CN113376629A - In-well radar least square inversion method based on non-uniform input parameter grid - Google Patents
In-well radar least square inversion method based on non-uniform input parameter grid Download PDFInfo
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- CN113376629A CN113376629A CN202110522569.4A CN202110522569A CN113376629A CN 113376629 A CN113376629 A CN 113376629A CN 202110522569 A CN202110522569 A CN 202110522569A CN 113376629 A CN113376629 A CN 113376629A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
Abstract
The invention discloses a least square inversion method of a radar in a well based on a non-uniform input parameter grid, which is characterized by comprising the following steps: s1, determining the shape of the target through offset imaging; s2, carrying out initial model mesh division through a k-means algorithm; s3, inputting the initial model after the grid division into an inversion code to perform inversion calculation; and S4, iterating the model parameter updating matrix, and ending iteration to output an inversion result. According to the invention, the pulse signal is used as an unknown inversion method, the pulse signal is generated by means of forward simulation, the calculated amount is optimized by building a non-uniform model grid, the calculation speed is accelerated by a parallel calculation scheme, the target inversion of a simulation model is obtained, the calculation speed and the calculation precision are improved, and the inversion convergence condition is optimized.
Description
Technical Field
The invention relates to the technical field of inversion imaging of a radar waveform in a well, in particular to a least square inversion method of a radar in a well based on a non-uniform input parameter grid.
Background
The radar in the well places radar components such as a transmitting-receiving antenna, a transmitting source, receiving acquisition, communication and the like in the well, so that in-well detection is carried out. The radar wave transmitting frequency of the radar in the well usually works in a lower radar frequency range (10 MHz-1 GHz), and a high-frequency pulse signal is adopted, so that a target with a wide frequency band and high resolution is achieved. The radar in the well is different from the conventional ground surface ground penetrating radar, and can be placed in a drill hole due to the special structural form of the radar, so that the geological environment around the drill hole is detected, and the radar in the well has unique advantages. Firstly, compared with a ground penetrating radar on the ground surface, the radar in the well can be placed in the borehole, the detection range depends on the radial depth perpendicular to the borehole wall and also comprises the axial depth of the well, so the detection modes are different, and the detection range is larger; secondly, the radar is arranged in the well, and the underground electromagnetic environment is clean, so that the ground electromagnetic interference is small, and the underground abnormal target can be accurately reflected.
An important scheme for visually explaining radar data in a well is waveform inversion of the radar, inversion is a feasible means for realizing qualitative analysis to quantitative explanation of data, the principle is mainly based on the acquired radar data in the well, the distribution condition of dielectric parameters of a target area is determined or positioned by analyzing information such as amplitude, phase and frequency of a waveform in echo data, the radar waveform inversion is similar to radar imaging, radar signals also need to be preprocessed, but for the waveform inversion of the radar, the radar signals need to be ensured to reach a very high signal-to-noise ratio degree, and compared with imaging, the requirement on the quality of the radar signals is more strict.
In the last few years, full-wave inversion of radar data has become a new solution to solve the geophysical inversion problem due to the continuous enhancement of computing power, and the ground penetrating radar full-wave inversion is time domain full-waveform inversion based on a traditional objective function and is performed by using all information of radar waveforms in a well. By utilizing all information inversion, an inversion result with high resolution can be obtained, so that a method capable of solving the nonlinear problem of the traditional full waveform inversion is urgently needed.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a least square inversion method of a radar in a well based on a non-uniform input parameter grid, which takes a pulse signal as an unknown inversion method, generates the pulse signal by means of forward simulation, optimizes the calculated amount by building a non-uniform model grid, accelerates the calculation speed by a parallel calculation scheme, obtains the target inversion of a simulation model, and solves the problems in the background art.
In order to achieve the purpose, the invention provides the following technical scheme: the well radar least square inversion method based on the non-uniform input parameter grid comprises the following steps:
s1, determining the shape of the target through offset imaging;
s2, carrying out initial model mesh division through a k-means algorithm;
s3, inputting the initial model after the grid division into an inversion code to perform inversion calculation;
and S4, iterating the model parameter updating matrix, and ending iteration to output an inversion result.
Preferably, the step S1 of determining the target shape through offset imaging specifically includes the following steps:
s11, preprocessing the collected radar B scanning data;
and S12, performing offset imaging on the preprocessed B-scan data to obtain an initial model imaging result image array containing the target shape.
Preferably, the signal preprocessing in step S11 specifically includes removing direct waves and direct current offsets by an average filtering method, and removing out-of-band noise interference by a band-pass filtering algorithm.
