CN110376655A - The calculation method that dipole source electromagnetic field in any position responds under the conditions of layered geology - Google Patents
The calculation method that dipole source electromagnetic field in any position responds under the conditions of layered geology Download PDFInfo
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Abstract
The present invention provides the numerical computation methods that any position dipole source electromagnetic field under the conditions of a kind of layered geology responds, comprising the following steps: step S100: defines each stratum according to position of the dipole source in layered medium；Step S200: Orthogonal Decomposition dipole source；Step S300: the Lorentz vector potential expression formula that unit dipole source generates on each stratum is derived；Step S400: according to Lorentz vector potential expression formula, electromagnetic field expressions in each stratum are derived；Step S500: it is integrated using Bessel function in Gauss calculation by extrapolation electromagnetic field expressions, obtains the numerical solution of electromagnetic field；Step S600 obtains dipole source electromagnetic field multiplied by dipole source polar moment using numerical solution and responds.The relational expression that the present invention is met with Lorentz vector potential between adjacent earth formations obtains all stratum Lorentz vector potential expression formulas using stratum particular solution circulation recursion where dipole source, then obtains electromagnetic field expressions by Lorentz vector potential.It is finally integrated using Bessel function in Gauss calculation by extrapolation electromagnetic field expressions, obtains the electromagnetic field response of dipole source.With theoretical clear, the high feature of computational accuracy.
Description
Technical field
The present invention relates to electromagnetism calculating fields, particularly, are related to any position dipole source electricity under the conditions of a kind of layered geology
The calculation method of magnetic responsiveness.
Background technique
One-dimensional electromagnetic field method of response calculation includes numerical solution and analytic solutions two major classes.
Numerical solution includes differential equation method and integral equation method, it is critical that being discrete list by underground medium subdivision
Member forms equation group using electromagnetic field correlation in each discrete unit, and solve system of equation obtains electromagnetism number of fields in all units
Value solution.Numerical solution generally requires a large amount of units, and the relation equation group for causing unit electromagnetic field to be formed is huge, solves the time
It is long.
Any position dipole source electromagnetic field responds under the conditions of the one-dimensional layered geology of analytical Calculation, with conventional finite element, limited
The numerical algorithms such as difference and integral equation are compared, and are had the characteristics that efficient.Dipole source electricity in any position under the conditions of layered geology
Magnetic responsiveness calculating is widely used in numerical simulation, Research on Methods, the physical prospectings field such as instrument research.Current one-dimensional layered medium one
Dimension electromagnetic field analytic solutions generally use matrix Law of Communication directly against electromagnetic field Solving Partial Differential Equations, and present invention introduces Lorentzs
Vector potential has following two points advantage as intermediate variable
(1) it is expressed by Lorentz vector potential, electromagnetic field will divide into electric current item and Charge Terms two parts, be conducive to analyze
Different frequency Electromagnetic Wave Propagation physical mechanism in layered medium；
(2) it is sought in the present invention comprising Lorentz vector potential, for the Three-dimensional simulation side based on Lorentz vector potential
Method provides analytic solutions basis；
The Bessel function integral in the one-dimensional analytic solutions formula of electromagnetic field generally uses fixed quantity filter factor method meter at present
It calculates, the present invention uses Gauss extrapolation, has following two points advantage
(1) Bessel function integrating range length and point quantity can be arbitrarily set；
(2) integral accuracy can be controlled by defining absolute error and relative error parameter；
Present invention introduces Lorentz vector potentials as intermediate variable derivation electromagnetic field expressions, uses Gauss calculation by extrapolation
Bessel function integral in expression formula has the characteristics that theory is clear, computational solution precision is high.
Summary of the invention
It is an object of that present invention to provide dipole source electromagnetic field method of response calculation in any position under the conditions of a kind of layered geology,
To solve the computational accuracy technical problems such as not enough.
To achieve the above object, the present invention provides any position dipole source electromagnetic fields under the conditions of a kind of layered geology to respond
Calculation method, comprising the following steps:
Step S100: each stratum is defined according to position of the dipole source in layered medium；
Step S200: Orthogonal Decomposition dipole source；
Step S300: Lorentz vector potential expression formula of the unit dipole source in each stratum is derived；
Step S400: measuring point electromagnetic field expressions in any position in each stratum are derived；
Step S500: it is integrated using Bessel function in Gauss calculation by extrapolation expression formula, obtains the numerical solution of electromagnetic field；
Step S600: numerical solution obtains dipole source multiplied by dipole moment and responds in observation point electromagnetic field.
