Natural electric field-electric field joint detection and inversion method based on GMM prior

Abstract

The application discloses a natural electric field-electric field combined detection and inversion method based on a GMM prior, relates to the technical field of tunnel engineering geological detection, and obtains resistivity and natural electric potential observed in a region to be inverted; equivalent body source of the natural electric potential is parameterized into a body source vector on a grid unit, a weighted L1 sparse regular constraint is introduced to the body source vector, a GMM prior model is taken as an underground electrical structure prior shared across physical fields, a multi-task combined inversion objective function sharing a label of the underground electrical structure is established; inversion iteration is carried out by using maximum posterior, and a maximum expectation algorithm is used to update parameters of the GMM prior model and the label of the underground electrical structure until a termination condition is met, so that a combined inversion imaging result of a water-rich abnormal body of a tunnel is obtained. The method combines the advantages of multiple source electric methods, introduces an underground electrical structure prior, and combines Bayesian uncertainty analysis, and thus high-resolution and high-credibility identification of a water-rich abnormal body in front of a tunnel is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of tunnel engineering geological exploration, in particular to a natural electric field-electric field combined exploration and inversion method based on GMM prior. BACKGROUND

[0002] In the process of tunnel construction, unfavorable geological bodies such as fault fracture zones, karst development zones and fissure water-rich areas often develop in front of the working face. Once the water-bearing structure is penetrated during excavation, it is easy to cause sudden gushing water, sudden mud and surrounding rock collapse and other disasters, which seriously threaten the safety of construction and the progress of the project. Therefore, the advanced prediction and identification of disaster water body and groundwater distribution in front of the construction is a key problem that needs to be solved in tunnel engineering construction.

[0003] Geophysical methods are widely used in front disaster source exploration due to their wide coverage, non-destructive detection and small construction interference. Among them, inversion imaging technology, as an important part of geophysical methods, can realize the identification and characterization of the position and boundary of underground abnormal body through parameterization and numerical optimization of the collected signals, and is an important technical means for positioning and quantifying tunnel disaster bodies.

[0004] In electrical exploration, resistivity inversion methods have been widely used, but the resolution is insufficient in deep weak abnormal bodies and complex interference environment. The natural electric field method is a passive observation method, which is highly sensitive to groundwater migration and water-rich abnormal bodies, and has the advantages of simple layout, light equipment and small construction interference, which can make up for the shortcomings of resistivity inversion to a certain extent.

[0005] In recent years, researchers have proposed joint inversion of different electrical data to integrate multi-source information and improve imaging accuracy. Natural electric field and resistivity joint inversion, as a potential fusion mode, can not only use resistivity data to provide overall stability, but also use natural electric potential to provide high sensitivity to water body anomalies, so it has unique advantages in resolution and abnormal body focusing.

[0006] However, the existing joint inversion method still has many shortcomings in theory and practice:

[0007] (1) Current joint inversion is mostly focused on seismic-electric, resistivity-inductive, etc. Combination, and the collaborative imaging of natural electric field and electric field is not sufficient, and lacks systematic application.

[0008] (2) Natural electric field and resistivity data have significant differences in scale, amplitude and signal-to-noise ratio. The existing joint inversion often fails to achieve a reasonable balance, leading to situations where strong signal data dominates optimization and weak signal data contributes to attenuation, thereby reducing the positioning accuracy of deep abnormal bodies.

[0009] (3) Most traditional joint inversion relies on fixed smoothing constraints or cross-gradient and other relational constraints, which force different physical fields to be bound together. Such methods are prone to over-blurring of the anomaly boundary on the one hand, and artificially flattening the physical differences that should exist on the other hand, so that the imaging results of different physical fields are mechanically coupled and lack adaptability. Especially in the scene of narrow, scattered or buried anomaly bodies, imaging distortion and detail loss are prone to occur, thereby limiting the anomaly body recognition ability.

[0010] (4) Most existing methods do not realize dynamic updating of priori and quantification of uncertainty in the Bayesian inversion framework, and it is difficult to adaptively adjust the priori during the iteration process, resulting in insufficient imaging stability and reliability.

[0011] (5) Traditional inversion results are mainly single imaging maps, which lack posterior sampling and uncertainty evaluation based on probability, and cannot provide quantitative indicators such as boundary confidence, ambiguity or regional probability distribution, which is not conducive to reliable judgment of disaster risk in construction. SUMMARY

[0012] In order to solve the above problems, the application provides a natural electric field-electric field joint detection and inversion method based on GMM priori, which combines the advantages of multi-source electrical methods, introduces the priori of underground electrical structure, and realizes high-resolution and high-reliability identification of water-rich anomaly bodies in front of the tunnel by combining Bayesian uncertainty analysis.

