CN108873103A - A kind of two-dimentional gravity gradient and magnetotelluric joint inversion method of structural constraint - Google Patents
A kind of two-dimentional gravity gradient and magnetotelluric joint inversion method of structural constraint Download PDFInfo
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- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
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Abstract
The present invention relates to a kind of two-dimentional gravity gradient of structural constraint and magnetotelluric joint inversion methods, establish multi -components gravity gradient and magnetotelluric joint inversion objective function;Calculate separately gravity gradient and magnetotelluric method forward response and Jacobian matrix;It seeks forward response value and observation data is fitted poor threshold value.The present invention is that multi -components gravity gradient method is introduced into joint inversion, substitutes Conventional gravity exploitation method.Ground electromagnetic method has frequency information abundant, and depth of exploration is big, and this method is added in joint inversion, can effectively make up the defect of gravity gradient and gravity vertical resolution difference, preferably recover inversion of Density model;It is a kind of based on the joint inversion method for intersecting gradient-structure coupling, compared with independent inverting and other traditional physical property coupling joint inversion methods, this method is independent of physical properties of rock relationship, true model structure can preferably be recovered, no matter physical property numerically, or in geometric space form.
Description
Technical field:
The present invention relates to invertings while multi -components gravity gradient and magnetotelluric (MT) two kinds of geophysical methods, especially
It is to utilize the two-dimentional multi -components gravity gradient and magnetotelluric joint inversion method for intersecting gradient-structure constraint.
Background technique:
Gravity, which is prospected, to be become using earth's surface gravity acceleration value caused by density variation between the various rock mass of the composition earth's crust, ore body
Change and carry out geological prospecting kind method, have light, fast, the advantages of less investment, is widely used in Research on Crustal internal junction
Structure constructs, detects Solid Mineral and petroleum resources distribution etc..With the raising and GPS skill of gravimetric prospecting measuring instrument precision
The progress of art, high-precision gradiometry technology are rapidly developed.Observed gravity position is capable of in gradiometry
Second dervative has higher resolution ratio to shallow-layer geologic body, can preferably reflect superficial part compared with traditional gravity measurement
The boundary of anomalous body.Gravity gradient includes multiple gradient components, and the information that each gradient data component includes is not quite similar, comprehensive
The accuracy of geologic interpretation is helped to improve using multiple component informations.
Magneto-electrotelluric exploration is a kind of geophysical exploration side using natural alternating electromagnetic field research earth electrical structure
Method, has at low cost, and work is convenient, and not by the shielding of resistive formation, to resistive layer high resolution, and depth of exploration is with electromagnetic field
Frequency variation, the shallow stratum of high-frequency detection, low-frequency acquisition deep stratum, since frequency range is abundant, depth of exploration has reached ten
Kilometers several or up to a hundred.Therefore, in recent years in the generaI investigation and exploration of oil and natural gas, the investigation of underground heat and earthquake
The fields such as forecast are all successfully applied.
Gravity gradient method has lateral resolution capability well, but vertical resolution is poor, is difficult to divide deep
Construction.For magnetotelluric method since spectral range is abundant, Observational depth is larger, very strong to vertical resolution, but laterally differentiates energy
Power is relatively weak.Both of which can only evaluate the physical properties of rock feature of underground medium from single angle, only according to a kind of earth
Physical method is difficult accurate exploring subsurface structure.Therefore, more accurate subsurface information in order to obtain, need magnetotelluric method and
Gravity gradient method Combined Treatment is explained, is absorbed the advantage of each method, is abandoned the disadvantage of each method, finally obtains more accurate underground
Structural information.
Joint inversion is one of the important means of Comprehensive Geophysical Method explanation, is broadly divided into two ways.The first,
Based on the coupling process of physical properties of rock relationship, but this method needs to rely on physical properties of rock relationship, and complex area is difficult to determine standard
True physical properties of rock relationship has certain limitation;Second, based on the method for spatial distribution structure coupling, this side
Method only emphasizes the similitude in rock texture independent of physical properties of rock relationship, has universal adaptability.Currently, both at home and abroad
The joint inversion research of traditional gravity methods and other geophysical methods is had studied, but there is no propose and study
The joint inversion of the more gravity gradient methods of multi -components, information content and other geophysical methods is studied.
Summary of the invention:
The purpose of the present invention is in view of the above shortcomings of the prior art, provide a kind of two-dimentional gravity gradient of structural constraint
With magnetotelluric joint inversion method, existing gravimetric prospecting method is replaced.
