CN106980736A - A kind of ocean controllable source electromagnetic method finite element forward modeling method of anisotropic medium - Google Patents
A kind of ocean controllable source electromagnetic method finite element forward modeling method of anisotropic medium Download PDFInfo
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Abstract
The present invention is a kind of ocean controllable source electromagnetic method finite element forward modeling method of anisotropic medium.The present invention sets a reference conductivity rate first, and three non-zero diagonal entries of the reference conductivity rate are the electrical conductivity in three main shaft x, y, z directions, then sets three Euler's anglecs of rotation, is rotated by three Eulers, just can obtain the conductivity tensor model of any direction.Then from maxwell equation group, the finite element equation that magnetic vector potential, scalar potential under Coulomb specifications are met in the case where electrical conductivity is in any Anisotropic Condition.Secondly, discrete subdivision is carried out to survey region with unstructured grid, complicated earth-electricity model can be built.The incomplete factorization fore condition factor is combined with IDR (s) algorithms realizes large scale sparse linear equations efficiently, accurate to solve.Derivation is carried out to secondary field vector position, scalar potential finally by weighting Moving Least, each component of electromagnetic field is obtained.The present invention has good versatility, can promote for complicated distribution of conductivity, high-precision electromagnetic method numerical simulation.
Description
Technical field
The present invention relates to any anisotropic problem of the electrical conductivity of underground medium in field of geophysical exploration, it is proposed that one
The Three-dimensional unstructured numerical simulation method of ocean controllable source electromagnetism based on secondary field vector position, scalar potential is planted, is applicable
The geophysical exploration method numerical simulation such as electromagnetism, land face electromagnetism is ground in geometry complexity, the aviation electromagnetic of physical property distribution, well
Study carefully.
Background technology
The structure and attribute of earth interior are the core contents of geophysics's research.21 century is geoscience entrance pair
Medium, the epoch of the anisotropic further investigation of construction and deep layer dynamic process.With constantly entering for modern observation technology
The continuous improvement of step and the level of understanding, anisotropic problem gradually causes domestic and foreign scholars and widely paid attention to, as the earth
The focus of physics research.
Ocean controllable source electromagnetic method is a kind of geophysical exploration using artificial source's Research of electromagnetic field earth electrical structure
Method.Nearly ten years, this method is quickly grown, and is had become and is realized the exploration mesh such as look for oil and gas field, research backdeeps construction
A kind of effective exploitation method.Existing ocean controllable source electromagnetism method for numerical simulation mainly has integral equation method
(IEM), finite difference calculus (FDM), Finite Element (FEM) etc..
So far, mostly it is only to examine for the ocean controllable source electromagnetism numerical simulation of electrical conductivity anisotropic medium
Three main shaft electrical conductivity anisotropy are considered, this no doubt simplifies problem, however, protuberance, upset as the stratum caused by geological movement
The electrical conductivity anisotropy Deng caused by is often not limited to three main shafts, in some instances it may even be possible to increasingly complex, and in actual detection,
Explanation of the anisotropic influence of complicated sea-floor relief and electrical conductivity to real data may produce certain deviation.
The content of the invention
The technical problems to be solved by the invention are that the ocean controllable source electromagnetic method for providing a kind of anisotropic medium has
The first forward modeling method of limit, realizes the numerical simulation of efficient, quick marine electromagnetic anisotropic medium.
The present invention is achieved in that
A kind of ocean controllable source electromagnetic method finite element forward modeling method of anisotropic medium, this method includes：
1) unstructured grid subdivision is carried out to survey region, obtains grid cell numbering, node serial number and coordinate parameters；
2) the earth-electricity model parameter of design, including background layer parameter, frequency parameter, reference conductivity rate, three Eulers are read
The anglec of rotation, grid cell numbering and node coordinate；
3) the corresponding each component of primary field electromagnetism of background layer is calculated；
4) cycle calculations unit coefficient matrix is carried out to all grid cells, then overall all grid cells of synthesis is
Matrix number, then according to step 3) right-hand vector of an Electromagnetic Calculation system of linear equations calculated of background layer；
5) essential boundary condition is loaded, system of linear equations is solved, secondary field vector position and the scalar potential of each node is obtained；
6) derivation is carried out to secondary field vector position, scalar potential, obtains each component of electromagnetic field of all nodes.
Further, survey region is split into limited multiple tetrahedron element e.