Preferably, the dipole source can be placed in any stratum.
Preferably, the dipole source includes electric dipole source and magnetic dipole source at any angle.
Preferably, the specific method of step S100 is: being determined according to z coordinate of the dipole source in layered medium and contains dipole source
Stratum defines source upper layer and each stratum of source lower layer, stratum is numbered, and redefine each stratum according to prime stratum parameter
Thickness, conductivity and boundary depth information.
Preferably, the specific method of step S200 is: calculating the dipole moment size of dipole source, and obtains it at x, y, z points
Amount divides size.
It is further preferred that calculating electricity according to current density in conducting wire and conductor length when dipole source is electric line source
Dipole source polar moment, and determine electric dipole source polar moment in x, y, z durection component size according to conducting wire direction.
It is further preferred that when dipole source is the magnetic dipole source that belt current coil is formed, according to current density and coil
Areal calculation magnetic dipole source electrode according to flat orientation where coil away from determining magnetic dipole source electrode away from x, y, z durection component size.
It is further preferred that calculating dipole source pole span, root according to current strength and volume when dipole source is volumetric energy
Determine electric dipole source polar moment in x, y, z durection component size according to current direction.
Preferably, the specific method of step S300 is: the relationship met using adjacent earth formations contact surface Lorentz vector potential
Formula derives the Lorentz vector potential general solution that unit dipole source generates in each stratum.
It is further preferred that the particular solution met using stratum Lorentz vector potential where dipole source, determines each stratum Lip river
The expression of human relations hereby vector potential.
Preferably, the specific method of step S400 is: stratum where determining observation point according to observation point z coordinate utilizes ground
The relational expression that Lorentz vector potential and electromagnetic field meet in layer derives observation point electromagnetic field expressions.
It is further preferred that the observation point can be placed in any stratum.
Preferably, the specific method of step S500 is: using Bezier letter in Gauss calculation by extrapolation electromagnetic field expressions
Scalar product point, obtains electromagnetic field x, y, z-component electromagnetic field exact numerical by the Accuracy Controlling Parameter of setting.
It is further preferred that step S500 the following steps are included:
Step S510: it defines the maximum integrating range section of Bessel function integral and is divided into n；
Step S520: integrated value of the m point Gauss integration as this section is defined in section in each interval；
Step S530: each section of integrated value of this transformation calculations of Shanks is used, and is added up, until accumulation result meets phase
To error and absolute error requirement；
Wherein, m and n is the integer greater than zero.
It is further preferred that being the sum of n finite interval integral to infinite interval Bessel function integration phase；
It is integrated it is further preferred that being further broken into m Gauss point to each finite interval integral；
It is further preferred that limiting using relative error limit with absolute error, integral result accumulated value in integrating range is evaluated
Whether restrain, to judge whether inifinite integral is accurately calculated；
It is further preferred that stopping integral when finite interval integrates and meets the setting limits of error.
Preferably, the specific method of step S600 is: logarithm solution is multiplied by corresponding direction dipole source polar moment, by x, y, z points
Amount synthesis obtains dipole source and responds in observation point electromagnetic field.
It is further preferred that y, z-component electromagnetic field numerical solution is obtained multiplied by step 200 to the x that unit dipole source generates
Corresponding dipole moment size obtains observation point x, y, the response of z-component electromagnetic field.
The invention has the following advantages:
The present invention obtains all stratum in the presence of circulation using particular solution with the relationship of Lorentz vector potential between adjacent earth formations
Lorentz vector potential expression formula, then electromagnetic field expressions are obtained by Lorentz vector potential, finally use Gauss calculation by extrapolation
Bessel function integrates in expression formula, and it is theoretical clear to have, the high feature of computational accuracy.
It is specific as follows:
1, dipole dipole source electromagnetic field method of response calculation in any position under the conditions of layered geology provided by the invention, is based on
Lorentz vector potential relation derivation obtains observation point electromagnetic field in each stratum, has strict logic, the characteristics of should be readily appreciated that.
