CN110398782A - A kind of gravimetric data and gravity gradient data combine regularization inversion method - Google Patents
A kind of gravimetric data and gravity gradient data combine regularization inversion method Download PDFInfo
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Abstract
The present invention relates to a kind of gravimetric datas and gravity gradient data to combine regularization inversion method, includes the following steps: step 1: obtaining gravimetric data, carries out Inversion Calculation to gravimetric data, obtain inversion result；Step 2: the inversion result m obtained to step 1 takes absolute value, and is normalized, for the zero in result, is set as a minimum, result that treated is as weighting matrix；Step 3: obtaining gravity gradient data, gravity gradient data and the weighting matrix are applied in Inversion Calculation simultaneously, obtain the inversion result of gravity gradient data and weighting matrix joint inversion.The geological information that gravimetric data includes effectively is utilized in the present invention, constructs weighting matrix using gravimetric data, and weighting matrix is applied to Gravity Gradient Inversion and is calculated, improves the resolution ratio of inversion result, inversion result bottom boundary is apparent, accurate.
Description
Technical field
The present invention relates to target seeker gyro inversion method technical field, specifically a kind of gravimetric data and gravity gradient data connection
Close regularization inversion method.
Background technique
Gravimetric data is obtained by measuring the vertical component of potential field, and gravity gradient data is then by measuring gravitational field
Variation in three directions obtains, if being indicated vertically downward with Z axis positive direction by taking cartesian coordinate system as an example, gravimetric data is
For gravitational field in the first-order partial derivative of Z-direction, gravity gradient data is then Second Order Partial of the gravitational field in X, Y and three directions of Z axis
Derivative.Gravimetric data and gravity gradient data are compared in frequency domain, it is found that gravimetric data includes more low frequency
Information, gravity gradient data then include more high-frequency information.Therefore, gravity and gravity gradient data are applied to inverting simultaneously
In calculating, the complementation of information may be implemented, and improve efficiency of inverse process.
Since potential field lacks the resolution ratio of depth direction, so being needed in gravimetric data and gravity gradient data inverting
Introduce depth weighted function.The setting of depth weighted function and data rate of decay have relationship, and gravimetric data is with range attenuation speed
Rate is proportional to r-2, and gravity gradient is proportional to r-3 with range attenuation rate, wherein r indicates the distance between two mass blocks.But
It is, in most of gravity and gravity gradient joint inversion method, to gravity and gravity gradient data using same depth weighted
Function offsets rate of decay, both does not account for the difference with range attenuation rate.Meanwhile in common gravity and gravity ladder
Gravimetric data and gravity gradient data are generally directly constituted a matrix, participate in Inversion Calculation by degree according in joint inversion
In, since gravimetric data magnitude is lower than gravity gradient data, and in same matrix, different components can interact, using this
Kind method, the geological information extraction for including in gravimetric data and gravity gradient data cannot be come out, lead to inverting knot well
The vertical resolution of fruit is not high.
Summary of the invention
In view of the deficiencies of the prior art, it is an object of the invention to provide a kind of gravimetric datas and gravity gradient data to combine canonical
Change inversion method, the vertical resolution for being able to solve inversion result in gravimetric data and gravity gradient data joint inversion is not high
The problem of.
The technical solution achieved the object of the present invention are as follows: a kind of gravimetric data and gravity gradient data joint regularization inverting
Method includes the following steps:
Step 1: obtaining gravimetric data, Inversion Calculation is carried out to gravimetric data, obtains inversion result, gravimetric data is carried out
The objective function φ of invertingdFor formula (1):
Wherein,Indicate that the square operation of two-norms, d indicate observation data, A indicates that sensitivity matrix, m indicate model
Parameter, Aw=AW-1, mw=Wm, W indicate depth weighted function, are a diagonal matrix；
Step 2: the inversion result m obtained to step 1 takes absolute value, and is normalized, for the zero in result,
It is set as a minimum, result that treated is as weighting matrix；
Step 3: obtaining gravity gradient data, gravity gradient data and the weighting matrix are applied to Inversion Calculation simultaneously
In, obtain the inversion result of gravity gradient data and weighting matrix joint inversion.
