阅读说明：本技术 一种隧道磁共振准全空间反演参数不确定度分析方法 (Tunnel magnetic resonance quasi-full space inversion parameter uncertainty analysis method ) 是由 林婷婷 林小雪 万玲 于 2020-04-28 设计创作，主要内容包括：本发明属于地球物理反演领域,为一种隧道磁共振准全空间反演参数不确定度分析方法,包括:计算准全空间核函数,得到准全空间磁共振响应；根据准全空间磁共振响应,确认目标数据误差；根据目标数据误差,基于正演响应的线性近似,计算反演模型的协方差矩阵；根据协方差矩阵获取反演参数的标准偏差因子；根据标准偏差因子,对反演参数的不确定度进行定性评估；通过改变激发脉冲矩、探测天线尺寸和匝数,选择单一变量设置多组模型,重复不确定度计算过程,选择使得反演含水体不确定度最小的一组参数为最佳系统参数,得到不确定度分析结果。避免了盲目开展探测工作而造成不必要的人力物力消耗,提高了探测工作效率,达到获取最可靠探测结果的目的。(The invention belongs to the field of geophysical inversion, and discloses a method for analyzing uncertainty of tunnel magnetic resonance quasi-total space inversion parameters, which comprises the steps of calculating a quasi-total space kernel function to obtain a quasi-total space magnetic resonance response; confirming target data errors according to quasi-total space magnetic resonance response; calculating a covariance matrix of the inversion model based on a linear approximation of the forward response according to the target data error; acquiring a standard deviation factor of an inversion parameter according to the covariance matrix; according to the standard deviation factor, carrying out qualitative evaluation on the uncertainty of the inversion parameters; by changing the excitation pulse moment, the size and the number of turns of the detection antenna, selecting a single variable to set a plurality of groups of models, repeating the uncertainty calculation process, selecting a group of parameters which enable the uncertainty of the inversion water-containing body to be minimum as the optimal system parameters, and obtaining the uncertainty analysis result. The method avoids unnecessary manpower and material resource consumption caused by blind development of detection work, improves the detection work efficiency, and achieves the purpose of obtaining the most reliable detection result.)

1. A method for analyzing uncertainty of tunnel magnetic resonance quasi-full space inversion parameters is characterized by comprising the following steps:

calculating a quasi-total space kernel function to obtain a quasi-total space magnetic resonance response;

confirming target data errors according to quasi-total space magnetic resonance response;

calculating a covariance matrix of the inversion model based on a linear approximation of the forward response according to the target data error;

acquiring a standard deviation factor of an inversion parameter according to the covariance matrix;

according to the standard deviation factor, carrying out qualitative evaluation on the uncertainty of the inversion parameters;

by changing parameters of excitation pulse moment, the size of a detection antenna and the number of turns, selecting a single variable to set a plurality of groups of models, repeating the uncertainty calculation process, selecting a group of parameters which enable the uncertainty of the inversion water-containing body to be minimum as the optimal system parameters, and obtaining the uncertainty analysis result.

2. The analytical method according to claim 1,

calculating a quasi-total space kernel function to obtain a quasi-total space magnetic resonance response, comprising:

forward computing a quasi-full-space kernel K considering the excavated cavity of the tunnel_qw(q, x) acquiring the sensitivity distribution of magnetic resonance signals in front of and behind the tunnel face of the tunnel;

wherein x represents a coordinate along the tunneling direction; k (q; x, y, z) represents a full-space kernel function, and is determined by the size and the number of turns of the detection antenna, the intensity and the direction of the geomagnetic field, the excitation pulse and other parameters; l represents the tunnel face size;

using w around the tunnel in the inverse model_tunAnd target water content distribution w in front of the tunnel face_tarCalculating a quasi-total-space magnetic resonance response V of the tunnel, which is a magnetic resonance signal V generated by a water-containing body around the tunnel_tunAnd a magnetic resonance signal V generated by a target water-containing body in front of the palm face_tarJointly forming;

