CN107015285A - A kind of bearing calibration for observing apparent resistivity and system - Google Patents
A kind of bearing calibration for observing apparent resistivity and system Download PDFInfo
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Abstract
The invention discloses a kind of bearing calibration for observing apparent resistivity and system.This method includes：Obtain the updating formula that apparent resistivity is observed in tunnel；According to the fit solution of the actual observation apparent resistivity curve and two pole method correction function curve obtaineds of construction obtained in tunnel using two Ji Fa observation stations, determine the correctness of two pole method correction functions, utilize the combined transformation relation between three electrode method, symmetrical quadrupole method and two pole methods, determine that the three electrode method, symmetrical quadrupole method observe the correction function of apparent resistivity, and then determine corresponding updating formula；The observation apparent resistivity is corrected according to the updating formula of the observation apparent resistivity, the apparent resistivity after being corrected.The bearing calibration for the observation apparent resistivity that the present invention is provided and system can be good at being corrected tunnel observation apparent resistivity, exclude the interference of tunnel environment, reliable data foundation is provided for the forward probe in tunnel.
Description
Technical Field
The invention relates to the field of roadway advanced detection, in particular to a correction method and a correction system for observing apparent resistivity.
Background
Along with the rapid development of economy in China, the requirements on resources such as coal, metal ores and the like are increased. At present, most of mines in China enter the middle and late mining periods, the ascertained resource reserves and the available energy of a plurality of mine species are gradually reduced, the resources in superficial mine areas are exhausted, and the resource exploration is developed towards the three-dimensional and depth direction. In the underground engineering construction process, if faults, karst caves, collapse columns and other poor geologic bodies exist in front of a working face and near the periphery of a roadway, catastrophic accidents can be caused if the detection is not carried out in advance. Therefore, the accurate roadway advanced detection method and technology are researched, the disaster forecast is accurately carried out, and the method has wide application prospects in the aspects of coal fields, mines, tunnels, underground engineering construction and the like.
To research an accurate roadway advanced detection technology, the technology needs to be established on the basis of stable and reliable three-dimensional forward and backward modeling, an underground roadway environment is used as a complex three-dimensional underground structure, a roadway cavity, roadway rails and the like have great influence on the distribution of a current field, the resistivity is influenced by the roadway environment and often seriously distorted, so that great difficulty is increased for data interpretation of a resistivity method, and even wrong interpretation is caused.
Disclosure of Invention
The invention aims to provide a method and a system for correcting observed apparent resistivity, which can be used for correcting the observed apparent resistivity of a roadway well, eliminating the interference of the environment and providing a reliable data basis for the advanced detection of the roadway.
In order to achieve the purpose, the invention provides the following scheme:
a method of correcting observed apparent resistivity, the method comprising:
correction formula for acquiring observed apparent resistivity of roadwayWherein,for corrected apparent resistivity, psFor observing apparent resistivity to be corrected, k (r, b) is a correction function, the correction function is a correction function for observing apparent resistivity by a dipolar method, or an apparent resistivity by a tripolar method, or an apparent resistivity by a symmetric quadrapole method, and the correction function is a function related to observing polar moment r and roadway width b;
determining a dipolar method actual observation apparent resistivity curve obtained in the process of observing at different positions of a roadway, wherein the dipolar method actual observation apparent resistivity curve is obtained by a finite element analysis method;
fitting a curve obtained by a correction function of the apparent resistivity observed by the dipolar method with an actual observed apparent resistivity curve of the dipolar method, determining undetermined coefficients in the observed apparent resistivity correction function of the dipolar method, and determining the correction function of the observed apparent resistivity of the dipolar method;
converting the correction function of the apparent resistivity observed by the dipolar method, and determining the correction function of the apparent resistivity observed by the tripolar method and the correction function of the apparent resistivity observed by the symmetric quadrapole method;
respectively bringing the correction function of the apparent resistivity observed by the dipolar method, the correction function of the apparent resistivity observed by the tripolar method and the correction function of the apparent resistivity observed by the symmetric quadrapole method into the correction formula of the observed apparent resistivity, and determining the correction formula of the apparent resistivity observed by the dipolar method, the correction formula of the apparent resistivity observed by the tripolar method and the correction formula of the apparent resistivity observed by the symmetric quadrapole method;
and correcting the observation apparent resistivity to be corrected according to the correction formula of the observation apparent resistivity to obtain the corrected apparent resistivity.
Optionally, the determining a two-pole method actual observation apparent resistivity curve obtained when observing at different positions of the roadway specifically includes:
observing the resistivity of the roadway at different positions by adopting a dipolar method to obtain observed apparent resistivity of the dipolar method;
and determining an actual apparent resistivity curve of the dipolar method obtained when observation is carried out on different positions of the roadway by a finite element analysis method according to the observed apparent resistivity of the dipolar method obtained by observation on different positions of the roadway.
Optionally, fitting a curve obtained by the correction function of the apparent resistivity observed by the dipolar method with the actual observed apparent resistivity curve of the dipolar method, determining an undetermined coefficient in the correction function of the apparent resistivity observed by the dipolar method, and determining the correction function of the apparent resistivity observed by the dipolar method specifically includes:
when the tunnel apparent resistivity is observed by using a dipolar method, a correction function in the observed apparent resistivity correction formula is constructed in a way that k (r, b) is α e-βr+ gamma, and pre-drafting undetermined coefficients α, β and gamma values;
fitting a curve obtained by the correction function of the apparent resistivity observed by the dipolar method with the actual apparent resistivity curve observed by the dipolar method obtained in the observation of different positions of the roadway, and determining that the correction function k (r, b) is α e-βrThe values of gamma and undetermined coefficients α, β and gamma are correct;
changing the correction function k (r, b) to α e-βr+ gamma into said viewAnd obtaining a correction formula of the apparent resistivity observed by a dipolar method.
