CN102619504A - Method for determining radial detection depth index of electromagnetic wave resistivity instrument while drilling - Google Patents

Method for determining radial detection depth index of electromagnetic wave resistivity instrument while drilling Download PDF

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CN102619504A
CN102619504A CN2012101126281A CN201210112628A CN102619504A CN 102619504 A CN102619504 A CN 102619504A CN 2012101126281 A CN2012101126281 A CN 2012101126281A CN 201210112628 A CN201210112628 A CN 201210112628A CN 102619504 A CN102619504 A CN 102619504A
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electromagnetic wave
investigetion
resistivity
antenna
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段宝良
李郴
宋殿光
韩宏克
魏少华
方辉
郭巍
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China Research Institute of Radio Wave Propagation CRIRP
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Abstract

The invention relates to a method for determining a radial detection depth index of an electromagnetic wave resistivity instrument while drilling. The method comprises the following steps of: firstly, establishing an axial-symmetric radial three-layer annular stratum model, wherein three layer of media of the stratum model are a borehole, an invaded zone and an undisturbed zone sequentially from the inside to the outside, and placing the electromagnetic wave resistivity instrument while drilling on an axis of the stratum model; secondly, gradually increasing the invasion diameter of the invaded zone from zero, and calculating apparent resistivity response values of the electromagnetic wave resistivity instrument while drilling at different invasion diameters by adopting a radial layered green function method simultaneously; and thirdly, setting an apparent conductivity value, an invaded zone conductivity value and an undisturbed zone conductivity value, and at the time, the value of the invaded diameter of the invaded zone is a radial detection depth. The invention provides the method for determining the radial detection depth index of the electromagnetic wave resistivity instrument while drilling, which better accords with an actual logging environment.

Description

With the radial depth of investigetion determination of index method of boring electromagnetic wave resistivity instrument
(1), technical field: the present invention relates to a kind of technical device determination of index method, particularly relate to a kind of with the radial depth of investigetion determination of index method of boring electromagnetic wave resistivity instrument.
(2), background technology: in the oil drilling industry; Along with the increase of land horizontal well and high angle hole drilling effort and the demand of offshore drilling; The normal cable well logging can not have been satisfied the needs of logging technique, and therefore, logging while drilling technology has obtained very fast development.Logging while drilling technology can realize drilling well and log well and carry out simultaneously; It is that logger is installed in the position near drill bit; Do not receive on the stratum under the condition of obvious intrusion and pollution and carry out parameter measurement; Logging while drilling technology and traditional cable log facies relatively have that real-time is good, the logging accuracy advantages of higher.With boring the electromagnetic resistivity logger is one of instrument the most frequently used in the well logging during; It mainly measures the resistivity information on stratum; Because the resistivity of oil reservoir is higher generally speaking; Therefore, it can discern oil reservoir effectively, and also has and instruct the drill bit geosteering function that level is crept in oil reservoir.It is thus clear that, in oil drilling, having very important practical significance with boring the electromagnetic resistivity logger, it can strengthen the ability of well logging during, helps the oil field to find more oil and gas reservoir, alleviates petroleum resources situation in short supply.
Though with boring the electromagnetic resistivity logger has been prior art; But, also do not occur or imperfection about definite method of some technical indicators of this instrument, such as: the radial depth of investigetion index; The radial depth of investigetion index is with one of very important index of boring the electromagnetic resistivity logger; It is the same like the range index of a rifle, is the important indicator of judging with boring electromagnetic resistivity logger performance quality, is directly connected to the result of use of this instrument.Previously basically all be to adopt radially two-layer annular dielectric model to the calculating of investigation depth radially; The stratum of first floor for surveying; The second layer is an air, and radial depth of investigetion is the radius that response is taken up an area of 50% o'clock first floor stratum of layer, and this computational methods do not meet actual well logging environment.
(3), summary of the invention:
The technical problem that the present invention will solve is: overcome the defective of prior art, a kind of radial depth of investigetion determination of index method with the brill electromagnetic wave resistivity instrument that more meets actual well logging environment is provided.