The purpose of the present invention is what is be achieved through the following technical solutions:
The two-dimentional gravity gradient and magnetotelluric joint inversion method of structural constraint, include the following steps:
A, multi -components gravity gradient and magnetotelluric joint inversion objective function are established;
B, density and resistivity initial model are established;
C, gravity gradient method and magnetotelluric method forward response and Jacobian matrix are calculated separately;
D, gravity gradient and the independent inverting of magnetotelluric are sought respectively using gauss-newton method, obtains independent inverting density
And resistivity models;
E, the partial derivative and Lagrangian of the structural constraint item in objective function are sought;
F, it calculates and obtains joint inversion density and resistivity models;
G, forward modelling is carried out to joint inversion density and resistivity models respectively, seeks forward response value and observation data
Fitting it is poor, if fitting difference increase, reach maximum number of iterations or fitting difference reach threshold value, stop Inversion Calculation, it is defeated
Final joint inversion is as a result, otherwise return step c out.
Beneficial effect:Multi -components gravity gradient method is introduced into joint inversion by the present invention, instead of Conventional gravity
Exploitation method.Gravimeter only measures a vertical component of gravitational field, and full tensor gravity gradiometer can measure 9 gravitational fields
The information content of gradient tensor component, gravity gradient data is more, can more accurately reflect hard site source distribution, compared to weight
Power has higher resolution capability.Meanwhile magnetotelluric method has frequency information abundant, depth of exploration is big, by this method plus
Enter into joint inversion, effectively makes up the defect of gravity gradient and gravity vertical resolution difference, preferably recover density
Inverse model;Method of the invention is a kind of joint inversion method of intersection gradient-structure coupling, with independent inverting or based on object
Property coupling joint inversion method compare, this method can preferably recover true model knot independent of physical properties of rock relationship
Structure, no matter physical property numerically, or in geometric space form.
Detailed description of the invention:
The two-dimentional gravity gradient and magnetotelluric joint inversion method flow chart of Fig. 1 structural constraint.
Fig. 2 resistivity and density theory illustraton of model.
Fig. 3 gravity (a) and gravity gradient (b) forward response curve.
The independent inverting (a) of Fig. 4 gravity;The independent inverting (b) of gravity gradient.
Fig. 5 gravity and MT joint inversion, MT inverting (a);Gravitational inversion (b).
Fig. 6 gravity gradient and MT joint inversion, MT inverting (a);Gravity Gradient Inversion (b)
Specific embodiment:
With reference to the accompanying drawing with example to further detailed description of the invention.
The two-dimentional gravity gradient and magnetotelluric joint inversion method of structural constraint, include the following steps:
A, multi -components gravity gradient and magnetotelluric joint inversion objective function are established;
B, density and resistivity initial model are established;
C, gravity gradient method and magnetotelluric method forward response and Jacobian matrix are calculated separately;
D, gravity gradient and the independent inverting of magnetotelluric are sought respectively using gauss-newton method, obtains independent inverting density
And resistivity models;
E, the partial derivative and Lagrangian of the structural constraint item in objective function are sought;
F, it calculates and obtains joint inversion density and resistivity models;
G, forward modelling is carried out to joint inversion density and resistivity models respectively, seeks forward response value and observation data
Fitting it is poor, if fitting difference increase, reach maximum number of iterations or fitting difference reach threshold value, stop Inversion Calculation, it is defeated
Final joint inversion is as a result, otherwise return step c out.
Fig. 1 is the two-dimentional gravity gradient and magnetotelluric joint inversion method flow chart of structural constraint, is included the following steps:
A, multi -components gravity gradient and magnetotelluric joint inversion objective function are established;
Three component (V of gravity gradient are contained in objective functionzx,Vzz,Vxx) and magnetotelluric data fit term, together
When joined model smoothing bound term and intersect gradient constraint condition, expression formula is as follows:
Constraint condition:
Wherein:
Cd=diag [Cd1,Cd2,Cd3,Cd4],
Cm=diag [Cm1,Cm2],
α=[α1,α2].
It is expressed as data fit term,It is expressed as mould
Type bound term;Cd1Cd2And Cd3Respectively gravity gradient observes data d1,d2And d3Data covariance matrix;Cd4Number is observed for MT
According to d4Data covariance matrix;Cm1And Cm2Respectively density m1With resistivity m2Model covariance matrix;minf1And minf2For
Prior model parameter;α1And α2For damping parameter;f1(m), f2(m) and f3(m) it is expressed as the forward modeling of each component of gravity gradient
Response, f4It (m) is MT forward response;For gradient;τ is to intersect gradient function to be expressed as density and resistivity models parameter gradients
Multiplication cross;T and -1 is respectively matrix transposition and matrix inversion.