Optionally, the step of respectively substituting the correction function of the apparent resistivity observed by the dipolar method, the correction function of the apparent resistivity observed by the tripolar method, and the correction function of the apparent resistivity observed by the symmetric quadrapole method into the correction formula of the apparent resistivity observed by the dipolar method, and determining the correction formula of the apparent resistivity observed by the dipolar method, the correction formula of the apparent resistivity observed by the tripolar method, and the correction formula of the apparent resistivity observed by the symmetric quadrapole method includes:
the characteristics that a tripolar method and a symmetrical quadrupolar method can be regarded as the combination of a dipolar method are utilized, and correction functions of the observation apparent resistivity of the tripolar method and the symmetrical quadrupolar method can be deduced by a dipolar method correction formula;
the correction function of the apparent resistivity observed by the dipolar method is subjected to corresponding derivation transformation to determine the correction function of the apparent resistivity observed by the tripolar method and the symmetric quadrapole methodAnd the values of undetermined coefficients α and β;
applying the correction functionSubstituting the correction formula for observing the apparent resistivity to obtain the correction formula for observing the apparent resistivity by a tripolar method and a symmetric quadrapole method.
A correction system for observing apparent resistivity, the system comprising:
a correction formula obtaining unit for obtaining correction formula of observed apparent resistivity of the tunnelWherein,for corrected apparent resistivity, psTo be calibratedObserving the apparent resistivity positively, wherein k (r, b) is a correction function, the correction function is a correction function of observing the apparent resistivity by a dipolar method, or a correction function of observing the apparent resistivity by a tripolar method, or a correction function of observing the apparent resistivity by a symmetrical quadrapole method, and the correction function is a function related to the observed polar moment r and the roadway width b;
the actual observation apparent resistivity curve determining unit is used for determining a dipolar method actual observation apparent resistivity curve obtained in the process of observing at different positions of a roadway, and the dipolar method actual observation apparent resistivity curve is obtained by a finite element analysis method;
the dipolar method correction function determining unit is used for fitting a curve obtained by a correction function of the apparent resistivity observed by the dipolar method with an actual observed apparent resistivity curve of the dipolar method, determining undetermined coefficients in the dipolar method observed apparent resistivity correction function, and determining the correction function of the apparent resistivity observed by the dipolar method;
the calibration function determining unit of the tripolar method and the quadrapole method is used for converting the calibration function of the apparent resistivity observed by the dipolar method and determining the calibration function of the apparent resistivity observed by the tripolar method and the calibration function of the apparent resistivity observed by the symmetric quadrapole method;
a correction formula determining unit, configured to bring the correction function of the apparent resistivity observed by the dipolar method, the correction function of the apparent resistivity observed by the tripolar method, and the correction function of the apparent resistivity observed by the symmetric quadrapole method into the correction formula of the apparent resistivity, and determine the correction formula of the apparent resistivity observed by the dipolar method, the correction formula of the apparent resistivity observed by the tripolar method, and the correction formula of the apparent resistivity observed by the symmetric quadrapole method;
and the apparent resistivity correction unit is used for correcting the observation apparent resistivity to be corrected according to the correction formula of the observation apparent resistivity to obtain the corrected apparent resistivity.
Optionally, the unit for determining the apparent resistivity curve of the actual observation by the dipolar method specifically includes:
the two-pole observation apparent resistivity obtaining subunit is used for observing the resistivity of the roadway at different positions by adopting a two-pole method to obtain two-pole observation apparent resistivity;
and the determining subunit of the two-pole actual observation apparent resistivity curve is used for determining the two-pole actual observation apparent resistivity curve obtained when observation is carried out on different positions of the roadway by a finite element analysis method according to the two-pole observation apparent resistivity obtained by observation on different positions of the roadway.
Optionally, the dipolar method correction function determining unit specifically includes:
a correction function constructing subunit, configured to, when observing the tunnel apparent resistivity by the dipolar method, construct the correction function in the observation apparent resistivity correction formula as k (r, b) ═ α e-βr+ gamma, and pre-drafting undetermined coefficients α, β and gamma values;
a fitting subunit, configured to fit a curve obtained by the correction function of the apparent resistivity observed by the dipolar method to the actually observed apparent resistivity curve obtained by the dipolar method when the observation is performed at a different position in the roadway, and determine that the correction function k (r, b) ═ α e-βrThe values of gamma and undetermined coefficients α, β and gamma are correct;
a correction formula determination subunit for observing apparent resistivity by a dipolar method, for changing the correction function k (r, b) to α e-βrAnd substituting the + gamma into the correction formula for observing the apparent resistivity to obtain the correction formula for observing the apparent resistivity by a dipolar method.