Preferably, the shifting method in step S12 is F-K shifting, specifically, energy generated by each huygens secondary energy source is summarized and mapped to a power generation point, and each diffraction hyperbola is contracted to its vertex by diffraction summation.
Preferably, the step S2 of performing initial model meshing through a k-means algorithm is to perform non-uniform meshing on the imaging result image array generated in the step S12 to obtain a dielectric constant of the initial model, and the specific steps include: dividing all the observed values in the matrix after grid division into k clusters respectively, wherein each observed value belongs to a cluster which is close to the nearest average and serves as a prototype cluster, the average value of the clusters replaces a far observed value, the Euclidean distance is used as a metric, and the variance is used as a measure of cluster spread; and merging large-area uniform backgrounds, so that detailed parts are highlighted, and converting the differential grid calculation with huge quantity into non-uniform grid calculation.
Preferably, the inversion calculation in step S3 specifically includes the following steps:
s31 model initial electromagnetic parameter m0For the initial model dielectric constant matrix, Δ m is the model electromagnetic parameter variation, and the objective function is approximated as:
converting the problem of solving the inverse objective function into a solution
Inverse problem of function, according to the optimization principle, the objective is to
The function is extremely small, the partial derivative of the function on the electromagnetic parameter change quantity of the model is 0, and an inversion equation set is simplified as follows: J.JTΔm＝JTb; j is E (m) at m0Jacobian matrix of (i) e (m) for model matrix m0B is a partial derivative matrix of
JTRepresents a transpose of a matrix;
step S32, solving the Jacobian matrix J through a differential disturbance method, wherein the formula is as follows:
step S33, JacobianMatrix J.JTAdding damping coefficient to improve matrix pathological characteristics to make J.JTDenoted A, damping coefficient i.e
Set of inversion equations
Is Δ m ═ (a + λ I)-1k；
Preferably, in step S4, the model parameters are updated into a matrix, and the parameters are updated as follows: m isk＝mk-1+ Δ m is input to step S3 as new m0Performing iteration until the iteration end condition
When etak<And when the time is 0.01, iteration is stopped to output inversion results.
Preferably, the parallel computation matrix method used in the iteration of step S4 is a multi-thread computation method.
The invention has the beneficial effects that:
1) the method is suitable for inversion of the radar data in the well, electromagnetic parameters of the stratum of the radar data in the well can be calculated, through imaging and grid division, an inversion input parameter matrix is a non-uniform grid, the method is better for a model with small targets and sparse matrix characteristics, the calculation speed and the calculation accuracy can be effectively improved, the inversion equation set is corrected by using the damping factor, the ill-conditioned characteristics of the Jacobian matrix are optimized, and the inversion convergence condition is optimized.
2) The method for inverting the full wave of the radar in the well is based on a least square method, an inversion initial model is constructed by combining an imaging algorithm, an inversion equation set is calculated and optimized through a singular value decomposition method, a grid is segmented by using a classical k-means algorithm, and finally a whole algorithm framework of full wave inversion is formed.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a schematic diagram of the imaging effect of the present invention, in which FIG. 2(a) is a graph of the result after preprocessing of B-scan data signals, and FIG. 2(B) is a graph of the result of offset imaging;
FIG. 3 is a schematic diagram of a model and a meshing result of the present invention, FIG. 3(a) is a schematic diagram of a simulation model, and FIG. 3(b) is a schematic diagram of a non-uniform meshing result after k-means clustering;
FIG. 4 is a schematic diagram of the inversion results of the present invention; fig. 4(a) is a two-dimensional schematic diagram of a model result, and fig. 4(b) is a schematic diagram of a model inversion result.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Examples
Referring to fig. 1-4, the present invention provides a technical solution: a ground penetrating radar least square inversion method based on non-uniform input parameter grids comprises an initial model building part and an inversion part. The initial model building part builds an initial model by analyzing echo data from a radar in a well to the model. The inversion part is to take the initial model as an iteration entrance of well radar inversion, perform inversion iteration on the well radar model, and finally generate an inversion result containing an electromagnetic parameter matrix of a target, and the flow of the method disclosed by the invention is shown in figure 1 and comprises the following steps:
step 1: determining target shape by offset imaging
(1) The acquired radar B-scan data is subjected to signal preprocessing to remove interference such as direct waves, direct current offset, noise and the like, as shown in fig. 2 (a).
