CN112199859B - Gravity gradient data joint inversion method - Google Patents
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Abstract
The invention provides a gravity gradient data joint inversion method, relates to the technical field of geophysical inversion, aims at solving the problems of insufficient spatial resolution and the like of the existing gravity gradient data inversion, introduces a gradient depth weighting function and physical property constraint based on pair/index transformation and the like on the basis of focusing inversion, combines 6 components in full tensor gradient data, and realizes three-dimensional density inversion by using a nonlinear conjugate gradient method. Meanwhile, in order to improve the visualization effect and operability of inversion, a software platform with a visualization function is developed for the proposed inversion method based on tool packages such as Python language and PyQt, matplotlib, and the invention effectively improves the distinguishing capability of adjacent geologic bodies and the longitudinal space imaging capability of a target body; the software platform and the development method have the advantages of easy use, practicability and the like.
Description
Technical Field
The invention relates to the technical field of geophysical inversion, in particular to a gravity gradient data joint inversion method.
Background
The use of gravity survey data to implement three-dimensional inversion enables the acquisition of density distributions in subsurface space, a common interpretation method in geological exploration. Compared with the gravity anomaly data, the gravity gradient data has higher signal-to-noise ratio, particularly the full tensor gradient data contains more geological information, and the use of a plurality of gravity gradient data for joint inversion is beneficial to improving the defect of poor longitudinal spatial resolution of the current potential field data and is beneficial to further improving the distinguishing capability of adjacent geological bodies.
However, since inversion has multiple solutions, constraints or a priori information need to be introduced in the actual computation to improve the uniqueness of the solution. The method described in document [1] is to provide a range of physical properties, and if a certain result is not within the range, the upper limit or the lower limit of the range is forcibly given (wherein document [1] is Li Y.,. 2001,3-D Inversion of Gravity Gradiometer data.2001 SEG Annual Mening. Society of expression Geophysis.). But this approach breaks the conjugation in the known search process, i.e., each iteration forces a solution after the computation. Meanwhile, the gravity gradient data has the property of decaying along with the distance, so that the inversion result may have lower longitudinal resolution and other problems. Some scholars introduced depth weighted functions in literature [2-4] (where literature [2] is Li Y, oldenburg D W.3-D inversion of magnetic data [ J ]. Geophysics,1996,61 (2): 394-408.; literature [3] is Li Y, oldenburg D W.3-D inversion of gravity data [ J ]. Geophysics,1998,63 (1): 109-119.; literature [4] is Portniaguine O, zhdananov M.3-D magnetic inversion with data compression and image focusing [ J ]. Geophysics,2002,67 (5): 1532-1541.; these classical methods provide references for subsequent studies, but still suffer from poor bottom imaging of deep targets (mainly from excessive bottom depth in inversion results, unfocused density distribution of the geologic volume). Therefore, it is necessary to employ an efficient depth weighting function using a constraint method that preserves conjugation.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a gravity gradient data joint inversion method, which comprises the following steps:
step 1: constructing an objective function phi (m) of three-dimensional physical inversion according to the acquired gravity gradient data;
in phi d 、φ m Respectively representing a data non-fitting function and a model objective function; lambda is a regularization parameter; g represents a sensitivity matrix, d represents gravity gradient data; m represents the inverted model parameter vector, m j Representing in vector mThe j-th model parameter, M, represents the length of vector M; sigma represents a positive number that avoids generating singular values;
step 2: introducing a constraint range of model parameters through a formula (2) to construct a model parameter m j Conversion variable x of (2) j Let j=1, 2, …, M, obtain the conversion variable corresponding to each model parameter using equation (3), and represent all conversion variables with conversion vector x;
wherein a and b respectively represent model parameters m j Lower limit and upper limit of (2);
step 3: calculating a depth weighting function f (z);
wherein ω represents a constant, r represents a scale factor, dz and z represent the depth of a cube into which the subsurface is divided and the maximum depth of the inversion region, z c Representing depth coefficients based on a priori geological information;
step 4: and solving an objective function phi (m) by a nonlinear conjugate gradient method by combining the depth weighting function f (z) to obtain the optimal inversion model parameters.