[0013] In order to achieve the above purpose, the application adopts the following technical solutions:

[0014] In the first aspect, the application provides a natural electric field-electric field joint detection and inversion method based on GMM priori, comprising:

[0015] Initializing the parameters of the Gaussian mixture model according to the obtained geological information in front of the tunnel face to obtain a GMM priori model;

[0016] Obtaining the resistivity and natural potential observed in the area to be inverted;

[0017] Parameterizing the equivalent body source of the natural potential as a body source vector on the grid element, introducing a weighted L1 sparse regularization constraint to the body source vector, taking the GMM priori model as the underground electrical structure priori shared by cross-physical fields, and establishing a multi-task joint inversion objective function sharing the underground electrical structure label according to the weighted L1 sparse regularization constraint of the resistivity, natural potential and body source vector;

[0018] In the process of inversion iteration of the multi-task joint inversion objective function by maximum posteriori, the parameters of the GMM priori model and the underground electrical structure label are updated by using the expectation maximization algorithm, and the joint inversion imaging result of the water-rich anomaly body of the tunnel is obtained after the set iteration end condition is met.

[0019] As an alternative implementation, a two-dimensional array of measuring electrodes is deployed on the tunnel face, and at least two power supply electrode rings are deployed on the tunnel sidewall behind the tunnel face. Each power supply electrode ring consists of four power supply electrodes. The detection host is connected to the measuring electrodes and the power supply electrodes. The detection host first collects the natural potential through the measuring electrodes, then supplies power through the power supply electrodes, and then collects the resistivity through the measuring electrodes.

[0020] As an alternative implementation method, the collected resistivity is preprocessed to remove outliers.

[0021] The preprocessing of the collected natural potentials includes: each time the natural potential is measured, at the same detection depth, the four power supply electrodes of a power supply electrode ring participate in the power supply respectively, thereby obtaining four sets of natural potentials. The arithmetic mean of the four sets of natural potentials is calculated and used as the final value of the natural potential.

[0022] As an alternative implementation, after obtaining the volume source vector, the natural potential is then subjected to forward modeling. The forward modeling of the natural potential is as follows:

[0023] ;

[0024] ;

[0025] in, Resistivity; Here is the stiffness matrix; L is the volume source assembly matrix; L is the measurement operator; It means that it is always equal to; For volume source vector; The distribution is based on natural potential. This is the result of forward modeling of spontaneous potential; For linear operators; This is the boundary equivalent term.

[0026] As an alternative implementation method, the objective function for multi-task joint inversion is:

[0027] ;

[0028] In the formula, Resistivity; For volume source vector; The soft tag for the kth component of voxel i; The coefficient for adjusting the body source threshold according to the components; This represents the weight of the resistivity component; The weight of the natural potential component; For resistivity observation data; is the observed data of the self-potential; is the forward result of the resistivity; is the linear operator; is the soft label of the i-th resistivity distribution; is the prior strength coefficient of the i-th resistivity distribution; is the voxel source coefficient strength; is the voxel source vector of the i-th self-potential; is the i-th resistivity distribution vector; are the mean and covariance in the GMM prior model, respectively.

[0029] As an alternative implementation, the process of updating the parameters of the GMM prior model and the underground electrical structure label using the expectation-maximization algorithm includes:

[0030] According to the current , the soft label is calculated:

[0031] ;

[0032] Under the fixed , the σ is updated:

[0033] ;

[0034] Under the fixed and , the s is updated:

[0035] ;

[0036] According to the statistical quantity of , the is updated; when the preset error tolerance is reached, the iteration is terminated, and the inversion result is obtained;

[0037] wherein, is the resistivity; are the mixing weight, mean and covariance in the GMM prior model, respectively; is the i-th resistivity distribution vector; is the soft label of the i-th resistivity distribution; is the weight of the resistivity part; is the observed data of the resistivity; is the forward result of the resistivity; is the soft label of the i-th resistivity distribution; is the prior strength coefficient of the i-th resistivity distribution; is the weight of the self-potential part; is the observed data of the self-potential; is the voxel source coefficient strength; is the voxel source vector of the i-th self-potential; is the linear operator; is the voxel source vector; a coefficient for adjusting the body-source threshold value according to components.

[0038] As an alternative embodiment, after obtaining the joint inversion result, a Markov Chain Monte Carlo method is used to sample the model posterior distribution; the confidence interval, boundary ambiguity and regional probability distribution of the water-rich abnormal body boundary are calculated based on the MCMC posterior sample sequence obtained by sampling, so as to obtain a 95% confidence interval map, a boundary ambiguity map and a regional probability heat map.

[0039] As an alternative embodiment, the position of the abnormal boundary point on each cross section is counted to construct a boundary envelope range, so as to obtain a 95% confidence interval map.

[0040] As an alternative embodiment, the boundary ambiguity is defined as: ; in the formula, is the midpoint of the region to be inverted is the posterior probability of the water-rich abnormal body.

[0041] As an alternative embodiment, the region to be inverted is divided into a plurality of sub-blocks, the frequency of the occurrence of the water-rich abnormal body in each sub-block is counted, and a regional probability heat map is constructed.