Further, this method also includes one reference conductivity rate of setting, three diagonal line elements of non-zero of the reference conductivity rate
The electrical conductivity of element, then sets three Euler's anglecs of rotation, is rotated by three Eulers, obtains the conductivity tensor of any direction
Model.
Further, then from maxwell equation group, introduce based on the magnetic vector potential A under Coulomb specifications, mark
Measure position Ψ to represent electric field, magnetic field, in secondary field, total magnetic vector potential and scalar resolve into secondary field and ambient field sum, obtain
To on the secondary position expression formula of electromagnetic field：
Wherein,For abnormal electrical conductivity, ApFor a field vector position, AsFor secondary field vector position, ΨpFor primary field scalar
Position, ΨsFor secondary field scalar potential.
Further, the secondary position expression formula of electromagnetic field is deployed successively according to xyz axles, using the golden method of gal the Liao Dynasty to expansion
It is weighted, with reference to vector identity and divergence theorem, obtains the volume integral equations group on secondary position.
Further, step 4) in system of linear equations：
Ku=b
K is coefficient matrix, and u is solves the field value that each node in domain is to be asked, and b is right-hand vector.
Further, step 5) middle solution system of linear equations：Ku=b, adds Dirichlet boundary conditions：(As,Ψs)Γ=
0。
Further, system of linear equations is carried out using IDR (s) iterative algorithms of the fore condition factor of incomplete factorization
Solve.
Further, step 6) secondary field vector position, scalar potential are solved using exponentially weighted moving average (EWMA) least square method
To x, y, z partial derivative.
Compared with prior art, beneficial effect is the present invention：
The present invention propose it is a kind of based on secondary field vector position, scalar potential unstructured finite element numerical simulation algorithm come
Simulate any anisotropic ocean controllable source electromagnetic problem of electrical conductivity.This method can both avoid the shadow of the singularity of source point
Ring, continuity requirement of the nodal finite element for field can be met again, while using unstructured grid, being conducive to structure geometry to answer
Miscellaneous earth-electricity model, the more preferable real geological condition of simulation, it is thereby achieved that efficiently, quick marine electromagnetic anisotropy
The numerical simulation of medium.
It is each to different present invention is generally directed to the electrical conductivity any direction being widely present in controllable source electromagnetic surveying underground medium
Property the problem of, assume initially that a conductivity tensor and three Euler's anglecs of rotation, rotated by carrying out three Eulers, constructed
The anisotropic conductivity tensor model of any direction.And the electricity based on secondary field magnetic vector potential, scalar potential has been derived first
The unstructured finite element equation of controllable source electromagnetism under any Anisotropic Condition of conductance, it is possible to prevente effectively from source point singularity
Influence, improves the precision of numerical solution, successional requirement of the nodal finite element for field is disclosure satisfy that again.It is multiple in order to more preferably simulate
Miscellaneous geologic structure, the present invention carries out discrete subdivision using unstructured grid to survey region, can build the geologic structure of complexity
Transitivity is distributed, while avoiding the encryption to region-wide progress equal extent, reduces amount of calculation.For conventional iterative algorithm
Solve the problem of system of linear equations convergence is slow, it is proposed that using incomplete factorization preprocess method and Krylov subspace iteration
IDR (S) method in algorithm is combined to Solving Linear, is effectively improved computational efficiency.Using the cunning of exponential weighting
Dynamic mean least squares carry out derivation to secondary field vector position, scalar potential, relative to conventional Method of Seeking Derivative, further improve
The precision that derivative is solved.Therefore, the present invention can realize high accuracy, quick electrical conductivity under any Anisotropic Condition
Ocean controllable source electromagnetic method numerical simulation.
