CN103278855B - Method for eliminating influence of roadways and terrains on apparent resistivity in direct-current exploration - Google Patents
Method for eliminating influence of roadways and terrains on apparent resistivity in direct-current exploration Download PDFInfo
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- CN103278855B CN103278855B CN201310173286.9A CN201310173286A CN103278855B CN 103278855 B CN103278855 B CN 103278855B CN 201310173286 A CN201310173286 A CN 201310173286A CN 103278855 B CN103278855 B CN 103278855B
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Abstract
The invention discloses a method for eliminating the influence of roadways and terrains on the apparent resistivity in direct-current exploration. The method comprises the following steps of establishing a model according to a roadway shape, the roadway cutting depth, topographic relief elevation and the like; taking the minimum value of the formation resistivity of an exploration area as the resistivity of a uniform half-space containing the roadways and the terrains; putting a power supply electrode at a corresponding position in the model according to the type of the adopted device for direct-current exploration and the electrode distribution mode; performing one-time three-dimensional numerical simulation every time the power supply electrode moves, obtaining potential response of a background field, and interpolating to obtain potential difference between receiving electrodes as potential difference of the background field; deducing an apparent resistivity formula from a potential formula of a point current source in the horizontal uniform self-space; and subtracting the potential difference of the background field from the measured potential difference to obtain potential different without the influence of the roadways and the terrains, and substituting the potential difference into an apparent resistivity formula of a current source in an underground self-space to obtain the relative apparent resistivity. The method can be widely applied to direct-current resistivity exploration projects.
Description
Technical field
The invention belongs to electricity and electromagnetic prospecting field, be specifically related to eliminate the technology that in DC resistivity exploration, tunnel and landform affect apparent resistivity.
Background technology
Apparent resistivity is one of important method of resistivity prospecting data interpretation.In underground and direct current of ground electrical survey (-ing), the apparent resistivity by tunnel and the influence of topography distorts, and often mixes with the exception of geologic objective body, causes interpretation errors even to be judged by accident.Tunnel repair distorts to the one of constant current field normal distribution, and with device form, cloth pole mode, topographic relief degree and tunnel geometric configuration, the many factors such as stratum electric conductivity are relevant.This impact is nonlinear with the change of transmitting electrode, attempts to find factor of influence
[1]it is difficult for realizing correcting.The influence of topography is also distort to the one of constant current field.Common ratiometric correction method
[2], because the homogeneous half space resistivity value of simulating the response of pure landform is not easily determined, when underground electrical structure becomes complexity, the precision of this correcting method reduces, and even draws error result.If rely on the three-dimensional numerical value inverting comprising tunnel and landform completely
[3], ingredient necessary during this Data Inversion of disappearance apparent resistivity is explained.And the ill-posedness of Geophysical Inverse Problem, the problems such as the instability in 3-d inversion and multi-solution, calculated amount are huge need to solve.For this reason, the present invention is according to the sumproperties of current field in linear medium, utilize three-dimensional numerical value just drilling the impact of peeling off tunnel, landform, from the homogeneous half space current potential of point electric current source in underground, provide underground and direct current of ground explores the blanket apparent resistivity formula of various device.
There is following defect in prior art:
1., in the DC electrical method detection on underground and ground, the apparent resistivity by tunnel and the influence of topography distorts, and often mixes with the exception of geologic objective body, causes interpretation errors even to be judged by accident;
2. tunnel repair and device form, cloth pole mode, topographic relief degree and tunnel geometric configuration, the many factors such as stratum electric conductivity are relevant, and non-linearly change with polar distance of supplying power, and it is difficult for attempting to find factor of influence to realize correcting;
3. the method for the common ratiometric correction influence of topography, because the homogeneous half space resistivity value of simulating the response of pure landform is not easily determined, when underground electrical structure becomes complexity, the precision of this correcting method reduces, and even draws error result;
If 4. rely on the three-dimensional numerical value inverting comprising tunnel and landform completely, by ingredient necessary in this data interpretation of disappearance apparent resistivity.Moreover 3-d inversion self also also exists the problem such as instability and height nonuniqueness;
5. original underground and direct current of ground apparent resistivity, respectively from homogeneous half space current source current potential formula on the surface, and in the even total space, the current potential formula of current source is derived, can not be general.For overhead nearer subsurface investigation, the apparent resistivity that the current potential formula of original current source from the even total space is derived has larger error.
Documents
[1] Yue Jianhua, Li Zhidan. the tunnel repair in mine direct current method exploration. coal journal, 1999,24 (1): 7-10
[2] Holcomble HT, Jiracek G R. Three dimensional terrain correction in resistivitysurveys. Geophysics, 1984, 49(4): 439~452
[3] Wu little Ping. resistivity inversion under non-equilibrium drilling condition. Chinese Journal of Geophysics, 2005,48 (4): 932-936.
Summary of the invention
The object of the present invention is to provide a kind of method eliminated tunnel and landform and direct-current exploration apparent resistivity is affected, on the impact of apparent resistivity, improve the Explanation Accuracy of D.C. method to eliminate tunnel and landform in DC resistivity exploration.