(2) And (3) performing offset imaging on the preprocessed B-scan data to obtain an initial model imaging result image array containing the target shape, wherein the offset imaging result is shown in fig. 2 (B). The migration method is F-K migration, i.e. summarizing the energy generated by each Wheatstone secondary energy source, mapping it to the point of power generation, and contracting each diffraction hyperbola to its vertex by diffraction summation.
Step 2: inverse initial model meshing by k-means algorithm
Carrying out non-uniform grid division on the imaging result image array generated in the step 1(2) to obtain the dielectric constant of the initial model, and specifically comprising the following steps: dividing all the observed values in the matrix after grid division into k clusters respectively, wherein each observed value belongs to a cluster which is close to the nearest average and serves as a prototype cluster, the average value of the clusters replaces a far observed value, the Euclidean distance is used as a metric, and the variance is used as a measure of cluster spread; merging large-area uniform backgrounds, so as to highlight detail parts, and converting differential grid calculation with huge number into non-uniform grid calculation, as shown in fig. 3, wherein fig. 3(a) is a model schematic diagram, and fig. 3(b) is a non-uniform grid division result after k-means clustering.
And step 3: inputting the initial model after the grid division into an inversion code to perform inversion calculation
1) Model initial electromagnetic parameter m0The initial model dielectric constant matrix comprises dielectric constant, conductivity, permeability and the like, the delta m is the model electromagnetic parameter change quantity, namely iteration step length, and the objective function is approximated as:
converting the problem of solving the inverse objective function into a solution
Inverse problem of function, according to the optimization principle, the objective is to
The function is extremely small, the partial derivative of the function on the electromagnetic parameter change quantity of the model is 0, and an inversion equation set is simplified as follows: J.JTΔm＝JTb; j is E (m) at m0The jacobian matrix of (a) is,i.e. E (m) for the model matrix m0B is a partial derivative matrix of
JTRepresenting the transpose of the matrix.
2) Solving the jacobian matrix J by a differential disturbance method, wherein the formula is as follows:
3) to Jacobian matrix J.JTAdding damping coefficient to improve matrix pathological characteristics to make J.JTDenoted A, damping coefficient i.e
Set of inversion equations
Is Δ m ═ (a + λ I)- 1k。
And 4, step 4: and iterating the model parameter updating matrix, and ending iteration to output an inversion result.
Updating the model parameters into a matrix, wherein the parameters are updated as follows: m isk＝mk-1+ Δ m, input to step 3 as new m0Performing iteration until the iteration end condition
When etak<And when the time is 0.01, iteration is stopped to output inversion results. The calculation of the jacobian is designed to be a large amount of parallel calculation, the jacobian calculation is concurrently executed by using a thread pool, the method is a multi-thread calculation method, the inversion result is shown in fig. 4, fig. 4(a) is a model two-dimensional schematic diagram, the target is a white part, the dielectric constant is about 1, the other parts are stratum dielectric constants are about 7, fig. 4(b) is a model at a position where trace number is extracted 15, a dotted line is an initial model, a dotted line is a real model, and a solid line is an inversion calculation result.
In the examples, simulationsThe principle is FDTD, and the simulation software is GprMax. The simulation model is shown in FIG. 3(a), in which the relative permittivity of the stratum is εr7, the conductivity is 1e-4S/m, the target model establishes a two-dimensional FDTD simulation model for a triangular target, and the target filler is air (the dielectric constant is epsilon)r1, the conductivity sigma is 1e-4S/m), the distance from the borehole is 1.3m, the distance between a transmitting antenna and a receiving antenna is 0.2m, the transmitting waveform is a 180MHz zero-order Gaussian pulse signal, the time window length is 6e-8S, and the sampling rate is 8.5 GHz.
As a result of imaging, as shown in fig. 2(b), the position, size, etc. of the target model can be found intuitively, and as a result of mesh division, as shown in fig. 3(b), it can be seen that the target model is divided into non-uniform meshes, and model optimization is performed as an initial model and an inversion entry.
The two-dimensional graph of the model result obtained through the inversion calculation is shown in fig. 4(a), and through the inversion calculation, the stratum dielectric constant can be effectively calculated to be about 7, the node constant of the target model is about 1, and the node constant is close to that of the actual model. The case of the dielectric constant subsection of line 15 of the model is truncated as shown in FIG. 4 (b). Wherein, the dot-dash line is an initial model, the relative dielectric constant of the target area is between 2 and 17, and the dielectric constant of the stratum part is 3; the dotted line is a real model, and the inversion calculation result is a solid line.