Technical scheme of the present invention:
A kind of with the radial depth of investigetion determination of index method of boring electromagnetic wave resistivity instrument, contain following steps:
Step 1, set up radially three layers layer model circlewise of an axial symmetry; Three layers of medium of this stratigraphic model are followed successively by well, invaded zone, undisturbed formation from inside to outside; By the medium parameter of actual given these the three layers of media of well logging environment, medium parameter contains the resistivity value of invaded zone and the resistivity value of undisturbed formation; To be placed on the axis of this stratigraphic model with boring electromagnetic wave resistivity instrument, consistent with the axis that bores electromagnetic wave resistivity instrument with the direction of the axis of this stratigraphic model;
Step 2, the invasion diameter of invaded zone started from scratch gradually to be increased, simultaneously, and the apparent resistivity response value that records with the measurement antenna that bores electromagnetic wave resistivity instrument when adopting stratification green function method radially to calculate different invasion diameter;
Step 3, will measure the apparent resistivity response value that antenna records inverse as apparent conductivity value σ, with the inverse of the resistivity value of invaded zone as invaded zone conductivity value σ Xo, with the inverse of the resistivity value of undisturbed formation as undisturbed formation conductivity value σ t
During as
Figure BDA0000154266600000021
, the value of the invasion diameter of the invaded zone of this moment is this with the radial depth of investigetion of measurement antenna under said stratigraphic model of boring electromagnetic wave resistivity instrument.
With containing N transmitting antenna and two reception antennas in the measurement antenna that bores electromagnetic wave resistivity instrument; N transmitting antenna timesharing and two reception antenna couplings are formed the N group and are measured antenna; Measure antenna for every group; All can obtain one group according to the method for step 2~step 3 and measure the corresponding radial depth of investigetion of antenna with this group, N is the natural number more than or equal to 1.
Measure in the antenna at every group, transmitting antenna sends the signal of two kinds of different operating frequencies, and two reception antennas receive the signal of these two kinds of different operating frequencies respectively, and then, the signal that again each reception antenna is received carries out phase measurement and amplitude measurement respectively; Radial depth of investigetion under the radial depth of investigetion under radial depth of investigetion under radial depth of investigetion when containing phase measurement under first operating frequency in one group of radial depth of investigetion, second operating frequency during phase measurement, first operating frequency during amplitude measurement and second operating frequency during amplitude measurement.
Medium parameter also contains relative dielectric constant value and the magnetic permeability value of relative dielectric constant value and magnetic permeability value, the invaded zone of mud in the resistivity value, well of mud in relative dielectric constant and magnetic permeability value, the well of resistivity value, the drill collar of drill collar diameter, borehole diameter, drill collar, the relative dielectric constant value and the magnetic permeability value of undisturbed formation.