3. the analytical method according to claim 2,

confirming the target data error according to the quasi-total space magnetic resonance response comprises:

when the uncertainty of the advance detection inversion parameters of the tunnel is analyzed, a detection target is positioned in front of a tunnel face, and the target data error is caused by a magnetic resonance signal V generated by water-containing bodies around the tunnel_tunAnd data observation error e_obsJointly constitute:

e_tar＝V_tun+e_obs；

when the uncertainty of the inversion parameters at the back of the tunnel face is analyzed, the target data error is caused by the magnetic resonance signal V generated by the target water-containing body at the front of the tunnel face_tarAnd data observation error e_obsJointly constitute:

e_tar＝V_tar+e_obs。

4. the analytical method according to claim 1,

calculating a covariance matrix of the inverse model based on a linear approximation of the forward response from the target data error comprises: covariance matrix C_est：

Wherein, C_estIs the covariance matrix of the inverse model; g is a Jacobian matrix; c_obsIs the covariance of the observed data; r is a roughness matrix; c_RRepresenting the strength of the constraint;

wherein the covariance C of the observed data_obsReflecting the noise content in the data, from the target data error e_tarAnd contains the following elements:

C_obs,ij＝cov(e_tar,i,e_tar,j)。

5. the analytical method according to claim 1,

obtaining the standard deviation factor of the inversion parameters according to the covariance matrix comprises: in the tunnel magnetic resonance detection, the water-containing distribution w is an inversion key parameter, and a standard deviation factor STDF (w) of the water-containing distribution w is obtained by utilizing diagonal elements of a covariance matrix;

wherein, C_estA covariance matrix.

6. The analytical method according to claim 1,

the qualitative assessment of the uncertainty of the inversion parameters according to the standard deviation factor comprises dividing the assessment into the following 6 levels:

1) stdf (w) <1.1, corresponding to an inversion parameter level of "very definite";

2) when the STDF (w) is more than or equal to 1.1 and less than or equal to 1.2, the corresponding inversion parameter level is high in certainty degree;

3) when the STDF is more than or equal to 1.2 and less than or equal to (w) and less than 1.5, the corresponding inversion parameter level is 'determinable';

4) when the STDF (w) is more than or equal to 1.5 and less than 2.0, the corresponding inversion parameter level is low in certainty degree;

5) when STDF (w) is more than or equal to 2.0 and less than or equal to 3.0, the corresponding inversion parameter level is 'very low certainty';

6) stdf (w) >3.0 corresponds to an inversion parameter level of "completely uncertain".

Technical Field

The invention belongs to the field of geophysical inversion, and particularly relates to a method for analyzing uncertainty of tunnel magnetic resonance quasi-full space inversion parameters.

Background

As an emerging geophysical exploration technique, the Underground Magnetic Resonance Sounding (UMRS) method has been used in the past decade to detect water inrush conditions in Underground structures. Due to direct sensitivity to water molecules, the non-invasive UMRS technology has important significance in preventing water inrush disasters of tunnels. Previous research results show that the UMRS technology has the capability of directly and quantitatively tracking the water body in the tunnel, so that the tunnel water inrush accident can be effectively prevented.

However, unlike ground detection conditions: (1) the limited space available within the tunnel greatly limits the size of the probe antenna-which results in weak magnetic resonance probe signals in the tunnel (typically, for small volume groundwater detection, a narrow underground space limits the signal amplitude to less than 100 nV); (2) large electrical equipment in the tunnel is distributed in a centralized manner and is not easy to move, which causes the influence of electromagnetic noise on magnetic resonance signals to be larger and the signal-to-noise ratio to be lower; (3) the calculation of the magnetic resonance kernel in the tunnel is based on quasi-total space-this results in that the presence of water-containing bodies around the tunnel will also generate magnetic resonance signals, thus affecting the results of the advanced detection. The above problems seriously affect the accuracy of the inversion result of the tunnel magnetic resonance, especially the water content which is one of the important results of the data inversion. This indicates that it is necessary to calculate the uncertainty of the tunnel magnetic resonance inversion result to evaluate the reliability of the detection effect; it is necessary to know the influence trend of various key parameters (such as the size and the number of turns of a detection antenna, the excitation pulse moment, the size of a tunnel, the water content of geological bodies around the tunnel, the noise level and the like) on the uncertainty of the water content of the tunnel detection in the tunnel magnetic resonance detection, and further guide the configuration of system parameters so as to expect to obtain more reliable results in field tests. At present, no relevant research is published at home and abroad, so that the research on the uncertainty analysis method of the tunnel magnetic resonance inversion parameters is of great significance for improving the accuracy of detection results.

