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

Abstract

The invention discloses a natural electric field-electric field joint detection and inversion method based on GMM prior, and relates to the technical field of tunnel engineering geological detection, and the method comprises the steps: obtaining the resistivity and natural potential observed in a to-be-inverted region; an equivalent body source of a natural potential is parameterized into a body source vector on a grid unit, weighted L1 sparse regular constraint is introduced into the body source vector, a GMM prior model is used as underground electrical structure prior shared across physics fields, and a multi-task joint inversion objective function of a shared underground electrical structure label is established; and performing inversion iteration by adopting maximum posteriori, updating parameters of the GMM prior model and the underground electrical structure label by adopting an expectation maximization algorithm until an end condition is met, and obtaining a joint inversion imaging result of the tunnel water-rich anomalous body. The advantages of a multi-source electrical method are fused, underground electrical structure priori is introduced, Bayesian uncertainty analysis is combined, and high-resolution and high-reliability recognition of the water-rich anomalous body in front of the tunnel is achieved.

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 detection 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 detection 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 environments. 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 some 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: (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.

[0007] (2) Natural electric field and resistivity data have significant differences in scale, amplitude and signal-to-noise ratio. Existing joint inversion often fails to achieve a reasonable balance, leading to strong signal data dominating optimization and weak signal data contributing to attenuation, thus reducing the positioning accuracy of deep abnormal bodies.

[0008] (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. On the one hand, this kind of method is easy to cause the abnormal body boundary to be excessively blurred, and on the other hand, the physical differences that should exist are artificially smoothed, so that the imaging results of different physical fields are mechanically coupled and lack of adaptability. Especially in the scene of narrow, scattered or buried abnormal body, imaging distortion and detail loss are easy to occur, thereby limiting the abnormal body recognition ability.

[0009] (4) Most of the existing methods do not realize the dynamic update of priori and the 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.

[0010] (5) The traditional inversion result is mainly single imaging map, which lacks 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

[0011] 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 method, introduces the priori of underground electrical structure and combines the Bayesian uncertainty analysis to realize the high-resolution and high-reliability identification of the water-rich abnormal body in front of the tunnel.

[0012] In order to achieve the above purpose, the application adopts the following technical solutions: In the first aspect, the application provides a natural electric field-electric field joint detection and inversion method based on GMM priori, comprising: 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; Obtaining the resistivity and natural electric potential observed in the area to be inverted; Parameterizing the equivalent body source of the natural electric 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, the natural electric potential and the body source vector; In the process of inversion iteration of the multi-task joint inversion objective function by maximum posterior, 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 abnormal body of the tunnel is obtained after the set iteration end condition is met.

[0013] 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.

[0014] As an alternative implementation method, the collected resistivity is preprocessed to remove outliers. 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.

[0015] 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: ; ; 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.

[0016] As an alternative implementation method, the objective function for multi-task joint inversion is: ; 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; This is data from spontaneous potential observations; This is the result of resistivity forward modeling; For linear operators; for The prior strength coefficient; The intensity of the volume source coefficient; is the i-th body source vector of the natural potential; is the i-th resistivity distribution vector; are the mean and covariance of the GMM prior model, respectively.

[0017] As an alternative embodiment, the process of updating the parameters of the GMM prior model and the underground electrical structure label using the expectation-maximization algorithm comprises: According to the current Calculate the soft label: ; Update σ under the fixed ; ; Update s under the fixed and ; ; Update according to the statistical quantity of ; when the preset error tolerance is reached, the iteration is terminated, and the inversion result is obtained; wherein, is the resistivity; are the mixing weight, mean and covariance of the GMM prior model, respectively; is the i-th resistivity distribution vector; is the soft label of the 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 intensity coefficient of ; is the weight of the natural potential part; is the natural potential observation data; is the body source coefficient intensity; is the i-th body source vector of the natural potential; is the linear operator; is the body source vector; is the coefficient of adjusting the body source threshold according to the component.

[0018] As an alternative embodiment, after obtaining the joint inversion result, the Markov chain Monte Carlo method is used to sample the model posterior distribution; based on the MCMC posterior sample sequence obtained by sampling, the confidence interval, boundary ambiguity and regional probability distribution of the water-rich abnormal body boundary are calculated, thereby obtaining the 95% confidence interval map, boundary ambiguity map and regional probability heat map.

[0019] As an alternative embodiment, the position of the abnormal boundary point on each cross section is counted to construct the boundary envelope range, thereby obtaining a 95% confidence interval graph.

[0020] 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.

[0021] 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.

[0022] Compared with the prior art, the present application has the following beneficial effects: The present application proposes a natural electric field-electric field combined detection and inversion method based on GMM prior, which reduces the imaging multi-solution, 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 property model, and quantifies the result reliability by using the uncertainty evaluation index, so as to realize high-resolution imaging and high-credibility identification of the front water-rich abnormal body, and provide reliable basis for support design and risk prediction.