The step 4 comprises the following steps:
step 4.1: setting the maximum iteration number k max Initializing a model parameter vector, and calculating to obtain an initial conversion vector x through a formula (3) 0 Calculating an initial gradient g using a depth weighting function f (z) 0 ；
Wherein lambda is 0 Represents the initial regularization parameters, lambda 0 ＝0；
Step 4.2: let λ at iteration 1 k=1 1 ＝λ 0 Acquiring regularization parameters of the 1 st iteration, and initializing a search direction vector p 0 ＝g 0 ；
Step 4.3: calculation of search step alpha at the kth iteration using Armijo search method k Where k=1, 2,.. max ；
Step 4.4: using formula x k ＝x k-1 +α k p k Calculating the conversion vector x at the kth iteration k ；
Step 4.5: will transform vector x k Each element x of (a) j Calculating by using a formula (2) to obtain a corresponding model parameter m j Using vector m for all model parameters k Representation, using formula d k ＝Gm k Calculating a fitting value d at the kth iteration k ；
Step 4.6: according to d k D calculating the mean square error rms at the kth iteration k ；
Step 4.7: judging rms k If not, stopping iteration; if not, entering the next iteration;
step 4.8: at iteration 2, k=2, the formula Φ is first used d ＝||Gm-d|| 2 Calculating phi d Using formulasCalculating phi m Using the formula lambda 2 ＝φ d /φ m Calculating regularization parameters of the 2 nd iteration;
when k is more than or equal to 3, the formula lambda is directly utilized k ＝λ k-1 Update regularization parameter lambda for the kth iteration k ；
Step 4.9: updating gradient g using equation (6) k ；
Step 4.10: calculating the intermediate variable beta by using the formula (7) k ；
Step 4.11: updating the search direction p using equation (8) k ；
p k ＝g k +β k p k-1 (8)
Step 4.12: let k=1, 2,.. max When k is<k max Repeating the steps 4.3 to 4.11 for iterative calculation; mean square error rms at the kth iteration k Stopping iteration and outputting a vector m when epsilon is less than or equal to epsilon k Vector m k All elements in the model are the optimal inversion model parameters.
The beneficial effects of the invention are as follows:
the invention provides a gravity gradient data joint inversion method, which effectively utilizes priori geological information such as physical properties, depth ranges and the like, and further improves the result precision compared with the existing method; the combination of the multi-component gravity gradient data improves the resolution of three-dimensional density imaging of the underground space, better distinguishes adjacent geologic bodies and determines the top and bottom burial depths of the target body.
Drawings
FIG. 1 is a flow chart of a method of gravity gradient data joint inversion in the present invention;
FIG. 2 is a software development flow chart of the gravity gradient data joint inversion method of the present invention;
FIG. 3 is a diagram of a theoretical model location in the present invention;
FIG. 4 is a graph of inversion results in the present invention;
FIG. 5 is a graph of measured data of the venturi region of the present invention, wherein the graph (a) shows gravity gradient data V xx Component, graph (b) represents gravity gradient data V xy Component, graph (c) represents gravity gradient data V xz Component, graph (d) represents gravity gradient data V yy Component, graph (e) represents gravity gradient data V yz Component, graph (f) represents gravity gradient data V zz A component;
fig. 6 is a graph of inversion results of measured data of a venturi region according to the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings and examples of specific embodiments.
As shown in FIG. 1, the method for joint inversion of gravity gradient data can accurately calculate three-dimensional density distribution and effectively improve the spatial resolution of the result, and comprises the following steps:
step 1: constructing an objective function phi (m) of three-dimensional physical inversion according to the acquired gravity gradient data, wherein the gravity gradient data can be obtained through simulation by constructing a theoretical model or obtained by utilizing a measuring instrument;
in phi d 、φ m Respectively representing a data non-fitting function and a model objective function; lambda is a regularization parameter; g represents a sensitivity matrix, d represents gravity gradient data; m represents the inverted model parameter vector, m j Representing the j-th model parameter in the vector M, M representing the length of the vector M; sigma represents a positive number that avoids generating singular values;
in the present embodiment, the acquired gravity gradient data is first subjected to conventional gridding processing, and V in the full tensor gravity gradient data is selected xx 、V xy 、V xz 、V yy 、V yz 、V zz The six components are jointly inverted.