In order to solve above technical matters, the present invention by the following technical solutions.
Eliminate the method that tunnel and landform affect direct-current exploration apparent resistivity, it is characterized in that the additivity according to constant current field in linear medium, the tunnel in homogeneous half space and landform are separated from ground electricity structure, specifically comprises the following steps:
Step one, according to roadway shape and the Modling model such as cutting depth, topographic relief elevation;
Step 2, using the resistivity of the minimum value of exploration area formation resistivity as the homogeneous half space containing tunnel and band landform;
Step 3, by transmitting electrode
with
the type of device adopted according to direct-current exploration and cloth pole mode, place correspondence position in a model;
Step 4, transmitting electrode is often mobile once carries out a Three-dimensional simulation, obtain the potential response of ambient field, then interpolation obtains receiving electrode
with
between potential difference (PD)
the potential difference (PD) of field as a setting;
Step 5, is arranged in horizontal homogeneous semispace current potential formula from point electric current source, derivation apparent resistivity formula: transmitting electrode in ground
with
form current return, have any point in ground
current potential formula
（1）
In formula
be ground resistivity,
supply current,
with
power supply respectively
and virtual source
arrive
distance,
with
power supply respectively
and virtual source
arrive
distance, any point in ground
current potential be
（2）
Formula (1) and formula (2) subtract each other, and obtain receiving electrode
with
between potential difference (PD)
（3）
Formula (3) is derived
as apparent resistivity, computing formula is as follows
（4）
When in formula (4)
for actual measurement potential difference (PD), the earth be non-horizontal homogeneous half space time, the ground resistivity in formula
be apparent resistivity, above formula is the formula calculating apparent resistivity, wherein
（5）
For electrode coefficient;
Step 6, by described actual measurement potential difference (PD)
deduct the potential difference (PD) of field as a setting
, obtain the potential difference (PD) without tunnel and the influence of topography
, utilize following formula
（6）
Calculate restivity
, be namely a cancellation the apparent resistivity of tunnel and the influence of topography.
Described restivity is added described homogeneous half space resistivity has been eliminated the absolute apparent resistivity of tunnel and the influence of topography.
The described step 5 apparent resistivity that current source current potential formula is derived from homogeneous half space, can be applicable to subsurface investigation and ground location simultaneously.
Described method can be applicable to whole electrical resistivity survey methods on underground and ground, comprise section and depth measurement, forward probe, roof and floor and lateral wall detection etc., and one pole-dipole, dipole-monopole, one pole-one pole, dipole-dipole etc. four kinds basic device type and combination in any.
The present invention has beneficial effect.The rock forming mineral of the overwhelming majority except ferromagnetic mineral, in the field strength range of D.C. method, is linear medium.Utilize the sumproperties of constant current field, eliminate tunnel and the influence of topography by partition method.This separation null method, solves the difficulty correcting and determine factor of influence in tunnel repair, does not have common ratioing technigue topographic correction homogeneous half space resistivity to determine the improper error brought.In the apparent resistivity of inversion interpretation important component part, applying three-dimensional numerical value is just drilled, and avoids and relies on the problems such as 3-d inversion instability, multi-solution and the calculated amount brought be huge completely.The apparent resistivity that current source current potential formula is derived from homogeneous half space, can switching naturally in underground and ground location, not only need not transformation for mula, and ensure that the precision of the apparent resistivity when tunnel is near ground.Whole electrical resistivity survey methods on the present invention compatibly lower and ground, as section and depth measurement, forward probe, roof and floor and lateral wall detection etc., and one pole-dipole, dipole-monopole, one pole-one pole, dipole-dipole etc. four kinds basic device type and combination in any.
Accompanying drawing explanation
Fig. 1 is underground point current field distribution plan, wherein
be point electric current source in ground,
the virtual source of symmetric position,
source and the virtual source distance to ground,
be any point in ground, the dotted line of band arrow is current line.
Fig. 2 is the rugged topography homogeneous half space computation model schematic diagram containing tunnel, wherein
be the earth with Air Interface,
be tunnel and Air Interface,
underground cutoff boundary,
emitting electrode, wherein
be power supply positive electrode,
power cathode,
receiving electrode,
source point to frontier point radius vector,
the outer normal vector on border, arrow indication device
moving direction.
Embodiment
Below in conjunction with accompanying drawing, technical scheme of the present invention is described in further detail.
For symmetrical quadrupole section detection in tunnel, mountain region.