[0042] Compared with the prior art, the beneficial effects of the present application are:

[0043] The present application proposes a natural electric field-electric field joint detection and inversion method based on GMM prior, which reduces the imaging multi-solution and improves the focusing degree and boundary clarity of the water-rich abnormal body positioning through the joint inversion strategy of natural potential body source explicitization and shared label; combines the Bayesian inversion framework to optimize the underground electrical model, and uses the uncertainty evaluation index to quantify the result reliability, so as to realize high-resolution imaging and high-confidence identification of the water-rich abnormal body in front, and provide reliable basis for support design and risk prediction.

[0044] In the observation and data processing link, the present application uses the same set of electrode array and observation system to simultaneously acquire resistivity and natural potential data, realizes the acquisition of natural potential with zero additional layout cost, greatly simplifies the field construction layout process, and reduces interference and cost. At the same time, in the inversion process, the natural potential data is processed by equivalent body source explicitization, the body source is parameterized as a body source vector on the grid element, and a weighted L1 sparse regularization constraint is introduced, so that the body source is only activated in the area with sufficient evidence. This design effectively weakens the non-uniqueness of natural potential imaging, suppresses the noise-induced pseudo-anomaly and strip effect, and significantly improves the focusing of abnormal body positioning and boundary clarity.

[0045] The application introduces a Gaussian mixture model as an underground electrical structure prior in an inversion imaging framework, uses the multi-modal characteristics to express the difference between the background surrounding rock and the water-rich abnormal body, and realizes the dynamic update of the prior parameters and structure labels through the maximum expectation algorithm in iteration. Compared with the traditional smoothing or cross gradient constraint, the underground electrical structure prior can be closer to the actual geological conditions, avoiding excessive blurring of the boundary and improving the identification ability of narrow, dispersed or buried abnormal bodies. At the same time, the noise level adaptive weighting mechanism is combined in the inversion objective function, so that the resistivity and the natural potential data can be balancedly constrained in the unified structure framework, and the stability of the multi-source joint imaging is significantly enhanced.

[0046] In the inversion result evaluation stage, the application adopts a Bayesian inversion framework to unify the observation data and the prior information, and combines Markov chain Monte Carlo sampling to obtain the model posterior distribution. Based on this, multi-dimensional results such as 95% confidence interval graph, boundary ambiguity graph and regional probability heat map are output, and the quantitative evaluation of the uncertainty of the inversion result is realized. Unlike the traditional method which only relies on a single imaging result, this way can intuitively reflect the reliability and ambiguity of the abnormal body boundary, and provide a more reliable basis for the tunnel front hazard body identification and construction safety decision.

[0047] The advantages of the additional aspects of the application will be partially given in the following description, partially become obvious from the following description, or be understood through the practice of the application. BRIEF DESCRIPTION OF DRAWINGS

[0048] In order to more clearly illustrate the technical solutions in the embodiments of the application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description only are the embodiments of the application, and for those skilled in the art, other drawings can be obtained without creative labor on the basis of the provided drawings.

[0049] Figure 1 A flow chart of the natural electric field-electric field joint detection and inversion method based on the GMM prior provided for the embodiment 1 of the application is shown in the figure;

[0050] Figure 2 A principle diagram of the natural electric field-electric field joint detection and inversion method based on the GMM prior provided for the embodiment 1 of the application is shown in the figure;

[0051] Figure 3 A natural electric field-electric field joint detection arrangement schematic diagram provided for the embodiment 1 of the application is shown in the figure;

[0052] Figure 4 A Markov chain Monte Carlo sampling flow chart provided for the embodiment 1 of the application is shown in the figure;

[0053] Figure 5A joint inversion resistivity image provided for the verification example of the present application;

[0054] Figure 6 A 95% confidence interval map provided for the verification example of the present application;

[0055] Figure 7 A boundary ambiguity map provided for the verification example of the present application;

[0056] Figure 8 A regional probability heat map provided for the verification example of the present application;

[0057] Wherein, 1, power supply electrode; 2, detection host; 3, measurement electrode; 4, abnormal water body. DETAILED DESCRIPTION

[0058] The present application will be further described below in conjunction with the accompanying drawings and embodiments.

[0059] It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless otherwise indicated, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present application belongs.

[0060] It should be noted that the terms used herein are only for the purpose of describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, the singular form is intended to include the plural form unless the context clearly indicates otherwise, and it should be understood that the terms "comprise" and "include" and any variations thereof are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device comprising a series of steps or units does not have to be limited to those steps or units clearly listed, but can include other steps or units not clearly listed or inherent to the process, method, product or device.

