CN106646625A - Transient electromagnetic inversion method for sharp boundary model - Google Patents
Transient electromagnetic inversion method for sharp boundary model Download PDFInfo
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- CN106646625A CN106646625A CN201610857249.3A CN201610857249A CN106646625A CN 106646625 A CN106646625 A CN 106646625A CN 201610857249 A CN201610857249 A CN 201610857249A CN 106646625 A CN106646625 A CN 106646625A
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- G01V3/00—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation
- G01V3/08—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation operating with magnetic or electric fields produced or modified by objects or geological structures or by detecting devices
- G01V3/10—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation operating with magnetic or electric fields produced or modified by objects or geological structures or by detecting devices using induction coils
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Abstract
The invention discloses a transient electromagnetic inversion method for a sharp boundary model. The method comprises the following steps: secondary field data observed via a transient electromagnetic method is input, inversion parameters are input and an inversion initial model is built; a mismatch general function between observed data and forward modeling theory data is built, a minimum gradient support general function used for restraining resistivity change is built, an inversion object function is built via the mismatch general function and the minimum gradient support general function, the initial model is used as initial conditions, a Gauss-Newton method is used for solving resistivity corresponding to a minimum target function, and an inversion result is obtained. Via the inversion method, a resolution of a underground resistivity abrupt change surface, a defect of unclear electrical interface reflection in an Occam inversion algorithm can be compensated, characteristics of stability and simplicity of the Occam inversion algorithm are kept in the transient electromagnetic inversion method, and the transient electromagnetic inversion method is of great significance for transient electromagnetic data inversion and late stage data interpretation.
Description
Technical field
The present invention relates to geophysical probing technique field, particularly to a kind of transient electromagnetic inverting of sharp boundary model
Method.
Background technology
Transient electromagnetic method as a kind of powerful measure of geophysical exploration, can solve the problem that mineral exploration, the energy, engineering,
Various geophysical problems such as the hydrology, environment geology survey, archaeology detection.It is issued using step wave or other pulse currents
Pulsatile once magnetic field is penetrated, underground conduction geologic body produces inductive loop under a field excitation, and then inspires secondary magnetic field.When
When emission current is turned off, primary field disappears, and underground vortex decays with the time, the electrical parameter of its die-away time and conductive geologic body
(volume, structure, resistivity, buried depth) is relevant.By observing secondary field value, the electrical parameter of underground heterogeneous body can be rebuild,
This process is referred to as inverting.Conversely, the process of secondary field change is calculated using the underground structure of known electrical parameter, referred to as just
Drill.
Conventional transient electromagnetic one-dimensional inversion method has Marquardt methods and Occam methods.Marquardt methods are led to
The data of just drilling for crossing hypothesized model are directly fitted with measured data, and iteration obtains every thickness degree and its resistance of Earth model
Rate.The method calculating speed is fast, and principle is simple, as a result can reflect the abrupt boundary of ground resistivity, but refutation process is unstable,
Easily it is absorbed in locally optimal solution.Occam methods are applied with longitudinal smoothness constraint on the basis of Marquardt method constraint functions,
Two Norm minimums of longitudinal resistivity gradient are made, it is big using gauss-newton method iterative using fixed Earth model thickness
Ground is per layer resistivity.The method refutation process is stablized, and can find the globally optimal solution for meeting longitudinal smoothness constraint, but to some
The ground electric interface resolution ratio of resistivity mutation is not good, it is impossible to accurately portrays the hierarchy of the earth.
The content of the invention
(1) technical problem to be solved
The invention provides a kind of transient electromagnetic inversion method of sharp boundary model, anti-to solve Marquardt methods
Drill unstable, Occam methods as far as possible to smooth ground resistivity change, the layered boundary resolution ratio to resistivity mutation
It is not good, it is impossible to which that the hierarchy and above two method for accurately portraying the earth is used in mixed way in practical engineering application not enough letter
Just problem.