Introduction about stratification green function method radially is following:
If radially stratified medium has n+1 layer (as shown in Figure 1), each layer Media ID is l=0 from inside to outside, 1 ..., n, the source is at the j layer, and each layer parameter is respectively μ l, ε l, then
Figure BDA0000154266600000031
κ l 22μ lε l
Can the Green's function in any l layer of stratified medium radially be expressed as following form:
Γ l ( r , r ′ ) = δ lj r ′ π ∫ 0 ∞ K ~ 1 ( Λ j R ) I ~ 1 ( Λ j R ′ ) exp [ Λ j ( R ′ - R ) ] cos [ λ ( z - z ′ ) ] dλ
+ r ′ ∫ 0 ∞ A l ( λ ) I ~ 1 ( Λ l r ) exp [ Λ l ( r - r l ) ] cos [ λ ( z - z ′ ) ] dλ
+ r ′ ∫ 0 ∞ B l ( λ ) K ~ 1 ( Λ l r ) exp [ - Λ l ( r - r l - 1 ) ] cos [ λ ( z - z ′ ) ] dλ . - - - ( 1 )
First on formula (1) equal sign right side is a source item, for non-source layer (l ≠ j), then this item not of containing.A l(λ) and B l(λ) be undetermined coefficient, by cylindrical layer at the interface the condition of continuity in electric field and magnetic field confirm.Can know by the fringe conditions of r → 0 and r → ∞ in addition, if l=0 then has only A 0(λ), if l=n then has only B n(λ).At bed boundary place, the tangent vector in electric field and magnetic field is continuous, promptly μ Γ (r, r ') and
Figure BDA0000154266600000035
Continuously, can obtain confirming all undetermined coefficient A thus l(λ) (l=0,1 ..., n-1) and B l(λ) (l=1 ..., system of linear equations n).Can be expressed as following matrix form through this equation group of arrangement
AX=S,(2)
In the formula: A ∈ C 2n * 2n, X, S ∈ C 2nEach nonzero element of A is:
A 11 = μ 0 I ~ 1 ( Λ 0 r 0 ) , A 12 = - μ 1 I ~ 1 ( Λ 1 r 0 ) exp [ Λ 1 ( r 0 - r 1 ) ] , A 13 = - μ 1 K ~ 1 ( Λ 1 r 0 ) ;
A 21 = Λ 0 I ~ 0 ( Λ 0 r 0 ) , A 22 = - Λ 1 I ~ 0 ( Λ 1 r 0 ) exp [ Λ 1 ( r 0 - r 1 ) ] , A 23 = Λ 1 K ~ 0 ( Λ 1 r 0 ) ;
A 2 i - 1,2 i - 2 = μ i - 1 I ~ 1 ( Λ i - 1 r i - 1 ) , A 2 i - 1,2 i - 1 = μ i - 1 K ~ 1 ( Λ i - 1 r i - 1 ) exp [ - Λ i - 1 ( r i - 1 - r i - 2 ) ] ,
A 2 i - 1,2 i = - μ i I ~ 1 ( Λ i r i - 1 ) exp [ Λ i ( r i - 1 - r i ) ] , A 2 i - 1,2 i + 1 = - μ i K ~ 1 ( Λ i r i - 1 ) ;
A 2 i , 2 i - 2 = Λ i - 1 I ~ 0 ( Λ i - 1 r i - 1 ) , A 2 i , 2 i - 1 = - Λ i - 1 K ~ 0 ( Λ i - 1 r i - 1 ) exp [ - Λ i - 1 ( r i - 1 - r i - 2 ) ] ,
A 2 i , 2 i = - Λ i I ~ 0 ( Λ i r i - 1 ) exp [ Λ i ( r i - 1 - r i ) ] , A 2 i , 2 i + 1 = Λ i K ~ 0 ( Λ i r i - 1 ) ; (i=2,…,n-1)
A 2 n - 1 , 2 n - 2 = μ n - 1 I ~ 1 ( Λ n - 1 r n - 1 ) , A 2 n - 1,2 n - 1 = μ n - 1 K ~ 1 ( Λ n - 1 r n - 1 ) exp [ - Λ n - 1 ( r n - 1 - r n - 2 ) ] ,
A 2 n - 1,2 n = - μ n K ~ 1 ( Λ n r n - 1 ) ;
A 2 n , 2 n - 2 = Λ n - 1 I ~ 0 ( Λ n - 1 r n - 1 ) , A 2 n , 2 n - 1 = - Λ n - 1 K ~ 0 ( Λ n - 1 r n - 1 ) exp [ - Λ n - 1 ( r n - 1 - r n - 2 ) ] , A 2 n , 2 n = Λ n K ~ 0 ( Λ 0 r n - 1 )
Each element of X is:
X 1=A 0,X 2n=B n,X 2i=A i,X 2i+1=B i,(i=1,…,n-1)
Each nonzero element of S is:
S 2 j - 1 = μ j π K ~ 1 ( Λ j r ′ ) I ~ 1 ( Λ j r j - 1 ) exp ( - Λ j | r j - 1 - r ′ | ) , S 2 j = Λ j π K ~ 1 ( Λ j r ′ ) I ~ 0 ( Λ j r j - 1 ) exp ( - Λ j | r j - 1 - r ′ | ) ,
S 2 j + 1 = - μ j π K ~ 1 ( Λ j r j ) I ~ 1 ( Λ j r ′ ) exp ( - Λ j | r j - r ′ | ) , S 2 j + 2 = Λ j π K ~ 0 ( Λ j r j ) I ~ 1 ( Λ j r ′ ) exp ( - Λ j | r j - r ′ | ) .
If j=0 then has only S 2j+1And S 2j+2If j=n then has only S 2j-1And S 2jAll the other elements are 0.
