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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- CN107015285A CN107015285A CN201710139390.4A CN201710139390A CN107015285A CN 107015285 A CN107015285 A CN 107015285A CN 201710139390 A CN201710139390 A CN 201710139390A CN 107015285 A CN107015285 A CN 107015285A
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- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V3/00—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation
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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 present invention relates to Roadway Leading Prospecting field, more particularly to a kind of bearing calibration for observing apparent resistivity and it is
System.
Background technology
With China's rapid economic development, the demand to resources such as coal, metallic ores is also increased therewith.At present, China is most
Number mines have been enter into, the late productive life, many identified resource reserves of mineral and be available for ability to decline increasingly, superficial mining area money
Source faces exhaustion, and resource exploration develops to three-dimensional, depth direction.During underground engineering construction, if working face front, tunnel
When there is the unfavorable geologic bodies such as tomography, solution cavity, karst collapse col umn near surrounding, if do not detected in advance, it is possible to cause catastrophic failure.
Therefore, accurate Roadway Leading Prospecting methods and techniques are studied, accurate hazard forecasting is carried out, coalfield, mine, tunnel,
Had broad application prospects in terms of lower engineering construction.
Accurate Roadway Leading Prospecting technology is studied, need to be set up on reliable and stable three-dimensional FORWARD AND INVERSE PROBLEMS basis, ground
Lower tunnel environment is as a complicated three-dimensional underground structure, and tunnel cavity is in itself and the distribution to current field such as tunnel rail
In the presence of very big influence, by tunnel ambient influnence, Severe distortion often occurs for resistivity, the data interpretation increase to resistivity method
Many difficulty, or even the explanation of mistake is caused, and not in view of environment in existing Roadway Leading Prospecting technology
Interference, makes the accuracy of Roadway Leading Prospecting technology there is very big dispute.
The content of the invention
It is an object of the invention to provide a kind of bearing calibration for observing apparent resistivity and system, it can be good at seeing tunnel
Survey apparent resistivity to be corrected, exclude the interference of environment, reliable data foundation is provided for the forward probe in tunnel.
To achieve the above object, the invention provides following scheme:
A kind of bearing calibration for observing apparent resistivity, methods described includes:
Obtain the updating formula of the observation apparent resistivity in tunnelWherein,For regarding after correction
Resistivity, ρsFor observation apparent resistivity to be corrected, k (r, b) is correction function, and the correction function is two pole method observation apparent resistances
Rate correction function or three electrode method observation apparent resistivity correction function or symmetrical quadrupole method observation apparent resistivity correction function, institute
It is the function relevant with span length b with observation polar moment r to state correction function;
It is determined that the two pole method actual observation apparent resistivity curves obtained when being observed on the diverse location of tunnel, described
Two pole method actual observation apparent resistivity curves are obtained by limited element analysis technique;
The curve and the two pole method actual observation apparent resistance that the correction function that apparent resistivity is observed by two pole methods is obtained
Rate curve is fitted, and is determined the undetermined coefficient in two pole method observation apparent resistivity correction functions, is determined two pole method observation
The correction function of apparent resistivity;
The correction function that two pole method observes apparent resistivity is changed, the three electrode method observation apparent resistivity is determined
Correction function, symmetrical quadrupole method observe apparent resistivity correction function;
Two pole method is observed into the correction function of apparent resistivity, it is the correction function of three electrode method observation apparent resistivity, symmetrical
The correction function of four-electrode method observation apparent resistivity brings the updating formula of the observation apparent resistivity into respectively, determines two pole method
Observe the updating formula, the updating formula of three electrode method observation apparent resistivity, symmetrical quadrupole method observation apparent resistivity of apparent resistivity
Updating formula;
The observation apparent resistivity to be corrected is corrected according to the updating formula of the observation apparent resistivity, school is obtained
Apparent resistivity after just.
Optionally, the two pole method actual observation apparent resistances obtained when the determination is observed on the diverse location of tunnel
Rate curve, is specifically included:
Resistivity observation is carried out to the tunnel in diverse location using two pole methods, two pole method observation apparent resistivities are obtained;
According to the two pole method observation apparent resistivities observed and obtained on the diverse location of tunnel, pass through limited element analysis technique
It is determined that when being observed on the diverse location of tunnel, the two pole method actual observation apparent resistivity curves obtained.
Optionally, the curve that the correction function that apparent resistivity is observed by two pole methods is obtained and two pole method are actual
Observation apparent resistivity curve is fitted, and the undetermined coefficient in two pole method observation apparent resistivity correction functions is determined, it is determined that described
Two pole methods observe the correction function of apparent resistivity, specifically include:
When being observed using two pole methods to tunnel apparent resistivity, by the school in the observation apparent resistivity updating formula
Positive function is configured to k (r, b)=α e-βr+ γ, and undetermined coefficient α, β, γ value are drafted in advance;
The curve that the correction function that apparent resistivity is observed by two pole method is obtained, with described on the diverse location of tunnel
The two pole method actual observation apparent resistivity curves obtained when being observed are fitted, and determine correction function k (r, b)=α e-βr
+ γ and its undetermined coefficient α, β, γ value correctness;
By the correction function k (r, b)=α e-βr+ γ substitutes into the updating formula of the observation apparent resistivity, obtains two poles
Method observes the updating formula of apparent resistivity.
