Data processing for ground penetrating radar using the continuous wavelet transform

2016 ◽  
Vol 03 ◽  
pp. 85
Author(s):  
Tin, D.Q.C. ◽  
Dau, D.H.
Keyword(s):  
Wavelet Transform ◽  
Data Processing ◽  
Ground Penetrating Radar ◽  
Continuous Wavelet Transform ◽  
Continuous Wavelet ◽  
Ground Penetrating

scholarly journals The continuous wavelet transform in processing data of high frequency electromagnetic prospecting

2016 ◽  
Vol 19 (2) ◽  
pp. 81-93
Author(s):  
Tin Quoc Chanh Duong ◽  
Dau Hieu Duong ◽  
Van Thanh Nguyen ◽  
Thuan Van Nguyen
Keyword(s):  
Wavelet Transform ◽  
Data Processing ◽  
Continuous Wavelet Transform ◽  
High Frequency ◽  
Theoretical Models ◽  
Vital Role ◽  
Continuous Wavelet ◽  
Ground Penetrating ◽  
Non Destructive ◽  
Shallow Structure

Ground Penetrating Radar (GPR), a high frequency electromagnetic prospecting method (10 to 3000 MHz) has been rapidly developed in recent decades. With many advantages such as non-destructive, fast data collection, high precision and resolution, this method is a useful means to detect underground targets. It is currently used in the research of studying the shallow structure for examples: forecast landslide, subsidence, mapping urban underground works, traffic, construction, archaeology and other various fields of engineering, GPR data processing is becoming increasingly urgent. Wavelet transform is one of the new signal analysis tools, plays a vital role in numerous domains like image processing, graphics, data compression, gravitational, electromagnetic and geomagnetic data processing, GPR and some others. In this study, we used the continuous wavelet transform (CWT) and multiscale edge detection (MED) with the wavelet functions which were appropriately selected to determine underground targets. The accuracy of this technique was tested on some theoretical models before being applied on experimental data. The obtained results showed that this was a feasible method that could be used to detect the size and position of the anomaly objects.

scholarly journals Processing seismic ambient noise data with the continuous wavelet transform to obtain reliable empirical Green's functions

2020 ◽  
Vol 222 (2) ◽  
pp. 1224-1235
Author(s):  
Yang Yang ◽  
Chunyu Liu ◽  
Charles A Langston
Keyword(s):  
Wavelet Transform ◽  
Data Processing ◽  
Continuous Wavelet Transform ◽  
Ambient Noise ◽  
Continuous Wavelet ◽  
Denoising Method ◽  
Transient Signals ◽  
Empirical Green’S Functions ◽  
Noise Data ◽  
Correlated Signals

SUMMARY Obtaining reliable empirical Green's functions (EGFs) from ambient noise by seismic interferometry requires homogeneously distributed noise sources. However, it is difficult to attain this condition since ambient noise data usually contain highly correlated signals from earthquakes or other transient sources from human activities. Removing these transient signals is one of the most essential steps in the whole data processing flow to obtain EGFs. We propose to use a denoising method based on the continuous wavelet transform to achieve this goal. The noise level is estimated in the wavelet domain for each scale by determining the 99 per cent confidence level of the empirical probability density function of the noise wavelet coefficients. The correlated signals are then removed by an efficient soft thresholding method. The same denoising algorithm is also applied to remove the noise in the final stacked cross-correlogram. A complete data processing workflow is provided with the overall data processing procedure divided into four stages: (1) single station data preparation, (2) removal of earthquakes and other transient signals in the seismic record, (3) spectrum whitening, cross-correlation and temporal stacking and (4) remove the noise in the stacked cross-correlogram to deliver the final EGF. The whole process is automated to make it accessible for large data sets. Synthetic data constructed with a recorded earthquake and recorded ambient noise is used to test the denoising method. We then apply the new processing workflow to data recorded by the USArray Transportable Array stations near the New Madrid Seismic Zone where many seismic events and transient signals are observed. We compare the EGFs calculated from our workflow with commonly used time domain normalization method and our results show improved signal-to-noise ratios. The new workflow can deliver reliable EGFs for further studies.

scholarly journals Continuous Wavelet Transform of Schwartz Distributions in DL2′(Rn), n ≥ 1

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1106
Author(s):  
Jagdish N. Pandey
Keyword(s):  
Wavelet Transform ◽  
Function Space ◽  
Continuous Wavelet Transform ◽  
Inversion Formula ◽  
Continuous Wavelet ◽  
The Real ◽  
Schwartz Distributions ◽  
Distributional Sense ◽  
Wavelet Inversion

We define a testing function space DL2(Rn) consisting of a class of C∞ functions defined on Rn, n≥1 whose every derivtive is L2(Rn) integrable and equip it with a topology generated by a separating collection of seminorms {γk}|k|=0∞ on DL2(Rn), where |k|=0,1,2,… and γk(ϕ)=∥ϕ(k)∥2,ϕ∈DL2(Rn). We then extend the continuous wavelet transform to distributions in DL2′(Rn), n≥1 and derive the corresponding wavelet inversion formula interpreting convergence in the weak distributional sense. The kernel of our wavelet transform is defined by an element ψ(x) of DL2(Rn)∩DL1(Rn), n≥1 which, when integrated along each of the real axes X1,X2,…Xn vanishes, but none of its moments ∫Rnxmψ(x)dx is zero; here xm=x1m1x2m2⋯xnmn, dx=dx1dx2⋯dxn and m=(m1,m2,…mn) and each of m1,m2,…mn is ≥1. The set of such wavelets will be denoted by DM(Rn).

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