Because each interline element of matrix A has the exponential damping of being, formula (2) can adopt recursive matrix method rapid solving, and recursive process spillover can not occur.This recursive algorithm that contains the banded sparse matrix of exponential damping item of finding the solution need not to carry out matrix inversion operation, only needs a forward recursive and a backward induction method to get final product.Its forward recursive process only needs iteration n time, and the backward induction method process also only needs n time iteration, has accelerated computational speed greatly.In addition because
Figure BDA0000154266600000048
and
Figure BDA0000154266600000049
in the formula (1) deducted exponential term; The integrand of this formula is exponential damping, and there is not the overflow phenomenon in computational process.Can obtain the Green's function of each layer after the result of calculation substitution formula (1) with formula (2), and the electromagnetic field that in stratified medium radially, produces of the circular current-carrying coil that obtains any radius through following three formulas.
A(r,z)=μ bN TIΓ(r,r′).(3)
E = - ∂ A ∂ t = - iωA - - - ( 4 )
B = ▿ × A = - ∂ A ∂ z e ^ r + 1 r ∂ ∂ r ( rA ) e ^ z - - - ( 5 )
Because acceptance point is in the l layer, so the μ in the formula (3) bMust change μ into lOnly need the positions of elements of interior the source item S of change formula (2), just can obtain all undetermined coefficients when source point r ' and field are put r at random layer easily, and and then calculate the Green's function of each layer.Above expression formula has the electromagnetic field that the round electric of any radius produces in the different medium layer applicable to calculating, its result has more universal significance.The above in addition recursive matrix method that adopts is easy to provide under the different situations universal expression formula of Green's function in the stratified medium radially, no matter is from the angle of expression way or sees all very succinct from the angle of programming.
About the further detailed content of stratification green function method radially, can be with reference to the interim article of " China University Of Petroleum Beijing's journal (natural science edition) " 2009 the 33rd volumes the 3rd " radially the Green function of stratified medium and with boring the application of electromagnetic resistivity in a measuring " literary composition.
Beneficial effect of the present invention:
1, the present invention has been for having provided quantitative index with the radial depth of investigetion of boring electromagnetic wave resistivity instrument, and is clear and definite in different wells and invade the effect and the response characteristic of this instrument under the environment; Having under the stratum of intrusion; The log of this instrument segregation phenomenon occurs because of the difference of investigation depth generally speaking; But the influence of anisotropy and country rock also can produce the phenomenon that curve separates, and the invention enables us that this segregation phenomenon has been had more accurately and judges, helps judging the true cause that curve separates; Realize formation resistivity evaluation accurately, and then obtain reserves estimation accurately.
2, the present invention compares with the existing method of calculating radial depth of investigetion; More approach actual well logging environment; The radial depth of investigetion index of utilizing the present invention to calculate has more practical significance, and this method that Theoretical Calculation is combined with actual environment is the development trend of Theoretical Calculation.
(4), description of drawings:
Fig. 1 is the model sketch map of radially stratified medium;
One of Fig. 2 curve map that to be the apparent resistivity response value change with the invasion diameter of invaded zone;
Two of Fig. 3 curve map that to be the apparent resistivity response value change with the invasion diameter of invaded zone.
(5), the specific embodiment:
Radial depth of investigetion determination of index method with boring electromagnetic wave resistivity instrument contains following steps:
Step 1, set up radially three layers layer model circlewise of an axial symmetry; Three layers of medium of this stratigraphic model are followed successively by well, invaded zone, undisturbed formation from inside to outside; By the medium parameter of actual given these the three layers of media of well logging environment, medium parameter contains the resistivity value of invaded zone and the resistivity value of undisturbed formation; To be placed on the axis of this stratigraphic model with boring electromagnetic wave resistivity instrument, consistent with the axis that bores electromagnetic wave resistivity instrument with the direction of the axis of this stratigraphic model;
Step 2, the invasion diameter of invaded zone started from scratch gradually to be increased, simultaneously, and the apparent resistivity response value that records with the measurement antenna that bores electromagnetic wave resistivity instrument when adopting stratification green function method radially to calculate different invasion diameter;
Step 3, will measure the apparent resistivity response value that antenna records inverse as apparent conductivity value σ, with the inverse of the resistivity value of invaded zone as invaded zone conductivity value σ Xo, with the inverse of the resistivity value of undisturbed formation as undisturbed formation conductivity value σ t
During as
Figure BDA0000154266600000061
, the value of the invasion diameter of the invaded zone of this moment is this with the radial depth of investigetion of measurement antenna under said stratigraphic model of boring electromagnetic wave resistivity instrument.
