CN116047614A - Semi-aviation transient electromagnetic data regularized Newton inversion method based on model space constraint - Google Patents
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Abstract
The invention discloses a semi-aviation transient electromagnetic data regularization Newton inversion method based on model space constraint, which comprises the following steps: selecting N according to the distribution of the measuring lines L A measuring line, and selecting N on any one of the measuring lines P Measuring points; presetting a survey line constraint operator R according to the quantity of survey lines and survey points L And a transverse constraint operator R of any one of the measuring lines P The method comprises the steps of carrying out a first treatment on the surface of the Collecting electromagnetic data of a measurement area, constructing a one-dimensional observation data vector, and generating a data fitting item by making a difference with a forward result; constraint operator R of the survey line L And a transverse constraint operator R of any one of the measuring lines P And combining the regularized target function with the data fitting term, searching the minimum value of the regularized problem by adopting a Newton method with high convergence efficiency, obtaining an optimal solution, and obtaining an underground three-dimensional electrical structure distribution image. Through the scheme, the invention has the advantages of simple logic, accuracy, reliability and the like.
Description
Technical Field
The invention relates to the technical field of geophysical aviation electromagnetic exploration, in particular to a semi-aviation transient electromagnetic data regularization Newton inversion method based on model space constraint.
Background
The semi-aviation transient electromagnetic method adopts a fixed grounding wire source as a transmitting source, adopts an aircraft to carry a receiving coil to survey a region, and has outstanding effects in various geological survey practical applications due to high exploration efficiency and large detection depth. The half aviation transient electromagnetic receiving system has high sampling rate and high aircraft speed, and massive data can be generated in the actual detection process, and a great deal of time and energy are required to be consumed when a three-dimensional forward and backward method is adopted for imaging, so that the field work requirement can not be met. Therefore, the rapid one-dimensional inversion method is widely applied to practical work, however, the simple one-dimensional inversion method is poor in interface continuity of an inversion result and even has false abnormality of interface mutation due to the influence of data quality and noise level.
For example, chinese invention patent with patent application number "CN202210160358.5", entitled "method and apparatus for inversion of semi-aviation transient electromagnetic data based on L1L2 mixed norms", includes the following steps: collecting electromagnetic response data of the region to be tested by using a receiving device; building a stratum model of a region to be detected, and presetting iteration termination conditions; obtaining a transverse constraint weighting matrix corresponding to an L2 norm constraint term of electromagnetic response data; obtaining or updating a longitudinal constraint matrix corresponding to an L1 norm constraint term of electromagnetic response data; fitting the data to a gradient term, an L1 norm constraint term and an L2 norm constraint term to form an objective function, and developing a formula after model increment derivative is equal to zero; and inversion calculation is carried out by using an expansion formula to obtain a model increment and a model is corrected, and an inversion imaging image is obtained after the iteration termination condition is reached.
The above-described technique has the following problems:
the inversion imaging algorithm only considers the transverse continuity between each measuring point in one measuring line; when inversion imaging of a plurality of measuring lines is carried out, the situation that the resistivity value and the layer interface information between the adjacent measuring lines are discontinuous or even suddenly change can occur, and the problem that the subsequent electrical interface explanation is difficult to explain is caused.
Therefore, it is highly desirable to provide a space constraint-based semi-aviation transient electromagnetic data regularization Newton inversion method which is simple in logic, accurate and reliable.
Disclosure of Invention
Aiming at the problems, the invention aims to provide a semi-aviation transient electromagnetic data regularization Newton inversion method based on model space constraint, which adopts the following technical scheme:
the semi-aviation transient electromagnetic data regularization Newton inversion method based on model space constraint comprises the following steps:
selecting N according to the distribution of the measuring lines L A measuring line, and selecting N on any one of the measuring lines P Measuring points; the N is L and NP Are all positive integers;
presetting a survey line constraint operator R according to the quantity of survey lines and survey points L And a transverse constraint operator R of any one of the measuring lines P ；
Collecting electromagnetic data of a measurement area, constructing a one-dimensional observation data vector, and generating a data fitting item by making a difference with a forward result;
constraint operator R of the survey line L And a transverse constraint operator R of any one of the measuring lines P Combining the regularized target function with the data fitting term;
searching the minimum value of the regularization problem by adopting a Newton method with high convergence efficiency, obtaining an optimal solution, and obtaining an underground three-dimensional electrical structure distribution image.
Further, the method further comprises the following steps:
acquiring any transceiver parameter and observed data time channel number N of semi-aviation transient electromagnetic system T And arranging the observation data of all the measuring lines along the column direction to form a one-dimensional first column direction array.