B, density and resistivity initial model are established;
The density and resistivity initial model of two-dimensional rectangle mesh generation are established, initial model is set as homogeneous half space mould
Type, density value 0g/cm3Value after taking logarithm with resistivity is 102.5Ω·m;
C, gravity gradient method and magnetotelluric method forward response and Jacobian matrix are calculated separately;
Magnetotelluric forward response, which is calculated, carries out forward modeling meter using the triangle subdivision finite element algorithm that Wanamaker is proposed
It calculates, which derives the L. Van Hée of secondary field from Maxwell equation, carry out by FInite Element to inclined
The solution of the differential equation, finally obtains forward response.The Jacobian matrix of magnetotelluric method carries out solution meter using theory of reciprocity
It calculates.
Gravity gradient forward response is according to the law of universal gravitation, and a residual mass is m, and residual density is the geology of ρ
First derivative, available gravity are asked to gravitation position in the gravitation position (V) that body generates at its exterior space any point in the z-direction
Forward response (gz), second dervative available gravity gradient forward response (V is asked in direction along x, z to gravitation positionxx,Vzz,Vzx)。
Gravity gradient forward response and residual density are in a linear relationship, only need to will be remaining so gravity gradient Jacobian matrix is sought
Density value is set as 1, and forward response at this time is Jacobian matrix.
D, gravity gradient and the independent inverting of magnetotelluric are sought respectively using gauss-newton method, obtains independent inverting density
And resistivity models;
Firstly, carrying out Taylor series expansion, such as following formula to forward response f (m):
f(m)≈f(m0)+A(m-m0) (2)
Wherein, A is the Jacobian matrix of forward response, m0For model initial model.
Formula (2) is brought into the formula (1) for not intersecting gradient constraint condition, it is as follows to obtain expression formula
Extreme value is asked to formula (5)Independent inverse model is obtained, expression formula is as follows:
E, the partial derivative and Lagrangian of the structural constraint item in objective function are sought;
Intersect gradient constraint condition to be added in objective function by Lagrangian method, such as following formula:
Wherein, Λ is Lagrangian, and B is to intersect gradient partial derivative.
Derivation, available joint inversion model knots modification are carried out to formula (7):
Formula (8) is updated to the expression of available Lagrangian Λ in the constraint condition in target function type (1)
Formula:
F, it calculates and obtains joint inversion density and resistivity models;
Formula (10) is brought into formula (8), joint inversion model may finally be arrived
G, forward modelling is carried out to joint inversion density and resistivity models respectively, seeks forward response value and observation data
Fitting it is poor, if fitting difference increase, reach maximum number of iterations or fitting difference reach threshold value, stop Inversion Calculation, it is defeated
Final joint inversion is as a result, otherwise return step c out.
Fitting difference is such as formula (14)
Wherein, N is observation data amount check.
Modeling computation:
The application devises density and resistivity models as shown in Figure 2, carries out independent inverting and joint to generated data
Inverting, and gravity and Gravity Gradient Inversion result are compared and analyzed.Density model and resistivity models are in joint inversion area
Domain uses identical mesh generation (140 × 60), and outside joint inversion region, resistivity models also need Expanding grid size
(156×76).If anomalous body there are two in subsurface model space, background density is 0g/cm in density model3, two anomalous bodys
Density be respectively -2.0g/cm3、-2.0g/cm3;Background resistivity is 10 in resistivity models2.5Ω m, two anomalous body electricity
Resistance rate is respectively 101.5Ω m and 104Ω·m.Buried depth is 0.5km at the top of two anomalous bodys, and bottom buried depth is respectively
0.9km and 1.4km.Gravity and gravity gradient method use identical observation point, and point spacing is 0.2km, and measuring point number is 30;
Magnetotelluric data contains view phase and apparent resistivity under two kinds of polarization modes of TM, TE, and frequency points are 10, frequency model
It is trapped among between 1~1000Hz, 9 observation points equidistantly distribute between 0~6km of survey line.Before Inversion Calculation, needed herein to reason
Forward modelling is carried out by model, and the gravity anomaly and gravity gradient that Fig. 3 a and Fig. 3 b, which are respectively theoretical model, to be generated in earth's surface are just
Drill response curve
No matter independent inverting or joint inversion, initial model is all made of homogeneous half space, and Fig. 4 a and Fig. 4 b attach most importance to respectively
Power and the independent inversion result figure of gravity gradient, wherein black box indicate true model boundary figure 4, it is seen that
There is the false anomaly phenomenon of large area diverging below high density anomalous body in gravitational inversion result.However, due to gravity gradient
Data contain multiple components, can provide more subsurface informations, therefore can be found that gravity gradient degree inversion result is calibrated
Really reflect spatial position and the geometric shape of true anomalous body, but the absolute value of residual density value is smaller than true value, and
And there are still certain deviations for inverting anomalous body boundary and real border.Compared to independent inverting, the joint inversion of Fig. 5 and Fig. 6
As a result the anomalous body boundary obtained is more clear, and especially longitudinal resolution ratio is significantly improved;In addition, it is also seen that gravity
Gradient joint inversion result (Fig. 6 b) compared to gravity Inversion result (Fig. 5 b), the residual density value of high density anomalous body from
0.6g/cm3It is restored to 0.9g/cm3, while the boundary of anomalous body has obtained better recovery;For resistivity models, gravity ladder
Joint inversion of the joint inversion result compared to gravity and MT of degree and MT are as a result, in terms of spatial shape and physical property numerical value recovery
All obtain better effect.