2, the calculation method that any position dipole source electromagnetic field responds under the conditions of layered geology provided by the invention, can provide
The electromagnetic field of all kinds of artificial emission sources of controllable source electromagnetic method responds analytic solutions.Existing method for numerical simulation is compensated for need stratum
Subdivision is a large amount of discrete units, needs to take considerable time electromagnetic field in solution discrete unit, inefficient disadvantage.
3, the calculation method that any position dipole source electromagnetic field responds under the conditions of layered geology provided by the invention, uses height
This calculation by extrapolation Bessel function integral, has the characteristics that high-efficiency high-accuracy.
4, the calculation method that any position dipole source electromagnetic field responds under the conditions of layered geology provided by the invention, system meter
Electromagnetic field caused by having calculated any position eelctric dipole and magnetic dipole at an arbitrary position responds, and work covering scope is wide, practical
The characteristics of.
Other than objects, features and advantages described above, there are also other objects, features and advantages by the present invention.
Below with reference to figure, the present invention is described in further detail.
Detailed description of the invention
The attached drawing constituted part of this application is used to provide further understanding of the present invention, schematic reality of the invention
It applies example and its explanation is used to explain the present invention, do not constitute improper limitations of the present invention.In the accompanying drawings:
Fig. 1 is calculation method flow diagram of the invention；
Fig. 2 is horizontal multilayer formation schematic diagram；
Fig. 3 is the ocean master pattern that the response of electric dipole source electromagnetic field is calculated for verifying the method for the present invention；
Fig. 4 is the method for the present invention to electric dipole source response computation result and ocean standard results comparison diagram；
Fig. 5 is the sheet model that electromagnetic field response in magnetic dipole source is calculated for verifying the method for the present invention；
Fig. 6 is the method for the present invention to magnetic dipole source response computation result and standard results comparison diagram；
Fig. 7 is seven layer model schematic diagram；
Fig. 8 is horizontal electric dipole source electromagnetic field response cross-section diagram；
Fig. 9 is Vertical electric dipole electromagnetic field response cross-section diagram；
Figure 10 is horizontal magnetic dipole source electromagnetic field response cross-section diagram；
Figure 11 is vertical magnetic dipole source electromagnetic field response cross-section diagram；
Figure 12 be the present invention Marine Electromagnetic Approach practical application horizontal electric dipole source in measurement point caused by electric field response
Curve graph；
Figure 13 is horizontal electric dipole source survey line vertical cross section caused by electricity of the present invention in Marine Electromagnetic Approach practical application
Flow response diagram；
Figure 14 is that the present invention causes in aeroelectromagnetic method actual application level magnetic dipole source in horizontal profile and survey line section
Current-responsive figure.
Specific embodiment
The embodiment of the present invention is described in detail below in conjunction with attached drawing, but the present invention can be limited according to claim
Fixed and covering multitude of different ways is implemented.
Embodiment:
As shown in Figure 1, the calculation method that dipole source electromagnetic field in any position responds under the conditions of a kind of layered geology, including with
Lower step:
Step S100: each stratum is defined according to position of the dipole source in layered medium；
Step S200: Orthogonal Decomposition dipole source；
Step S300: unit dipole source is derived in the Lorentz vector potential expression formula of measuring point；
Step S400: electromagnetic field expressions are obtained according to measuring point Lorentz vector potential；
Step S500: it is integrated using Bessel function in Gauss calculation by extrapolation expression formula, obtains measuring point electromagnetism Flow Field Numerical
Solution；
Step S600: numerical solution obtains dipole source electromagnetic field multiplied by dipole moment and responds.
It is specific as follows:
1, dipole source and layered geology condition geometrical model are established
Observation point and geometry site of the dipole source position under rectangular coordinate system are as shown in Figure 2.The z of rectangular coordinate system
Vertically downward, and defining air layer and ground contact surface z coordinate value is 0 in direction；Dipole source coordinate is (x ', y ', z '), and fixed
Stratum where adopted dipole source is 0 layer；Side is existed by N layers of medium on the emitter, and top layer is defined as n-th layer, for i-th layer
(i=1,2...N is from bottom to top) dielectric conductance rate σ, interface ordinate Z are marked using "-" number；There are M layers of Jie below dipole source
Matter exists, and the bottom is defined as M layers, vertical for i-th layer of (i=1,2...M are from top to bottom) dielectric conductance rate σ, interface
Coordinate Z is marked using "+" number；The magnetic conductivity of all layered mediums is set to constant identical with air permeability.
