CN105447314A - Ground penetrating radar (GPR) data analysis method - Google Patents

Abstract

The present invention discloses a ground penetrating radar (GPR) data analysis method. The method comprises the steps of: firstly, designing a GPR data analysis formula as shown in the description, optimizing the formula, defining an optimized formula as shown in the description, and performing mixed iteration optimization by use of an omega k calculation step and a mu k calculation step. The GPR data analysis method has the beneficial effects of being capable of decomposing GPR data efficiently, thereby improving the visualization efficiency of the data collected by the GPR in later period.

Description

A kind of method of ground penetrating radar (GPR) data decomposition

Technical field

The invention belongs to the radar exploration technique field, relate to the method for a kind of ground penetrating radar (GPR) data decomposition.

Background technology

Ground penetrating radar (GroundPenetratingRadar; GPR) be Detection Techniques with carrying out to descend definitely dielectric distribution rule without electric wave; be widely used in human survival and service for life, comprise oil mineral resources, foundation works construction, military affairs, environmental protection and diaster prevention and control etc.Spy ground data analysis and decipher are core links GPR data being converted to useful information.Specifically, being exactly the parameters such as the scattered field according to obtaining, and phase place, frequency and velocity of wave in scattering data, inferring space structure distribution and the attributive character of different medium in region.

Current GPR data analysis and decipher work still rest on the stage of strong depend-ence decipher personnel experience, the generation of its result usually because of personal view and experience difference and have very large difference.Reason is that the decipher of the uncertainty of data processing to data brings great difficulty.This difficulty is not merely because the defect of disposal route or skill cause, but observation technology itself also also exists the obstacle being difficult to go beyond.

The dynamic range of GPR system is at least 60dB, and the dynamic range of computer screen epigraph display is approximately 10 ~ 20dB, this means only have small part available information directly to show in the form of images, other additional information are not well shown and are utilized.This technology is fully excavated the attribute information accumulate in raw data and is associated, and the rule being in the past difficult to discover ground is revealed.

Complicated for ground penetrating radar GPR data earlier stage processing method at present, cause the visual efficiency of later stage ground penetrating radar image data low, precision is low.

Summary of the invention

A kind of method that the object of the present invention is to provide Coherent Noise in GPR Record to decompose, solves Coherent Noise in GPR Record and can not obtain effective resolution process, causes the visual inefficient problem of later stage ground penetrating radar image data.

The technical solution adopted in the present invention is carried out according to following steps:

Step 1:GPR data decomposition formula is expressed as:

$f\left(t\right)=\underset{k=1}{\overset{P}{\Σ}}{u}_k\left(t\right)=\underset{k=1}{\overset{P}{\Σ}}{A}_k\left(t\right)e^{{\mathrm{j\ω}}_{k}t}+\mathrm{\η};$

F (t) is GPR data or observation signal, u _kfor K the subband of f (t), A _kand ω _kbe respectively k subband amplitude and frequency, for the complex exponential of signal represents, η is noise;

Step 2: formula is optimized in definition:

$L({\mathrm{\ω}}_k,u_k,\mathrm{\ρ})=\mathrm{\α}\underset{k}{\Σ}\left|\right|\∂f_L\left({\mathrm{\ω}}_k\right)|{|}_2^2+||f-\Σu_k|{|}_2^2+\mathrm{\ρ}\left|f-\Σu_k\right|;$

F _lrepresent 1D forms data road information, ρ and α is respectively regulating parameter, represent and carry out partial differential calculating;

Step 3: adopt ω _kcalculation procedure and u _kcalculation procedure mixed iteration is optimized:

ω _kcalculation procedure: solve ω _kminimization problem, ω _kiterative formula be:

${\mathrm{\ω}}_k^{n+1}=\underset{{\mathrm{\ω}}_k}{\arg \min }L({\mathrm{\ω}}_k^n,u_k^n);$

U _kstep: solve u _kminimization problem, iterative formula is:

$u_k^{n+1}=\underset{u_k}{\arg \min }L({\mathrm{\ω}}_k^n,u_k^n).$

The invention has the beneficial effects as follows a kind of method providing GPR data efficient and decompose, the visual efficiency of later stage ground penetrating radar image data is improved.

Accompanying drawing explanation

Fig. 1 is GPR data decomposition schematic diagram;

Fig. 1 (a) is GPR data;

Sub-band division result when Fig. 1 (b) is K=1;

Sub-band division result when Fig. 1 (c) is K=2;

Sub-band division result when Fig. 1 (d) is K=3;

Sub-band division result when Fig. 1 (e) is K=4;

Sub-band division result when Fig. 1 (f) is K=5.

Embodiment

Below in conjunction with embodiment, the present invention is described in detail.

The present invention decomposes original GPR data, forms the sub-section in multiple independently arrowbands.Because GPR data have asynchronous attribute (horizontal and vertical), so we are based on VMD model, specialized designs decomposition model.