Optionally, it is described that two pole method is observed into the school that the correction function of apparent resistivity, three electrode method observe apparent resistivity
Positive function, the correction function of symmetrical quadrupole method observation apparent resistivity bring the updating formula of the observation apparent resistivity into respectively, really
Updating formula, updating formula, the symmetrical quadrupole method of three electrode method observation apparent resistivity of fixed two pole method observation apparent resistivity are seen
The updating formula of apparent resistivity is surveyed, is specifically included:
The characteristic of the combination of two pole methods is considered as using three electrode method, symmetrical quadrupole method, can be pushed away by two pole method updating formulas
Export three electrode method, the correction function of the observation apparent resistivity of symmetrical quadrupole method;
The correction function of apparent resistivity will be observed by two pole method, converted by corresponding derive, determine three pole
Method, symmetrical quadrupole method observe the correction function of apparent resistivity
And the value of undetermined coefficient α, β;
By the correction functionThe observation is substituted into regard
The updating formula of resistivity, obtains the updating formula that three electrode method, symmetrical quadrupole method observe apparent resistivity.
A kind of correction system for observing apparent resistivity, the system includes:
Updating formula acquiring unit, the updating formula of the observation apparent resistivity for obtaining tunnel
Wherein,For the apparent resistivity after correction, ρsFor observation apparent resistivity to be corrected, k (r, b) is correction function, the correction letter
Number is that two pole method observation apparent resistivity correction functions or three electrode method observation apparent resistivity correction function or symmetrical quadrupole method are seen
Apparent resistivity correction function is surveyed, the correction function is the function relevant with span length b with observation polar moment r;
Actual observation apparent resistivity curve determining unit, is obtained during for determining and be observed on the diverse location of tunnel
Two pole method actual observation apparent resistivity curves, the two pole method actual observation apparent resistivity curve obtains by limited element analysis technique
Arrive;
Two pole method correction function determining units, for the curve that the correction function of apparent resistivity is obtained will to be observed by two pole methods
It is fitted with the two pole method actual observation apparent resistivity curve, determines treating in two pole method observation apparent resistivity correction functions
Determine coefficient, determine that two pole method observes the correction function of apparent resistivity;
Three electrode method four-electrode method correction function determining unit, the correction function for observing two pole method apparent resistivity enters
Row conversion, determines that the correction function of the three electrode method observation apparent resistivity, symmetrical quadrupole method observe the correction function of apparent resistivity;
Updating formula determining unit, is regarded for two pole method to be observed to the correction function of apparent resistivity, three electrode method observation
Correction function, the correction function of symmetrical quadrupole method observation apparent resistivity of resistivity bring the school of the observation apparent resistivity into respectively
Positive formula, determines the updating formula of two pole method observation apparent resistivity, the updating formula of three electrode method observation apparent resistivity, symmetrical
Four-electrode method observes the updating formula of apparent resistivity;
Apparent resistivity corrects unit, and the observation to be corrected is regarded for the updating formula according to the observation apparent resistivity
Resistivity is corrected, the apparent resistivity after being corrected.
Optionally, the two pole method actual observation apparent resistivity curve determining unit, is specifically included:
Two pole method observation apparent resistivities obtain subelement, for carrying out electricity to the tunnel in diverse location using two pole methods
Resistance rate is observed, and obtains two pole method observation apparent resistivities;
Two pole method actual observation apparent resistivity curve determination subelements, for being observed according to described on the diverse location of tunnel
Two obtained pole method observation apparent resistivities, when determining to be observed on the diverse location of tunnel by limited element analysis technique, are obtained
The two pole method actual observation apparent resistivity curves obtained.
Optionally, the two pole method correction function determining unit, is specifically included:
Correction function constructs subelement, for when being observed using two pole methods to tunnel apparent resistivity, being seen described
The correction function surveyed in apparent resistivity updating formula is configured to k (r, b)=α e-βr+ γ, and draft undetermined coefficient α, β, γ in advance
Value;
Subelement is fitted, it is and described for the obtained curve of correction function will apparent resistivity observed by two pole method
The two pole method actual observation apparent resistivity curves obtained when being observed on the diverse location of tunnel are fitted, it is determined that correction
Function k (r, b)=α e-βr+ γ and its undetermined coefficient α, β, γ value correctness;
Two pole methods observe the updating formula determination subelement of apparent resistivities, for by the correction function k (r, b)=α e-βr
+ γ substitutes into the updating formula of the observation apparent resistivity, obtains the updating formula that two pole methods observe apparent resistivity.
Optionally, the updating formula determining unit, is specifically included:
Correction function determination subelement, the spy of the combination for being considered as two pole methods using three electrode method, symmetrical quadrupole method
Property, three electrode method, the correction function of the observation apparent resistivity of symmetrical quadrupole method can be derived by two pole method updating formulas;
Updating formula determination subelement, for the correction function by apparent resistivity is observed by two pole method, is converted by corresponding derive,
Determine that the three electrode method, symmetrical quadrupole method observe the correction function of apparent resistivity
And the value of undetermined coefficient α, β;
By the correction functionThe observation is substituted into regard
The updating formula of resistivity, obtains the updating formula that three electrode method, symmetrical quadrupole method observe apparent resistivity.
The specific embodiment provided according to the present invention, the invention discloses following technique effect:The present invention is to empty in tunnel
Apparent resistivity under chamber ambient influnence carries out three-dimensional finite element analysis, obtains the real background under the influence of the cavity environment of tunnel and regards electricity
Resistance rate, by being studied with using two pole methods, three electrode method to observe obtained observation apparent resistivity real background apparent resistivity,
Real background apparent resistivity and the relational expression for observing apparent resistivity under the influence of the cavity of tunnel have been obtained, can be right using this relational expression
The apparent resistivity observed is corrected, and is translated into real background apparent resistivity, eliminates the influence of tunnel cavity.So
One, the bearing calibration provided using measuring instrument and the present invention can obtain accurate apparent resistivity, without being answered again
Miscellaneous three-dimensional finite element analysis, improve efficiency.