[0061] The embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0062] Embodiment 1

[0063] This embodiment proposes a natural electric field-electric field joint detection and inversion method based on GMM prior, as shown in Figure 1 , comprising:

[0064] According to the obtained geological information in front of the tunnel face, the parameters of the Gaussian mixture model are initialized to obtain the GMM prior model;

[0065] Obtain the resistivity and natural potential observed in the area to be inverted;

[0066] The equivalent body source of the natural potential is parameterized as a body source vector on a grid cell, a weighted L1 sparse regularization constraint is introduced to the body source vector, a GMM prior model is taken as a cross-physical-field shared underground electrical structure prior, and a multi-task joint inversion objective function sharing the underground electrical structure label is established according to the weighted L1 sparse regularization constraint of the resistivity, the natural potential and the body source vector.

[0067] In the process of inversion iteration of the multi-task joint inversion objective function by using the maximum posterior, the parameters of the GMM prior model and the underground electrical structure label are updated by using the expectation maximization algorithm, until the set iteration end condition is met, and the joint inversion imaging result of the tunnel water-rich abnormal body is obtained.

[0068] The method of the embodiment will be described in detail below in combination with the flow shown in Figures 1-2

[0069] S1: According to the geological design data and the field survey data, the geological information in front of the tunnel face is obtained, such as lithology information, topographic information, geological structure information, underground water conditions and the like, to provide prior conditions for subsequent inversion modeling.

[0070] Specifically: According to the geological design data and the field survey data, combined with the real-time exposed stratum of the tunnel face and the surrounding monitoring data, a macro-geological framework model of the region to be inverted is established to determine the main stratum unit and the spatial range of the possible water-rich abnormal body, thereby providing geological background support for subsequent inversion modeling.

[0071] Among them, the reference geological design data includes but is not limited to geological profile, drilling information, actual lithology and rock resistivity test results and the like.

[0072] S2: By arranging an electrode array in the tunnel, a joint observation of the natural potential and the resistivity is carried out at the same time, and the synchronous acquisition of multi-source data is realized by using the same measurement system, thereby simplifying the arrangement and reducing the construction interference.

[0073] Specifically:

[0074] As shown in Figure 3 , there is an abnormal water body 4 behind the tunnel face, then a focused sounding observation mode is selected for the arrangement of the electrode array; at least two rows of measurement electrodes 3 are arranged on the tunnel face, each row including a plurality of measurement electrodes 3, the left and right spacing d1 of the measurement electrodes 3 in the same row and the upper and lower spacing d2 of the measurement electrodes 3 between different rows can be set according to the actual situation on site.

[0075] ​At least two rows of power supply electrode rings are arranged on the tunnel sidewall behind the tunnel face, each power supply electrode ring is surrounded by four power supply electrodes 1, the four power supply electrodes are in the same section, and the ring distance d between the power supply electrode rings can be set according to the actual situation, such as 5m, 6m, 7m, 8m, etc.

[0076] The detection host 2 is connected with the measuring electrode 3 and the power supply electrode 1. During each measurement, after being excited by the artificial current source, the detection host 2 first collects the natural electric potential through the measuring electrode 3, collects the natural electric potential, and then supplies power through the power supply electrode 1, and then collects the resistivity through the measuring electrode 3. In this embodiment, the four-electrode method is adopted, the B electrode refers to the infinite electrode, and the N electrode refers to the reference electrode in the measuring electrode 3; the Ai electrode and the B electrode in the power supply electrode ring supply power, and the M electrode and the N electrode in the measuring electrode measure.

[0077] S3: Obtain electric field and natural electric field data; wherein the electric field data refers to resistivity, and the natural electric field data refers to natural electric potential; thus, the obtained resistivity and natural electric potential are preprocessed to enhance data stability and comparability.

[0078] Specifically:

[0079] For resistivity observation data, in combination with collection logs and instrument state monitoring records, abnormal points in the resistivity observation data are marked and removed by construction personnel for data preprocessing.

[0080] For natural electric field observation data, in the focused depth observation mode, when measuring the natural electric potential each time, the four power supply electrodes on one power supply electrode ring participate in power supply at the same detection depth, so that four sets of natural electric potential data are obtained. In order to enhance the stability of the natural electric potential, the four sets of natural electric potential data are calculated by arithmetic mean, and the final input value of the natural electric potential at this point is: ; wherein, is the natural electric potential obtained based on the i-th power supply electrode on the power supply electrode ring when measuring the resistivity.

[0081] S4: Initialize Gaussian mixture model (GMM) parameters according to stratum information.

[0082] The parameters of the Gaussian mixture model are initialized according to the geological information in front of the tunnel face and engineering experience, including the mixing weight, the resistivity mean and the covariance, to obtain the GMM prior model, which is used to describe the underground electrical structure characteristics of various geological units such as background stratum and water-rich abnormal body.

[0083] S5: Construct the Bayesian joint inversion framework based on the GMM prior model, including the explicitization of the natural electric field body source sparse regularization processing and the joint inversion strategy of sharing GMM labels, and input the preprocessed natural electric potential and resistivity data into the joint inversion framework.