Claims (1)
1. the two-dimentional gravity gradient and magnetotelluric joint inversion method of a kind of structural constraint, include the following steps:
A, multi -components gravity gradient and magnetotelluric joint inversion objective function are established;
B, density and resistivity initial model are established;
C, gravity gradient method and magnetotelluric method forward response and Jacobian matrix are calculated separately;
D, gravity gradient and the independent inverting of magnetotelluric are sought respectively using gauss-newton method, obtains independent inverting density and electricity
Resistance rate model;
E, the partial derivative and Lagrangian of the structural constraint item in objective function are sought;
F, it calculates and obtains joint inversion density and resistivity models;
G, forward modelling is carried out to joint inversion density and resistivity models respectively, seek forward response value and observes the quasi- of data
It is poor to close, and reaches threshold value if being fitted difference increase, reaching maximum number of iterations or being fitted difference, stops Inversion Calculation, output is most
Whole joint inversion is as a result, otherwise return step c.
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CN109633762A (en) * | 2019-01-07 | 2019-04-16 | 吉林大学 | The method of correlation constraint conditional joint inverting gravity and magnetic data based on SIN function |
CN110286416A (en) * | 2019-05-13 | 2019-09-27 | 吉林大学 | A kind of fast two-dimensional inversion of Density method based on physical property function |
CN111142170A (en) * | 2020-02-25 | 2020-05-12 | 中国地质大学(北京) | Submarine position detection method based on gravity gradient extreme point |
CN111323830A (en) * | 2020-01-14 | 2020-06-23 | 东华理工大学 | Joint inversion method based on magnetotelluric and direct-current resistivity data |
CN112199859A (en) * | 2020-10-26 | 2021-01-08 | 东北大学 | Method for joint inversion of gravity gradient data |
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CN116466402A (en) * | 2023-04-24 | 2023-07-21 | 中国地震局地球物理研究所 | Electromagnetic inversion method based on geological information and electromagnetic data combined driving |
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CN110286416B (en) * | 2019-05-13 | 2020-12-22 | 吉林大学 | Fast two-dimensional density inversion method based on physical property function |
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CN112199859B (en) * | 2020-10-26 | 2023-08-08 | 东北大学 | Gravity gradient data joint inversion method |
CN112835122B (en) * | 2021-01-05 | 2022-01-25 | 吉林大学 | Discontinuous three-dimensional joint inversion method based on smooth focusing regularization |
CN112835122A (en) * | 2021-01-05 | 2021-05-25 | 吉林大学 | Discontinuous three-dimensional joint inversion method based on smooth focusing regularization |
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CN114200541A (en) * | 2021-12-02 | 2022-03-18 | 吉林大学 | Three-dimensional gravity-magnetic joint inversion method based on cosine dot product gradient constraint |
CN114721044A (en) * | 2022-04-21 | 2022-07-08 | 湖南工商大学 | Method and system for joint inversion of crust structure by using multi-frequency receiving function and amplitude ratio |
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CN116466402A (en) * | 2023-04-24 | 2023-07-21 | 中国地震局地球物理研究所 | Electromagnetic inversion method based on geological information and electromagnetic data combined driving |
CN116466402B (en) * | 2023-04-24 | 2024-02-06 | 中国地震局地球物理研究所 | Electromagnetic inversion method based on geological information and electromagnetic data combined driving |
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