[0023] In the observation and data processing link, the present application simultaneously acquires resistivity and natural potential data by using the same set of electrode array and observation system, realizes the acquisition of natural potential with zero additional layout cost, greatly simplifies the field construction layout process, and reduces the 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 regular constraint is introduced, so that the body source is only activated in the area with sufficient evidence. The design effectively weakens the non-uniqueness of natural potential imaging, suppresses the noise-induced pseudo-anomaly and strip effect, and significantly improves the focusing and boundary clarity of the abnormal body positioning.

[0024] In the inversion imaging framework, the present application introduces a Gaussian mixture model as an underground electrical property structure prior, uses its 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 in the iteration through the maximum expectation algorithm. Compared with the traditional smoothing or cross gradient constraint, the underground electrical property structure prior can be closer to the actual geological conditions, avoids excessive ambiguity of the boundary, and improves the identification ability of narrow, dispersed or buried abnormal bodies. At the same time, in the inversion objective function, a noise level adaptive weighting mechanism is combined, so that the resistivity and natural potential data can be balancedly constrained in a unified structure framework, and the stability of multi-source joint imaging is significantly enhanced.

[0025] In the inversion result evaluation stage, the application adopts the Bayesian inversion framework to unify the observation data and prior information, and combines the Markov chain Monte Carlo sampling to obtain the model posterior distribution. Based on this, multi-dimensional results such as 95% confidence interval chart, boundary ambiguity chart 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 single imaging results, this method can intuitively reflect the reliability and ambiguity of the anomaly body boundary, and provide more reliable basis for the identification of disaster bodies in front of the tunnel and the safety decision of construction.

[0026] Advantages of the additional aspects of the application will be partially given in the following description, partially will become obvious from the following description, or will be known by the practice of the application. BRIEF DESCRIPTION OF DRAWINGS

[0027] 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.

[0028] Figure 1 The flow chart of the natural electric field-electric field joint detection and inversion method based on GMM prior provided for the embodiment 1 of the application is shown in the figure; Figure 2 The principle diagram of the natural electric field-electric field joint detection and inversion method based on GMM prior provided for the embodiment 1 of the application is shown in the figure; Figure 3 The natural electric field-electric field joint detection arrangement schematic diagram provided for the embodiment 1 of the application is shown in the figure; Figure 4 The Markov chain Monte Carlo sampling flow chart provided for the embodiment 1 of the application is shown in the figure; Figure 5 The joint inversion resistivity imaging chart provided for the verification example of the application is shown in the figure; Figure 6 The 95% confidence interval chart provided for the verification example of the application is shown in the figure; Figure 7 The boundary ambiguity chart provided for the verification example of the application is shown in the figure; Figure 8 The regional probability heat chart provided for the verification example of the application is shown in the figure; Wherein, 1, power supply electrode; 2, detection host; 3, measurement electrode; 4, abnormal water body. DETAILED DESCRIPTION

[0029] The application will be further described below in combination with the drawings and embodiments.

[0030] It should be noted that the following detailed description is exemplary in nature and is intended to provide further description of the application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

[0031] It is to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments in accordance with the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and / or "comprising," when used in this specification, specify the presence of stated features, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and / or groups thereof.

[0032] The embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0033] Embodiment 1 This embodiment proposes a natural electric field-electric field joint detection and inversion method based on GMM prior, as shown in Figure 1 , which includes: 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; Obtain the resistivity and natural potential observed in the area to be inverted; The equivalent body source parameter of the natural potential is parameterized as a body source vector on the grid element, and the weighted L1 sparse regularization constraint is introduced to the body source vector. The GMM prior model is used as the underground electrical structure prior 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 vector; In the process of inversion iteration of the multi-task joint inversion objective function by maximum posterior, the parameters of the GMM prior model and the underground electrical structure label are updated by the expectation maximization algorithm, and the joint inversion imaging result of the tunnel water-rich abnormal body is obtained after the set iteration end condition is met.

[0034] The method of this embodiment will be described in detail in combination with the flow shown in Figures 1-2 .

[0035] S1: According to the geological design data and field survey data, obtain the geological information in front of the tunnel face, such as lithology information, topographic information, geological structure information, groundwater conditions, etc., to provide prior conditions for subsequent inversion modeling.

[0036] Specifically: according to the geological design data and the site survey data, combining the real-time exposed strata at 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 units and the spatial range of possible water-rich abnormal bodies, thereby providing geological background support for subsequent inversion modeling.

[0037] 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 other data.

[0038] S2: By arranging an electrode array in the tunnel, combined 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.

[0039] Specifically: As Figure 3 shown, 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.