[0084] Wherein, the natural electric potential is explicitly parameterized by the body source vector and the weighted L1 sparse regularization constraint is introduced, and the resistivity is used to stabilize the overall structure, and both are optimized under the shared GMM label, and the expectation-maximization algorithm (EM) is used to dynamically update the GMM parameters and labels, so that the prior distribution is adaptively adjusted with the observation data, and the joint inversion imaging of the water-rich abnormal body is realized.

[0085] Specifically:

[0086] (1) In order to explicitly characterize the equivalent body source in the natural electric potential, the equivalent body source of the natural electric potential is parameterized as a body source vector s on the grid element, which can be understood as a body source intensity for each grid element.

[0087] This step is actually a further simplification of the natural electric potential forward processing, because in the resistivity inversion, the supply source term is known, so only the resistivity distribution needs to be changed to perform the resistivity inversion, but in the natural electric field, the resistivity distribution and the source term distribution are unknown, but in the natural electric field inversion, the current density distribution is used for inversion (source term inversion). Therefore, this can be directly understood as a source term / body source.

[0088] The purpose of this operation on the natural electric potential is to regard the source term as an invertible unknown term and to discretize it to the element for the convenience of subsequent use of the finite element method. The advantage of this is that after discretization, the inversion calculation can be directly performed on the level of "where the body source is needed and how strong it is". The purpose of displaying the body source representation is to directly invert the source term of the natural electric potential, which is parameterized as s, and to estimate it together with the resistivity in the multi-task joint inversion objective function.

[0089] (2) After obtaining the body source vector, the natural electric potential is discretely processed, and the relationship of stiffness x potential = body source load is formed in the discrete forward processing, so as to separate the medium contrast and body source effect, which is convenient for subsequent joint optimization and uncertainty evaluation.

[0090] The discrete forward processing of the natural electric potential is represented as:

[0091] ;

[0092] ;

[0093] Wherein, The medium electrical parameter, i.e. resistivity (such as rock resistivity, abnormal body resistivity, etc.); The stiffness matrix (the stiffness matrix is a change from the numerical solution of the Poisson equation to the finite element solution); The body source assembly matrix (i.e. the body source intensity in the grid element is distributed to the right end item of the adjacent nodes of the element); L is a measurement operator (field to observation mapping, i.e. a linear converter for converting the potential field into the data displayed in the instrument); Indicates the identity; The body source vector; The natural potential distribution; The natural potential forward result; The linear operator; The boundary external force or boundary equivalent item, when the outer boundary takes zero flux and the reference potential is pinned in the tunnel application, let .

[0094] Based on this, in the joint inversion, the resistivity is used to stabilize the medium electrical parameter, and the natural potential is used to identify the body source activity; the resistivity part and the natural potential part share the same set of underground electrical structure labels given by the GMM prior model (soft distribution), so that the medium geometry and the body source active area are cooperatively constrained under the unified underground electrical structure prior, thereby realizing the structure isotope and the mechanism division of labor joint inversion; wherein the label does not refer to the hard classification result, but the membership probability of each stratum element under different Gaussian components, which is used to reflect the soft constraint relationship of its structure attribution.

[0095] Therefore, taking the GMM prior model as the underground electrical structure prior shared across physical fields, the natural potential forward result is combined with the resistivity forward result , and at the same time, the weighted L1 sparse regular constraint is introduced to the body source vector, to establish a multi-task joint inversion objective function sharing the underground electrical structure label;

[0096] Specifically:

[0097] ;

[0098] In the formula, The medium electrical parameter; The body source vector; The soft label of voxel i belonging to the k component (the sum is 1); The coefficient for adjusting the body source threshold according to the component; The weight of the resistivity part; The weight of the natural potential part; The resistivity observation data; The natural potential observation data; The resistivity forward result; is the prior strength coefficient of the GMM; is the body source coefficient strength; is the body source vector of the ith natural potential; is the ith resistivity distribution vector; are the mean and covariance in the GMM prior model, respectively.

[0099] where the first term refers to the resistivity part, the second term refers to the natural potential part, the third term refers to the GMM prior model part, and the fourth part refers to the weighted L1 sparse regularization constraint part of the body source vector s (label-adjusted L1) for automatically compressing most of the is zero, and only activates the body source when the evidence is sufficient, thereby suppressing noise and pseudo-anomalies and improving the focusing degree of the anomaly body positioning.

[0100] To make the underground electrical structure label adaptively update with the priori and inversion, an EM framework is adopted to alternately optimize the two types of unknown quantities in M steps.

[0101] Specifically:

[0102] (1) In the E step, the soft label is calculated according to the current

[0103]

[0104] where is the mixing weight in the GMM prior model.

[0105] (2) In the M step, first, update under the fixed :

[0106]

[0107] Then, update s (the solution can be obtained by using a convex optimization method containing a soft threshold, such as an alternating direction multiplier method) under the fixed and :

[0108]

[0109] (3) If necessary, update according to the statistics of ; when the data residual and the parameter change meet the convergence or reach the preset error tolerance, the iteration is terminated, and the inversion result is obtained.