Further, the method further comprises the following steps:
presetting the layer number N of the inversion initial model, the thickness of any layer and the resistivity value of any layer of model according to the detection depth;
and arranging the model parameters of any measuring point along the column direction to form a one-dimensional second column direction array.
Preferably, the expression of the observation data vector is:
wherein ,
nth of the i-th line P And measuring points.
Preferably, the line constraint operator R L The expression of (2) is:
where N represents the number of layers of the inversion initial model.
Further, the lateral constraint operator R P The construction process of (2) is as follows:
electromagnetic data of any measuring line are obtained, and a transverse smooth operator r is obtained, wherein the expression is as follows:
arranging the transverse smooth operators R of the single measuring lines along diagonal lines to form a transverse constraint operator R P The expression is:
further, the data fitting term
The expression of (2) is:
wherein T represents the transpose of the matrix; d, d obs Representing an observation data vector; w (W) d Representing a data weighting matrix; f is a positive operator, M is a model parameter vector.
Further, the line constraint operator R L And a transverse constraint operator R of any one of the measuring lines P Combining the regularized target function with the data fitting term, and carrying out iterative solution by adopting a Newton method, wherein the regularized target function comprises the following steps:
constraint operator R of the survey line L And a transverse constraint operator R of any one of the measuring lines P Merging with the data fitting term, and applying weight to form a regularization minimization problem of space constraint, wherein the expression is as follows:
wherein α represents a regularization factor; s is(s) w (M) represents a spatially constrained regularization term;
the spatial constraint regularization term s w The expression of (M) is:
wherein ,WL Representing a line constraint operator R L Is a model constrained weighting matrix; w (W) p Transverse constraint operator R representing a line P Is a model constraint of the model.
Further, searching for the minimum value of the regularization problem by adopting a Newton method with high convergence efficiency, and updating an equation by using an inversion model in the (k+1) th iteration:
wherein ,Mk+1 Representing the inversion model at the (k+1) th iteration; m is M k Representing an inversion model at the kth iteration; j (J) k Representing the jacobian matrix in the kth iteration process; t represents the transpose of the matrix; alpha k Representing a regularization factor in a kth iteration process; m is M k Representing the model parameter vector during the kth iteration.
Further, the inversion model is updated until the error of the model forward modeling data and the observed data of the observed data vector is smaller than or equal to a preset fitting difference or the iteration number reaches a preset upper limit, and an underground three-dimensional electrical structure distribution image is obtained.
Compared with the prior art, the invention has the following beneficial effects:
(1) The three-dimensional inversion method based on the one-dimensional model skillfully inverts the three-dimensional data body, and simultaneously considers the transverse line continuity of resistivity physical properties between adjacent measuring points in one measuring line and the physical property continuous characteristics of corresponding measuring points between the adjacent measuring lines.
(2) The invention controls the weights of two continuity constraints in inversion by applying different weight factors to the model line constraint operator and the line transverse constraint operator.
(3) According to the invention, the Newton method with high convergence speed is adopted for iterative solution, and regularization constraint conditions are introduced, so that the inversion process is fast and stable, continuous bottom layer interface information is obtained, and the trouble of subsequent explanation caused by unsmooth interfaces is avoided.
In conclusion, the method has the advantages of simple logic, accuracy, reliability and the like, can quickly invert to obtain the underground three-dimensional ground structure, and has high practical value and popularization value in the technical field of geophysical exploration.
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For a clearer description of the technical solutions of the embodiments of the present invention, the drawings to be used in the embodiments will be briefly described below, it being understood that the following drawings only illustrate some embodiments of the present invention and should not be considered as limiting the scope of protection, and other related drawings may be obtained according to these drawings without the need of inventive effort for a person skilled in the art.
FIG. 1 is a logic flow diagram of the present invention.
FIG. 2 is a schematic diagram of the detection in the present invention.
FIG. 3 is a schematic diagram of a survey line of a region according to the present invention.
FIG. 4 is an inversion imaging chart of measured data of a certain area in the invention.
Detailed Description
For the purposes, technical solutions and advantages of the present application, the present invention will be further described with reference to the accompanying drawings and examples, and embodiments of the present invention include, but are not limited to, the following examples. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the present disclosure, are within the scope of the present application based on the embodiments herein.
In this embodiment, the term "and/or" is merely an association relationship describing the association object, and indicates that three relationships may exist, for example, a and/or B may indicate: a exists alone, A and B exist together, and B exists alone.
The terms first and second and the like in the description and in the claims of the present embodiment are used for distinguishing between different objects and not for describing a particular sequential order of objects. For example, the first target object and the second target object, etc., are used to distinguish between different target objects, and are not used to describe a particular order of target objects.