2, unit dipole source and Lorentz vector potential fundamental relation are established
When in short lead there are electric current, and observation point with a distance from wire center more than 5 times of conductor lengths when, short lead transmitting
Source can be considered as electric dipole source: in the controllable source electromagnetic method of ocean, horizontal live wire emission source is considered as horizontal electric dipole source；
In well logging or borehole electromagnetics work, the vertical short lead that charges often is considered as Vertical electric dipole.Under normal conditions I
Can ignore influence of the dislocation charge to electromagnetic field, selection electrode couple source signal use time-harmonic factor eiωtWhen description, referring to
Ward,S.H.andHohmann,G.W.,1987.Electromagnetic theory for geophysical
applications in Electromag-netic Methods in Applied Geophysics,Nabighian,
M.N., derivation method disclosed in Society of Exploration Geophysicists.131-311. obtains
Wherein ω is the angular speed with dipole source, and I is unit imaginary number, and μ is air permeability,It is Hamiltonian, Eei
With HeiIt is that electromagnetic field responds in the i-th stratum respectively.AeiIt is unit electric dipole source Lorentz vector potential caused by the i-th stratum,
Meet following non-homogeneous ordinary differential equation
To small circular coil band logical with alternating current, when observation point positional distance hub of a spool distance is greater than roundlet coil radius 5
Times when, coil can be considered as magnetic dipole source.In aeroelectromagnetic method work, horizontal magnetic dipole source is common with vertical magnetic dipole source
Dipole source.Measuring point is at the i-th stratum
EmiWith HmiIt is that electromagnetic field responds in the i-th stratum respectively.AmiIt is unit electric dipole source long-range navigation caused by the i-th stratum
Hereby vector potential meets following non-homogeneous ordinary differential equation
We can obtain the Lorentz vector that electromagnetism dipole source is generated at i-th layer by calculating solution equation (3) and (6)
Then gesture calculates again and uses the electromagnetic field that generates in i layers of measuring point of (1) and (2) unit of account electric dipole source respectively, use (4) and
(5) electromagnetic field that unit of account magnetic dipole source is generated in i layers of measuring point.Level can be decomposed into due to calculating any direction dipole source
The combining form in direction and vertical direction dipole source, it is necessary to the electromagnetism that horizontal dipole source respectively and vertical electric dipole source generate for we
Field response
3, unit level electric dipole source Lorentz vector potential calculates (Fig. 3)
Because layered medium is symmetrical about x-axis, y-component is not present in the Lorentz vector potential that the direction x horizontal electric dipole generates,
Therefore for horizontal dipole source, we, which only need to study the direction x dipole source, to obtain the direction y dipole source electromagnetic field sound in bucket
It answers.Referring to Wait, J.R., 1981.Wave propagation theory.Pergamon Press, 110-115. are at i-th layer
Lorentz vector potential in medium meets the following conditions
Wherein A represents Lorentz vector potential, and upper right mark represents the direction in source, and bottom right mark represents component direction.F with
W is the intermediate variable seeking Lorentz gesture and introducing, and is met
dzIt is observation point respectively with ρ to source point z direction coordinate difference and horizontal distance.ai、bi、ci、diIt is wait seek respectively
Unknowm coefficient, J0Zero Bessel function is represented, λ is Bessel function integral term, uiIt is related with formation conductivity.By electromagnetism
Continuity of the field in the i-th bed boundary is available
In order to acquire ai、bi, we define intermediate variableIntermediate variable v is introduced simultaneouslyi
WhereinIt is poor for observation point and the i-th bed boundary z coordinate
And
vi=1/ui, (19)
TM=vM, (20)
TN=-vN. (21)
According to (16) and (17), i-th layer of a, b meet above stratum where dipole source
The i-th layer of a below of the stratum where dipole source, b meet
In order to acquireWe introduce a0、b0With R intermediate variable
ForIt is available according to (13), (14), (15)
Wi-1=Wi, (33)
In conjunction with (11) and (12), can be obtained with abbreviation (34)
In order to acquire ci、di, we define intermediate variableIntermediate variable is introduced simultaneously
γi
And
YM=γM, (38)
YN=-γN. (39)
It only needs to replace a, d that b, Y is replaced to replace T, γ that v is replaced to obtain c using c in (16)~(25)iWith di.In addition,
In order to acquire We introduce c0、d0With X intermediate variable
4, specific vertical electric dipole source Lorentz vector potential calculates
In a steady stream for vertical electric dipole, Lorentz vector potential only exists z durection component, is in i-th layer of expression formula
According to electromagnetic field in boundary continuity
It is available in the i-th bed boundary according to (48) and (49)
Wi-1=Wi, (50)
(48) and (49) are just the same with (33) and (35), similarly defineObtain ciWith
diExpression formula is completely as horizontal electric dipole expression formula.WithIt needs to replace a, d using c in formula (26)~(32)
V, Y is replaced to replace T, X that R is replaced to obtain instead of b, γ.