[0110] ​​​​​S6: After obtaining the joint inversion result by solving with Maximum A Posteriori (MAP), the Markov Chain Monte Carlo Method (MCMC) is used to sample the model posterior distribution.

[0111] As shown in Figure 4 , the process of MCMC posterior sampling to generate a posterior sample sequence includes: initializing a state, setting a sampling step and a total number of steps; constructing a candidate sample; calculating an acceptance probability; judging whether the probability is accepted, if yes, generating a posterior sample, otherwise, continuing to calculate the acceptance probability until the calculation is completed, and generating a posterior sample sequence.

[0112] Among them, the MCMC sampling strategy can be selected, including but not limited to Metropolis-Hastings algorithm, Hamiltonian Monte Carlo (HMC) method, Adptive Metropolis (AM) method or parallel chain sampling, etc. Sampling algorithm, extracting parameter uncertainty information.

[0113] S7: Based on the MCMC posterior sample sequence, calculate the inversion evaluation indexes such as the confidence interval of the water-rich abnormal body boundary, the boundary ambiguity and the regional probability distribution, and finally output the joint inversion imaging result and the uncertainty evaluation result, which are used for supporting design and risk prediction.

[0114] Specifically:

[0115] (1) Confidence interval of water-rich abnormal body boundary: the position of the abnormal boundary point on each cross section is counted, and the boundary envelope range is constructed, and thus a 95% confidence interval map is drawn.

[0116] (2) Boundary ambiguity: by defining the boundary ambiguity, a boundary ambiguity map is drawn; the boundary ambiguity is:

[0117] ;

[0118] In the formula, is the point is the posterior probability of the water-rich abnormal body.

[0119] (3) Regional probability distribution: the region to be inverted is divided into several sub-blocks, and the frequency of the water-rich abnormal body in each sub-block is counted, and thus a regional probability heat map is constructed.

[0120] (4) The output results include joint inversion resistivity imaging, 95% confidence interval map, boundary ambiguity map and regional probability heat map, which are used to assist tunnel support design, risk warning and construction optimization.

[0121] The above scheme of the embodiment takes the GMM prior as the underground electrical structure prior shared across physical fields, jointly inverts the natural electric field (body source explicitization + sparse regularization) and electrical method parameters in the same framework, and gives uncertainty measurement outputs such as confidence interval / ambiguity / probability heat map under the Bayesian-MCMC framework, taking into account resolution, robustness and engineering usability.

[0122] Verification example.

[0123] In a certain large tunnel construction project, the construction area is located in a mountainous area with complex geological conditions. Common adverse geology includes fault fracture zone, karst and soft interlayer. In the rainy season, mud gushing disasters are prone to occur during tunnel excavation. In order to find out the source of mud gushing disaster in front of the tunnel face, the tunnel water-rich abnormal body natural electric field-electric field joint detection method provided in the above embodiment is used to locate and image the mud gushing disaster source in front of the tunnel.

[0124] Specifically, the following steps are included:

[0125] (1) According to the geological design data and field investigation data, obtain the geological information in front of the tunnel face, and provide prior conditions for subsequent inversion modeling.

[0126] Among them, according to the geological design data and field investigation data, combined with the real-time exposed stratum of the tunnel face and the surrounding monitoring data, a macro-geological framework model of the region to be inverted is established to determine the main stratum unit and the spatial range of possible water-rich abnormal bodies, and to provide geological background support for subsequent inversion modeling.

[0127] Specifically, in this verification example, according to the geological design data, the surrounding rock in front of the tunnel face is limestone and sandstone, the resistivity of limestone is about 1200Ω·m, and the resistivity of sandstone is about 700Ω·m; The water in the horizontal advanced drill hole is obvious, indicating the existence of aquifer.

[0128] (2) By arranging electrode arrays in the tunnel, joint observation of natural potential and resistivity is carried out, and synchronous acquisition of multi-source data is realized by using the same measurement system, thereby simplifying the arrangement and reducing the construction interference.

[0129] The measurement electrodes are arranged on the tunnel face, and 2 rows*6 columns are arranged, the left-right spacing d1 can be selected as 0.5 m, and the upper-lower spacing d2 can be selected as 1 m; meanwhile, the current source power supply electrode ring is arranged on the tunnel side wall behind the tunnel face, and there are 4 power supply electrodes in each ring, and the ring spacing d can be selected as 5 m, 5 m, 7 m and 8 m. In actual work, the measurement electrode spacing and the power supply electrode ring spacing can be adjusted according to the actual situation. At the same time of artificial current source excitation and obtaining resistivity response data, the same measurement electrode group is used to record the natural potential signal.

[0130] (3) Obtain the electric field and the natural electric field data; wherein the electric field data refers to the resistivity, and the natural electric field data refers to the natural potential; thus, the obtained resistivity and the natural potential are preprocessed to enhance the data stability and comparability.

