scholarly journals Slowness vector estimation over large-aperture sparse arrays with the Continuous Wavelet Transform (CWT): application to Ocean Bottom Seismometers

2020 ◽  
Vol 223 (3) ◽  
pp. 1919-1934
Author(s):  
Roberto Cabieces ◽  
Frank Krüger ◽  
Araceli Garcia-Yeguas ◽  
Antonio Villaseñor ◽  
Elisa Buforn ◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Direct Search ◽  
Ocean Bottom ◽  
Continuous Wavelet ◽  
Search Methods ◽  
Direct Search Methods ◽  
Large Aperture ◽  
Slowness Vector ◽  
Vector Estimation

SUMMARY This work presents a new methodology designed to estimate the slowness vector in large-aperture sparse Ocean Bottom Seismometer (OBS) arrays. The Continuous Wavelet Transform (CWT) is used to convert the original incoherent traces that span a large array, into coherent impulse functions adapted to the array aperture. Subsequently, these impulse functions are beamformed in the frequency domain to estimate the slowness vector. We compare the performance of this new method with that of an alternative solution, based on the Short-/Long-Term Average algorithm and with a method based on the trace envelope, with the ability to derive a very fast detection and slowness vector estimation of seismic signal arrivals. The new array methodology has been applied to data from an OBS deployment with an aperture of 80 km and an interstation distance of about 40 km, in the vicinity of Cape Saint Vincent (SW Iberia). A set of 17 regional earthquakes with magnitudes 2 < mbLg < 5, has been selected to test the capabilities of detecting and locating regional seismic events with the Cape Saint Vincent OBS Array. We have found that there is a good agreement between the epicentral locations obtained previously by direct search methods and those calculated using the slowness vector estimations resulting from application of the CWT technique. We show that the proposed CWT method can detect seismic signals and estimate the slowness vector from regional earthquakes with high accuracy and robustness under low signal-to-noise ratio conditions. Differences in epicentral distances applying direct search methods and the CWT technique are between 1 and 21 km with an average value of 12 km. The backazimuth differences range from 1° to 7° with an average of 1.5° for the Pwave and ranging from 1° to 10° with an average of 3° for the Swave.

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).

scholarly journals Automatic ECG Classification Using Continuous Wavelet Transform and Convolutional Neural Network

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 119
Author(s):  
Tao Wang ◽  
Changhua Lu ◽  
Yining Sun ◽  
Mei Yang ◽  
Chun Liu ◽  
...  
Keyword(s):  
Neural Network ◽  
Wavelet Transform ◽  
Convolutional Neural Network ◽  
Continuous Wavelet Transform ◽  
Continuous Wavelet ◽  
Time Frequency ◽  
Ecg Signals ◽  
Rr Interval ◽  
Frequency Components ◽  
Fully Connected

Early detection of arrhythmia and effective treatment can prevent deaths caused by cardiovascular disease (CVD). In clinical practice, the diagnosis is made by checking the electrocardiogram (ECG) beat-by-beat, but this is usually time-consuming and laborious. In the paper, we propose an automatic ECG classification method based on Continuous Wavelet Transform (CWT) and Convolutional Neural Network (CNN). CWT is used to decompose ECG signals to obtain different time-frequency components, and CNN is used to extract features from the 2D-scalogram composed of the above time-frequency components. Considering the surrounding R peak interval (also called RR interval) is also useful for the diagnosis of arrhythmia, four RR interval features are extracted and combined with the CNN features to input into a fully connected layer for ECG classification. By testing in the MIT-BIH arrhythmia database, our method achieves an overall performance of 70.75%, 67.47%, 68.76%, and 98.74% for positive predictive value, sensitivity, F1-score, and accuracy, respectively. Compared with existing methods, the overall F1-score of our method is increased by 4.75~16.85%. Because our method is simple and highly accurate, it can potentially be used as a clinical auxiliary diagnostic tool.

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