Disclosure of Invention

In view of the above problems in the prior art, the present invention is directed to a method for analyzing uncertainty of parameters of quasi-full space inversion of magnetic resonance in a tunnel,

the present invention is achieved in such a way that,

a method for analyzing uncertainty of tunnel magnetic resonance quasi-full space inversion parameters comprises the following steps:

calculating a quasi-total space kernel function to obtain a quasi-total space magnetic resonance response;

confirming target data errors according to quasi-total space magnetic resonance response;

calculating a covariance matrix of the inversion model based on a linear approximation of the forward response according to the target data error;

acquiring a standard deviation factor of an inversion parameter according to the covariance matrix;

according to the standard deviation factor, carrying out qualitative evaluation on the uncertainty of the inversion parameters;

parameters such as excitation pulse moment, the size of a detection antenna, the number of turns and the like are changed, a single variable is selected to set a plurality of groups of models, the uncertainty calculation process is repeated, a group of parameters which enable the uncertainty of the inversion water-containing body to be minimum is selected as the optimal system parameters, and the uncertainty analysis result is obtained.

Further, calculating a quasi-total-space kernel function to obtain a quasi-total-space magnetic resonance response includes:

forward computing a quasi-full-space kernel K considering the excavated cavity of the tunnel_qw(q, x) acquiring the sensitivity distribution of magnetic resonance signals in front of and behind the tunnel face of the tunnel;

wherein x represents a coordinate along the tunneling direction; k (q; x, y, z) represents a full-space kernel function, and is determined by the size and the number of turns of the detection antenna, the intensity and the direction of the geomagnetic field, the excitation pulse and other parameters; l represents the tunnel face size;

using w around the tunnel in the inverse model_tunAnd target water content distribution w in front of the tunnel face_tarCalculating a quasi-total-space magnetic resonance response V of the tunnel, which is a magnetic resonance signal V generated by a water-containing body around the tunnel_tunAnd a magnetic resonance signal V generated by a target water-containing body in front of the palm face_tarAre formed jointly；

Further, confirming the target data error based on the quasi-total space magnetic resonance response comprises:

when the uncertainty of the advance detection inversion parameters of the tunnel is analyzed, a detection target is positioned in front of a tunnel face, and the target data error is caused by a magnetic resonance signal V generated by water-containing bodies around the tunnel_tunAnd data observation error e_obsJointly constitute:

e_tar＝V_tun+e_obs；

when the uncertainty of the inversion parameters at the back of the tunnel face is analyzed, the target data error is caused by the magnetic resonance signal V generated by the target water-containing body at the front of the tunnel face_tarAnd data observation error e_obsJointly constitute:

e_tar＝V_tar+e_obs。

further, calculating a covariance matrix of the inverse model based on a linear approximation of the forward response from the target data error comprises: covariance matrix C_est：

Wherein, C_estIs the covariance matrix of the inverse model; g is a Jacobian matrix; c_obsIs the covariance of the observed data; r is a roughness matrix; c_RRepresenting the strength of the constraint;

wherein the covariance C of the observed data_obsReflecting the noise content in the data, from the target data error e_tarAnd contains the following elements:

C_obs,ij＝cov(e_tar,i,e_tar,j)。

further, obtaining the standard deviation factor of the inversion parameters according to the covariance matrix comprises: in the tunnel magnetic resonance detection, the water-containing distribution w is an inversion key parameter, and a standard deviation factor STDF (w) of the water-containing distribution w is obtained by utilizing diagonal elements of a covariance matrix;

wherein, C_estA covariance matrix.