According to the step one in technical scheme, according to roadway shape and the Modling model such as cutting depth, topographic relief elevation, as shown in Figure 2;
According to the step 2 in technical scheme, the minimum value of Qu Ce district formation resistivity
as the homogeneous half space resistivity containing tunnel and band landform;
According to the step 3 in technical scheme, by the transmitting electrode of symmetrical quadrupole device
with
place correspondence position in a model, as shown in Figure 2;
According to the step 4 in technical scheme, transmitting electrode often moves once, carries out a Three-dimensional simulation.If adopt the field domain Meta algorithm such as finite element, there is following boundary condition:
At the interface of earth's surface and air
on
（7）
At the interface of tunnel and air
on
（8）
At the cutoff boundary of underground infinite space
on, the first kind, Equations of The Second Kind, third boundary condition can be set.Wherein third boundary condition is general form
（9）
Above in formula,
current potential,
the distance that initial point is shown up a little,
the radial vector of source point to border
with outer normal vector
between angle.If tunnel is buried comparatively dark, ground-air border can be moved down, become border in ground, adopt the boundary condition of formula (9).Boundary condition formula (7) and (8) are accurate, and the boundary condition (9) of underground boundary is approximate.If possible, coboundary extends to ground as far as possible, obtains the Three-dimensional simulation result of degree of precision.
After utilizing Three-dimensional simulation to obtain the potential response of ambient field, then interpolation obtains receiving electrode
with
between potential difference (PD)
the potential difference (PD) of field as a setting;
According to formula (5) the calculation element coefficient of step 5 in technical scheme, the peak of the liftoff shape of roadway
if,
, so
（10）
Formula (10) is substituted into formula (5), and electrode coefficient is
（11）
According to the step 6 in technical scheme, potential difference (PD) will be surveyed
deduct the potential difference (PD) of field as a setting
, obtain the potential difference (PD) without tunnel and the influence of topography
, utilize formula (6)
（12）
Obtain the restivity without tunnel and the influence of topography;
Described in technical scheme, by restivity
add upper half-space resistivity
, the absolute apparent resistivity of be eliminated tunnel and the influence of topography.
Claims (4)
1. eliminate the method that tunnel and landform affect direct-current exploration apparent resistivity, it is characterized in that the additivity according to constant current field in linear medium, the tunnel in homogeneous half space and landform are separated from ground electricity structure, specifically comprises the following steps:
Step one, according to roadway shape and cutting depth, topographic relief elevation Modling model;
Step 2, using the resistivity of the minimum value of exploration area formation resistivity as the homogeneous half space containing tunnel and band landform;
Step 3, type of device electrodes of A and B adopted according to direct-current exploration and cloth pole mode, place correspondence position in a model;
Step 4, transmitting electrode is often mobile once carries out a Three-dimensional simulation, obtain the potential response of ambient field, then interpolation obtains the potential difference (PD) Δ U between receiving electrode M and N "
mNthe potential difference (PD) of field as a setting;
Step 5, is arranged in horizontal homogeneous semispace current potential formula from point electric current source, derivation apparent resistivity formula: in ground, electrodes of A and B form current return, have the current potential formula of any point M in ground
In formula, ρ is ground resistivity, I is supply current, AM and A ' M is the distance of power supply A and virtual source A ' to M respectively, BM and B ' M is the distance of power supply B and virtual source B ' to M respectively, and in ground, the current potential of any point N is
Formula (1) and formula (2) subtract each other, and obtain the potential difference (PD) Δ U between receiving electrode M and N
mN
The ρ that formula (3) is derived is as apparent resistivity, and computing formula is as follows
As Δ U in formula (4)
mNfor actual measurement potential difference (PD), the earth be non-horizontal homogeneous half space time, the ground resistivity ρ in formula is apparent resistivity, above formula be calculating apparent resistivity formula, wherein
For electrode coefficient;
Step 6, by described actual measurement potential difference (PD) Δ U
mNdeduct the potential difference (PD) Δ U of field as a setting "
mN, obtain the potential difference (PD) Δ U ' without tunnel and the influence of topography
mN, utilize following formula
Calculate restivity ρ ' for eliminating the apparent resistivity in tunnel and the influence of topography.
2. the as claimed in claim 1 method eliminated tunnel and landform and affect direct-current exploration apparent resistivity, is characterized in that, described restivity is added described homogeneous half space resistivity has been eliminated the absolute apparent resistivity of tunnel and the influence of topography.
3. the as claimed in claim 1 method eliminated tunnel and landform and affect direct-current exploration apparent resistivity, it is characterized in that, the apparent resistivity of described step 5 current source current potential formula derivation from homogeneous half space, can be applicable to subsurface investigation and ground location simultaneously.
4. the as claimed in claim 1 method eliminated tunnel and landform and direct-current exploration apparent resistivity is affected, it is characterized in that, described method can be applicable to whole electrical resistivity survey on underground and ground, comprises section and depth measurement, forward probe, roof and floor and lateral wall detection.
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| CN110297016A (en) * | 2019-06-19 | 2019-10-01 | 安徽国科骄辉科技有限公司 | The calculation method and imaging device of the apparent resistivity of cylinder model |
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| CN113885086B (en) * | 2021-08-05 | 2023-06-13 | 中煤科工集团西安研究院有限公司 | Underground direct-current equatorial direction dipole dynamic source abnormity self-explicit advanced detection method |
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