Further, in the step 1, the detailed process for carrying out Inversion Calculation to gravimetric data includes:
(1) the number of iterations is indicated with i, maximum number of iterations is set as n, and the initial value of i is 0, i=0,1,2 ..., n, really
Determine initial model m0Value, obtain formula (2):
mw0=Wm0------(2)
(2) the gradient I of objective function when calculating initial by formula (3)0:
I0=Aw(Awmw0-d)------(3)
First time is iterated to calculate, direction of search d0=-I0；
(3) i-th step-size in search k is calculated by formula (4)(i):
Wherein, diIndicate the observation data of i-th iteration, IiIndicate the gradient of the corresponding objective function of i-th iteration；
(7) the result m of i-th iteration is calculated by formula (5)i, and intermediate variable r is calculated by formula (6):
Wherein, mw(i-1)Indicate (i-1)-th iteration as a result, mw(i)For intermediate variable；
R=Ami-d------(6)
(8) whenWhen reaching maximum number of iterations n less than or equal to preset value or the number of iterations, terminate iteration, otherwise after
It is continuous to be carried out by step (6)；
(6) the gradient I of the corresponding objective function of i+1 time iteration is calculated(i+1), calculate intermediate parametersThe new direction of search is set as di+1=-Ii+1+βi+1di, and (3) processing that gos to step.
Further, in the step 3, Inversion Calculation is applied to simultaneously to gravity gradient data and the weighting matrix
In, constraint condition is added by regularization method, the target of joint inversion is carried out to gravity gradient data and the weighting matrix
Function phi is formula (7):
φ=φd+αφs------(7)
Wherein, φsIt indicates stability function, is calculated by formula (8):
φs=αs∫∫∫Vm2dv+αx∫∫∫Vmx 2dv+αy∫∫∫Vmy 2dv+αz∫∫∫Vmz 2dv------(8)
Wherein, αs、αx、αy、αzIt indicates the weight of each component, is constant, mx、my、mzIndicate model parameter m in x, y, z
The first-order partial derivative in three directions, V indicate integral domain, and weighting function W, therefore, formula (7) are introduced in objective function φ
Objective function φ becomes formula (9):
Formula (9) is gravity gradient data and weighting matrix is applied to the objective function in Inversion Calculation, using conjugation
Gradient algorithm solution formula (9), obtains inversion result, which is gravimetric data and gravity gradient data joint canonical
Inversion result after changing inverting.
The invention has the benefit that the geological information that gravimetric data includes effectively is utilized in the present invention, gravity is utilized
Data construct weighting matrix, and weighting matrix is applied to Gravity Gradient Inversion and is calculated, the resolution ratio of inversion result, inverting are improved
As a result bottom boundary is apparent, accurate.
Detailed description of the invention
Fig. 1 is flow diagram of the invention；
Fig. 2 is to realize gravimetric data and gravity gradient data joint inversion result using system method；
Fig. 3 is gravimetric data of the invention and gravity gradient data joint inversion result.
Specific embodiment
In the following, being described further in conjunction with attached drawing and specific embodiment to the present invention:
As shown in Figure 1 to Figure 3, a kind of gravimetric data and gravity gradient data combine regularization inversion method, including as follows
Step:
Step 1: obtaining gravimetric data, Inversion Calculation, objective function φ are carried out to gravimetric datadSuch as formula (1), namely
Gravimetric data inverting is calculated by formula (1):
Wherein,It indicates that the square operation of two-norms, d indicate observation data, is a vector, size n1× 1, n1
Indicate observation point number, A indicates sensitivity matrix, can obtain using existing universal calculation equation, size n1×n2,
n2Indicate the small cuboid number of survey Division, AijFor the element in A, the survey that the small cuboid that number is i is j in number is indicated
Gravity caused by point or gravity gradient value, density 1g/cm3, m indicate model parameter, be vector, that is to say that this step passes through public affairs
Formula (1) needs obtained inversion result, φdIndicate fitting function.