5, Lorentz vector potential in horizontal magnetic dipole source calculates
The Lorentz vector potential that the horizontal magnetic dipole source in the direction x generates does not have y-component, the Lorentz arrow in i-th layer
Measuring gesture expression formula is
It can be obtained by using the continuity of electromagnetic field
For interface two sidesDefinitionThe a of interface two sidesiWith biMeet following relationship
Wherein
vi=σi/ui, (61)
TMWith TNExpression formula is (20) and (21).According to (58) and (59), in a and b where dipole source below layer in stratum
Meet
In a and b satisfaction where dipole source above stratum in stratum
WithExpression formula same level Electric Dipole (26)~(32) are consistent
For interface two sidesAccording to (53), (55), (56) and (57) are available
Wi-1=Wi, (66)
It uses (52), (54) and (11) obtain W and meet at the i-th interface to z directional derivative
DefinitionA, d is replaced to replace b, Y that T, γ is replaced to replace v using c in (16)~(25)
To obtain c and the d expression formula of adjacent interfaces.WithSame formula (40)~(46).
6, vertical magnetic dipole source Lorentz vector potential calculates
The magnetic dipole source of vertical direction only generates the Lorentz vector potential in the direction z, in the Lorentz vector potential of i-th layer of medium
Meet
It can be obtained according to electromagnetic field in the continuity that the i-th bed boundary meets
(69)~(71) and (7), (12), (13) are just the same, so (69)~(71) and (7), (12), (13) have equally
Solution, that is, have same a, b.
7, it is integrated using Gauss calculation by extrapolation Bessel function
There can be Bessel function integrated form by the electromagnetic field expressions that (1)~(6) are acquired
Wherein
Wherein n be 0~∞ of calculating integral truncation section quantity, it usually needs the value taken come accurately calculate height concussion J0
With J1Integral.Gauss extrapolation uses Gauss integration to calculate the integral in each stage section first
Wherein m is Gauss integration point number, and w is point of cut-off Bessel function weight.To (74), adds up and take in the section i >=2
Value is
Si=Si-1+Fi, (75)
Wherein S1=F1.Gauss extrapolation using ∈ algorithm in conjunction with restriction or checking relation in five elements and convert the convergence to accelerate (72), for
I times cumulative, judges whether to restrain in the following way
|Si-Si-1|≤α|Si-Si-1|+β, (76)
Wherein β and α is the absolute error and relative error allowed respectively.Gauss extrapolation continues to add up always to calculate
(72) until meeting inequality (76)
8, the response of dipole source electromagnetic field is calculated
To unit dipole source electromagnetic field response numerical solution multiplied by the x obtained from dipole source Orthogonal Decomposition, y, the direction z dipole
Square obtains the electromagnetic field response of dipole source.
Any position dipole source electromagnetic field under the conditions of layered geology provided by the invention is responded below in conjunction with specific example
The application of calculation method is described in detail.