(2) technical scheme
The invention provides a kind of transient electromagnetic inversion method of sharp boundary model, the inverting is by surveying secondary field
Data, rebuild the electrical parameter of heterogeneous body, and the transient electromagnetic inversion method includes building inverting initial model, it is characterised in that
Also comprise the steps：
Treat that inverting electrical parameter builds minimal gradient supporting functional according to the inverting initial model；And
Inversion objective function is built according to minimal gradient supporting functional.
In such scheme, also include：
The inverting initial model is just being drilled, theoretical response value is being obtained；
Built with the theoretical response value according to the secondary field data of the actual measurement and mismatch functional.
In such scheme, the structure inversion objective function also includes：
Inversion objective function is built according to the mismatch functional.
In such scheme, building the minimal gradient supporting functional using equation below is：
In formula, PsFor minimal gradient supporting functional, β is referred to as (ionospheric) focussing factor, is a positive number much smaller than 1, and m is to treat inverting
Electrical parameter, R be describe graded matrix：N is the inverting number of plies.
In such scheme, building the inversion objective function using equation below is：
P=Pt+Ps
In formula P be inversion objective function, PtFor mismatch functional, α is regularization factors, for adjusting refutation process in not
Proportion between matching functional and minimal gradient supporting functional, PsFor minimal gradient supporting functional.
In such scheme, also include：
With initial model as primary condition, solve inversion objective function and take corresponding electrical parameter during minimum of a value, obtain anti-
Drill result.
(3) beneficial effect
The method that the present invention is provided, can obtain following beneficial effect：
1st, the inventive method inherits the stable advantage of Occam invertings, inversion result by using regularization object function
Initial model is independent of, globally optimal solution can be found.
2nd, the inventive method chooses minimal gradient supporting functional as resistivity constraints, produces similar Marquardt
The result of inverting, can project the stratigraphic boundary of resistivity mutation, compensate for Occam invertings unclear to electrical interface reflection scarce
Fall into.
3rd, the inventive method gives the concrete formula of each step during use, easy to operate, can step realization
The inversion result that Occam invertings are used in mixed way with Marquardt invertings.
Description of the drawings
Fig. 1 diagrammatically illustrates the flow process of the transient electromagnetic inversion method of sharp boundary model according to embodiments of the present invention
Figure.
Fig. 2 diagrammatically illustrates transient electromagnetic secondary field corresponding data according to embodiments of the present invention.
Fig. 3 diagrammatically illustrates sharp boundary model inversion result according to embodiments of the present invention.
Specific embodiment
To make the object, technical solutions and advantages of the present invention become more apparent, below in conjunction with specific embodiment, and reference
Accompanying drawing, the present invention is described in further detail.
Fig. 1 diagrammatically illustrates the flow process of the transient electromagnetic inversion method of sharp boundary model according to embodiments of the present invention
Figure.As illustrated,
In step S1, input reverse parameter, inverted parameters include emission current I, transmitting coil radius R, transmitting coil circle
Number Nt, observe offset distance r, receiving coil effective area S.According to embodiments of the present invention, the transmitting coil number of turn is Nt=1, transmitting electricity
Flow for I=5A, launch radius R=50m, observation station offset distance r=0m, receiving coil effective area is 2000m2。
In step S2, inverting initial model is built, inverting initial model includes inverting number of plies N, each thickness degree h=[h1,
h2..., hN-1], inverting initial electrical resistivity m=[m1, m2..., mN].Due to reducing with change in depth resolution of inversion, generally
Make hi+1/hi＞ 1.According to embodiments of the present invention, inverse model is 30 layers, thickness growth ratio hi+1/hi=1.12, the first thickness
Degree h1=5m, per layer of initial electrical resistivity is 100 Ω m.
In step S3, just drilling initial model and obtaining gross data.According to embodiments of the present invention, the inverting introductory die is just being drilled
Type, obtains theoretical response F (m).