Optionally, the correction formula determining unit specifically includes:
the correction function determination subunit is used for deducing the correction functions of the observation apparent resistivity of the tripolar method and the symmetric quadrupole method by using the characteristic that the tripolar method and the symmetric quadrupole method can be regarded as the combination of the dipolar method;
a correction formula determination subunit for determining the correction formula of the second unitThe correction function of the apparent resistivity observed by the polar method is determined by corresponding derivation transformationAnd the values of undetermined coefficients α and β;
applying the correction functionSubstituting the correction formula for observing the apparent resistivity to obtain the correction formula for observing the apparent resistivity by a tripolar method and a symmetric quadrapole method.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects: the invention carries out three-dimensional finite element analysis on the apparent resistivity under the influence of the tunnel cavity environment to obtain the actual background apparent resistivity under the influence of the tunnel cavity environment, and obtains the relation between the actual background apparent resistivity and the observation apparent resistivity under the influence of the tunnel cavity by researching the actual background apparent resistivity and the observation apparent resistivity obtained by adopting a dipolar method and a tripolar method, and the observed apparent resistivity can be corrected by adopting the relation to convert the observed apparent resistivity into the actual background apparent resistivity, thereby eliminating the influence of the tunnel cavity. Therefore, the accurate apparent resistivity can be obtained by adopting the measuring instrument and the correction method provided by the invention, complex three-dimensional finite element analysis is not needed, and the efficiency is improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a schematic flow chart of a calibration method for observing apparent resistivity according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of the whole effect (a), the central cross section (b) and the tetrahedron subdivision (c) of the three-dimensional finite element mesh subdivision according to the embodiment of the present invention;
FIG. 3 is a schematic diagram of a layout position of a survey line in a finite element simulation roadway according to an embodiment of the invention;
FIG. 4 is a graph of tau-r curves of different survey lines in a roadway observed by a dipolar method according to an embodiment of the invention;
FIG. 5 is a tau-r curve observed by a dipolar method for roadways with different cross sections in the embodiment of the invention;
FIG. 6 is a fitting curve for observing influence of survey lines of roadway surfaces with different cross sections by a dipolar method according to an embodiment of the present invention;
FIG. 7 is a graph fitting of the two-pole method for observing the influence of the lane angle measurement line in the embodiment of the present invention;
FIG. 8 is a schematic diagram of a three-pole cross-section observation model according to an embodiment of the present invention;
FIG. 9 is a graph of the three-pole section method of the present invention before (a) and after (b) the correction of the effect of the cavity of the apparent resistance roadway;
FIG. 10 is a schematic structural diagram of a calibration system for observing apparent resistivity according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a method and a system for correcting observed apparent resistivity, which can be used for correcting the observed apparent resistivity of a roadway well, eliminating the interference of the environment and providing a reliable data basis for the advanced detection of the roadway.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Fig. 1 is a schematic flow chart of a correction method for observing apparent resistivity according to an embodiment of the present invention, and as shown in fig. 1, the correction method for observing apparent resistivity of a roadway includes the following steps:
step 101: correction formula for acquiring observed apparent resistivity of roadwayWherein,for corrected apparent resistivity, psFor observing apparent resistivity to be corrected, k (r, b) is a correction function, the correction function is a two-pole method observation apparent resistance correction function or a three-pole method observation apparent resistance correction function or a symmetrical four-pole method observation apparent resistance correction function, and the correction function is a function related to observation polar moment r and roadway width b;
step 102: determining a dipolar method actual observation apparent resistivity curve obtained in the process of observing at different positions of a roadway, wherein the dipolar method actual observation apparent resistivity curve is obtained by a finite element analysis method;
step 103: fitting a curve obtained by a correction function of the apparent resistivity observed by the dipolar method with an actual observed apparent resistivity curve of the dipolar method, determining undetermined coefficients in the observed apparent resistivity correction function of the dipolar method, and determining the correction function of the observed apparent resistivity of the dipolar method;
step 104: correspondingly converting the correction function of the apparent resistivity observed by the two-pole method, and determining the correction function of the apparent resistivity observed by the three-pole method and the correction function of the apparent resistivity observed by the symmetrical four-pole method;
step 105: respectively bringing the correction function of the apparent resistivity observed by the dipolar method, the correction function of the apparent resistivity observed by the tripolar method and the correction function of the apparent resistivity observed by the symmetric quadrapole method into the correction formula of the observed apparent resistivity, and determining the correction formula of the apparent resistivity observed by the dipolar method, the correction formula of the apparent resistivity observed by the tripolar method and the correction formula of the apparent resistivity observed by the symmetric quadrapole method;
step 106: and correcting the observation apparent resistivity to be corrected according to the correction formula of the observation apparent resistivity to obtain the corrected apparent resistivity.
Step 102, determining a two-pole actual observation apparent resistivity curve obtained when observing at different positions of a roadway, specifically comprising:
observing the resistivity of the roadway at different positions by adopting a dipolar method to obtain observed apparent resistivity of the dipolar method;
and determining an actual apparent resistivity curve of the dipolar method obtained when observation is carried out on different positions of the roadway by a finite element analysis method according to the observed apparent resistivity of the dipolar method obtained by observation on different positions of the roadway.
Step 103 specifically comprises:
fitting a curve obtained by a correction function of apparent resistivity observed by a dipolar method with an actual observed apparent resistivity curve of the dipolar method, determining undetermined coefficients in the observed apparent resistivity correction function of the dipolar method, and determining the correction function of the observed apparent resistivity of the dipolar method, specifically comprising the following steps:
when the tunnel apparent resistivity is observed by using a dipolar method, a correction function in the observed apparent resistivity correction formula is constructed in a way that k (r, b) is α e-βr+ gamma, and pre-drafting undetermined coefficients α, β and gamma values;
will be provided byFitting a curve obtained by the correction function of the apparent resistivity observed by the dipolar method with the actually observed apparent resistivity curve obtained by the dipolar method when the observation is carried out on the different positions of the roadway, and determining that the correction function k (r, b) is α e-βrAnd the values of the gamma and undetermined coefficients α, β and the gamma are correct.