Brief description of the drawings
In order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, below will be to institute in embodiment
The accompanying drawing needed to use is briefly described, it should be apparent that, drawings in the following description are only some implementations of the present invention
Example, for those of ordinary skill in the art, without having to pay creative labor, can also be according to these accompanying drawings
Obtain other accompanying drawings.
Fig. 1 is the bearing calibration schematic flow sheet that the embodiment of the present invention observes apparent resistivity;
Fig. 2 is three-dimensional finite element mesh subdivision whole structure of the embodiment of the present invention (a), central cross-section (b), Tetrahedron subdivision
(c) schematic diagram;
Fig. 3 is Hydrographic General Line position view in finite element modelling of embodiment of the present invention tunnel;
Fig. 4 is different survey line τ~r curves in the pole method observation tunnel of the embodiment of the present invention two;
Fig. 5 is the pole method observation τ~r curves of different cross section of embodiment of the present invention tunnel two;
Fig. 6 is the matched curve of the pole method observation different cross section tunnel face survey line influence of the embodiment of the present invention two;
Fig. 7 is the curve matching of the pole method observation tunnel angle survey line influence of the embodiment of the present invention two;
Fig. 8 is the pole profile method observation model schematic diagram of the embodiment of the present invention three;
Fig. 9 is that the pole profile method observation apparent resistance tunnel cavity of the embodiment of the present invention three influences (a) before correction, after correction (b)
Curve;
Figure 10 is the correction system structure diagram that the embodiment of the present invention observes apparent resistivity.
Embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete
Site preparation is described, it is clear that described embodiment is only a part of embodiment of the invention, rather than whole embodiments.It is based on
Embodiment in the present invention, it is every other that those of ordinary skill in the art are obtained under the premise of creative work is not made
Embodiment, belongs to the scope of protection of the invention.
It is an object of the invention to provide a kind of bearing calibration for observing apparent resistivity and system, it can be good at seeing tunnel
Survey apparent resistivity to be corrected, exclude the interference of environment, reliable data foundation is provided for the forward probe in tunnel.
In order to facilitate the understanding of the purposes, features and advantages of the present invention, it is below in conjunction with the accompanying drawings and specific real
Applying mode, the present invention is further detailed explanation.
Fig. 1 is the bearing calibration schematic flow sheet that the embodiment of the present invention observes apparent resistivity, as shown in figure 1, tunnel is observed
The bearing calibration step of apparent resistivity is as follows:
Step 101:Obtain the updating formula of the observation apparent resistivity in tunnelWherein,For school
Apparent resistivity after just, ρsFor observation apparent resistivity to be corrected, k (r, b) is correction function, and the correction function is that two pole methods are seen
Apparent resistance correction function or three electrode method observation apparent resistance correction function or symmetrical quadrupole method observation apparent resistance correction function are surveyed,
The correction function is the function relevant with span length b with observation polar moment r;
Step 102:It is determined that the two pole method actual observation apparent resistivities obtained when being observed on the diverse location of tunnel
Curve, the two pole method actual observation apparent resistivity curve is obtained by limited element analysis technique;
Step 103:The curve that the correction function that apparent resistivity is observed by two pole methods is obtained and the actual sight of two pole method
Survey apparent resistivity curve to be fitted, determine the undetermined coefficient in two pole method observation apparent resistivity correction functions, determine described two
Pole method observes the correction function of apparent resistivity;
Step 104:The correction function that two pole method observes apparent resistivity is changed accordingly, three pole is determined
The correction function of method observation apparent resistivity, symmetrical quadrupole method observe the correction function of apparent resistivity;
Step 105:Two pole method is observed into the correction letter that the correction function of apparent resistivity, three electrode method observe apparent resistivity
Number, the correction function of symmetrical quadrupole method observation apparent resistivity bring the updating formula of the observation apparent resistivity into respectively, determine institute
The updating formula, the updating formula of three electrode method observation apparent resistivity, the observation of symmetrical quadrupole method for stating two pole method observation apparent resistivities are regarded
The updating formula of resistivity;
Step 106:School is carried out to the observation apparent resistivity to be corrected according to the updating formula of the observation apparent resistivity
Just, the apparent resistivity after being corrected.
Wherein, step 102 determines that the two pole method actual observations obtained when being observed on the diverse location of tunnel regard electricity
Resistance rate curve, is specifically included:
Resistivity observation is carried out to the tunnel in diverse location using two pole methods, two pole method observation apparent resistivities are obtained;
According to the two pole method observation apparent resistivities observed and obtained on the diverse location of tunnel, pass through limited element analysis technique
It is determined that when being observed on the diverse location of tunnel, the two pole method actual observation apparent resistivity curves obtained.
Step 103 is specifically included:
The curve and the two pole method actual observation apparent resistance that the correction function that apparent resistivity is observed by two pole methods is obtained
Rate curve is fitted, and is determined the undetermined coefficient in two pole method observation apparent resistivity correction functions, is determined two pole method observation
The correction function of apparent resistivity, is specifically included:
When being observed using two pole methods to tunnel apparent resistivity, by the school in the observation apparent resistivity updating formula
Positive function is configured to k (r, b)=α e-βr+ γ, and undetermined coefficient α, β, γ value are drafted in advance;
The curve that the correction function that apparent resistivity is observed by two pole method is obtained, with described on the diverse location of tunnel
The two pole method actual observation apparent resistivity curves obtained when being observed are fitted, and determine correction function k (r, b)=α e-βr
+ γ and its undetermined coefficient α, β, γ value correctness.