In step S4, the secondary field data of actual measurement is input into, is input into the secondary field data observed by transient electromagnetic method, including adopting
Collection time T and its corresponding field value dobs.Wherein, field value dobsMeet attenuation characteristic, portion of the early stage comprising primary field need to be rejected
Divide and late period is because noise produces the part shaken.According to embodiments of the present invention, as shown in Fig. 2 the data are by three layers big topotypes
Type is just drilled and tried to achieve, and its thickness is respectively 100m, 200m, homogeneous half space.Corresponding resistivity is respectively 300 Ω m, 90 Ω m,
300Ωm。
In step S5, the secondary field data of actual measurement and the mismatch functional of theoretical response value are built.According to present invention enforcement
Example, mismatching functional can be written as：
Pt=| | Wd(F(m)-dobs)||2
In formula, WdTo describe the weight matrix of data proportion, F (m) is theoretical response value, WdMay be selected to be：
In formula, σiThe noise in road is surveyed for each time, M is to survey road sum the time.
According to embodiments of the present invention, it is assumed herein that each time surveys, track data proportion is consistent, i.e., weight matrix is unit
Diagonal matrix.
In step S6, minimal gradient supporting functional is built.According to embodiments of the present invention, constraint change in resistance is built most
Little gradient supporting functional, can be written as：
In formula, β is referred to as (ionospheric) focussing factor, is a positive number much smaller than 1.R is the matrix for describing graded, can be written as：
According to embodiments of the present invention, in order to project the abrupt boundary of ground resistivity, β should be as far as possible little, takes β=5 × 10-11。
In step S7, inversion objective function is built by mismatch functional and minimal gradient supporting functional, according to of the invention real
Example is applied, inversion objective function can be written as：
P=Pt+αPs
In formula, α is referred to as regularization factors, for adjusting refutation process in mismatch functional and minimal gradient supporting functional it
Between proportion, embodiments in accordance with the present invention, arrange α hunting zone be 10-4-100。
In step S8, with initial model as primary condition, correspondence when object function takes minimum is solved using gauss-newton method
Resistivity, obtain inversion result.Theoretical response value F (m) is approximately written as：
F (m)=F (m0)+J0(m1-m0)
In formula, m0For the primary condition of certain step iteration, m1For the resistivity to be asked of current iteration, J0For certain step iteration when just
The Jacobian matrix of function pair primary condition is drilled, each of which element is：
By F (m)=F (m0)+J0(m1-m0) substitute into object function P=Pt+αPsIn, orderObtain iterative formula：
Often walk after iteration and update primary condition with the result newly tried to achieve, it is poor when being fitted
During less than expecting fitting difference, iteration ends.Often walking iterative process need to reach object function in certain interval interior dynamic select α value
To minimum.The embodiment of the present invention selects but is not limited only to gauss-newton method.
In step S9, the electrical parameter of final inversion result, i.e. heterogeneous body is obtained, as a result as shown in figure 3, can see
Arrive, sharp boundaries inversion result has the fitting of higher degree with theoretical model, has higher resolution ratio to resistivity abrupt boundary.
Particular embodiments described above, has been carried out further in detail to the purpose of the present invention, technical scheme and beneficial effect
Describe in detail bright, it should be understood that the foregoing is only the specific embodiment of the present invention, be not limited to the present invention, it is all
Within the spirit and principles in the present invention, any modification, equivalent substitution and improvements done etc. should be included in the protection of the present invention
Within the scope of.
Claims (6)
1. a kind of transient electromagnetic inversion method of sharp boundary model, the inverting is by surveying secondary field data, rebuilding uneven
The electrical parameter of even body, the transient electromagnetic inversion method includes building inverting initial model, it is characterised in that also including following step
Suddenly：
Treat that inverting electrical parameter builds minimal gradient supporting functional according to the inverting initial model；And
Inversion objective function is built according to minimal gradient supporting functional.