[0040] At least two columns of 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 1, the four power supply electrodes are in the same section, and the ring spacing d between the power supply electrode rings can be set according to the actual situation on site, such as 5m, 6m, 7m, 8m, etc.

[0041] The detection host 2 is connected with the measurement electrodes 3 and the power supply electrodes 1, and each time the measurement is carried out, after being excited by the artificial current source, the detection host 2 first collects the natural potential through the measurement electrodes 3, then supplies power through the power supply electrodes 1 after collecting the natural potential, and then collects the resistivity through the measurement electrodes 3. Among them, 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 measurement 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 measurement electrode measure.

[0042] 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 potential; thus, the obtained resistivity and natural potential are preprocessed to enhance the data stability and comparability.

[0043] Specifically: For resistivity observation data, combined with the collection log and instrument state monitoring record, the abnormal points in the resistivity observation data are marked and removed by the construction personnel for data preprocessing.

[0044] For natural electric field observation data, in the focused sounding observation mode, when measuring the natural electric potential each time, four power supply electrodes on the same power supply electrode ring at the same sounding depth participate in power supply respectively, then four groups of natural electric potential data are obtained, in order to enhance the stability of the natural electric potential, the four groups of natural electric potential data are calculated by arithmetic mean, and the final input value of the natural electric potential at the point is taken as: ; wherein, is the natural electric potential obtained based on the measurement of the resistivity of the i th power supply electrode on the power supply electrode ring.

[0045] S4: initialize Gaussian mixture model (GMM) parameters according to stratum information.

[0046] Among them, 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 covariance of the resistivity, 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.

[0047] S5: build a Bayesian joint inversion framework based on the GMM prior model, including natural electric field body source explicitization sparse regularization processing and shared GMM label joint inversion strategy, and input the preprocessed natural electric potential and resistivity data into the joint inversion framework.

[0048] Among them, the natural electric potential is parameterized by the body source vector and introduced into the weighted L1 sparse regularization constraint, and the resistivity is used to stabilize the overall structure, and the two are optimized under the shared GMM label, and the GMM parameters and label are dynamically updated by using the expectation-maximization algorithm (EM), 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.

[0049] Specifically: (1) In order to make the equivalent body source in the natural electric potential explicit, 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.

[0050] This step is actually a further simplification of the natural electric potential forward processing, because in the resistivity inversion, the power supply source term is known, so only the resistivity distribution needs to be changed to perform the resistivity inversion. However, 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 is performed). Therefore, this can be directly understood as a source term / body source.

[0051] The purpose of this step for the natural potential is to take the source term as an invertible unknown term and discretize it to the unit, which is convenient for the subsequent use of the finite element method for solving. The advantage is that after discretization, the inversion calculation can be directly performed at 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 potential, parameterize it as s, and estimate it together with the resistivity in the multi-task joint inversion objective function.

[0052] (2) After obtaining the body source vector, the natural potential is discretely forward processed again. In the discrete forward, the relationship of stiffness x potential = body source load is formed, the medium contrast and body source effect are separated and expressed, which is convenient for subsequent joint optimization and uncertainty assessment.

[0053] The discrete forward of the natural potential is expressed as: ; ; Among them, is the medium electrical parameter, that is, the resistivity (such as the resistivity of the rock layer, the resistivity of the abnormal body, etc.); is the stiffness matrix (the stiffness matrix is a change from the numerical solution of the Poisson equation to the finite element solution); is the body source assembly matrix (that is, the body source intensity in the grid cell is distributed to the right end item of the adjacent nodes of the cell); L is the measurement operator (field to observation mapping, which is a linear converter that converts the potential field into the data displayed in the instrument); represents the identity; is the body source vector; is the natural potential distribution; is the natural potential forward result; is the linear operator; is the boundary external force or boundary equivalent term. In the application of the tunnel, when the zero flux and the reference potential pinning are taken on the outer boundary, .

[0054] 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 allocation), so that the medium geometry and the body source active area are cooperatively constrained under the unified underground electrical structure prior, so as to realize the joint inversion of structure homology and mechanism division; Among them, the label does not mean the hard classification result, but the membership probability of each stratum unit under different Gaussian components, which is used to reflect the soft constraint relationship of its structure attribution.

[0055] Therefore, taking the GMM prior model as the underground electrical structure prior shared across physical fields, the natural potential forward result With resistivity forward modeling results In conjunction with the introduction of weighted L1 sparse regularization constraints on the volume source vector, a multi-task joint inversion objective function sharing underground electrical structure labels is established. Specifically: ; In the formula, These are the electrical parameters of the dielectric. For volume source vector; The soft tag for the kth component of voxel i (totaling 1); 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; This is data from spontaneous potential observations; This is the result of resistivity forward modeling; for The prior strength coefficient; The intensity of the volume source coefficient; Let be the volume source vector of the i-th natural potential; Let i be the resistivity distribution vector; These are the mean and covariance in the GMM prior model, respectively.