Changing the correction function k (r, b) to α e-βrAnd substituting the + gamma into the correction formula for observing the apparent resistivity to obtain the correction formula for observing the apparent resistivity by a dipolar method.
Step 105, the step of respectively substituting the correction function of the apparent resistivity observed by the dipolar method, the correction function of the apparent resistivity observed by the tripolar method, and the correction function of the apparent resistivity observed by the symmetric quadrapole method into the correction formula of the apparent resistivity observed by the dipolar method, and determining the correction formula of the apparent resistivity observed by the dipolar method, the correction formula of the apparent resistivity observed by the tripolar method, and the correction formula of the apparent resistivity observed by the symmetric quadrapole method includes the following steps:
the characteristics that a tripolar method and a symmetrical quadrupolar method can be regarded as the combination of a dipolar method are utilized, and correction functions of the observation apparent resistivity of the tripolar method and the symmetrical quadrupolar method can be deduced by a dipolar method correction formula;
the correction function of the apparent resistivity observed by the dipolar method is subjected to corresponding derivation transformation to determine the correction function of the apparent resistivity observed by the tripolar method and the symmetric quadrapole methodAnd the values of the undetermined coefficients α and β.
Applying the correction functionSubstituting the correction formula for observing the apparent resistivity to obtain the correction formula for observing the apparent resistivity by a tripolar method and a symmetric quadrapole method.
The invention carries out three-dimensional finite element analysis on the apparent resistivity under the influence of the tunnel cavity environment to obtain the actual background apparent resistivity under the influence of the tunnel cavity environment, and obtains the relation between the actual background apparent resistivity and the observation apparent resistivity under the influence of the tunnel cavity by researching the actual background apparent resistivity and the observation apparent resistivity obtained by adopting a dipolar method and a tripolar method, and the observed apparent resistivity can be corrected by adopting the relation to convert the observed apparent resistivity into the actual background apparent resistivity, thereby eliminating the influence of the tunnel cavity. Therefore, the accurate apparent resistivity can be obtained by adopting the measuring instrument and the correction method provided by the invention, complex three-dimensional finite element analysis is not needed, and the efficiency is improved.
As an embodiment of the present invention, when determining a correction formula of the observed apparent resistivity of a roadway, a three-dimensional radial full-space tetrahedral mesh is divided around the roadway as a center, as shown in fig. 2 (fig. 2 is a schematic diagram of an overall effect (a), a central cross section (b), and a tetrahedral mesh (c) of the three-dimensional finite element mesh division according to the embodiment of the present invention), in order to study the influence of the layout position of survey lines in the roadway on the observed apparent resistivity, the roadway is set to be infinitely long, the width b is 4m, the height c is 4m, the center of the roadway is a coordinate origin, the resistivity of the cavity of the roadway is infinite, and the calculation time is 1 × 1012Omega m, the surrounding rock is a uniform medium, and the resistivity is 1 omega m. Taking a roadway bottom plate as an example, 3 measuring lines are arranged totally, the influence of the roadway cavity on the apparent resistivity observed by the dipolar method is calculated respectively, and the 3 measuring lines are respectively: the power supply point coordinate positions are respectively a1(0,2,2), a2(0,1,2) and A3(0,0,2), as shown in fig. 3 (fig. 3 is a schematic diagram of the layout position of the finite element simulation roadway internal measuring line in the embodiment of the invention).
FIG. 4 is a schematic diagram of a two-pole method for observing curves tau-r of different lateral lines in a roadway (where tau is rho)s/ρ0) As shown in fig. 4, comparing the curves of the different measurement lines τ to r, the main characteristics of the influence of the roadway cavity on the point source field are as follows: 1. because of the repulsion action of the tunnel on the current, the observed potential near the power supply point is larger than the normal potential without the influence of the tunnel, tau>1, the tunnel cavity has positive influence on the observation potential and is far away from the observation potentialThe observed potential of the power supply point tends to have no influence on the source field potential value of the same medium point by the tunnel cavity. 2. The influence of the roadway cavity is related to the relative position of the measuring lines, the influence degree of different measuring lines by the roadway cavity is different, the influence of the cavity on the measuring line of the roadway surface is large, and the influence of the cavity on the angle measuring line is relatively small. 3. The tau-r curves of different position surface survey lines (y is 1 and 2) on the roadway surface are similar in shape, only have slight difference in the descending section of the curve, and the influence rules are basically the same. 4. For a point source field, the curve variation trends of tau-r curves of different measuring lines are the same, and the curve consists of a first descending section and a tail horizontal asymptote. The first branch τ tends to be a fixed value (a surface measurement line τ → 2, an angle measurement line τ → 4/3), and the curve gradually decreases with increasing polar distance (r ═ AM); when r is>At 20m (about 5 times the width b of the roadway), the curve τ -r tends to be a straight line, τ → 1.