Since gravimetric data is proportional to r-2 with range attenuation rate, gravity gradient is proportional to r-3 with range attenuation rate,
It needs to introduce depth weighted function W to offset this influence, obtains formula (2):
Wherein, Aw=AW-1, mw=Wm, W are a diagonal matrix, are asked using conjugate gradient algorithms formula (2)
Solution, obtains m, detailed process is as follows:
(1) indicate the number of iterations with i, maximum number of iterations is set as n, and the initial value of i is 0 namely i=0,1,2 ...,
N determines initial model m0Value generally take 0 value in the case where lacking prior information, to obtain formula (3):
mw0=Wm0------(3)
(2) the gradient I of objective function when calculating initial by formula (4)0:
I0=Aw(Awmwi-d)------(4)
First time is iterated to calculate, direction of search d0=-I0；
(3) i-th step-size in search k is calculated by formula (5)(i):
Wherein, diIndicate the observation data of i-th iteration, IiIndicate the gradient of the corresponding objective function of i-th iteration；
(4) the result m of i-th iteration is calculatedi, such as formula (6), if miLess than or equal to preset value, then show the element in A
Value meet geological information, and calculate intermediate variable r by formula (7):
Wherein, mw(i-1)Indicate (i-1)-th iteration as a result, mw(i)For intermediate variable；
R=Ami-d------(7)
(5) whenLess than or equal to preset minimum (such as 10-6Or smaller) or iteration
When number reaches maximum number of iterations n, iteration is terminated, is otherwise continued by step (6)
It carries out:
(6) the gradient I of the corresponding objective function of i+1 time iteration is calculated(i+1), calculate intermediate parametersThe new direction of search is set as di+1=-Ii+1+βi+1di, and (3) processing that gos to step.
Step 2: the inversion result m obtained to step 1 takes absolute value, and is normalized, for the zero in result,
It is set as minimum (such as 10-6Or smaller), result that treated is as weighting matrix；
Step 3: obtaining gravity gradient data, by weighting matrix that gravity gradient data and step 2 obtain while being applied to
In Inversion Calculation, inversion result is obtained.
Inversion Calculation in this step is calculated using smooth inversion algorithm, and detailed process is as follows:
Constraint condition is added by regularization method, objective function φ is formula (8):
φ=φd+αφs------(8)
Wherein, φsIt indicates stability function, is calculated by formula (9):
φs=αs∫∫∫Vm2dv+αx∫∫∫Vmx 2dv+αy∫∫∫Vmy 2dv+αz∫∫∫Vmz 2dv------(9)
Wherein, αs、αx、αy、αzThe weight for indicating each component is coefficient, is constant, can preset or based on experience value
It provides, mx、my、mzModel parameter m is indicated in the first-order partial derivative in three directions of x, y, z, V indicates integral domain, φsIt can also be with
It is indicated with matrix form, such as formula (10):
Wi=αiDi, i=x, y, z, wherein WiIndicate difference operator, DiIt is to be calculated according to different directions finite difference operator
Obtained matrix introduces weighting function W in objective function, and therefore, the objective function φ of formula (8) becomes formula (11):
Formula (11) is that the objective function that is applied in Inversion Calculation of gravity gradient data and weighting matrix is equally adopted
With conjugate gradient algorithms solution formula (11), inversion result is obtained, which that is to say final inversion result of the invention,
It is the inversion result after gravimetric data and gravity gradient data joint regularization inverting, detailed process and step 1 solve target
Function is a kind of, and detailed process does not repeat.
As can be seen from the above description, the geological information that gravimetric data includes effectively is utilized in the present invention, utilizes gravity number
According to building weighting matrix, weighting matrix is applied to Gravity Gradient Inversion and is calculated, the resolution ratio of inversion result, inverting knot are improved
Fruit bottom boundary is apparent, accurate.
It as shown in Figures 2 and 3, is the result that inverting is carried out to U.S. Vinton salt dome A/W and gravity gradient data
Figure, left side one is classified as horizontal profile in Fig. 2 and Fig. 3, and transverse and longitudinal coordinate indicates East and West direction and north-south position coordinates, in Fig. 2 and Fig. 3
The column of centre one and right side one be classified as vertical section, ordinate indicates depth, and abscissa indicates horizontal position.It is given respectively in Fig. 2
Gravimetric data gz and four groups of difference gravity gradient component combination (g are gone outzz、gxx|gyy|gzz、gxx|gxy|gyy|gzz、gxx|gxy|gxz
|gyy|gyz|gzz) joint inversion as a result, then given in Fig. 3 respective components combination using the method for the present invention inverting obtain knot
Fruit.
