determined by accepting the probability alpha, wherein the calculation formula of alpha is as follows:
in the middle ofRepresenting the probability ratio of a jump from the candidate model to the current model and the current model to the candidate model, +.>Representing the ratio of the candidate model to the current model likelihood function;
the likelihood function is used for calculating the fitting degree between the model data and the real data, and the likelihood function is defined as multidimensional normal distribution:
wherein N represents the number of observed data, d obs Representing measured data, g (m) representing magnetic resonance and transient electromagnetic combined forward response of a given model, C d Represents the data covariance matrix, |C d The I represents a matrix corresponding determinant; when the data does not meet the normal distribution, the Laplace distribution is adopted for representation:
finally, generating a random number mu between [0,1], accepting the transition if mu is smaller than the acceptance probability alpha, otherwise rejecting;
and 4, continuously updating and sampling the model according to the steps 1-3 until the iteration times are reached, carrying out probability statistics on all the sampled models, and finally outputting the maximum probability and posterior probability distribution of the model parameters.
5. The method of claim 1, wherein the analysis of uncertainty and correlation in step S3 is to obtain a map of uncertainty and correlation of model resistivity and resistivity layer interface positions and model water content and aquifer interface positions based on markov chain monte carlo inversion results, and analyze the correlation and distribution probability of resistivity, water content and their corresponding layer interface positions.
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| CN117075212A (en) * | 2023-10-16 | 2023-11-17 | 吉林大学 | Tunnel magnetic resonance fracture structure imaging method |
| CN117075212B (en) * | 2023-10-16 | 2024-01-26 | 吉林大学 | Tunnel magnetic resonance fracture structure imaging method |
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