By the correction function k (r, b)=α e-βr+ γ substitutes into the updating formula of the observation apparent resistivity, obtains two poles
Method observes the updating formula of apparent resistivity.
Two pole method is observed into the school that the correction function of apparent resistivity, three electrode method observe apparent resistivity described in step 105
Positive function, the correction function of symmetrical quadrupole method observation apparent resistivity bring the updating formula of the observation apparent resistivity into respectively, really
Updating formula, updating formula, the symmetrical quadrupole method of three electrode method observation apparent resistivity of fixed two pole method observation apparent resistivity are seen
The updating formula of apparent resistivity is surveyed, is specifically included:
The characteristic of the combination of two pole methods is considered as using three electrode method, symmetrical quadrupole method, can be pushed away by two pole method updating formulas
Export three electrode method, the correction function of the observation apparent resistivity of symmetrical quadrupole method;
The correction function of apparent resistivity will be observed by two pole method, converted by corresponding derive, determine three pole
Method, symmetrical quadrupole method observe the correction function of apparent resistivity
And the value of undetermined coefficient α, β.
By the correction functionThe observation is substituted into regard
The updating formula of resistivity, obtains the updating formula that three electrode method, symmetrical quadrupole method observe apparent resistivity.
The present invention carries out three-dimensional finite element analysis to the apparent resistivity under the influence of the cavity environment of tunnel, obtains tunnel cavity
Real background apparent resistivity under ambient influnence, by being observed to real background apparent resistivity and using two pole methods, three electrode method
To observation apparent resistivity studied, obtained real background apparent resistivity and observation apparent resistivity under the influence of the cavity of tunnel
Relational expression, can be corrected to the apparent resistivity observed using this relational expression, be translated into real background apparent resistivity,
Eliminate the influence of tunnel cavity.So, the bearing calibration provided using measuring instrument and the present invention can obtain standard
True apparent resistivity, the three-dimensional finite element analysis without carrying out complexity again, improves efficiency.
As one embodiment of the present of invention, it is determined that tunnel observation apparent resistivity updating formula when, using tunnel as
Center carries out three-dimensional radial total space tetrahedron mesh generation, and (Fig. 2 is Three-D limited of the embodiment of the present invention as shown in Figure 2
First mesh generation whole structure (a), central cross-section (b), Tetrahedron subdivision (c) schematic diagram).For Hydrographic General Line position in research tunnel
The influence to observing apparent resistivity is put, if tunnel endless, wide b=4m, high c=4m, tunnel center are the origin of coordinates, and tunnel is empty
Chamber resistivity is infinity, and 1 × 10 is taken as during calculating12Ω m, country rock is uniform dielectric, and resistivity is 1 Ω m.With tunnel bottom
Exemplified by plate, 3 surveys line are laid altogether, and the influence that tunnel cavity observes two pole methods apparent resistivity, 3 survey line difference are calculated respectively
For:Positioned at the base angle survey line (y=2) of roadway floor and side intersection, tunnel face survey line (y=1) and positioned at roadway floor center line
Base surface survey line (y=0), supply terminals coordinate position is respectively A1 (0,2,2), A2 (0,1,2), A3 (0,0,2), such as accompanying drawing 3
Shown (Fig. 3 is Hydrographic General Line position view in finite element modelling of embodiment of the present invention tunnel).
Accompanying drawing 4 is different side line τ~r curves (wherein τ=ρ in the pole method observation tunnel of the embodiment of the present invention twos/ρ0), such as scheme
Shown in 4, different survey line τ~r curves are contrasted, tunnel cavity is mainly characterized by point source influence:1st, because tunnel is right in itself
The repulsive interaction of electric current, nearby observation voltage is more than the normal current potential without tunnel repair, τ to power supply point>1, tunnel cavity is to observation
Current potential shows as active influence, and no tunnel cavity influence same media point source field potential value is tended to away from power supply point observation voltage.2、
Tunnel cavity influence is relevant with survey line relative position, and different surveys line are different by tunnel cavity influence degree, and tunnel face survey line is by sky
Chamber influence is big, and angle survey line is influenceed relatively small by cavity.3rd, diverse location face survey line (y=1,2) τ~r shaped forms on the face of tunnel
State is similar, and only drop section has fine difference under the curve, and affecting laws are essentially identical.4th, for point source, different survey line τ~r is bent
Line variation tendency is identical, and curve is made up of first branch descending branch and tail branch horizontal asymptote two parts.First branch τ tends to definite value, and (face is surveyed
Line τ → 2, angle survey line τ → 4/3), as the increase τ of pole span (r=AM) is gradually reduced, curve slowly declines;Work as r>20m is (about
5 times of span length b) when, τ~r curves tend to straight line, τ → 1.