Step 2: introducing a constraint range of model parameters through a formula (2) to construct a model parameter m j Conversion variable x of (2) j Let j=1, 2, …, M, obtain the conversion variable corresponding to each model parameter using equation (3), and represent all conversion variables with conversion vector x;
wherein a and b respectively represent model parameters m j Lower limit and upper limit of (2);
step 3: calculating a depth weighting function f (z);
where ω represents an empirical constant, r represents a proportionality coefficient, dz and z represent the depth of the cube into which the subsurface is partitioned and the maximum depth of the inversion region, z c Representing depth coefficients based on a priori geological information;
step 4: solving an objective function phi (m) by a nonlinear conjugate gradient method in combination with a depth weighting function f (z) to obtain optimal inversion model parameters, wherein the method comprises the following steps:
step 4.1: setting the maximum iteration number k max Initializing a model parameter vector, and calculating to obtain an initial conversion vector x through a formula (3) 0 Calculating an initial gradient g using a depth weighting function f (z) 0 ；
Wherein lambda is 0 Represents the initial regularization parameters, lambda 0 ＝0；
Step 4.2: let λ at iteration 1 k=1 1 ＝λ 0 Acquiring regularization parameters of the 1 st iteration, and initializing a search direction vector p 0 ＝g 0 ；
Step 4.3: calculation of search step alpha at the kth iteration using Armijo search method k Where k=1, 2,.. max ；
Step 4.4: using formula x k ＝x k-1 +α k p k Calculating the conversion vector x at the kth iteration k ；
Step 4.5: will transform vector x k Each element x of (a) j Calculating by using a formula (2) to obtain a corresponding model parameter m j Using vector m for all model parameters k Representation, using formula d k ＝Gm k Calculating a fitting value d at the kth iteration k ；
Step 4.6: according to d k D calculating the mean square error rms at the kth iteration k ；
Step 4.7: judging rms k If not, stopping iteration; if not, entering the next iteration;
step 4.8: at iteration 2, k=2, the formula Φ is first used d ＝||Gm-d|| 2 Calculating phi d Using formulasCalculating phi m Using the formula lambda 2 ＝φ d /φ m Calculating regularization parameters of the 2 nd iteration;
when k is more than or equal to 3, the formula lambda is directly utilized k ＝λ k-1 Update regularization parameter lambda for the kth iteration k ；
Step 4.9: updating gradient g using equation (6) k ；
Step 4.10: calculating the intermediate variable beta by using the formula (7) k ；
Step 4.11: updating the search direction p using equation (8) k ；
p k ＝g k +β k p k-1 (8)
Step 4.12: let k=1, 2,.. max When k is<k max Repeating the steps 4.3 to 4.11 for iterative calculation; mean square error rms at the kth iteration k Stopping iteration and outputting a vector m when epsilon is less than or equal to epsilon k Vector m k All elements in the model are the optimal inversion model parameters; when k is greater than or equal to k max When this occurs, the operation is stopped.
To improve the practicability of the application, a software development method based on a gravity gradient data joint inversion method is provided below, as shown in fig. 2, and includes the following steps:
1) Building a development environment on a Windows system by utilizing tools such as Eric, microsoft Visual Studio and the like by utilizing tool packages such as Python language, pyQt, matplotlib and the like;
2) Aiming at the characteristics of data formats of input data and output results, a PyQt, matplotlib is utilized to design a graphical interface, data management, drawing and other modules of a software platform;
3) Inversion code is written in the C language, and dll files are generated by Microsoft Visual Studio, wherein the pseudo code is programmed as follows:
wherein k is max Is the maximum number of iterations.
4) The "init" function is customized, all variables (input, output, intermediate variables and the like) involved in calculation are added into the function, and the function is used for transferring parameters; custom class "class CustomClass", algorithm function in incoming dll;
5) The input parameter design module (comprising functions of calculation, drawing, data storage and the like) and the graphical interface thereof are designed aiming at inversion; connecting the graphical interface with the function through a signal slot mechanism in PyQt;
6) The main function is called with a user-defined init function and a class class CustomClass to realize an inversion function;
7) After compiling and running, testing the software.
By using the software written above, the spatial imaging capability and noise immunity of the inversion method are tested by adopting a double cube combination model containing 5% Gaussian noise, the position and inversion result of the theoretical model are respectively shown in fig. 3 and 4, and inversion parameters are set as follows: lambda (lambda) 0 =0, density constraint value a= -0.1, b= 0.5, ω=0.001, r=20, z in the depth weighting function c =325, dz=1000. Comparing the inversion result with the actual position of the model, the inversion method provided by the invention well distinguishes adjacent cubes and calculates the top and bottom depths of the two cubes, and the numerical range of the result is matched with the model, so that the effectiveness and noise resistance of the method are proved.