[0131] Specifically:

[0132] For the resistivity observation data, in combination with the collection log and the instrument state monitoring record, the abnormal points in the resistivity observation data are marked and removed by the construction personnel, so as to perform data preprocessing.

[0133] For the natural electric field observation data, in the focused sounding observation mode, when measuring the natural potential, four power supply electrodes on the same power supply electrode ring participate in power supply at the same detection depth, so that four groups of natural potential data are obtained. In order to enhance the stability of the natural potential, the four groups of natural potential data are calculated by arithmetic average, and the final input value of the natural potential at the point is: ; wherein, is the natural potential obtained based on the i th power supply electrode on the power supply electrode ring when measuring the resistivity.

[0134] (4) Initialize the Gaussian mixture model (Gaussian Mixture Module, GMM) parameters according to the stratum information.

[0135] Wherein, according to the geological information in front of the tunnel face and engineering experience, the parameters of the Gaussian mixture model are initialized, including the mixing weight, the mean and the covariance, to obtain the GMM prior model, which is used to describe the underground electrical structure characteristics of various geological units such as background stratum and water-rich abnormal body.

[0136] Specifically, in the present verification example, in the area of 30m*30m*30m in front of the tunnel face, there are two kinds of background strata and a kind of water-rich abnormal body, so three groups of Gaussian components can be set, and the parameters are shown in Table 1.

[0137] Table 1 Parameters of Gaussian Mixture Model

[0138] .

[0139] (5) Construct a Bayesian joint inversion framework based on the GMM prior model, including the explicitization of the natural electric field body source, sparse regularization processing, and joint inversion strategy of sharing GMM labels. The preprocessed natural potential and resistivity data are input into the joint inversion framework.

[0140] (6) After obtaining the joint inversion result by using the maximum a posteriori (MAP) method, the Markov chain Monte Carlo (MCMC) method is used to sample the model posterior distribution.

[0141] (7) Based on the MCMC posterior sample sequence, calculate the inversion evaluation indexes such as the confidence interval of the water-rich abnormal body boundary, the boundary ambiguity, and the regional probability distribution, and finally output the joint inversion imaging result and uncertainty evaluation result for supporting design and risk prediction. The output result is shown in Figures 5-8

[0142] As shown in Figure 5 , the joint inversion resistivity imaging map reflects the underground electrical distribution; wherein, x refers to the distance in the tunneling direction starting from the working face.

[0143] As shown in Figure 6 , the 95% confidence interval map shows the value range of the model parameters in the posterior distribution, which is used to evaluate the stability and reliability of the model parameters at different depths. The width of the interval directly reflects the reliability of the result. When the interval is narrow, the parameter estimation is stable and the result is reliable; when the interval is wide, the uncertainty is high and needs to be interpreted carefully. If the mean curve and the background interval are obviously separated at the position of the water-rich abnormal body, even if the interval is widened, it can be considered that the conclusion of the existence of the water-rich abnormal body is reliable, but the boundary or electrical contrast exists uncertainty; if the interval is too wide and overlaps with the background range, it means that the reliability of the water-rich abnormal body identification result at this position is insufficient.

[0144] As shown in Figure 7 , the boundary ambiguity map is used to quantify the uncertainty of the water-rich abnormal body boundary imaging. The lower the value, the clearer and more reliable the boundary is, and the higher the value, the more fluctuation the boundary position has. Generally, the ambiguity is higher at the edge of the water-rich abnormal body or the stratigraphic interface, and lower inside the water-rich abnormal body and in the background area. It can be determined which boundary determination result needs to be interpreted carefully; wherein, x refers to the distance in the tunneling direction starting from the working face.

[0145] As shown in Figure 8 ​As shown, the regional probability heat map is used to assist in risk block identification and tunneling path planning. The result represents the probability of each position being determined as a water-rich anomaly body in the posterior sampling, and the high-value area represents a high possibility of the water-rich anomaly body. If the probability of a certain area is close to 1, it indicates that the water-rich anomaly body exists with high credibility; if the probability is lower than a certain threshold, it can be basically determined as a background area; the boundary probability is in the transition zone, which indicates that there is a certain uncertainty in the boundary range; wherein x refers to the distance in the tunneling direction from the tunnel face as the starting point.

[0146] Although the specific embodiments of the present application are described above with reference to the drawings, the description is not a limitation on the scope of protection of the present application, and those skilled in the art should understand that various modifications or changes made by those skilled in the art on the basis of the technical solutions of the present application without creative labor are still within the scope of protection of the present application.