[0056] In the formula, 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 volume source vector s (label-adjusted L1), which is used to automatically compress most of the data while ensuring data fit. The value is zero, and the volume source is activated only where there is sufficient evidence, thereby suppressing noise and false anomalies and improving the focus of anomaly localization.

[0057] To enable the underground electrical structure labels to be adaptively updated with priors during inversion, the EM framework is adopted and the two types of unknowns are alternately optimized in the M-step.

[0058] Specifically: (1) Step E, based on the current Calculate soft tags: ; In the formula, These are the mixed weights in the GMM prior model.

[0059] (2) M step, first, in the fixed Next update : .

[0060] Then, in the fixed and Update s (the solution can employ a convex optimization method containing a soft threshold, such as an alternating direction multiplier method) as follows: .

[0061] (3) Update s according to the statistic of if necessary; when the data residual and the parameter change satisfy convergence or reach a preset error tolerance, the iteration is terminated, and the inversion result is obtained.

[0062] S6: After obtaining the joint inversion result by solving using the maximum a posteriori (MAP), the Markov chain Monte Carlo (MCMC) method is used to sample the model posterior distribution.

[0063] As shown in Figure 4 , the process of generating a posterior sample sequence by MCMC posterior sampling 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.

[0064] Among them, the MCMC sampling strategy can be selected, but is not limited to, a Metropolis-Hastings algorithm, a Hamiltonian Monte Carlo (HMC) method, an adaptive Metropolis (AM) method or a parallel chain sampling, etc. sampling algorithms, and the parameter uncertainty information is extracted.

[0065] 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.

[0066] Specifically: (1) Confidence interval of the 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 graph is drawn.

[0067] (2) Boundary ambiguity: by defining the boundary ambiguity, a boundary ambiguity graph is drawn; the boundary ambiguity is: ; In the formula, is the point​ Posterior probability of water-rich anomaly.

[0068] (3) Regional probability distribution: divide the region to be inverted into several sub-blocks, and count the frequency of water-rich anomaly in each sub-block to construct a regional probability heat map.

[0069] (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.

[0070] The above scheme of the embodiment takes GMM prior as the underground electrical structure prior shared by cross-physical fields, jointly inverts the natural electric field (body source explicitization + sparse regularization) and the 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.

[0071] Verification example.

[0072] 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 anomaly 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.

[0073] Specifically includes the following steps: (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.

[0074] 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 where the water-rich anomaly may exist, and to provide geological background support for subsequent inversion modeling.

[0075] Specifically, in the 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.

[0076] (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 layout and reducing construction interference.

[0077] The measurement electrodes are arranged on the tunnel face, and are arranged in 2 rows * 6 columns, and the left-right spacing d1 can be selected as 0.5 m, and the up-down 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 or 8 m. In actual work, the measurement electrode spacing and the power supply electrode ring spacing can be adjusted according to the actual situation. While the artificial current source excitation and the resistivity response data are obtained, the same measurement electrode group is used to record the natural potential signal.

[0078] (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.

[0079] Specifically: 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.

[0080] For the natural electric field observation data, in the focused sounding observation mode, when the natural potential is measured each time, under the same detection depth, the four power supply electrodes on one power supply electrode ring participate in power supply respectively, 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 mean, 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 the resistivity is measured.

[0081] (4) Initialize the Gaussian mixture model (Gaussian Mixture Module, GMM) parameters according to the stratum information.

[0082] 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.

[0083] Specifically, in the present verification example, in the area of 30 m * 30 m * 30 m in front of the tunnel face, there are two kinds of background strata and one kind of water-rich abnormal body, so three groups of Gaussian components can be set, and the parameters are shown in Table 1.

[0084] Table 1 Parameters of Gaussian Mixture Model .

[0085] (5) Construct a Bayesian joint inversion framework based on the GMM prior model, including the explicitization of the natural electric field body source and the sparse regularization processing and the joint inversion strategy of sharing the GMM label, and input the preprocessed natural potential and resistivity data into the joint inversion framework.

[0086] (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.

[0087] (7) Based on the MCMC posterior sample sequence, the inversion evaluation indexes such as the confidence interval of the water-rich abnormal body boundary, the boundary ambiguity and the regional probability distribution are calculated, and finally the joint inversion imaging result and the uncertainty evaluation result are output, which are used for supporting design and risk prediction. The output result is as shown in Figures 5-8

[0088] 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 with the working face as the starting point.

[0089] 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, and the width of the interval directly reflects the reliability of the result. When the interval is narrow, it means that the parameter estimation is stable and the result is reliable; when the interval is wide, it means that 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.

[0090] 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 with the working face as the starting point.

[0091] 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 means 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.

[0092] 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. Those skilled in the art should understand that various modifications or variations made 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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