Compared to the existing method for carrying out joint inversion to gravimetric data and gravity gradient data, inverting knot of the invention
Fruit is apparent on deep boundary, and inversion result convergence is more preferable, inversion result increase resolution.
Embodiment disclosed in this specification is an illustration to folk prescription region feature of the present invention, protection model of the invention
Embodiment without being limited thereto is enclosed, the equivalent embodiment of other any functions is fallen within the protection scope of the present invention.For this field
Technical staff for, various other corresponding changes and change can be made according to the above description of the technical scheme and ideas
Shape, and all these change and deformation all should belong within the scope of protection of the claims of the present invention.
Claims (3)
1. a kind of gravimetric data and gravity gradient data combine regularization inversion method, which comprises the steps of:
Step 1: obtaining gravimetric data, Inversion Calculation is carried out to gravimetric data, obtains inversion result, inverting is carried out to gravimetric data
Objective function φdFor formula (1):
Wherein,Indicate that the square operation of two-norms, d indicate observation data, A indicates that sensitivity matrix, m indicate model ginseng
Number, Aw=AW-1, mw=Wm, W indicate depth weighted function, are a diagonal matrix；
Step 2: the inversion result m obtained to step 1 takes absolute value, and is normalized, for the zero in result, setting
For a minimum, result that treated is as weighting matrix；
Step 3: gravity gradient data is obtained, gravity gradient data and the weighting matrix are applied in Inversion Calculation simultaneously,
Obtain the inversion result of gravity gradient data and weighting matrix joint inversion.
2. gravimetric data according to claim 1 and gravity gradient data combine regularization inversion method, which is characterized in that
In the step 1, the detailed process for carrying out Inversion Calculation to gravimetric data includes:
(1) indicate that the number of iterations, maximum number of iterations are set as n with i, the initial value of i is 0, i=0,1,2 ..., n, is determined just
Beginning model m0Value, obtain formula (2):
mw0=Wm0------(2)
(2) the gradient I of objective function when calculating initial by formula (3)0:
I0=Aw(Awmw0-d)------(3)
First time is iterated to calculate, direction of search d0=-I0；
(3) i-th step-size in search k is calculated by formula (4)(i):
Wherein, diIndicate the observation data of i-th iteration, IiIndicate the gradient of the corresponding objective function of i-th iteration；
(4) the result m of i-th iteration is calculated by formula (5)i, and intermediate variable r is calculated by formula (6):
Wherein, mw(i-1)Indicate (i-1)-th iteration as a result, mw(i)For intermediate variable；
R=Ami-d------(6)
(5) whenWhen reaching maximum number of iterations n less than or equal to preset value or the number of iterations, terminate iteration, otherwise continue by
Step (6) carries out；
(6) the gradient I of the corresponding objective function of i+1 time iteration is calculated(i+1), calculate intermediate parameters
The new direction of search is set as di+1=-Ii+1+βi+1di, and (3) processing that gos to step.
3. gravimetric data according to claim 1 and gravity gradient data combine regularization inversion method, which is characterized in that
In the step 3, gravity gradient data and the weighting matrix are applied in Inversion Calculation simultaneously, by regularization method plus
Enter constraint condition, the objective function φ that joint inversion is carried out to gravity gradient data and the weighting matrix is formula (7):
φ=φd+αφs------(7)
Wherein, φsIt indicates stability function, is calculated by formula (8):
φs=αs∫∫∫Vm2dv+αx∫∫∫Vmx 2dv+αy∫∫∫Vmy 2dv+αz∫∫∫Vmz 2dv------(8)
Wherein, αs、αx、αy、αzIt indicates the weight of each component, is constant, mx、my、mzIndicate model parameter m in three sides of x, y, z
To first-order partial derivative, V indicate integral domain, in objective function φ introduce weighting function W, therefore, the target letter of formula (7)
Number φ becomes formula (9):
Formula (9) is gravity gradient data and weighting matrix is applied to the objective function in Inversion Calculation, using conjugate gradient
Algorithm solution formula (9), obtains inversion result, which is that gravimetric data and gravity gradient data joint regularization are anti-
Inversion result after drilling.