Brief description of the drawings
Fig. 1 is the node serial number schematic diagram of unstructured grid subdivision unit provided in an embodiment of the present invention；
Fig. 2 is corresponding three Eulers of structure of forward modeling in arbitrary anisotropic media conductivity tensor provided in an embodiment of the present invention
Rotate schematic diagram；Wherein, Fig. 2 (a) is along x-axis, and Fig. 2 (b) is along y-axis, and Fig. 2 (c) is along z-axis；
Fig. 3 is the unstructured finite element of forward modeling in arbitrary anisotropic media ocean controllable source electromagnetic method provided in an embodiment of the present invention
Numerical simulation flow chart；
Fig. 4 is the horizontal layer electrical conductivity anisotropic medium model that the embodiment of the present invention is set up；
Fig. 5 is the contrast of anisotropy of embodiment of the present invention stratiform model quasi-associative part and Finite Element Numerical Solution；
Fig. 6 is containing the abnormal body Model of high resistant in the forward modeling in arbitrary anisotropic media that the embodiment of the present invention is set up；
Fig. 7 is containing the abnormal unstructured net of body Model of high resistant in the forward modeling in arbitrary anisotropic media that the embodiment of the present invention is set up
Lattice subdivision schematic diagram；
Fig. 8 is containing abnormal each point of the body Model electromagnetic field of high resistant in the forward modeling in arbitrary anisotropic media that the embodiment of the present invention is set up
The plan of amplitude first is measured, wherein Fig. 8 (a), Fig. 8 (b), Fig. 8 (c) are electric field amplitude plan when reference conductivity rate does not rotate；8
(d), 8 (e), 8 (f), for reference conductivity rate along y-axis rotate 30.When electric field amplitude plane equivalence figure；8(g)、8(h)、
8 (l) is that reference conductivity rate rotates 45 along y-axis.When electric field amplitude plane equivalence；8 (m), 8 (n), 8 (o) are with reference to electricity
Conductance rotates 60 along y-axis.When electric field amplitude plane equivalence；
Fig. 9 is containing abnormal each point of the body Model electromagnetic field of high resistant in the forward modeling in arbitrary anisotropic media that the embodiment of the present invention is set up
The plan of amplitude second is measured, Fig. 9 (a), Fig. 9 (b), Fig. 9 (c) are respectively that reference conductivity rate rotates 30 along z-axis.When electric field shake
Width plane equivalence；Fig. 9 (d), Fig. 9 (e), Fig. 9 (f) are that reference conductivity rate rotates 45 along z-axis.When electric field amplitude plane
Isogram；Fig. 9 (g), Fig. 9 (h), Fig. 9 (l) are that reference conductivity rate rotates 60 along z-axis.When electric field amplitude plane isopleth
Figure.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to embodiments, to the present invention
It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to
Limit the present invention.
Referring to Fig. 1, the tetrahedron element node (1,2,3,4) of unstructured grid subdivision provided in an embodiment of the present invention is compiled
Number schematic diagram.
Using ready-made mesh generation software, discrete subdivision is carried out to survey region using any tetrahedral grid unit,
It is encrypted in electrical boundary and source point region, it is more sparse from the local subdivision of excitaton source farther out, just it can so avoid pair
The region-wide encryption for carrying out equal extent, saves calculating internal memory, reduces amount of calculation.
Referring to Fig. 3, any electrical conductivity anisotropic medium controllable source electromagnetic finite member analogy method flow chart, including it is as follows
The step of：
1) unstructured grid subdivision is carried out to survey region, obtains grid cell numbering, the ginseng such as node serial number and coordinate
Number；
2) the earth-electricity model parameter of design, including background layer parameter, frequency parameter, reference conductivity rate, three Eulers are read
The anglec of rotation, grid cell numbering, node coordinate etc.；
3) the corresponding each component of primary field electromagnetism of background layer is calculated；
4) cycle calculations coefficient matrix is carried out to all grid cells, then the unit coefficient square of overall all units of synthesis
Battle array, meanwhile, the right-hand vector of the Electromagnetic Calculation system of linear equations calculated according to background layer.
5) essential boundary condition is loaded, system of linear equations is solved, secondary field vector position and the scalar potential of each node is obtained；
6) derivation is carried out to secondary field vector position, scalar potential, obtains each component of electromagnetic field of all nodes.
In the controllable source electromagnetism boundary value problem geophysical exploration of electrical conductivity forward modeling in arbitrary anisotropic media, often using low
Frequency electromagnetic signal, ignores displacement current, using the humorous change time factor e of sine-(wt, Maxwell ' s equations can be expressed as follows form:
Wherein：W is angular frequency, μ0For the magnetic conductivity in vacuum..sFor field source CURRENT DISTRIBUTION.For any anisotropic electric
Conductance tensor, the electric field that E is represented, the magnetic field that H is represented is as follows：
In order to calculate conductivity tensorA reference conductivity rate σ is generally previously set4(wherein three cornerwise elements
Represent the electrical conductivity of three main shafts), it is as follows：
Then rotated by three Eulers, referring to Fig. 2 (a), Fig. 2 (b), Fig. 2 (c), just can obtain any anisotropy and be situated between
The conductivity tensor of matter：
Wherein spin matrix is：
α is reference axis along the x-axis anglec of rotation；β is reference axis along the y-axis anglec of rotation；γ is that reference axis is revolved along z-axis
Gyration., this process correspondence step 3.