Further, qualitatively evaluating the uncertainty of the inversion parameters according to the standard deviation factor includes classifying the evaluation into the following 6 levels:

1) stdf (w) <1.1, corresponding to an inversion parameter level of "very definite";

2) when the STDF (w) is more than or equal to 1.1 and less than or equal to 1.2, the corresponding inversion parameter level is high in certainty degree;

3) when the STDF is more than or equal to 1.2 and less than or equal to (w) and less than 1.5, the corresponding inversion parameter level is 'determinable';

4) when the STDF (w) is more than or equal to 1.5 and less than 2.0, the corresponding inversion parameter level is low in certainty degree;

5) when STDF (w) is more than or equal to 2.0 and less than or equal to 3.0, the corresponding inversion parameter level is 'very low certainty';

6) stdf (w) >3.0 corresponds to an inversion parameter level of "completely uncertain".

Compared with the prior art, the invention has the beneficial effects that:

the method disclosed by the invention not only realizes the uncertainty calculation method of the tunnel magnetic resonance inversion parameters, but also effectively evaluates the reliability of the inversion result; and uncertainty analysis is carried out by changing different parameters, which is helpful for deeply knowing the influence trend of the uncertainty analysis on the accuracy of tunnel magnetic resonance inversion water-containing bodies; in addition, multiple forward simulations can be performed by using the method according to specific experimental conditions, the influence of multiple key parameters on the uncertainty of the inversion result is known before actual on-site detection is implemented, system parameters are guided to be reasonably configured, unnecessary manpower and material resource consumption caused by blind detection is avoided, and the purpose of obtaining the most reliable detection result is achieved while the detection work efficiency is improved.

Drawings

FIG. 1 is a flow chart of a method for analyzing uncertainty of a tunnel magnetic resonance quasi-full space inversion parameter;

FIG. 2 is a flow chart of the optimal system parameter analysis for magnetic resonance detection in a tunnel;

FIG. 3 is a schematic diagram of a tunnel MR probe water-containing model;

FIG. 4 is a water cut model diagram;

fig. 5 is a distribution diagram of the influence of the water content change around the tunnel on the uncertainty of the advanced detection water-containing body.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

As shown in fig. 1, a method for analyzing uncertainty of a tunnel magnetic resonance quasi-full space inversion parameter includes the following steps:

calculating a quasi-total space kernel function to obtain a quasi-total space magnetic resonance response;

confirming target data errors according to quasi-total space magnetic resonance response;

calculating a covariance matrix of the inversion model based on a linear approximation of the forward response according to the target data error;

acquiring a standard deviation factor of an inversion parameter according to the covariance matrix;

according to the standard deviation factor, carrying out qualitative evaluation on the uncertainty of the inversion parameters;

parameters such as excitation pulse moment, the size of a detection antenna, the number of turns and the like are changed, a single variable is selected to set a plurality of groups of models, the uncertainty calculation process is repeated, a group of parameters which enable the uncertainty of the inversion water-containing body to be minimum is selected as the optimal system parameters, and the uncertainty analysis result is obtained.

Calculating a quasi-total space kernel function to obtain a quasi-total space magnetic resonance response, comprising: forward computing a quasi-full-space kernel K considering the excavated cavity of the tunnel_qw(q, x) acquiring the sensitivity distribution of magnetic resonance signals in front of and behind the tunnel face of the tunnel;

wherein x represents a coordinate along the tunneling direction; k (q; x, y, z) represents a full-space kernel function, and is determined by the size and the number of turns of the detection antenna, the intensity and the direction of the geomagnetic field, the excitation pulse and other parameters; l denotes the tunnel face size.