GPR data decomposition:

Step 1: GPR data decomposition is the sub-band information with different attribute feature by the target of decomposition.Be formulated as:

$f\left(t\right)=\underset{k=1}{\overset{P}{\Σ}}{u}_k\left(t\right)=\underset{k=1}{\overset{P}{\Σ}}{A}_k\left(t\right)e^{{\mathrm{j\ω}}_{k}t}+\mathrm{\η};$

F (t) is GPR data or observation signal.U _kfor K the subband of f (t), A _kand ω _kbe respectively k subband amplitude and frequency, for the complex exponential of signal represents, η is noise.

Step 2: decomposition method is based on VMD (VariationModeDecomposition) decomposition strategy.2DVMD method representation is minimization problem:

$\begin{array}{cc}\underset{u_k,{\mathrm{\ω}}_k}{\min }\left\{\underset{k}{\Σ}\right||\▿\[u_k(x,y)e^{-{\mathrm{j\ω}}_k}\]|{|}_2^2\},s.t.& \underset{k}{\Σ}{u}_k=f\end{array};$

Because 2DGPR data sequentially arrange by forms data road the section formed along horizontal survey line (transverse axis), so horizontal direction and vertical direction have obvious asynchronous nature, can not 1DVMD or 2DVMD be directly used to decompose.The improvement that we do devises a kind of hybrid optimization pattern, defines optimization formula:

$L({\mathrm{\ω}}_k,u_k,\mathrm{\ρ})=\mathrm{\α}\underset{k}{\Σ}\left|\right|\∂f_L\left({\mathrm{\ω}}_k\right)|{|}_2^2+||f-\Σu_k|{|}_2^2+\mathrm{\ρ}\left|f-\Σu_k\right|;$

Here, f _lrepresent 1D forms data road information.Above formula is that mixed structure is tieed up in 1 peacekeeping 2.ρ and α is respectively regulating parameter, represent and carry out partial differential calculating.

Step 3: adopt two step (ω _kcalculation procedure and u _kcalculation procedure) mixed iteration optimization:

ω _kcalculation procedure: solve ω _kminimization problem.ω _kiterative formula be:

${\mathrm{\ω}}_k^{n+1}=\underset{{\mathrm{\ω}}_k}{\arg \min }L({\mathrm{\ω}}_k^n,u_k^n);$

U _kstep: solve u _kminimization problem.Iterative formula is:

$u_k^{n+1}=\underset{u_k}{\arg \min }L({\mathrm{\ω}}_k^n,u_k^n).$

As shown in Figure 1, Fig. 1 (a) is GPR data; Sub-band division result when Fig. 1 (b) is K=1; Sub-band division result when Fig. 1 (c) is K=2; Sub-band division result when Fig. 1 (d) is K=3; Sub-band division result when Fig. 1 (e) is K=4; Sub-band division result when Fig. 1 (f) is K=5.Can find out, ω _konly with the directly related pass of 1D data track of vertical direction, indirect correlation between data track.And u _kaccording to 2D data section calculate, here be decomposition after result and corresponding histogram.

Claims (1)

1. a method for ground penetrating radar GPR data decomposition, is characterized in that carrying out according to following steps:

Step 1:GPR data decomposition formula is expressed as:

$f\left(t\right)=\underset{k=1}{\overset{P}{\Σ}}{u}_k\left(t\right)=\underset{k=1}{\overset{P}{\Σ}}{A}_k\left(t\right)e^{{\mathrm{j\ω}}_{k}t}+\mathrm{\η};$

F (t) is GPR data or observation signal, u _kfor K the subband of f (t), A _kand ω _kbe respectively k subband amplitude and frequency, for the complex exponential of signal represents, η is noise;

Step 2: formula is optimized in definition:

$L({\mathrm{\ω}}_k,u_k,\mathrm{\ρ})=\mathrm{\α}\underset{k}{\Σ}\left|\right|\∂f_L\left({\mathrm{\ω}}_k\right)|{|}_2^2+||f-{\mathrm{\Σu}}_k|{|}_2^2+\mathrm{\ρ}|f-{\mathrm{\Σu}}_k|;$

F _lrepresent 1D forms data road information, ρ and α is respectively regulating parameter, represent and carry out partial differential calculating;

Step 3: adopt ω _kcalculation procedure and u _kcalculation procedure mixed iteration is optimized:

ω _kcalculation procedure: solve ω _kminimization problem, ω _kiterative formula be:

${\mathrm{\ω}}_k^{n+1}=\underset{{\mathrm{\ω}}_k}{\arg \min }L({\mathrm{\ω}}_k^n,u_k^n);$

U _kstep: solve u _kminimization problem, iterative formula is:

$u_k^{n+1}=\underset{u_k}{\arg \min }L({\mathrm{\ω}}_k^n,u_k^n).$