By taking the observation of two pole normal plane surveys line (bottom plate center line) as an example, the influence of analysis tunnel cavity and the relation of tunnel size.For
Without loss of generality, it is assumed that span length b and height c are equal, survey line is located on roadway floor center line, other model electrical parameters
It is identical with the model of a upper embodiment.Accompanying drawing 5 is the pole method observation τ~r curves of different cross section of embodiment of the present invention tunnel two, is such as schemed
Shown in 5, the curve in Fig. 5 is respectively 2m × 2m, 4m × 4m, 6m × 6m, 8m × 8m, five kinds of sectional dimension tunnels skies of 10m × 10m
τ~r curve of the chamber on Single Point Source influence.Analysis understands that cavity influence is in close relations with tunnel sectional dimension, and tracing pattern is special
Levy and show as:1st, different size section tunnel τ~r tracing patterns are similar, first branch τ → 2 of curve.2nd, curve stage casing (1<x<5b),
As pole span (r=AM) increases, τ gradually gradually decreases to 1 by 2, and different size roadway curve decrease speeds are different, tunnel section
Bigger curve decrease speed is slower.3rd, the tunnel of different cross section, works as r>During 5b, τ → 1, curve is horizontal linear.
By above-mentioned analysis, it is known that, tunnel cavity to observe the influence of apparent resistivity and observation pole span r, span length b and
The factors such as survey line position are relevant, and main influence pole span is less than the small pole span (r of 5 times of span lengths<5b) observe apparent resistivity.Now
If directly calculating apparent resistivity by actual measurement potential difference and corresponding electrode coefficient, even in the electrically uniform bar of roadway surrounding rock medium
Under part, tunnel resistivity method apparent resistivity value is also no longer equal to the true resistance rate of country rock, and be approximately equal to shoulder-bed resistivity (SBR) with
The product of tunnel cavity influence coefficient k (r, b), i.e.,K (r, b) is defined as wide with observation pole span r, tunnel
Spend b and the relevant function in survey line position.The apparent resistivity ρ observed with tunnelsDivided by tunnel cavity influence coefficient k (r, b), you can
Be eliminated the apparent resistivity value after the ambient influnence of tunnelI.e.:
Present invention construction k (r, b) function and τ~r curves (τ=ρ of actual measurements/ρ0) be fitted, and to observation apparent resistance
Rate carries out approximate correction.Influence in view of tunnel to apparent resistivity is the feature for increasing with pole span and decaying, and is constructed using e the bottom of as
Exponential function k (r, b)=α e-βr+ γ, carries out least square fitting using each bar curve of the function pair, determines that function is undetermined
Coefficient simultaneously provides approximate formula.For the pole method observation of Single Point Source two, tunnel cavity influence function k (r, b) approximate formula is:
Face survey line α=1, γ=1,Angle survey lineγ=
1, β=1/ (2b).
Therefore, for general roadway floor face survey line and angle survey line situation, k (r, b) formula is deteriorated to:
Accompanying drawing 6 is the matched curve of the pole method observation different cross section tunnel face survey line influence of the embodiment of the present invention two, and accompanying drawing 7 is
The curve matching of the pole method observation tunnel angle survey line influence of the embodiment of the present invention two, as shown in fig. 7, solid line is correspondence fitting function k
(r, b) curve, dotted line is that country rock is 1 Ω m correspondence tunnel τ~r observation curves, and b is span length.5 differences shown in Fig. 6
The maximum error of fitting of the matched curve in tunnel is 1.88%, and mean error is 0.45%;Angle survey line observation fitting shown in accompanying drawing 7
Curve maximum error of fitting is 2.87%, and mean error is 0.57%.It follows that the tunnel cavity influence two that the present invention is provided
Pole method updating formula formula (2) and τ~r curves of actual measurement have higher fitting precision, real available for tunnel is observed to two pole methods
Survey the approximate correction that data carry out tunnel cavity influence.
The combination of two pole devices is considered as observation devices such as three electrode method, symmetrical quadrupole methods, therefore can be by two pole methods
Updating formula derives the tunnel environment correction function of other devices.For three poles, quadrupole observation device, tunnel repair coefficient can
It is expressed as:kMN=Δ UMN/ΔU′MN, Δ U in formulaMNIt is potential difference, Δ U ' between two measuring electrodes when there is tunnel environmentMNFor phase
With under condition of power supply without potential difference between the ambient influnence measuring electrode of tunnel.For three electrode method, Δ U is represented with two pole methodsMN:
ΔUMN=UA(M)-UA(N)=kA(M)UA0(M)-kA(N)UA0(N) (3)
The tunnel environment coefficient of measurement potential difference is expressed as
Wherein, UA0(M)、UA0(N) the normal current potential to be powered respectively without A, B under the ambient influnence of tunnel.AM:Represent electrode A
The distance between with electrode M, M, N are observation electrode N.If two measuring electrode spacing MN=d, AM=r, then have kA(M)=α e-βr+
1、kA(N)=α e-β(r+d)+ 1, (4) formula is substituted into, is obtained:
In formula, face survey line α=1, β=1/b;Angle survey line α=1/3, β=1/2b, then (5) formula is variable turns to:
The observation apparent resistivity correction of roadway floor symmetrical four-pole sounding:1st, design and there is a tunnel, country rock in uniform country rock
Resistivity is 100 Ω m, sets the long endless in tunnel, and wide b=4m, high c=4m, tunnel cavity resistivity are taken as 1 × 1012
Ω·m.2nd, in roadway floor placement-face survey line, depth sounding with apparent resistivity is carried out using symmetrical quadrupole device, and calculating observation regards electricity
Resistance rate ρs.3rd, will observation apparent resistivity ρsAnd updating formula (6) formula brings (1) formula into, both are divided by the tunnel environment that can be eliminated
Apparent resistivity value after influenceI.e.