Claims

1. A method for natural electric field-electric field joint detection and inversion based on GMM prior, characterized in that, The application comprises the following steps: Parameters of a Gaussian Mixture Model (GMM) are initialized according to the acquired geological information in front of the tunnel face, and a GMM prior model is obtained; Resistivity and natural potential observed in the area to be inverted are acquired; Equivalent body source parameters of the natural potential are parameterized as body source vectors on the grid cells, a weighted L1 sparse regularization constraint is introduced to the body source vectors, the GMM prior model is used as a prior of the underground electrical structure shared across physical fields, and a multi-task joint inversion objective function sharing the underground electrical structure label is established according to the weighted L1 sparse regularization constraint of the resistivity, the natural potential and the body source vectors; In the process of inversion iteration of the multi-task joint inversion objective function by maximum a posteriori, the parameters of the GMM prior model and the underground electrical structure label are updated by the expectation-maximization algorithm until the set iteration end condition is met, and a joint inversion imaging result of the water-rich abnormal body in the tunnel is obtained.

2. The natural electric field-electric field joint detection and inversion method based on GMM prior according to claim 1, characterized in that, A two-dimensional array of measuring electrodes is arranged on the tunnel face, at least two power supply electrode rings are arranged on the tunnel side wall behind the tunnel face, each power supply electrode ring is surrounded by four power supply electrodes, a detection host is connected with the measuring electrodes and the power supply electrodes, the detection host collects the natural potential through the measuring electrodes first, then supplies power through the power supply electrodes, and then collects the resistivity through the measuring electrodes.

3. The natural electric field-electric field joint detection and inversion method based on GMM prior according to claim 2, characterized in that, The collected resistivity is preprocessed by removing abnormal points; The preprocessing of the collected natural potential includes: when measuring the natural potential each time, the four power supply electrodes of one power supply electrode ring participate in power supply at the same detection depth, thereby obtaining four groups of natural potential, and calculating the arithmetic mean of the four groups of natural potential as the final value of the natural potential.

4. The natural electric field-electric field joint detection and inversion method based on GMM prior according to claim 1, characterized in that, After obtaining the body source vectors, the natural potential is further forward processed, and the forward of the natural potential is represented as: ； ； wherein, is resistivity; is stiffness matrix; is volume source assembly matrix; L is measurement operator; denotes identity; is volume source vector; is natural potential distribution; is natural potential forward result; is linear operator; is boundary equivalent term.

5. The natural electric field-electric field joint detection and inversion method based on GMM prior according to claim 1, characterized in that, The multi-task joint inversion objective function is ； where, is resistivity; is the volume source vector; is the soft label of voxel i belonging to the k-th component; is the coefficient for adjusting the volume source threshold by component; is the weight of the resistivity part; is the weight of the natural potential part; is the resistivity observation data; is the natural potential observation data; is the resistivity forward result; is the linear operator; is is the prior strength coefficient of is the volume source coefficient strength; is the volume source vector of the i-th natural potential; is the resistivity distribution vector of the i-th; are the mean and covariance in the GMM prior model, respectively.

6. The natural electric field-electric field joint detection and inversion method based on GMM prior according to claim 1, characterized in that, The process of updating the parameters of the GMM prior model and the underground electrical structure label by the expectation-maximization algorithm includes: According to the current Compute soft labels: ； In the fixed First update σ: ； At the fixing and Update s: ； According to statistical quantity updating ; when a preset error tolerance is reached, iteration is terminated, and an inversion result is obtained; where, is the resistivity; are the mixing weight, mean and covariance in the GMM prior model, respectively; is the i-th resistivity distribution vector; is the soft label of voxel i belonging to the k-th component; is the weight of the resistivity part; is the resistivity observation data; is the resistivity forward result; is the prior strength coefficient of ; is the weight of the spontaneous potential part; is the spontaneous potential observation data; is the body source coefficient strength; is the i-th spontaneous potential body source vector; is the linear operator; is the body source vector; is the coefficient to adjust the body source threshold by component.

7. The natural electric field-electric field joint detection and inversion method based on GMM prior according to claim 1, characterized in that, After obtaining the joint inversion result, the model posterior distribution is sampled by the Markov Chain Monte Carlo method; the boundary confidence interval, boundary ambiguity and regional probability distribution of the water-rich abnormal body are calculated based on the MCMC posterior sample sequence obtained by sampling, thereby obtaining a 95% confidence interval map, a boundary ambiguity map and a regional probability heat map.

8. The natural electric field-electric field joint detection and inversion method based on GMM prior according to claim 7, characterized in that, The boundary envelope range is constructed by counting the positions of the abnormal boundary points on each cross section, thereby obtaining the 95% confidence interval map.

9. The natural electric field-electric field joint detection and inversion method based on GMM prior according to claim 7, characterized in that, Boundary ambiguity is defined as: ; where, is the midpoint of the region to be inverted is the posterior probability of a water-rich anomaly.

10. The natural electric field-electric field joint detection and inversion method based on GMM prior according to claim 7, characterized in that, The area to be inverted is divided into a plurality of sub-blocks, the frequency of the occurrence of the water-rich abnormal body in each sub-block is counted, and thereby the regional probability heat map is constructed.

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