In the embodiments of the present application, words such as "exemplary" or "such as" are used to mean serving as examples, illustrations, or descriptions. Any embodiment or design described herein as "exemplary" or "for example" should not be construed as preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary" or "such as" is intended to present related concepts in a concrete fashion.
In the description of the embodiments of the present application, unless otherwise indicated, the meaning of "a plurality" means two or more. For example, the plurality of processing units refers to two or more processing units; the plurality of systems means two or more systems.
Example 1
As shown in fig. 1 to 2, the present embodiment provides a semi-aviation transient electromagnetic data regularization newton inversion method based on model space constraint, which includes the following steps:
the first step is to select proper line according to the distribution of the line in the area, i.e. N in the area L The line is then N from left to right P And measuring points. Wherein N is L The measuring lines are distributed at equal intervals, and N on the same measuring line P The measuring points are distributed at equal intervals. First to Nth lines L The data of the strip line are arranged along the column direction. Specifically:
the whole three-dimensional data volume is arranged into a one-dimensional observation data vector expressed as:
wherein, the observed data vector contains a first column array and a second column array, and the first column array is obtained as follows: acquiring any transceiver parameter and observed data time channel number N of semi-aviation transient electromagnetic system T And arranging the observation data of all the measuring lines along the column direction to form a one-dimensional first column direction array. Likewise, the second column-wise array acquisition process is as follows: presetting the layer number N of the inversion initial model, the thickness of any layer and the resistivity value of any layer of model according to the detection depth; and arranging the model parameters of any measuring point along the column direction to form a one-dimensional second column direction array.
Secondly, designing a line constraint operator R according to the number of the selected line and the measuring points L Transverse constraint operator R P . Specifically: when the inversion model is an N-layer model, two constraint operator expressions:
for all the line data, the transverse smooth operator R of a single line is arranged along the diagonal line to form a transverse constraint operator R P ：
Thirdly, combining the two constraint conditions and the data fitting term to form a regularized objective function, and adopting a Newton method to carry out iterative solution, specifically:
combining the data fitting term and the regularization model constraint term, and simultaneously applying corresponding weights to the data fitting term and the two constraint terms to form a regularization minimization problem of spatial constraint:
where α is a regularization factor that acts to weigh the specific gravity of the data and model terms in the objective function.
In this embodiment, forward modeling is performed, and a difference is made between the one-dimensional observation data vector and the result of the forward modeling to generate a data fitting term,
fitting the term to the data: />
Where T represents the transpose of the matrix, d obs To observe the data vector, W d The data weighting matrix is formed by taking F as a positive algorithm and M as a model parameter vector;
s w (M) is a spatially constrained regularization term:
wherein ,WL Representing a line constraint operator R L Is a model constrained weighting matrix; w (W) p Transverse constraint operator R representing a line P Is a model constraint of the model.
In this embodiment, the minimum value of the regularization problem is searched by adopting the newton method with high convergence efficiency, and the inversion model update equation is as follows in the (k+1) th iteration:
wherein ,Mk+1 Representing the inversion model at the (k+1) th iteration; m is M k Representing an inversion model at the kth iteration; j (J) k Representing the jacobian matrix in the kth iteration process; t represents the transpose of the matrix; alpha k Representing a regularization factor in a kth iteration process; m is M k Representing the model parameter vector during the kth iteration.
And fourthly, updating the inversion model until the error of the model forward modeling data and the observed data of the observed data vector is smaller than or equal to a preset fitting difference or the iteration number reaches a preset upper limit, and obtaining an underground three-dimensional electrical structure distribution image.
Example 2
As shown in fig. 3 to 4, the present embodiment provides a model space constraint-based semi-aviation transient electromagnetic data regularized newton inversion method, specifically:
firstly, selecting five measuring lines in a measuring area, selecting 96 measuring point data for each measuring line, arranging all the data along the column direction to form a one-dimensional array, selecting an even half-space model for an initial model, and simultaneously inverting the five measuring lines. The inversion result is shown in fig. 4, and it can be seen from the results of five lines that the spatial distribution continuity is better in the lateral continuity of a single line and before each line.
The left side of the survey line can be seen to be distributed above the river in fig. 3, the low-resistance river layer of the left side surface layer can be seen from the inversion imaging result, and the three-dimensional trend structure of the underground river bed base can be seen from the result. The existence of a low-resistance thin layer on the upward shallow surface layer of the hillside is caused by the downward drainage of daily rainfall to the river direction, and the thickness distribution of the low-resistance thin layer is used as an important reference material for judging the subsequent landslide disasters. The actual geological survey finds that a fracture zone is distributed in the northwest direction in the area, and the resistivity results of the five measuring lines can clearly see that a ground electric section exists in the northwest direction, so that the underground fracture trend can be deduced, and the result also fully verifies the practicability of the embodiment.