Data are shown in Table 1 before and after the correction of roadway floor symmetrical four-pole sounding apparent resistivity, public using correction proposed by the present invention
Formula (6) formula is corrected the influence of tunnel cavity.As can be seen from Table 1, the apparent resistivity directly observed and actual country rock resistance
The Ω m of rate 100 have very big difference, and it is corrected after apparent resistivity substantially close to the true resistance rate of country rock, investigate
17 polar distance of supplying power on survey line, maximum correction error is 4.37%, and mean error is 0.93%, therefore correction proposed by the present invention
Its calibration result of method can meet the error requirements of field 5% substantially.
The tunnel cavity influence approximation method correction error of table 1
The pole profile method observation apparent resistivity correction of roadway floor three:1st, design tunnel size 4m × 4m × 4m, tunnel bottom surface
Underface exist volume be 4m × 3m × 3m, resistivity be 5 Ω m low-resistance cubes, shoulder-bed resistivity (SBR) be 100 Ω m, cube
Body centre distance tunnel bottom H=3.5m.2nd, survey line is arranged in tunnel bottom center, is observed using three pole profile methods (AMN),
Pole span AM=2m, MN=1m, calculating observation apparent resistivity ρs, (Fig. 8 is that the pole profile method of the embodiment of the present invention three is seen as shown in Figure 8
Survey model schematic).3rd, will observation apparent resistivity ρsAnd updating formula (6) formula brings (1) formula into, both are divided by the tunnel that is eliminated
Apparent resistivity value after ambient influnence
Fig. 9 is that the pole profile method observation apparent resistance tunnel cavity of the embodiment of the present invention three influences (a) before correction, after correction (b)
Curve, as shown in figure 9, the apparent resistivity value difference before and after correction is larger, the apparent resistivity after influenceing correction through tunnel cavity is bent
Line corrects worst error 4.76% with having preferably fitting angle value without the observation apparent resistivity curve under the influence of the cavity of tunnel,
Mean error 1.02%.
The present invention obtains tunnel by carrying out three-dimensional finite element analysis to the apparent resistivity under the influence of the cavity environment of tunnel
Real background apparent resistivity under the influence of cavity environment, by being seen to real background apparent resistivity and using two pole methods, three electrode method
The observation apparent resistivity measured is studied, and has obtained real background apparent resistivity and observation apparent resistance under the influence of the cavity of tunnel
The relational expression of rate, this relational expression can be corrected to the apparent resistivity observed, be translated into real background apparent resistivity,
Eliminate the influence of tunnel cavity.So, the bearing calibration provided using measuring instrument and the present invention can obtain standard
True apparent resistivity, the three-dimensional finite element analysis without carrying out complexity again, improves efficiency.
Present invention also offers a kind of correction system for observing apparent resistivity, Figure 10 is that the embodiment of the present invention observes apparent resistance
The structural representation of the correction system of rate, as shown in Figure 10, the system includes:
Updating formula acquiring unit 1001, the updating formula of the observation apparent resistivity for obtaining tunnel
Wherein,For the apparent resistivity after correction, ρsFor observation apparent resistivity to be corrected, k (r, b) is correction function, the correction letter
Number is that two pole method observation apparent resistance correction functions or three electrode method observation apparent resistance correction function or the observation of symmetrical quadrupole method are regarded
Resistance correction function, the correction function is the function relevant with span length b with observation polar moment r;
Actual observation apparent resistivity curve determining unit 1002, for determining progress-survey when institute on the diverse location of tunnel
The two pole method actual observation apparent resistivity curves obtained, the two pole method actual observation apparent resistivity curve is by limited element analysis technique
Obtain;
Two pole method correction function determining units 1003, for obtain the correction function that apparent resistivity is observed by two pole methods
Curve is fitted with the two pole method actual observation apparent resistivity curve, is determined in two pole method observation apparent resistivity correction functions
Undetermined coefficient, determine that two pole method observes the correction function of apparent resistivity;
Three electrode method four-electrode method correction function determining unit 1004, the correction letter for observing two pole method apparent resistivity
Number is changed accordingly, determines correction function, the symmetrical quadrupole method observation apparent resistivity of the three electrode method observation apparent resistivity
Correction function;
Updating formula determining unit 1005, sees for two pole method to be observed to the correction function of apparent resistivity, three electrode method
Survey the correction function of apparent resistivity, the correction function of symmetrical quadrupole method observation apparent resistivity and bring the observation apparent resistivity into respectively
Updating formula, determine the updating formula of two pole method observation apparent resistivity, the updating formula of three electrode method observation apparent resistivity,
Symmetrical quadrupole method observes the updating formula of apparent resistivity;
Apparent resistivity corrects unit 1006, for the updating formula according to the observation apparent resistivity to the sight to be corrected
Survey apparent resistivity to be corrected, the apparent resistivity after being corrected.
Wherein, the two pole method actual observation apparent resistivity curve determining unit 1001, is specifically included:
Two pole method observation apparent resistivities obtain subelement, for carrying out electricity to the tunnel in diverse location using two pole methods
Resistance rate is observed, and obtains two pole method observation apparent resistivities;
Two pole method actual observation apparent resistivity curve determination subelements, for being observed according to described on the diverse location of tunnel
Two obtained pole method observation apparent resistivities, when determining to be observed on the diverse location of tunnel by limited element analysis technique, are obtained
The two pole method actual observation apparent resistivity curves obtained.