Introduce based on the magnetic vector potential A under Coulomb specifications, scalar potential Ψ to represent electric field, magnetic field, it is as follows：
Equation (6), (7) are substituted into equation (1), (2) to obtain：
In secondary field calculates hair, total magnetic vector potential and scalar are as follows to be decomposed into secondary field and ambient field sum：
A=Ap+As(11)
Ψ=Ψp+Ψs(12)
Wherein,For background conductance rate,For abnormal electrical conductivity, ApFor a field vector position, AsFor secondary field vector position,
ΨpFor primary field scalar potential, ΨsFor secondary field scalar potential.
Equation (10)-(12) are substituted into equation (8) (9) to obtain on the secondary position expression formula of electromagnetic field：
By observation equation (13), (14), equation right-hand vector is on once position, and without electric current.Therefore can
Avoid the influence of the singularity of source point.And once position can be tried to achieve by layered medium or homogeneous half space for background layer.Consider
Following relation：
EpFor an electric field.
Equation (13) (14) is rewritable into following form：
So it is avoided that solving the gradient of primary field scalar potential, the precision of primary field is improved.
Finite element analysis:
Equation (13) (14) is deployed successively according to xyz axles, equation below can be obtained：
Equation (15) to (18) is weighted using gal the Liao Dynasty golden method, with reference to vector identity and divergence theorem, most
The volume integral equations group on secondary position can be obtained afterwards：
Wherein, N is linear interpolation function.
In the present invention, survey region is split into limited multiple tetrahedron element e, referring to Fig. 1, in unit, electricity
Conductance is changeless, and secondary vector position and scalar potential in unit linearly change：
Shown in linear interpolation function is defined as follows：
Wherein VeFor unit volume,The respectively coefficient of interpolating function.
(23) (24) equation substitution (19)-(22) can finally be obtained into Discrete Linear equation group：
Ku=b (25)
Wherein:
be=(bx e,by e,b2 e,bΨ e)T
ue=(ASx e,ASy e,AS2 e,Ψs e)T
In order to solve equation (25), in addition it is also necessary to add corresponding boundary condition.The present invention uses Dirichlet boundary conditions：
(As,Ψs)Γ=0 (26).
The solution of system of linear equations in step 5：Krlov subspace iterations algorithm is because of fast convergence rate, and solving precision is high, and
And stability it is good the advantages of and be widely used in solve large scale sparse linear equations, particularly when it is combined with preconditioning technique
The speed of solution system of linear equations can effectively be accelerated, in order to further improve the efficiency of solution, the present invention uses incomplete LU
IDR (s) iterative algorithms of the fore condition factor of decomposition are solved to system of linear equations.
Step 6 electromagnetic field each component is asked for：
Each component of electromagnetic field secondary field can be solved by below equation：
Exponentially weighted moving average (EWMA) least square method implements process：
The linear description of the secondary position in unit is set first：
fi=T1xi+T2yi+T3zi+d (29)
Here:xi、yi、ziFor the grid node x, y, z coordinate of the secondary position of required solution.
It is clear that coefficient T1、T2、T3The derivative of secondary position as to be solved, as each component of electromagnetic field secondary field,
The equation that the moving average least square method of Gauss weighting is formed is directly given herein, it is as follows：
T=(XTWX)-1XTWF (30),
Here
X=(x, y, z, m), x=(x1,x2,x3…xn)T
Y=(y1,y2,y3…yn)T, z=(z1,z2,z3…zn)T
M=(1,1,1 ... 1)T
Wherein, X is represents grid node three dimensional space coordinate array, and W is weight function, and r represents that grid node is former to coordinate
The distance of point.H is r maximums.
Weight function
H=max (r)；
Here β is weight function coefficient, typically takes 1.F is the secondary place value for waiting to ask N number of node near secondary position derivative point, x,
Y, z are the node coordinate for waiting to ask secondary position.
In order to verify the correctness of method in the present invention.A three levels bedded deposit model is designed, as shown in Figure 4.
Seawater-sedimentary two layer medium is used for background layer.If the air conductivity in upper half-space is 10^ (- 12) Sm-1.Seawater
Electrical conductivity is 3.2Sm-1, and depth is 0.3km.Apart from seawater bottom surface depth 1km have that a horizontal direction infinitely extends it is each to different
Property high resistance body, its thickness be 100m, reference conductivity rate be σc=diag (0.01,0.01,0.025) Sm-1, 30 are rotated to y-axis.