In order to verify the correctness that the present invention calculates the response of electric dipole source electromagnetic field, calculated result and recognised standard of the present invention
As a result it is compared, computation model is referring to Fig. 3.Four layers of geological model are established based on Marine Electromagnetic Approach, top layer is sky
Gas-bearing formation conductivity is 10-12S/m, air layer lower section are the sea water layer of 1000m thickness 3S/m conductivity, and there are 1000m thickness for sea bed
The low-resistance medium of 1S/m, the bottom are the marine rock circles of 0.1S/m, emission source be unit horizontal electric dipole source coordinate be (0,0,
950) m, observation point coordinate are (1000,1000,1950) m.
As shown in figure 4, the method for the present invention calculate gained z direction electric field kernel function and magnetic field kernel function change with λ, with generally acknowledge
Standard results have good degree of fitting.
As shown in figure 5, devising in space and depositing to verify the correctness that the present invention calculates the response of magnetic dipole source electromagnetic field
In the lamellar body Model that unit thickness conductivity is 0.01S/m, emission source is that horizontally or vertically unit magnetic dipole source, coordinate are
(0,0,-30)m；Observation point coordinate is (8,0, -30) m, and measuring coil has the characteristics that coaxial with transmitting coil.
As shown in fig. 6, the method for the present invention calculate horizontal component and vertical component secondary magnetic field and analytic solutions, 1hz~
There is good degree of fitting in 10000hz band limits.
Shown in Fig. 7, in order to study electromagnetic field in the propagation property of layered medium, devises 7 layer models and exist at the 4th layer
Electromagnetic field response condition under the conditions of 1hz frequency emission source in each layer medium, emission source coordinate are (0,0,1750) m, are ground respectively
The direction x and the direction z emission source have been studied carefully in the electromagnetic field situation of xy bisector section.
Shown in Fig. 8, there are obvious laminations at interface for the electric field that the direction x unit electric dipole source generates, and magnetic field is not deposited
With interface debonding situation.
Shown in Fig. 9, there is horizontal and vertical component in the electric field that the direction z unit electric dipole source generates, and deposit near interface
In significant change, the magnetic field of generation, which only exists horizontal component, does not have vertical component.
Shown in Figure 10, there are obvious laminations at interface for the electric field that the direction x unit magnetic dipole source generates, and magnetic field is not deposited
With interface debonding situation.
Shown in Figure 11, the electric field that the direction z unit magnetic dipole source generates only exists horizontal component, and electricity is nearby not present in interface
Field delamination, and magnetic field has horizontal and vertical component and there is no with interface debonding situation.
Fig. 7~11 illustrate that horizontal component of electric field has continuity at interface, and vertical electric field is generated because of the presence at interface
Mutation will lead to the discontinuity of electric field；No matter horizontal magnetic field is or vertical component, all has continuity at interface；Vertical electric field
To horizontal magnetic field is generated, vertical magnetic field only generates horizontal electric field.
The present invention has practicability in Marine Electromagnetic Approach research, and practical ocean model top layer is air layer, conductivity
The seabed that 1000m thickness sea water layer and conductivity for 3.3S/m are 1S/m, emission source are that the direction x horizontal electric dipole source is located at sea
Bottom and seawater interface 50m height coordinate are (0,0,950) m.Measurement point with emission source is collinear is distributed in seabed seawater interface
Upper and lower 0.1m.
Shown in Figure 12, in seabed, for 1000m depth there are when the 100m thickness oil-gas Layer that conductivity is 0.01S/m, level is electric
Field response ExE corresponding to vertical electric fieldzDecay slack-off.E when measuring point is located under interfacezHave when being located on interface with measuring point
Notable difference, ExBut it varies less.
Shown in Figure 13, have very greatly in the presence of 100m thickness high resistant oil-gas Layer with the electric current cross-section diagram in the presence of no 100m high resistant
Difference, it can be seen that Marine Electromagnetic Approach has good exploration effects to high resistant oil-gas Layer.
The present invention has practicability in aeroelectromagnetic method research, and it be air lower layer is 0.01S/m that model airplane, which is upper layer,
Homogeneous half space model, emission source coordinate be (0,0, -30) m, tranmitting frequency 100000hz.
Shown in Figure 14, magnetic dipole source is very fast in the current distribution decaying that the lower half-space generates, and horizontal magnetic dipole source
Range is small with vertical magnetic dipole source range.