The two pole method correction function determining unit 1003, is specifically included:
Correction function constructs subelement, for when being observed using two pole methods to tunnel apparent resistivity, being seen described
The correction function surveyed in apparent resistivity updating formula is configured to k (r, b)=α e-βr+ γ, and draft undetermined coefficient α, β, γ in advance
Value;
Subelement is fitted, it is and described for the obtained curve of correction function will apparent resistivity observed by two pole method
The two pole method actual observation apparent resistivity curves obtained when being observed on the diverse location of tunnel are fitted, it is determined that correction
Function k (r, b)=α e-βr+ γ and its undetermined coefficient α, β, γ value correctness.
Two pole methods observe the updating formula determination subelement of apparent resistivities, for by the correction function k (r, b)=α e-βr
+ γ substitutes into the updating formula of the observation apparent resistivity, obtains the updating formula that two pole methods observe apparent resistivity.
The updating formula determining unit 1005, is specifically included:
Correction function determination subelement, the spy of the combination for being considered as two pole methods using three electrode method, symmetrical quadrupole method
Property, three electrode method, the correction function of the observation apparent resistivity of symmetrical quadrupole method can be derived by two pole method updating formulas;
Updating formula determination subelement, for the correction function by apparent resistivity is observed by two pole method, is converted by corresponding derive,
Determine that the three electrode method, symmetrical quadrupole method observe the correction function of apparent resistivity
And the value of undetermined coefficient α, β.
By the correction functionThe observation is substituted into regard
The updating formula of resistivity, obtains the updating formula that three electrode method, symmetrical quadrupole method observe apparent resistivity.
The observation apparent resistivity that the correction system for the observation apparent resistivity that the present invention is provided is provided by using the present invention is public
Formula is corrected to the observation apparent resistivity obtained using the observation of the devices such as two pole subtraction units, three electrode method device, is corrected
Apparent resistivity afterwards, eliminates the influence of tunnel cavity.Three-dimensional finite element analysis without carrying out complexity again, improve efficiency.
The embodiment of each in this specification is described by the way of progressive, and what each embodiment was stressed is and other
Between the difference of embodiment, each embodiment identical similar portion mutually referring to.For system disclosed in embodiment
For, because it is corresponded to the method disclosed in Example, so description is fairly simple, related part is said referring to method part
It is bright.
Specific case used herein is set forth to the principle and embodiment of the present invention, and above example is said
The bright method and its core concept for being only intended to help to understand the present invention;Simultaneously for those of ordinary skill in the art, foundation
The thought of the present invention, will change in specific embodiments and applications.In summary, this specification content is not
It is interpreted as limitation of the present invention.
Claims (8)
1. a kind of bearing calibration for observing apparent resistivity, it is characterised in that methods described includes:
Obtain the updating formula of the observation apparent resistivity in tunnelWherein,For the apparent resistance after correction
Rate, ρsFor observation apparent resistivity to be corrected, k (r, b) is correction function, and the correction function is two pole method observation apparent resistivity schools
Positive function or three electrode method observation apparent resistivity correction function or symmetrical quadrupole method observation apparent resistivity correction function, the school
Positive function is the function relevant with span length b with observation polar moment r;
It is determined that the two pole method actual observation apparent resistivity curves obtained when being observed on the diverse location of tunnel, two pole
Method actual observation apparent resistivity curve is obtained by limited element analysis technique;
The curve and the two pole method actual observation apparent resistivity that the correction function that apparent resistivity is observed by two pole methods is obtained are bent
Line is fitted, and is determined the undetermined coefficient in two pole method observation apparent resistivity correction functions, is determined that two pole method observation regards electricity
The correction function of resistance rate;
The correction function that two pole method observes apparent resistivity is changed, determines that the three electrode method observes the school of apparent resistivity
Positive function, symmetrical quadrupole method observe the correction function of apparent resistivity;
Two pole method is observed into correction function, symmetrical quadrupole that the correction function of apparent resistivity, three electrode method observe apparent resistivity
The correction function of method observation apparent resistivity brings the updating formula of the observation apparent resistivity into respectively, determines two pole method observation
Updating formula, updating formula, the symmetrical quadrupole method of three electrode method observation apparent resistivity of apparent resistivity observe the correction of apparent resistivity
Formula;
The observation apparent resistivity to be corrected is corrected according to the updating formula of the observation apparent resistivity, obtained after correction
Apparent resistivity.
2. bearing calibration according to claim 1, it is characterised in that the determination is observed on the diverse location of tunnel
When the two pole method actual observation apparent resistivity curves that are obtained, specifically include:
Resistivity observation is carried out to the tunnel in diverse location using two pole methods, two pole method observation apparent resistivities are obtained;
According to the two pole method observation apparent resistivities observed and obtained on the diverse location of tunnel, determined by limited element analysis technique
When being observed on the diverse location of tunnel, the two pole method actual observation apparent resistivity curves obtained.
3. bearing calibration according to claim 1, it is characterised in that the correction that apparent resistivity will be observed by two pole methods
The curve that function is obtained is fitted with the two pole method actual observation apparent resistivity curve, determines two pole method observation apparent resistivities
Undetermined coefficient in correction function, determines that two pole method observes the correction function of apparent resistivity, specifically includes:
When being observed using two pole methods to tunnel apparent resistivity, by the correction letter in the observation apparent resistivity updating formula
Number is configured to k (r, b)=α e-βr+ γ, and undetermined coefficient α, β, γ value are drafted in advance;
The curve that the correction function that apparent resistivity is observed by two pole method is obtained, is carried out with described on the diverse location of tunnel
The two pole method actual observation apparent resistivity curves obtained during observation are fitted, and determine correction function k (r, b)=α e-βr+γ
And its correctness of undetermined coefficient α, β, γ value;
By the correction function k (r, b)=α e-βr+ γ substitutes into the updating formula of the observation apparent resistivity, obtains two pole methods and sees
Survey the updating formula of apparent resistivity.