The method for inverting the full wave of the radar in the well is based on a least square method, an inversion initial model is constructed by combining an imaging algorithm, an inversion equation set is calculated and optimized through a singular value decomposition method, a grid is segmented by using a classical k-means algorithm, and finally a whole algorithm framework of full wave inversion is formed. The method is suitable for inversion of the radar data in the well, electromagnetic parameters of the stratum of the radar data in the well can be calculated, through imaging and grid division, an inversion input parameter matrix is a non-uniform grid, the method is better for a model with small targets and sparse matrix characteristics, the calculation speed and the calculation accuracy can be effectively improved, the inversion equation set is corrected by using the damping factor, the ill-conditioned characteristics of the Jacobian matrix are optimized, and the inversion convergence condition is optimized.
Although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that various changes in the embodiments and/or modifications of the invention can be made, and equivalents and modifications of some features of the invention can be made without departing from the spirit and scope of the invention.
Claims (8)
1. The well radar least square inversion method based on the non-uniform input parameter grid is characterized by comprising the following steps of:
s1, determining the shape of the target through offset imaging;
s2, carrying out initial model mesh division through a k-means algorithm;
s3, inputting the initial model after the grid division into an inversion code to perform inversion calculation;
and S4, iterating the model parameter updating matrix, and ending iteration to output an inversion result.
2. The method of claim 1 for in-well radar least squares inversion based on non-uniform input parameter grids, comprising: the step S1 of determining the target shape through offset imaging specifically includes the steps of:
s11, preprocessing the collected radar B scanning data;
and S12, performing offset imaging on the preprocessed B-scan data to obtain an initial model imaging result image array containing the target shape.
3. The method of claim 2 for in-well radar least squares inversion based on non-uniform input parameter grids, wherein: the signal preprocessing in step S11 specifically includes removing direct waves and direct current offsets by an average filtering method, and removing out-of-band noise interference by a band-pass filtering algorithm.
4. The method of claim 2 for in-well radar least squares inversion based on non-uniform input parameter grids, wherein: the shifting method in step S12 is F-K shifting, specifically, energy generated by each huygens secondary energy source is summarized and mapped to a power generation point, and each diffraction hyperbola is contracted to its vertex by diffraction summation.
5. The method of claim 1 for in-well radar least squares inversion based on non-uniform input parameter grids, comprising: the step S2 of performing initial model meshing through a k-means algorithm refers to performing non-uniform meshing on the imaging result image array generated in the step S12 to obtain a dielectric constant of the initial model, and the specific steps include: dividing all the observed values in the matrix after grid division into k clusters respectively, wherein each observed value belongs to a cluster which is close to the nearest average and serves as a prototype cluster, the average value of the clusters replaces a far observed value, the Euclidean distance is used as a metric, and the variance is used as a measure of cluster spread; and merging large-area uniform backgrounds, so that detailed parts are highlighted, and converting the differential grid calculation with huge quantity into non-uniform grid calculation.
6. The method of claim 1 for in-well radar least squares inversion based on non-uniform input parameter grids, comprising: the inversion calculation in step S3 specifically includes the following steps:
s31 model initial electromagnetic parameter m0For the initial model dielectric constant matrix, Δ m is the model electromagnetic parameter variation, and the objective function is approximated as:
converting the problem of solving the inverse objective function into a solution
Inverse problem of function, according to the optimization principle, the objective is to
The function is extremely small, the partial derivative of the function on the electromagnetic parameter change quantity of the model is 0, and an inversion equation set is simplified as follows: J.JTΔm＝JTb; j is E (m) at m0Jacobian matrix of (i) e (m) for model matrix m0B is a partial derivative matrix of
JTRepresents a transpose of a matrix;
step S32, solving the Jacobian matrix J through a differential disturbance method, wherein the formula is as follows:
step S33, Jacobian matrix J.JTAdding damping coefficient to improve matrix pathological characteristics to make J.JTDenoted A, damping coefficient i.e
Set of inversion equations
Is Δ m ═ (a + λ I)-1k。
7. The method of claim 1 for in-well radar least squares inversion based on non-uniform input parameter grids, comprising: the step S4 updates the model parameters into an update matrix, where the parameters are: m isk＝mk-1+ Δ m is input to step S3 as new m0Performing iteration until the iteration end condition
When etak<And when the time is 0.01, iteration is stopped to output inversion results.
8. The method of claim 1 for in-well radar least squares inversion based on non-uniform input parameter grids, comprising: the parallel computation matrix method used in the iteration in step S4 is a multi-thread computation method.
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