Inventive algorithm calculates magnetic dipole source excitation secondary Flow Field Numerical caused by horizontal unit thin plate in homogeneous space
It is following (frequency is 1Hz~10000Hz, and thin plate conductivity is 0.01S/m) that solution decomposes specific implementation
Step 1: being to be by thin plate subdivision centered on thin plate projection by launch point by the lamellar body subdivision of unit thickness
It is 64m that 200 × 200 (x and each 200 units in the direction y) a side lengths, which are 8m volume,2Discrete rectangular body unit；
Step 2: under the conditions of calculating 1hz~10000hz using 3 layers of dielectric model (air layer, thin plate layer, air layer), water
The Lorentz vector potential that flat unit magnetic dipole source is generated in discrete unit i central point
Step 3: by using Lorentz vector potentialWith electromagnetic field relationship, unit magnetic dipole emission source is obtained discrete
Electric field response caused by unit center
Step 4: to electric field response caused by discrete unit centerDo volume point and multiplied by the conductivity of thin plate and air
Difference obtains the vector electric dipole source intensity of the center thin-plate element iWherein Δ σ is
Thin plate conductivity anomaly；
Step 5: calculating x in full air dielectric, y, and the direction z unit electric dipole source is rung in the horizontal magnetic field that observation point generates
It answers
Step 6: horizontal magnetic field is responded multiplied by vector electric dipole source intensity, so that it may obtain each discrete unit to sight
The field contribution of measuring pointFor
Step 7: the cumulative thin plate that can be obtained by is carried out to the horizontal magnetic field contribution of observation point to each discrete unit and is existed
Caused observation point secondary magnetic field HsFor
Those skilled in the art will be clear that the scope of the present invention is not limited to example discussed above, it is possible to carry out to it
Several changes and modification, the scope of the present invention limited without departing from the appended claims.Although oneself is through in attached drawing and explanation
The present invention is illustrated and described in book in detail, but such illustrate and describe is only explanation or schematical, and not restrictive.
The present invention is not limited to the disclosed embodiments.
Claims (7)
1. the calculation method that dipole source electromagnetic field in any position responds under the conditions of layered geology, which is characterized in that including following step
It is rapid:
Step S100: stratum is defined according to position of the dipole source in layered medium；
Step S200: Orthogonal Decomposition dipole source；
Step S300: unit dipole source is derived in the Lorentz vector potential expression formula on each stratum；
Step S400: any position electromagnetic field expressions in each stratum are derived；
Step S500: it is integrated using the Bessel function in Gauss calculation by extrapolation electromagnetic field expressions, obtains the numerical value of electromagnetic field
Solution；
Step S600: numerical solution obtains the response of dipole source electromagnetic field multiplied by dipole source polar moment.
2. calculation method according to claim 1, which is characterized in that the specific method of step S100 is: according to dipole source z
Coordinate determines stratum where dipole source, defines stratum and source lower section stratum above source, stratum is numbered, and according to primitively
Layer parameter each layer thickness, conductivity and boundary depth information after being numbered.
3. calculation method according to claim 1, which is characterized in that the specific method of step S200 is: calculating dipole source
Polar moment size, and it is obtained in x, y, z durection component size.
4. calculation method according to claim 1, which is characterized in that the specific method of step S300 is: using being adjacent to
It is logical to derive the Lorentz vector potential that unit dipole source generates in each stratum for the relational expression that layer contact surface Lorentz vector potential meets
Solution.
5. calculation method according to claim 1, which is characterized in that the specific method of step S400 is: according to observation point z
Coordinate determines stratum where observation point, derives observation point using the relational expression that corresponding stratum Lorentz vector potential and electromagnetic field meet
Electromagnetic field expressions.
6. calculation method according to claim 1, which is characterized in that the specific method of step S500 is: to unit dipole
The electromagnetic field expressions that source is generated in observation point integrate to obtain electromagnetism using Bessel function in Gauss calculation by extrapolation expression formula
Field x, y, z component electromagnetic field exact numerical solution.
7. calculation method according to claim 1, which is characterized in that the specific method of step S600 is: logarithm solution multiplies
With the dipole moment of corresponding direction dipole source, each component is synthesized to obtain the response of observation point electromagnetic field.