As shown in FIG. 2, the water-containing model of the quasi-total space tunnel magnetic resonance detection considers the water-containing distribution w of the target around the tunnel and in front of the tunnel face_tunAnd w_tarAnd calculating a tunnel quasi-total space magnetic resonance response V by using the two parameters as inversion model parameters, wherein the tunnel quasi-total space magnetic resonance response V is a magnetic resonance signal V generated by water-containing bodies around the tunnel_tunAnd a magnetic resonance signal V generated by a target water-containing body in front of the palm face_tarJointly forming;

V＝V_tar+V_tun

V_tar＝K_qw(x≥0)·w_tar

V_tun＝K_qw(x＜0)·w_tun

confirming the target data error according to the quasi-total space magnetic resonance response comprises: when the uncertainty of the advance detection inversion parameters of the tunnel is analyzed, a detection target is positioned in front of a tunnel face, and the target data error is represented by V_tunAnd data observation error e_obsJointly constitute, namely:

e_tar＝V_tun+e_obs

when the uncertainty of the inversion parameters at the back of the tunnel face is analyzed, the target data error is V_tarAnd data observation error e_obsJointly constitute, namely:

e_tar＝V_tar+e_obs

computing covariance matrix C of inversion model based on linear approximation of forward response_est；

Wherein, C_estIs an inverse modelThe covariance matrix of (a); g is a Jacobian matrix; c_obsIs the covariance of the observed data; r is a roughness matrix; c_RRepresenting the strength of the constraint.

Covariance of observed data C_obsReflecting the noise content in the data, which can be determined by the target data error e_tarAnd contains the following elements:

C_obs,ij＝cov(e_tar,i,e_tar,j)

and acquiring a standard deviation factor of the inversion parameters according to the covariance matrix: in the tunnel magnetic resonance detection, the water-containing distribution w is an inversion key parameter, and a standard deviation factor STDF (w) of the water-containing distribution w is obtained by utilizing diagonal elements of a covariance matrix;

because the calculation of the standard deviation factor of the inversion parameters is based on linear approximation, the uncertainty of the inversion parameters is qualitatively evaluated, and the evaluation is divided into the following 6 grades:

1) stdf (w) <1.1, corresponding to an inversion parameter level of "very definite";

2) when the STDF (w) is more than or equal to 1.1 and less than or equal to 1.2, the corresponding inversion parameter level is high in certainty degree;

3) when the STDF is more than or equal to 1.2 and less than or equal to (w) and less than 1.5, the corresponding inversion parameter level is 'determinable';

4) when the STDF (w) is more than or equal to 1.5 and less than 2.0, the corresponding inversion parameter level is low in certainty degree;

5) when STDF (w) is more than or equal to 2.0 and less than or equal to 3.0, the corresponding inversion parameter level is 'very low certainty';

6) stdf (w) >3.0 corresponds to an inversion parameter level of "completely uncertain".

As shown in fig. 3, theoretical simulations may be performed in advance to determine the optimal system parameters before actual tunnel magnetic resonance detection is performed. Parameters such as excitation pulse moment, the size of a detection antenna, the number of turns and the like are changed, a single variable is selected to set a plurality of groups of models, the uncertainty calculation process is repeated, and a group of parameters which enable the uncertainty of the inversion water-containing body to be minimum is selected as the optimal system parameters and serves as a guidance scheme for instrument parameter configuration. It is noted that when the antenna size a or the number of receive antenna turns Rx is taken as a variable, the noise level in the received signal also changes, namely:

Noise＝C_φ·Rx·A

in addition, in order to solve the influence of parameters such as tunnel size, water-containing distribution of geologic bodies around the tunnel, noise level and the like on the uncertainty of the tunnel magnetic resonance inversion water-containing body, a single variable can be constructed according to the process, the uncertainty calculation process is repeated, and the comprehensive situation of the inversion uncertainty of the water-containing body under different key parameters is finally obtained, so that the influence trend of different variables on the uncertainty of the tunnel magnetic resonance quasi-total space inversion parameters is determined.