4. bearing calibration according to claim 1, it is characterised in that the school that two pole method is observed to apparent resistivity
Positive function, the correction function of three electrode method observation apparent resistivity, the correction function of symmetrical quadrupole method observation apparent resistivity are brought into respectively
The updating formula of the observation apparent resistivity, determines that the updating formula of two pole method observation apparent resistivity, three electrode method observation are regarded
Updating formula, the symmetrical quadrupole method of resistivity observe the updating formula of apparent resistivity, specifically include:
The characteristic of the combination of two pole methods is considered as using three electrode method, symmetrical quadrupole method, can be derived by two pole method updating formulas
The correction function of three electrode method, the observation apparent resistivity of symmetrical quadrupole method;
The correction function of apparent resistivity will be observed by two pole method, will be converted by corresponding derive, the three electrode method is determined, right
Four-electrode method is claimed to observe the correction function of apparent resistivityAnd it is undetermined
Factor alpha, β value;
By the correction functionSubstitute into the observation apparent resistance
The updating formula of rate, obtains the updating formula that three electrode method, symmetrical quadrupole method observe apparent resistivity.
5. a kind of correction system for observing apparent resistivity, it is characterised in that the system includes:
Updating formula acquiring unit, the updating formula of the observation apparent resistivity for obtaining tunnelIts
In,For the apparent resistivity after correction, ρsFor observation apparent resistivity to be corrected, k (r, b) is correction function, the correction function
For two pole method observation apparent resistivity correction functions or three electrode method observation apparent resistivity correction function or the observation of symmetrical quadrupole method
Apparent resistivity correction function, the correction function is the function relevant with span length b with observation polar moment r;
Actual observation apparent resistivity curve determining unit, two obtained during for determining and be observed on the diverse location of tunnel
Pole method actual observation apparent resistivity curve, the two pole method actual observation apparent resistivity curve is obtained by limited element analysis technique;
Two pole method correction function determining units, for curve and the institute that the correction function of apparent resistivity is obtained will to be observed by two pole methods
State two pole method actual observation apparent resistivity curves to be fitted, determine the system undetermined in two pole method observation apparent resistivity correction functions
Number, determines that two pole method observes the correction function of apparent resistivity;
Three electrode method four-electrode method correction function determining unit, the correction function for observing two pole method apparent resistivity is turned
Change, determine that the correction function of the three electrode method observation apparent resistivity, symmetrical quadrupole method observe the correction function of apparent resistivity;
Updating formula determining unit, apparent resistance is observed for two pole method to be observed to the correction function of apparent resistivity, three electrode method
The correction that correction function, the correction function of symmetrical quadrupole method observation apparent resistivity of rate bring the observation apparent resistivity into respectively is public
Formula, determines the updating formula, the updating formula of three electrode method observation apparent resistivity, symmetrical quadrupole of two pole method observation apparent resistivity
Method observes the updating formula of apparent resistivity;
Apparent resistivity correct unit, for according to it is described observation apparent resistivity updating formula to the observation apparent resistance to be corrected
Rate is corrected, the apparent resistivity after being corrected.
6. correction system according to claim 5, it is characterised in that the two pole method actual observation apparent resistivity curve is true
Order member, is specifically included:
Two pole method observation apparent resistivities obtain subelement, for carrying out resistivity to the tunnel in diverse location using two pole methods
Observation, obtains two pole method observation apparent resistivities;
Two pole method actual observation apparent resistivity curve determination subelements, are obtained for being observed according on the diverse location of tunnel
Two pole methods observation apparent resistivities, when determining to be observed on the diverse location of tunnel by limited element analysis technique, obtained
Two pole method actual observation apparent resistivity curves.
7. correction system according to claim 5, it is characterised in that the two pole method correction function determining unit, specifically
Including:
Correction function constructs subelement, for when being observed using two pole methods to tunnel apparent resistivity, the observation to be regarded
Correction function in resistivity correction formula is configured to k (r, b)=α e-βr+ γ, and draft taking for undetermined coefficient α, β, γ in advance
Value;
Subelement is fitted, for the curve for obtaining the correction function that apparent resistivity is observed by two pole method, with described in lane
The two pole method actual observation apparent resistivity curves obtained when being observed on road diverse location are fitted, and determine correction function
K (r, b)=α e-βr+ γ and its undetermined coefficient α, β, γ value correctness;
Two pole methods observe the updating formula determination subelement of apparent resistivities, for by the correction function k (r, b)=α e-βr+γ
The updating formula of the observation apparent resistivity is substituted into, the updating formula that two pole methods observe apparent resistivity is obtained.
8. correction system according to claim 5, it is characterised in that the updating formula determining unit, is specifically included:
Correction function determination subelement, the characteristic of the combination for being considered as two pole methods using three electrode method, symmetrical quadrupole method, can
The correction function of three electrode method, the observation apparent resistivity of symmetrical quadrupole method is derived by two pole method updating formulas;
Updating formula determination subelement, for the correction function by apparent resistivity is observed by two pole method, warp
Cross corresponding derive to convert, determine that the three electrode method, symmetrical quadrupole method observe the correction function of apparent resistivityAnd the value of undetermined coefficient α, β;
By the correction functionSubstitute into the observation apparent resistance
The updating formula of rate, obtains the updating formula that three electrode method, symmetrical quadrupole method observe apparent resistivity.
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