2. the transient electromagnetic inversion method of sharp boundary model according to claim 1, it is characterised in that also include：
The inverting initial model is just being drilled, theoretical response value is being obtained；
Built with the theoretical response value according to the secondary field data of the actual measurement and mismatch functional.
3. the transient electromagnetic inversion method of sharp boundary model according to claim 1, it is characterised in that the structure inverting
Object function also includes：
Inversion objective function is built according to the mismatch functional.
4. the transient electromagnetic inversion method of sharp boundary model according to claim 1, it is characterised in that use equation below
Building the minimal gradient supporting functional is：
In formula, PsFor minimal gradient supporting functional, β is referred to as (ionospheric) focussing factor, is a positive number much smaller than 1, and m is the electricity for treating inverting
Property parameter, R be describe graded matrix：N is the inverting number of plies.
5. the transient electromagnetic inversion method of sharp boundary model according to claim 1, it is characterised in that use equation below
Building the inversion objective function is：
P=Pt+αPs
In formula P be inversion objective function, PtFor mismatch functional, α is regularization factors, for adjusting refutation process in mismatch
Proportion between functional and minimal gradient supporting functional, PsFor minimal gradient supporting functional.
6. the transient electromagnetic inversion method of sharp boundary model according to claim 1, it is characterised in that also include：
With initial model as primary condition, solve inversion objective function and take corresponding electrical parameter during minimum of a value, obtain inverting knot
Really.
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Cited By (6)
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| CN107977501A (en) * | 2017-11-24 | 2018-05-01 | 山东省煤田地质规划勘察研究院 | A kind of method of inverting resistivity and magnetic susceptibility based on the earth data |
| CN110244351A (en) * | 2019-04-22 | 2019-09-17 | 西安石油大学 | A kind of Uniform Construction inversion method of different constraint Geophysical Inverse Problems |
| CN112711065A (en) * | 2019-10-25 | 2021-04-27 | 中国石油天然气集团有限公司 | Pre-stack seismic inversion method and device |
| CN112835122A (en) * | 2021-01-05 | 2021-05-25 | 吉林大学 | Discontinuous three-dimensional joint inversion method based on smooth focusing regularization |
| CN113177330A (en) * | 2021-05-27 | 2021-07-27 | 吉林大学 | Transient electromagnetic rapid statistical inversion method |
| CN113176617A (en) * | 2021-03-15 | 2021-07-27 | 中煤科工集团西安研究院有限公司 | Sedimentary stratum transient electromagnetic multi-parameter constraint inversion imaging method |
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Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107977501A (en) * | 2017-11-24 | 2018-05-01 | 山东省煤田地质规划勘察研究院 | A kind of method of inverting resistivity and magnetic susceptibility based on the earth data |
| CN110244351A (en) * | 2019-04-22 | 2019-09-17 | 西安石油大学 | A kind of Uniform Construction inversion method of different constraint Geophysical Inverse Problems |
| CN112711065A (en) * | 2019-10-25 | 2021-04-27 | 中国石油天然气集团有限公司 | Pre-stack seismic inversion method and device |
| CN112835122A (en) * | 2021-01-05 | 2021-05-25 | 吉林大学 | Discontinuous three-dimensional joint inversion method based on smooth focusing regularization |
| CN112835122B (en) * | 2021-01-05 | 2022-01-25 | 吉林大学 | Discontinuous three-dimensional joint inversion method based on smooth focusing regularization |
| CN113176617A (en) * | 2021-03-15 | 2021-07-27 | 中煤科工集团西安研究院有限公司 | Sedimentary stratum transient electromagnetic multi-parameter constraint inversion imaging method |
| CN113177330A (en) * | 2021-05-27 | 2021-07-27 | 吉林大学 | Transient electromagnetic rapid statistical inversion method |
| CN113177330B (en) * | 2021-05-27 | 2022-07-22 | 吉林大学 | Transient electromagnetic rapid statistical inversion method |
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