With containing N transmitting antenna and two reception antennas in the measurement antenna that bores electromagnetic wave resistivity instrument; N transmitting antenna timesharing and two reception antenna couplings are formed the N group and are measured antenna; Measure antenna for every group; All can obtain one group according to the method for step 2~step 3 and measure the corresponding radial depth of investigetion of antenna with this group, N is the natural number more than or equal to 1.
Measure in the antenna at every group, transmitting antenna sends the signal of two kinds of different operating frequencies, and two reception antennas receive the signal of these two kinds of different operating frequencies respectively, and then, the signal that again each reception antenna is received carries out phase measurement and amplitude measurement respectively; Radial depth of investigetion under the radial depth of investigetion under radial depth of investigetion under radial depth of investigetion when containing phase measurement under first operating frequency in one group of radial depth of investigetion, second operating frequency during phase measurement, first operating frequency during amplitude measurement and second operating frequency during amplitude measurement.
Medium parameter also contains relative dielectric constant value and the magnetic permeability value of relative dielectric constant value and magnetic permeability value, the invaded zone of mud in the resistivity value, well of mud in relative dielectric constant and magnetic permeability value, the well of resistivity value, the drill collar of drill collar diameter, borehole diameter, drill collar, the relative dielectric constant value and the magnetic permeability value of undisturbed formation.
Explain with the radial depth of investigetion determination of index method of boring electromagnetic wave resistivity instrument with concrete instance below:
Under the decreased resistance invasion situation:
Given drill collar diameter is 7in, and borehole diameter is 8in, the resistivity R of mud in the well m=0.06Ohmm, the resistivity R of invaded zone Xo=0.55Ohmm, the resistivity R of undisturbed formation t=30Ohmm.It is as shown in Figure 2 to utilize stratification green function method radially to calculate the curve of the apparent resistivity response value Ra that changes with invasion diameter di; 12 curves among the figure represent that 3 groups are measured the measured data and curves of antenna; Measure antenna for every group and contain 2MHZ and two kinds of operating frequencies of 400KHZ, measure antenna for every group and record 4 data and curves.
With the inverse of apparent resistivity response value Ra as apparent conductivity value σ, with the resistivity R of invaded zone XoInverse as invaded zone conductivity value σ Xo, with the resistivity R of undisturbed formation tInverse as undisturbed formation conductivity value σ t
During as
Figure BDA0000154266600000071
, the value of the invasion diameter of the invaded zone of this moment is this with the radial depth of investigetion of boring electromagnetic wave resistivity instrument.Being
Figure BDA0000154266600000072
and pointing to 12 invasion diameter values respectively from the intersection point of horizon Rdoi and 12 curves arrow through vertically downward of the value of a horizon Rdoi among Fig. 2 representative, these 12 invasion diameter values are respectively 12 kinds of radial depth of investigetion values under the metering system.
Under the increased resistance invasion situation:
Given drill collar diameter is 7in, and borehole diameter is 8in, the resistivity R of mud in the well m=50Ohmm, the resistivity R of invaded zone Xo=30Ohmm, the resistivity R of undisturbed formation t=0.55Ohmm.It is as shown in Figure 3 to utilize stratification green function method radially to calculate the curve of the apparent resistivity response value Ra that changes with invasion diameter di; 12 curves among the figure represent that 3 groups are measured the measured data and curves of antenna; Measure antenna for every group and contain 2MHZ and two kinds of operating frequencies of 400KHZ, measure antenna for every group and record 4 data and curves.
According to foregoing description, adopt the computational methods identical with the decreased resistance invasion situation, can calculate 12 kinds of radial depth of investigetion values under the metering system.