Taking observation of a dipolar normal plane survey line (a bottom plate central line) as an example, the relationship between the influence of the roadway cavity and the size of the roadway is analyzed. For the sake of no loss of generality, it is assumed that the width b and the height c of the roadway are equal, the measuring line is located on the central line of the roadway bottom plate, and the electrical parameters of other models are the same as those of the model of the previous embodiment. Fig. 5 is a tau-r curve observed by a dipolar method for roadways with different cross sections in the embodiment of the present invention, and as shown in fig. 5, the curves in fig. 5 are tau-r curves of the influence of roadway cavities with five cross-sectional sizes of 2 mx 2m, 4 mx 4m, 6 mx 6m, 8 mx 8m, and 10 mx 10m on a single-point source field, respectively. Analysis shows that the cavity influence is closely related to the size of the cross section of the roadway, and the curve morphological characteristics are as follows: 1. the shapes of curves tau-r of the roadways with different cross sections are similar, and the first branch of the curve tau → 2. 2. In the middle section of the curve (1< x <5b), as the polar distance (r ═ AM) is increased, τ is gradually reduced from 2 to 1, the curve descending speeds of the roadways with different sizes are different, and the curve descending speed is slower as the roadway section is larger. 3. And when r is greater than 5b, tau → 1 and the curve is a horizontal straight line.
Through the analysis, the influence of the tunnel cavity on the observation apparent resistivity is related to the observation polar distance r, the tunnel width b, the line measurement position and other factors, and the small polar distance (r) mainly influencing the polar distance less than 5 times of the tunnel width<5b) The apparent resistivity was observed. At the moment, if the measured potential difference and the corresponding device coefficient are directly measuredCalculating the apparent resistivity, wherein even under the condition that the electrical property of the surrounding rock medium of the roadway is uniform, the apparent resistivity value of the roadway resistivity method is not equal to the real resistivity of the surrounding rock any more, but is approximately equal to the product of the resistivity of the surrounding rock and the influence coefficient k (r, b) of the roadway cavity, namelyk (r, b) is defined as a function of the observed pole pitch r, the lane width b, and the line location. Apparent resistivity rho observed with a roadwaysDividing by the influence coefficient k (r, b) of the tunnel cavity to obtain the apparent resistivity value after eliminating the influence of the tunnel environmentNamely:
the invention constructs k (r, b) function and actually measured tau-r curve (tau ═ rho)s/ρ0) Considering the characteristic that the influence of the roadway on the apparent resistivity is attenuated along with the increase of the polar distance, an exponential function k (r, b) taking e as a base is constructed as α e-βrAnd + gamma, performing least square fitting on each curve by using the function, determining undetermined coefficients of the function and giving an approximate formula. For single-point source field dipolar observation, the approximate formula of the tunnel cavity influence function k (r, b) is as follows:
the face line α is equal to 1, γ is equal to 1,angular measuring lineγ＝1,β＝1/(2b)。
Therefore, for the general case of floor profile and angle profile of a roadway, the k (r, b) equation degenerates to:
fig. 6 is a fitting curve of the dipolar method for observing influence of survey lines of roadway surfaces with different cross sections in the embodiment of the invention, fig. 7 is curve fitting of the dipolar method for observing influence of survey lines of roadway angles in the embodiment of the invention, as shown in fig. 7, a solid line is a curve corresponding to a fitting function k (r, b), a dotted line is an observation curve of a roadway tau-r corresponding to a surrounding rock of 1 Ω · m, and b is a roadway width. The maximum fitting error of the fitting curves of the 5 different roadways shown in fig. 6 is 1.88%, and the average error is 0.45%; the maximum fitting error of the goniometric observation fit curve shown in fig. 7 was 2.87%, and the average error was 0.57%. Therefore, the roadway cavity influence dipolar method correction formula (2) has higher fitting precision with the actually measured tau-r curve, and can be used for approximately correcting the roadway cavity influence on the actually measured data of the roadway observed by the dipolar method.
The observation devices such as the tripolar method, the symmetric quadrapole method and the like can be regarded as the combination of the dipolar devices, so that the roadway environment correction functions of other devices can be deduced by the dipolar method correction formula. For a tripolar, quadrapole observation device, the roadway influence coefficient can be expressed as: k is a radical ofMN＝ΔUMN/ΔU′MNIn the formula ofMNIs the potential difference between two measuring electrodes, delta U ', when a roadway environment exists'MNAnd measuring the potential difference between the electrodes without the influence of the roadway environment under the same power supply condition. For tripolar, Δ U is expressed by dipolar methodMNObtaining:
ΔUMN＝UA(M)-UA(N)＝kA(M)UA0(M)-kA(N)UA0(N) (3)
the roadway environmental influence coefficient of the measured potential difference is expressed as
Wherein, UA0(M)、UA0And (N) is the normal potential for supplying power to the A, B respectively under the influence of no roadway environment. AM represents the distance between the electrode A and the electrode M, and M, N is an observation electrode N. Let the distance between two measuring electrodes MN and AM be d and r, then k isA(M)＝αe-βr+1、kA(N)＝αe-β(r+d)+1, substituting into formula (4) to obtain:
wherein, the surface measuring line alpha is 1, beta is 1/b; when the angle α is 1/3 and β is 1/2b, equation (5) can be changed to:
1, designing a tunnel in uniform surrounding rock, setting the tunnel length as infinite length, setting the width b as 4m and the height c as 4m, and taking the tunnel cavity resistivity as 1 × 1012Omega.m. 2. Arranging a surface survey line on a roadway floor, carrying out apparent resistivity depth survey by adopting a symmetrical quadrupole device, and calculating an observed apparent resistivity rhos. 3. Will observe apparent resistivity ρsAnd substituting the formula (6) into the formula (1), and dividing the formula and the formula to obtain the apparent resistivity value after eliminating the influence of the roadway environmentNamely, it is
Data before and after the tunnel floor symmetric quadrupole depth-finding apparent resistivity correction are shown in a table 1, and the influence of the tunnel cavity is corrected by using the correction formula (6) provided by the invention. As can be seen from the table 1, the directly observed apparent resistivity is greatly different from the actual surrounding rock resistivity of 100 omega m, the corrected apparent resistivity is basically close to the actual resistivity of the surrounding rock, the maximum correction error is 4.37 percent and the average error is 0.93 percent by considering 17 power supply polar distances on a measuring line, so that the correction effect of the correction method provided by the invention can basically meet the requirement of 5 percent of error in the field.