The electrical conductivity of sedimentary is 1Sm-1.Use along the HORIZONTAL ELECTRIC DIPOLE in x directions as excitaton source, its coordinate be located at (0,0,
970).Tranmitting frequency is 0.25Hz.Dipole moment is 1.It is observed at along z=970.Divided region size (- 4km≤x, y≤
4km, -1km≤z≤5km), grid cell sum 1467492.In AMD Athlon (tm) x4 63quad-core
Performed in processor 2.6GHz, internal memory 12G calculating platforms.
Fig. 5 is Finite Element Numerical Solution and the electric field x-component amplitude comparison diagram of quasi-associative part in zoning, quasi-solution analysis
The source of solution is Loseth L O, Ursim B.Electromagnetic fields in planarly layered
anisotropic media[J].From figure 5 it can be seen that both Finite Element Numerical Solution and the data of quasi-associative part height are kissed
Close, fully demonstrate correctness of the present invention on the electromagnetic method numerical simulation algorithm of any anisotropic problem of electrical conductivity, can
The research for being other electromagnetic methods in terms of anisotropic medium provides a kind of new method.
Fig. 6 is, containing the abnormal body Model of high resistant, upper half-space air conductivity is set in the forward modeling in arbitrary anisotropic media of foundation
For 10^ (- 12), sea water advanced is 1km, and electrical conductivity is 3.3Sm-1.There is a high resistance body in sedimentary, top surface is apart from seawater bottom
Face 1km, size is 2kmx2kmx0.1km, and centre coordinate is (2000,0,2050), and electrical conductivity is 0.01Sm-1.Sedimentary
Reference conductivity rate is set to σc=diag (2,1,1).Excitaton source is the HORIZONTAL ELECTRIC DIPOLE along x directions, and tranmitting frequency is
0.25Hz, dipole moment is 100, source point coordinate (0,0,950).Receiver is located at sea water advanced z=950.Unstructured grid
Subdivision is as shown in fig. 7, divided region size (- 4km≤x, y≤4km, -1km≤z≤4km).Make sedimentary reference conductivity rate point
Not along y-axis, z-axis rotation 0.、30.、45.、60.The abnormal response of electric field three-component amplitude is studied afterwards.
Fig. 8, Fig. 9 are respectively that sedimentary reference conductivity rate is divided along y-axis with electric field amplitude plane after z-axis different rotation angle
Butut.Fig. 8 (a), 8 (b), 8 (c) are electric field amplitude plan when reference conductivity rate does not rotate in Fig. 8；8(d)、8(e)、8(f)、
For reference conductivity rate 30 are rotated along y-axis.When electric field amplitude plane equivalence figure；8 (g), 8 (h), 8 (l) are reference conductivity
Rate rotates 45 along y-axis.When electric field amplitude plane equivalence；8 (m), 8 (n), 8 (o) are that reference conductivity rate is revolved along y-axis
Turn 60.When electric field amplitude plane equivalence.
Fig. 9 is containing abnormal each point of the body Model electromagnetic field of high resistant in the forward modeling in arbitrary anisotropic media that the embodiment of the present invention is set up
The plan of amplitude second is measured, 9 (a), 9 (b), 9 (c) are respectively that reference conductivity rate rotates 30 along z-axis.When electric field amplitude plane
Isogram；9 (d), 9 (e), 9 (f) are that reference conductivity rate rotates 45 along z-axis.When electric field amplitude plane equivalence；9
(g), 9 (h), 9 (l) are that reference conductivity rate rotates 60 along z-axis.When electric field amplitude plane equivalence.