Set several frequently seen typical stratum, can draw a certain with the radial depth of investigetion index of boring electromagnetic wave resistivity instrument, as shown in table 1 according to radial depth of investigetion determination of index method of the present invention:
Table 1
Figure BDA0000154266600000073
From table 1, can find out, should be basically between 33in~200in with the investigation depth scope of boring electromagnetic wave resistivity instrument.

Claims (4)

1. one kind with the radial depth of investigetion determination of index method of boring electromagnetic wave resistivity instrument, it is characterized in that: contain following steps:
Step 1, set up radially three layers layer model circlewise of an axial symmetry; Three layers of medium of this stratigraphic model are followed successively by well, invaded zone, undisturbed formation from inside to outside; By the medium parameter of actual given these the three layers of media of well logging environment, medium parameter contains the resistivity value of invaded zone and the resistivity value of undisturbed formation; To be placed on the axis of this stratigraphic model with boring electromagnetic wave resistivity instrument, consistent with the axis that bores electromagnetic wave resistivity instrument with the direction of the axis of this stratigraphic model;
Step 2, the invasion diameter of invaded zone started from scratch gradually to be increased, simultaneously, and the apparent resistivity response value that records with the measurement antenna that bores electromagnetic wave resistivity instrument when adopting stratification green function method radially to calculate different invasion diameter;
Step 3, will measure the apparent resistivity response value that antenna records inverse as apparent conductivity value σ, with the inverse of the resistivity value of invaded zone as invaded zone conductivity value σ Xo, with the inverse of the resistivity value of undisturbed formation as undisturbed formation conductivity value σ t
During as
Figure FDA0000154266590000011
, the value of the invasion diameter of the invaded zone of this moment is this with the radial depth of investigetion of measurement antenna under said stratigraphic model of boring electromagnetic wave resistivity instrument.
2. according to claim 1 with the radial depth of investigetion determination of index method of boring electromagnetic wave resistivity instrument; It is characterized in that: said with containing N transmitting antenna and two reception antennas in the measurement antenna that bores electromagnetic wave resistivity instrument; N transmitting antenna timesharing and two reception antenna couplings are formed the N group and are measured antenna; Measure antenna for every group; All can obtain one group according to the method for step 2~step 3 and measure the corresponding radial depth of investigetion of antenna with this group, N is the natural number more than or equal to 1.
3. according to claim 2 with the radial depth of investigetion determination of index method of boring electromagnetic wave resistivity instrument; It is characterized in that: measure in the antenna at said every group; Transmitting antenna sends the signal of two kinds of different operating frequencies; Two reception antennas receive the signal of these two kinds of different operating frequencies respectively, and then, the signal that again each reception antenna is received carries out phase measurement and amplitude measurement respectively; Radial depth of investigetion under the radial depth of investigetion under radial depth of investigetion under radial depth of investigetion when containing phase measurement under first operating frequency in said one group of radial depth of investigetion, second operating frequency during phase measurement, first operating frequency during amplitude measurement and second operating frequency during amplitude measurement.
4. according to claim 1 with the radial depth of investigetion determination of index method of boring electromagnetic wave resistivity instrument, it is characterized in that: said medium parameter also contains relative dielectric constant value and the magnetic permeability value of relative dielectric constant value and magnetic permeability value, the invaded zone of mud in the resistivity value, well of mud in relative dielectric constant and magnetic permeability value, the well of resistivity value, the drill collar of drill collar diameter, borehole diameter, drill collar, the relative dielectric constant value and the magnetic permeability value of undisturbed formation.
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CN103670367B (en) * 2012-09-07 2016-08-03 中国石油天然气集团公司 A kind of array induction logging instrument detection performance test device
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CN102900423B (en) * 2012-09-29 2015-04-22 中国石油天然气集团公司 Gel-based solid physical simulator for electrical logging detector and forming method of gel-based solid physical simulator
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CN108547611A (en) * 2018-03-01 2018-09-18 杭州迅美科技有限公司 Horizontal well complex environment is with brill electromagnetic wave resistivity logging rapid simulation method
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CN111734404B (en) * 2019-03-24 2023-09-05 天津大学青岛海洋技术研究院 Transient electromagnetic array induction logging model and response solution thereof

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Application publication date: 20120801