TABLE 1 correction of errors by approximation of the effects of roadway cavities
1, correcting the apparent resistivity of a designed roadway by a three-pole section method, wherein the size of the designed roadway is 4m × 4m × 4m, a low-resistance cube with the volume of 4m × 3m × 3m and the resistivity of 5 omega m exists under the bottom surface of the roadway, the resistivity of surrounding rocks is 100 omega m, the distance from the center of the cube to the bottom surface of the roadway H is 3.5 m.2, a measuring line is arranged at the center of the bottom surface of the roadway, the observation is carried out by the three-pole section method (AMN), the distance between poles AM is 2m, the distance between poles MN is 1m, and the apparent resistivity rho is calculatedsAs shown in fig. 8 (fig. 8 is a schematic diagram of a three-pole cross-section observation model according to an embodiment of the present invention). 3. Will observe apparent resistivity ρsAnd substituting the formula (6) into the formula (1), and dividing the formula and the formula to obtain the apparent resistivity value after eliminating the influence of the roadway environment
Fig. 9 shows curves before (a) and after (b) correction for observing the influence of the tunnel cavity of the apparent resistance by the three-pole section method in the embodiment of the invention, as shown in fig. 9, the difference between the apparent resistivity values before and after correction is large, the apparent resistivity curve after the influence of the tunnel cavity and the observed apparent resistivity curve without the influence of the tunnel cavity have good fitting values, the maximum error of correction is 4.76%, and the average error is 1.02%.
According to the method, the actual background apparent resistivity under the influence of the tunnel cavity environment is obtained by performing three-dimensional finite element analysis on the apparent resistivity under the influence of the tunnel cavity environment, the actual background apparent resistivity and the observed apparent resistivity obtained by observing through a dipolar method and a tripolar method are researched to obtain a relational expression of the actual background apparent resistivity and the observed apparent resistivity under the influence of the tunnel cavity, the relational expression can be used for correcting the observed apparent resistivity, the observed apparent resistivity is converted into the actual background apparent resistivity, and the influence of the tunnel cavity is eliminated. Therefore, the accurate apparent resistivity can be obtained by adopting the measuring instrument and the correction method provided by the invention, complex three-dimensional finite element analysis is not needed, and the efficiency is improved.
The invention also provides a correction system for observing apparent resistivity, fig. 10 is a schematic structural diagram of the correction system for observing apparent resistivity according to the embodiment of the invention, and as shown in fig. 10, the system comprises:
a correction formula obtaining unit 1001 for obtaining a correction formula of the observed apparent resistivity of the roadwayWherein,for corrected apparent resistivity, psFor observing apparent resistivity to be corrected, k (r, b) is a correction function, the correction function is a two-pole method observation apparent resistance correction function or a three-pole method observation apparent resistance correction function or a symmetrical four-pole method observation apparent resistance correction function, and the correction function is a function related to observation polar moment r and roadway width b;
an actual observation apparent resistivity curve determining unit 1002, configured to determine a two-pole method actual observation apparent resistivity curve obtained by performing-time measurement on different positions of a roadway, where the two-pole method actual observation apparent resistivity curve is obtained by a finite element analysis method;
a dipolar method correction function determination unit 1003, configured to fit a curve obtained by a correction function of the dipolar method observation apparent resistivity with the dipolar method actual observation apparent resistivity curve, determine an undetermined coefficient in the dipolar method observation apparent resistivity correction function, and determine the correction function of the dipolar method observation apparent resistivity;
a tripolar method and quadrupole method correction function determining unit 1004, configured to perform corresponding conversion on the correction function of the apparent resistivity observed by the dipolar method, and determine the correction function of the apparent resistivity observed by the tripolar method and the correction function of the apparent resistivity observed by the symmetric quadrupole method;
a correction formula determining unit 1005, configured to bring the correction function of the two-pole observation apparent resistivity, the correction function of the three-pole observation apparent resistivity, and the correction function of the symmetric four-pole observation apparent resistivity into the correction formula of the observation apparent resistivity, and determine the correction formula of the two-pole observation apparent resistivity, the correction formula of the three-pole observation apparent resistivity, and the correction formula of the symmetric four-pole observation apparent resistivity;
and an apparent resistivity correction unit 1006, configured to correct the observation apparent resistivity to be corrected according to the correction formula of the observation apparent resistivity, so as to obtain a corrected apparent resistivity.