The practical applicability and feasibility of the method and software for testing and inverting the measured data in the Wen dune salt dome area in the United states are shown in the graphs (a) to (f) in FIG. 5 (E (early) in units of gravity gradient data), and the inversion results are shown in FIG. 6 respectively. The inversion parameters were set as follows: lambda (lambda) 0 =0, density constraint value a= -0.1, b= 0.5, ω=0.001, r=20, z in the depth weighting function c =225, dz=1000. The result shows that the density distribution calculated by the inversion method is similar to the existing geological data and other research results, but the effect on underground cover rock imaging is clearer, the developed software imaging effect is good, and the practicability and feasibility of the method are proved.
Claims (2)
1. A method of gravity gradient data joint inversion comprising the steps of:
step 1: constructing an objective function phi (m) of three-dimensional physical inversion according to the acquired gravity gradient data;
in phi d 、φ m Respectively representing a data non-fitting function and a model objective function; lambda is a regularization parameter; g tableSensitivity matrix, d represents gravity gradient data; m represents the inverted model parameter vector, m j Representing the j-th model parameter in the vector M, M representing the length of the vector M; sigma represents a positive number that avoids generating singular values;
step 2: introducing a constraint range of model parameters through a formula (2) to construct a model parameter m j Conversion variable x of (2) j Let j=1, 2, …, M, obtain the conversion variable corresponding to each model parameter using equation (3), and represent all conversion variables with conversion vector x;
wherein a and b respectively represent model parameters m j Lower limit and upper limit of (2);
step 3: calculating a depth weighting function f (z);
wherein ω represents a constant, r represents a scale factor, dz and z represent the depth of a cube into which the subsurface is divided and the maximum depth of the inversion region, z c Representing depth coefficients based on a priori geological information;
step 4: and solving an objective function phi (m) by a nonlinear conjugate gradient method by combining the depth weighting function f (z) to obtain the optimal inversion model parameters.
2. A method of gravity gradient data joint inversion according to claim 1, wherein said step 4 comprises:
step 4.1: setting the maximum iteration number k max Initializing a model parameter vector, and calculating by a formula (3)Initial conversion vector x 0 Calculating an initial gradient g using a depth weighting function f (z) 0 ；
Wherein lambda is 0 Represents the initial regularization parameters, lambda 0 ＝0；
Step 4.2: let λ at iteration 1 k=1 1 ＝λ 0 Acquiring regularization parameters of the 1 st iteration, and initializing a search direction vector p 0 ＝g 0 ；
Step 4.3: calculation of search step alpha at the kth iteration using Armijo search method k Where k=1, 2,.. max ；
Step 4.4: using formula x k ＝x k-1 +α k p k Calculating the conversion vector x at the kth iteration k ；
Step 4.5: will transform vector x k Each element x of (a) j Calculating by using a formula (2) to obtain a corresponding model parameter m j Using vector m for all model parameters k Representation, using formula d k ＝Gm k Calculating a fitting value d at the kth iteration k ；
Step 4.6: according to d k D calculating the mean square error rms at the kth iteration k ；
Step 4.7: judging rms k If not, stopping iteration; if not, entering the next iteration;
step 4.8: at iteration 2, k=2, the formula Φ is first used d ＝||Gm-d|| 2 Calculating phi d Using formulasCalculating phi m Using the formula lambda 2 ＝φ d /φ m Calculating regularization parameters of the 2 nd iteration;
when k is more than or equal to 3, the formula lambda is directly utilized k ＝λ k-1 Update regularization parameter lambda for the kth iteration k ；
Step 4.9: updating gradient g using equation (6) k ；
Step 4.10: calculating the intermediate variable beta by using the formula (7) k ；
Step 4.11: updating the search direction p using equation (8) k ；
p k ＝g k +β k p k-1 (8)
Step 4.12: let k=1, 2,.. max When k is<k max Repeating the steps 4.3 to 4.11 for iterative calculation; mean square error rms at the kth iteration k Stopping iteration and outputting a vector m when epsilon is less than or equal to epsilon k Vector m k All elements in the model are the optimal inversion model parameters.
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| CN110398782A (en) * | 2019-07-17 | 2019-11-01 | 广州海洋地质调查局 | A kind of gravimetric data and gravity gradient data combine regularization inversion method |
| CN110501751A (en) * | 2019-08-23 | 2019-11-26 | 东北大学 | It is a kind of to be combined and depth weighted dependent imaging method based on multi -components gradient data |
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| CN110398782A (en) * | 2019-07-17 | 2019-11-01 | 广州海洋地质调查局 | A kind of gravimetric data and gravity gradient data combine regularization inversion method |
| CN110501751A (en) * | 2019-08-23 | 2019-11-26 | 东北大学 | It is a kind of to be combined and depth weighted dependent imaging method based on multi -components gradient data |
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