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111832199A (en) * | 2020-06-04 | 2020-10-27 | 中国铁路设计集团有限公司 | Pier top displacement calculation method based on arbitrary section and temperature field |
| CN112327374A (en) * | 2020-10-15 | 2021-02-05 | 广州市市政工程设计研究总院有限公司 | DGTD forward modeling method for GPU ground penetrating radar complex medium |
| CN113466954A (en) * | 2021-07-19 | 2021-10-01 | 中南大学 | Self-feedback regularization inversion method |
| CN114491987A (en) * | 2022-01-07 | 2022-05-13 | 西北工业大学 | Modeling method for electromagnetic field during electromagnetic wave propagation in marine multilayer medium |
| CN115186520A (en) * | 2022-09-09 | 2022-10-14 | 北京大学 | Time-frequency electromagnetic response simulation method of vector dipole source in horizontal layered geodetic medium |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US8886497B1 (en) * | 2010-07-19 | 2014-11-11 | Terje Graham Vold | Computer simulation of electromagnetic fields |
| CN106054257A (en) * | 2016-05-11 | 2016-10-26 | 中国科学院地质与地球物理研究所 | Determination system containing magnetosphere-shaped dielectric electromagnetic response |
| CN108509693A (en) * | 2018-03-13 | 2018-09-07 | 中南大学 | Three-dimensional frequency domain controllable source method for numerical simulation |
-
2019
- 2019-07-25 CN CN201910676771.5A patent/CN110376655A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US8886497B1 (en) * | 2010-07-19 | 2014-11-11 | Terje Graham Vold | Computer simulation of electromagnetic fields |
| CN106054257A (en) * | 2016-05-11 | 2016-10-26 | 中国科学院地质与地球物理研究所 | Determination system containing magnetosphere-shaped dielectric electromagnetic response |
| CN108509693A (en) * | 2018-03-13 | 2018-09-07 | 中南大学 | Three-dimensional frequency domain controllable source method for numerical simulation |
Non-Patent Citations (6)
| Title |
|---|
| RONG LIU ET AL.: "A hybrid solver based on the integral equation method and vector finite-element method for 3D controlled-source electromagnetic method modeling", 《GEOPHYSICS》 * |
| SAMIRA T. BISHAY ET AL.: "Transient response of a vertical electric dipole above a two-layer medium", 《APPLIED MATHEMATICS AND COMPUTATION》 * |
| ZONGHOU XIONG: "Electromagnetic fields of electric dipoles embedded in a stratified anisotropic earth", 《GEOPHYSICS》 * |
| 刘永亮: "基于拟线性积分方程法的三维复电阻率正反演研究", 《中国博士学位论文全文数据库 基础科学辑》 * |
| 刘颖等: "海洋可控源电磁场的一维反演", 《海洋可控源电磁场的一维反演》 * |
| 王德智: "基于积分方程技术的三维电磁法正演模拟研究", 《中国优秀硕士学位论文全文数据库 基础科学辑》 * |
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111832199A (en) * | 2020-06-04 | 2020-10-27 | 中国铁路设计集团有限公司 | Pier top displacement calculation method based on arbitrary section and temperature field |
| CN111832199B (en) * | 2020-06-04 | 2022-12-23 | 中国铁路设计集团有限公司 | Pier top displacement calculation method based on arbitrary cross section and temperature field |
| CN112327374A (en) * | 2020-10-15 | 2021-02-05 | 广州市市政工程设计研究总院有限公司 | DGTD forward modeling method for GPU ground penetrating radar complex medium |
| CN113466954A (en) * | 2021-07-19 | 2021-10-01 | 中南大学 | Self-feedback regularization inversion method |
| CN114491987A (en) * | 2022-01-07 | 2022-05-13 | 西北工业大学 | Modeling method for electromagnetic field during electromagnetic wave propagation in marine multilayer medium |
| CN114491987B (en) * | 2022-01-07 | 2024-03-01 | 西北工业大学 | Modeling method for electromagnetic field during electromagnetic wave propagation in marine multilayer medium |
| CN115186520A (en) * | 2022-09-09 | 2022-10-14 | 北京大学 | Time-frequency electromagnetic response simulation method of vector dipole source in horizontal layered geodetic medium |
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