The above embodiments are only preferred embodiments of the present invention and are not intended to limit the scope of the present invention, but all changes made by adopting the design principle of the present invention and performing non-creative work on the basis thereof shall fall within the scope of the present invention.
Claims (10)
1. The semi-aviation transient electromagnetic data regularization Newton inversion method based on model space constraint is characterized by comprising the following steps of:
selecting N according to the distribution of the measuring lines L A measuring line, and selecting N on any one of the measuring lines P Measuring points; the N is L and NP Are all positive integers;
presetting according to the number of the measuring lines and the measuring pointsLine constraint operator R L And a transverse constraint operator R of any one of the measuring lines P ；
Collecting electromagnetic data of a measurement area, constructing a one-dimensional observation data vector, and generating a data fitting item by making a difference with a forward result;
constraint operator R of the survey line L And a transverse constraint operator R of any one of the measuring lines P Combining the regularized target function with the data fitting term;
searching the minimum value of the regularization problem by adopting a Newton method with high convergence efficiency, obtaining an optimal solution, and obtaining an underground three-dimensional electrical structure distribution image.
2. The model space constraint based semi-aviation transient electromagnetic data regularization newton inversion method of claim 1, further comprising:
acquiring any transceiver parameter and observed data time channel number N of semi-aviation transient electromagnetic system T And arranging the observation data of all the measuring lines along the column direction to form a one-dimensional first column direction array.
3. The model space constraint based semi-aviation transient electromagnetic data regularization newton inversion method of claim 2, further comprising:
presetting the layer number N of the inversion initial model, the thickness of any layer and the resistivity value of any layer of model according to the detection depth;
and arranging the model parameters of any measuring point along the column direction to form a one-dimensional second column direction array.
4. A model space constraint based semi-aviation transient electromagnetic data regularization newton inversion method according to claim 3, wherein the observation data vector has the expression:
wherein ,
nth of the i-th line P And measuring points.
5. The model space constraint-based semi-aviation transient electromagnetic data regularized newton inversion method according to claim 1, wherein the survey line constraint operator R L The expression of (2) is:
where N represents the number of layers of the inversion initial model.
6. The model space constraint-based semi-aviation transient electromagnetic data regularization newton inversion method of claim 5, wherein the transverse constraint operator R P The construction process of (2) is as follows:
electromagnetic data of any measuring line are obtained, and a transverse smooth operator r is obtained, wherein the expression is as follows:
arranging the transverse smooth operators R of the single measuring lines along diagonal lines to form a transverse constraint operator R P The expression is:
7. half-voyage based on model space constraints as claimed in claim 6The Newton inversion method based on regularization of the space transient electromagnetic data is characterized in that the data fitting term
The expression of (2) is:
wherein T represents the transpose of the matrix; d, d obs Representing an observation data vector; w (W) d Representing a data weighting matrix; f is a positive operator, M is a model parameter vector.
8. The model space constraint-based semi-aviation transient electromagnetic data regularized newton inversion method of claim 7, wherein a survey line constraint operator R is used to calculate the model space constraint vector L And a transverse constraint operator R of any one of the measuring lines P Combining the regularized target function with the data fitting term, and carrying out iterative solution by adopting a Newton method, wherein the regularized target function comprises the following steps:
constraint operator R of the survey line L And a transverse constraint operator R of any one of the measuring lines P Merging with the data fitting term, and applying weight to form a regularization minimization problem of space constraint, wherein the expression is as follows:
wherein α represents a regularization factor; s is(s) w (M) represents a spatially constrained regularization term;
the spatial constraint regularization term s w The expression of (M) is:
wherein ,WL Representing a line constraint operator R L Weighting matrix for model constraints of (a)；W p Transverse constraint operator R representing a line P Is a model constraint of the model.
9. The model space constraint-based semi-aviation transient electromagnetic data regularization newton inversion method of claim 8, wherein searching for a minimum value of a regularization problem by adopting a newton method with high convergence efficiency, and at the (k+1) th iteration, inverting a model update equation is:
wherein ,Mk+1 Representing the inversion model at the (k+1) th iteration; m is M k Representing an inversion model at the kth iteration; j (J) k Representing the jacobian matrix in the kth iteration process; t represents the transpose of the matrix; alpha k Representing a regularization factor in a kth iteration process; m is M k Representing the model parameter vector during the kth iteration.
10. The model space constraint-based semi-aviation transient electromagnetic data regularization newton inversion method of claim 9, wherein the inversion model is updated until an error of model forward modeling data and observation data of an observation data vector is less than or equal to a preset fitting difference or the number of iterations reaches a preset upper limit, and an underground three-dimensional electrical structure distribution image is obtained.
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