The unit 1001 for determining apparent resistivity curve actually observed by the dipolar method specifically includes:
the two-pole observation apparent resistivity obtaining subunit is used for observing the resistivity of the roadway at different positions by adopting a two-pole method to obtain two-pole observation apparent resistivity;
and the determining subunit of the two-pole actual observation apparent resistivity curve is used for determining the two-pole actual observation apparent resistivity curve obtained when observation is carried out on different positions of the roadway by a finite element analysis method according to the two-pole observation apparent resistivity obtained by observation on different positions of the roadway.
The dipolar method correction function determination unit 1003 specifically includes:
a correction function constructing subunit for observing the apparent resistivity of the tunnel by using a dipolar methodThe correction function in the observation apparent resistivity correction formula is configured such that k (r, b) is α e-βr+ gamma, and pre-drafting undetermined coefficients α, β and gamma values;
a fitting subunit, configured to fit a curve obtained by the correction function of the apparent resistivity observed by the dipolar method to the actually observed apparent resistivity curve obtained by the dipolar method when the observation is performed at a different position in the roadway, and determine that the correction function k (r, b) ═ α e-βrAnd the values of the gamma and undetermined coefficients α, β and the gamma are correct.
A correction formula determination subunit for observing apparent resistivity by a dipolar method, for changing the correction function k (r, b) to α e-βrAnd substituting the + gamma into the correction formula for observing the apparent resistivity to obtain the correction formula for observing the apparent resistivity by a dipolar method.
The correction formula determining unit 1005 specifically includes:
the correction function determination subunit is used for deducing the correction functions of the observation apparent resistivity of the tripolar method and the symmetric quadrupole method by using the characteristic that the tripolar method and the symmetric quadrupole method can be regarded as the combination of the dipolar method;
a correction formula determining subunit, for determining the correction function of the apparent resistivity observed by the dipolar method through corresponding derivation transformationAnd the values of the undetermined coefficients α and β.
Applying the correction functionSubstituting the correction formula for observing the apparent resistivity to obtain the correction formula for observing the apparent resistivity by a tripolar method and a symmetric quadrapole method.
The correction system for observing the apparent resistivity corrects the observed apparent resistivity obtained by observing devices such as a dipolar method device and a tripolar method device by adopting the observed apparent resistivity formula provided by the invention, so that the corrected apparent resistivity is obtained, and the influence of a tunnel cavity is eliminated. And complex three-dimensional finite element analysis is not required, so that the efficiency is improved.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (8)
1. A method of correcting observed apparent resistivity, the method comprising:
correction formula for acquiring observed apparent resistivity of roadwayWherein,for corrected apparent resistivity, psObserving apparent resistivity for correctionK (r, b) is a correction function, the correction function is a two-pole observation apparent resistivity correction function or a three-pole observation apparent resistivity correction function or a symmetrical four-pole observation apparent resistivity correction function, and the correction function is a function related to observation polar moment r and roadway width b;
determining a dipolar method actual observation apparent resistivity curve obtained in the process of observing at different positions of a roadway, wherein the dipolar method actual observation apparent resistivity curve is obtained by a finite element analysis method;
fitting a curve obtained by a correction function of the apparent resistivity observed by the dipolar method with an actual observed apparent resistivity curve of the dipolar method, determining undetermined coefficients in the observed apparent resistivity correction function of the dipolar method, and determining the correction function of the observed apparent resistivity of the dipolar method;
converting the correction function of the apparent resistivity observed by the dipolar method, and determining the correction function of the apparent resistivity observed by the tripolar method and the correction function of the apparent resistivity observed by the symmetric quadrapole method;
respectively bringing the correction function of the apparent resistivity observed by the dipolar method, the correction function of the apparent resistivity observed by the tripolar method and the correction function of the apparent resistivity observed by the symmetric quadrapole method into the correction formula of the observed apparent resistivity, and determining the correction formula of the apparent resistivity observed by the dipolar method, the correction formula of the apparent resistivity observed by the tripolar method and the correction formula of the apparent resistivity observed by the symmetric quadrapole method;
and correcting the observation apparent resistivity to be corrected according to the correction formula of the observation apparent resistivity to obtain the corrected apparent resistivity.
2. The correction method according to claim 1, wherein the determining of the actual observed apparent resistivity curve of the dipolar method obtained when the observation is performed at different positions in the roadway specifically comprises:
observing the resistivity of the roadway at different positions by adopting a dipolar method to obtain observed apparent resistivity of the dipolar method;
and determining an actual apparent resistivity curve of the dipolar method obtained when observation is carried out on different positions of the roadway by a finite element analysis method according to the observed apparent resistivity of the dipolar method obtained by observation on different positions of the roadway.
3. The method according to claim 1, wherein the step of fitting a curve obtained from the correction function of the apparent resistivity observed by the dipolar method to the actual observed apparent resistivity curve of the dipolar method, determining a to-be-determined coefficient in the correction function of the apparent resistivity observed by the dipolar method, and determining the correction function of the apparent resistivity observed by the dipolar method specifically comprises:
when the tunnel apparent resistivity is observed by using a dipolar method, a correction function in the observed apparent resistivity correction formula is constructed in a way that k (r, b) is α e-βr+ gamma, and pre-drafting undetermined coefficients α, β and gamma values;
fitting a curve obtained by the correction function of the apparent resistivity observed by the dipolar method with the actual apparent resistivity curve observed by the dipolar method obtained in the observation of different positions of the roadway, and determining that the correction function k (r, b) is α e-βrThe values of gamma and undetermined coefficients α, β and gamma are correct;
changing the correction function k (r, b) to α e-βrAnd substituting the + gamma into the correction formula for observing the apparent resistivity to obtain the correction formula for observing the apparent resistivity by a dipolar method.