As it can be observed in the picture that the angle 30 rotated along y-axis when reference conductivity rate tensor.、45.When, the amplitude of electric field Ex components
All extend in x, y direction, the especially extension in y directions becomes apparent；And electric field Ey component contrasts.Compared to Ex,
Ey components, Ez component amplitudes amplitude of variation is obvious asymmetric by being symmetric at the beginning than larger, and the response ratio on right side
Left side it is big.When reference conductivity rate tensor along y-axis rotate 60.When, the distribution of electric field Ex component amplitudes has been shunk；Ey points of electric field
Amount change is little；And electric field Ez amplitude distributions are obvious to external expansion, and the amplitude in left side becomes big, but right side amplitude is still than left side
Greatly.By observing Fig. 9, it is known that, reference conductivity rate rotates 30 along z-axis.、45.When, the distribution run-off the straight of electric field Ex components is outside
The amplitude of .Ey components is expanded as the angle of rotation increases and has increased, and has also been extended in x, y directional spreding；Ez points
Measure amplitude distribution and occur obvious tilt variation.When reference conductivity rate along z-axis rotate 60.When, the further hair of Ex components distribution
Raw extension；The amplitude distribution of Ey components has been shunk；The distribution of Ez component amplitudes becomes skew symmetry.Therefore, it is known that different directions
Electrical conductivity anisotropy caused by electric field exception response and the three anisotropic response characteristics of main shaft electrical conductivity have significantly
Difference.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all essences in the present invention
Any modifications, equivalent substitutions and improvements made within refreshing and principle etc., should be included in the scope of the protection.
Claims (9)
1. the ocean controllable source electromagnetic method finite element forward modeling method of a kind of anisotropic medium, it is characterised in that this method includes：
1) unstructured grid subdivision is carried out to survey region, obtains grid cell numbering, node serial number and coordinate parameters；
2) the earth-electricity model parameter of design, including background layer parameter, frequency parameter, reference conductivity rate, three Euler's rotations are read
Angle, grid cell numbering and node coordinate；
3) the corresponding each component of primary field electromagnetism of background layer is calculated；
4) cycle calculations unit coefficient matrix is carried out to all grid cells, then the coefficient square of overall all grid cells of synthesis
Battle array, then according to step 3) right-hand vector of an Electromagnetic Calculation system of linear equations calculated of background layer；
5) essential boundary condition is loaded, system of linear equations is solved, secondary field vector position and the scalar potential of each node is obtained；
6) derivation is carried out to secondary field vector position, scalar potential, obtains each component of electromagnetic field of all nodes.
2. in accordance with the method for claim 1, it is characterised in that survey region is split into limited multiple tetrahedron element e.
3. in accordance with the method for claim 1, it is characterised in that this method also includes one reference conductivity rate of setting, the ginseng
The electrical conductivity of three non-zero diagonal entries of electrical conductivity is examined, three Euler's anglecs of rotation are then set, rotated by three Eulers,
Obtain the conductivity tensor model of any direction.
4. in accordance with the method for claim 1, it is characterised in that then from maxwell equation group, introducing is based on
Magnetic vector potential A, scalar potential Ψ under Coulomb specifications represent electric field, magnetic field, in secondary field, total magnetic vector potential and scalar
Secondary field and ambient field sum are resolved into, is obtained on the secondary position expression formula of electromagnetic field：
Wherein,For abnormal electrical conductivity, ApFor a field vector position, AsFor secondary field vector position, ΨpFor primary field scalar potential,
ΨsFor secondary field scalar potential.
5. in accordance with the method for claim 1, it is characterised in that open up the secondary position expression formula of electromagnetic field successively according to xyz axles
Open, expansion is weighted using gal the Liao Dynasty golden method, with reference to vector identity and divergence theorem, obtained on secondary position
Volume integral equations group.
6. in accordance with the method for claim 1, it is characterised in that
Step 4) in system of linear equations：
Ku=b
K is coefficient matrix, and u is solves the field value that each node in domain is to be asked, and b is right-hand vector.
7. system of linear equations is solved in accordance with the method for claim 6, it is characterised in that step 5)：Ku=b, adds Di
Sharp Cray boundary condition：(As,Ψs)Γ=0.
8. in accordance with the method for claim 1, it is characterised in that using the IDR (s) of the fore condition factor of incomplete factorization
Iterative algorithm is solved to system of linear equations.
9. exponentially weighted moving average (EWMA) least square method is used in accordance with the method for claim 1, it is characterised in that step 6)
Secondary field vector position, scalar potential are solved to x, y, z partial derivative.
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| CN111638556A (en) * | 2020-06-09 | 2020-09-08 | 东华理工大学 | Magnetotelluric forward modeling method and device based on geospatial solution strategy and storage medium |
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| CN114638133B (en) * | 2022-02-28 | 2024-04-30 | 桂林理工大学 | Transient electromagnetic wavelet Galerkin 2.5D positive algorithm |
| CN115017782A (en) * | 2022-08-08 | 2022-09-06 | 中南大学 | Three-dimensional natural source electromagnetic field calculation method considering medium anisotropy |
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