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| CN111399074A (en) * | 2020-04-28 | 2020-07-10 | 中国自然资源航空物探遥感中心 | Gravity and gravity gradient modulus combined three-dimensional inversion method |
| CN112147709A (en) * | 2020-08-03 | 2020-12-29 | 中国海洋石油集团有限公司 | Gravity gradient data three-dimensional inversion method based on partial smoothness constraint |
| CN112199859A (en) * | 2020-10-26 | 2021-01-08 | 东北大学 | Method for joint inversion of gravity gradient data |
| CN112558164A (en) * | 2020-12-08 | 2021-03-26 | 广州海洋地质调查局 | Magnetotelluric regularization inversion method based on deviation principle and processing terminal |
| CN112835122A (en) * | 2021-01-05 | 2021-05-25 | 吉林大学 | Discontinuous three-dimensional joint inversion method based on smooth focusing regularization |
| CN113504575A (en) * | 2021-07-09 | 2021-10-15 | 吉林大学 | Joint inversion method based on weight intersection and multiple intersection gradient constraints |
| CN113514900A (en) * | 2021-07-12 | 2021-10-19 | 吉林大学 | Density constraint-based spherical coordinate system gravity and gravity gradient joint inversion method |
| CN113552620A (en) * | 2021-09-07 | 2021-10-26 | 中国地震局地球物理研究所 | Step length calculation method and system suitable for waveform inversion |
| CN113591030A (en) * | 2021-08-17 | 2021-11-02 | 东北大学 | Gravity gradient data sensitivity matrix compression and calling method based on multiple GPUs |
| CN115220119A (en) * | 2022-06-21 | 2022-10-21 | 广州海洋地质调查局 | Gravity inversion method suitable for large-scale data |
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| CN111399074A (en) * | 2020-04-28 | 2020-07-10 | 中国自然资源航空物探遥感中心 | Gravity and gravity gradient modulus combined three-dimensional inversion method |
| CN111399074B (en) * | 2020-04-28 | 2022-08-12 | 中国自然资源航空物探遥感中心 | Gravity and gravity gradient modulus combined three-dimensional inversion method |
| CN112147709A (en) * | 2020-08-03 | 2020-12-29 | 中国海洋石油集团有限公司 | Gravity gradient data three-dimensional inversion method based on partial smoothness constraint |
| CN112199859A (en) * | 2020-10-26 | 2021-01-08 | 东北大学 | Method for joint inversion of gravity gradient data |
| CN112199859B (en) * | 2020-10-26 | 2023-08-08 | 东北大学 | Gravity gradient data joint inversion method |
| CN112558164A (en) * | 2020-12-08 | 2021-03-26 | 广州海洋地质调查局 | Magnetotelluric regularization inversion method based on deviation principle and processing terminal |
| 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 |
| CN113504575A (en) * | 2021-07-09 | 2021-10-15 | 吉林大学 | Joint inversion method based on weight intersection and multiple intersection gradient constraints |
| CN113514900A (en) * | 2021-07-12 | 2021-10-19 | 吉林大学 | Density constraint-based spherical coordinate system gravity and gravity gradient joint inversion method |
| CN113591030A (en) * | 2021-08-17 | 2021-11-02 | 东北大学 | Gravity gradient data sensitivity matrix compression and calling method based on multiple GPUs |
| CN113591030B (en) * | 2021-08-17 | 2024-01-30 | 东北大学 | Gravity gradient data sensitivity matrix compression and calling method based on multiple GPUs |
| CN113552620A (en) * | 2021-09-07 | 2021-10-26 | 中国地震局地球物理研究所 | Step length calculation method and system suitable for waveform inversion |
| CN115220119A (en) * | 2022-06-21 | 2022-10-21 | 广州海洋地质调查局 | Gravity inversion method suitable for large-scale data |
| CN115220119B (en) * | 2022-06-21 | 2023-02-24 | 广州海洋地质调查局 | Gravity inversion method suitable for large-scale data |
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