4. The method according to claim 1, wherein the step of substituting the correction function of the apparent resistivity observed by the dipolar method, the correction function of the apparent resistivity observed by the tripolar method, and the correction function of the apparent resistivity observed by the symmetric quadrapole method into the correction formula of the apparent resistivity to determine the correction formula of the apparent resistivity observed by the dipolar method, the correction formula of the apparent resistivity observed by the tripolar method, and the correction formula of the apparent resistivity observed by the symmetric quadrapole method includes:
the characteristics that a tripolar method and a symmetrical quadrupolar method can be regarded as the combination of a dipolar method are utilized, and correction functions of the observation apparent resistivity of the tripolar method and the symmetrical quadrupolar method can be deduced by a dipolar method correction formula;
the correction function of the apparent resistivity observed by the dipolar method is subjected to corresponding derivation transformation to determine the correction function of the apparent resistivity observed by the tripolar method and the symmetric quadrapole methodAnd the values of undetermined coefficients α and β;
applying the correction functionSubstituting the correction formula for observing the apparent resistivity to obtain the correction formula for observing the apparent resistivity by a tripolar method and a symmetric quadrapole method.
5. A calibration system for observing apparent resistivity, the system comprising:
a correction formula obtaining unit for obtaining correction formula of observed apparent resistivity of the tunnelWherein,for corrected apparent resistivity, psFor observing apparent resistivity to be corrected, k (r, b) is a correction function, the correction function is a correction function for observing apparent resistivity by a dipolar method, or an apparent resistivity by a tripolar method, or an apparent resistivity by a symmetric quadrapole method, and the correction function is a function related to observing polar moment r and roadway width b;
the actual observation apparent resistivity curve determining unit is used for determining a dipolar method actual observation apparent resistivity curve obtained in the process of observing at different positions of a roadway, and the dipolar method actual observation apparent resistivity curve is obtained by a finite element analysis method;
the dipolar method correction function determining unit is used for fitting a curve obtained by a correction function of the apparent resistivity observed by the dipolar method with an actual observed apparent resistivity curve of the dipolar method, determining undetermined coefficients in the dipolar method observed apparent resistivity correction function, and determining the correction function of the apparent resistivity observed by the dipolar method;
the calibration function determining unit of the tripolar method and the quadrapole method is used for converting the calibration function of the apparent resistivity observed by the dipolar method and determining the calibration function of the apparent resistivity observed by the tripolar method and the calibration function of the apparent resistivity observed by the symmetric quadrapole method;
a correction formula determining unit, configured to bring the correction function of the apparent resistivity observed by the dipolar method, the correction function of the apparent resistivity observed by the tripolar method, and the correction function of the apparent resistivity observed by the symmetric quadrapole method into the correction formula of the apparent resistivity, and determine the correction formula of the apparent resistivity observed by the dipolar method, the correction formula of the apparent resistivity observed by the tripolar method, and the correction formula of the apparent resistivity observed by the symmetric quadrapole method;
and the apparent resistivity correction unit is used for correcting the observation apparent resistivity to be corrected according to the correction formula of the observation apparent resistivity to obtain the corrected apparent resistivity.
6. The calibration system according to claim 5, wherein the determination unit for the actual observed apparent resistivity curve of the dipolar method specifically comprises:
the two-pole observation apparent resistivity obtaining subunit is used for observing the resistivity of the roadway at different positions by adopting a two-pole method to obtain two-pole observation apparent resistivity;
and the determining subunit of the two-pole actual observation apparent resistivity curve is used for determining the two-pole actual observation apparent resistivity curve obtained when observation is carried out on different positions of the roadway by a finite element analysis method according to the two-pole observation apparent resistivity obtained by observation on different positions of the roadway.
7. The calibration system of claim 5, wherein the dipolar calibration function determination unit specifically comprises:
a correction function constructing subunit for observing the tunnel apparent resistivity by using a dipolar methodConstructing a correction function in the observation apparent resistivity correction formula such that k (r, b) is α e-βr+ gamma, and pre-drafting undetermined coefficients α, β and gamma values;
a fitting subunit, configured to fit a curve obtained by the correction function of the apparent resistivity observed by the dipolar method to the actually observed apparent resistivity curve obtained by the dipolar method when the observation is performed at a different position in the roadway, and determine that the correction function k (r, b) ═ α e-βrThe values of gamma and undetermined coefficients α, β and gamma are correct;
a correction formula determination subunit for observing apparent resistivity by a dipolar method, for changing the correction function k (r, b) to α e-βrAnd substituting the + gamma into the correction formula for observing the apparent resistivity to obtain the correction formula for observing the apparent resistivity by a dipolar method.
8. The calibration system according to claim 5, wherein the calibration formula determining unit specifically includes:
the correction function determination subunit is used for deducing the correction functions of the observation apparent resistivity of the tripolar method and the symmetric quadrupole method by using the characteristic that the tripolar method and the symmetric quadrupole method can be regarded as the combination of the dipolar method;
a correction formula determining subunit, for determining the correction function of the apparent resistivity observed by the dipolar method through corresponding derivation transformationAnd the values of undetermined coefficients α and β;
applying the correction functionSubstituting the correction formula for observing the apparent resistivity to obtain the correction formula for observing the apparent resistivity by a tripolar method and a symmetric quadrapole method.
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