scholarly journals Wavelet transform mapping of effective elastic thickness and plate loading: Validation using synthetic data and application to the study of southern African tectonics

2003 ◽  
Vol 108 (B12) ◽  
Author(s):  
C. P. Stark
Keyword(s):  
Wavelet Transform ◽  
Synthetic Data ◽  
Effective Elastic Thickness ◽  
Plate Loading

scholarly journals Fractional integration of seismic wavelets in anelastic media to recover multiscale properties of impedance discontinuities

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. V61-V71 ◽  
Author(s):  
Stephan Ker ◽  
Yves Le Gonidec
Keyword(s):  
Wavelet Transform ◽  
Fractional Integration ◽  
Synthetic Data ◽  
Seismic Source ◽  
Seismic Attributes ◽  
Data Set ◽  
Shaping Filter ◽  
Gaussian Derivative ◽  
Intrinsic Attenuation ◽  
Seismic Wavelet

Multiscale seismic attributes based on wavelet transform properties have recently been introduced and successfully applied to identify the geometry of a complex seismic reflector in an elastic medium. We extend this quantitative approach to anelastic media where intrinsic attenuation modifies the seismic attributes and thus requires a specific processing to retrieve them properly. The method assumes an attenuation linearly dependent with the seismic wave frequency and a seismic source wavelet approximated with a Gaussian derivative function (GDF). We highlight a quasi-conservation of the Gaussian character of the wavelet during its propagation. We found that this shape can be accurately modeled by a GDF characterized by a fractional integration and a frequency shift of the seismic source, and we establish the relationship between these wavelet parameters and [Formula: see text]. Based on this seismic wavelet modeling, we design a time-varying shaping filter that enables making constant the shape of the wavelet allowing retrieval of the wavelet transform properties. Introduced with a homogeneous step-like reflector, the method is first applied on a thin-bed reflector and then on a more realistic synthetic data set based on an in situ acoustic impedance sequence and a high-resolution seismic source. The results clearly highlight the efficiency of the method in accurately restoring the multiscale seismic attributes of complex seismic reflectors in anelastic media by the use of broadband seismic sources.

Application of wavelet analysis to the impact harshness of a vehicle

2000 ◽  
Vol 214 (11) ◽  
pp. 1331-1338 ◽  
Author(s):  
S K Lee ◽  
P R White
Keyword(s):  
Wavelet Transform ◽  
Ride Comfort ◽  
Synthetic Data ◽  
Objective Measure ◽  
Vibration Modes ◽  
Continuous Wavelet ◽  
Signal Parameters ◽  
Subjective Measurements ◽  
The Impact ◽  
Initial Peak

The impact harshness of cars is an important factor in ride comfort. Traditionally, impact harshness is evaluated via subjective measurements based on the experience of test drivers. Objective evaluations are more efficient and reproducible than subjective measurements. Thus, this paper develops an objective measure based on a few signal parameters, specifically the initial peak values and damping ratios of the major vibration modes. A method based on the continuous wavelet transform is presented for the measurement of damping ratios. The performance of the method for estimating damping ratios is illustrated by the use of synthetic data, while performance of the objective measure is assessed on the basis of a series of trials on real vehicles.

scholarly journals Solar hard X-ray imaging by means of compressed sensing and finite isotropic wavelet transform

2018 ◽  
Vol 615 ◽  
pp. A59 ◽  
Author(s):  
M. A. Duval-Poo ◽  
M. Piana ◽  
A. M. Massone
Keyword(s):  
Wavelet Transform ◽  
Compressed Sensing ◽  
Regularization Parameter ◽  
Synthetic Data ◽  
High Energy ◽  
Morphological Properties ◽  
X Rays ◽  
X Ray ◽  
Reconstruction Methods ◽  
Thresholding Algorithm

Aims. Compressed sensing realized by means of regularized deconvolution and the finite isotropic wavelet transform is effective and reliable in hard X-ray solar imaging. Methods. The method uses the finite isotropic wavelet transform with the Meyer function as the mother wavelet. Furthermore, compressed sensing is realized by optimizing a sparsity-promoting regularized objective function by means of the fast iterative shrinkage-thresholding algorithm. Eventually, the regularization parameter is selected by means of the Miller criterion. Results. The method is applied against both synthetic data mimicking measurements made with the Spectrometer/Telescope Imaging X-rays (STIX) and experimental observations provided by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The performances of the method are qualitatively validated by comparing some morphological properties of the reconstructed sources with those of the corresponding synthetic configurations. Furthermore, the results concerning experimental data are compared with those obtained by applying other visibility-based reconstruction methods. Conclusions. The results show that when the new method is applied to synthetic STIX visibility sets, it provides reconstructions with a spatial accuracy comparable to the accuracy provided by the most popular method in hard X-ray solar imaging and with a higher spatial resolution. Furthermore, when it is applied to experimental RHESSI data, the reconstructions are characterized by reliable photometry and by a notable reduction of the ringing effects caused by the instrument point spread function.

Wavelet‐transform‐based prestack multiscale Kirchhoff migration

Geophysics ◽  
2004 ◽  
Vol 69 (6) ◽  
pp. 1505-1512 ◽  
Author(s):  
Zhou Yu ◽  
George A. McMechan ◽  
Phil D. Anno ◽  
John F. Ferguson
Keyword(s):  
Wavelet Transform ◽  
Wavelet Decomposition ◽  
Computational Cost ◽  
Synthetic Data ◽  
Phase Distortion ◽  
Discrete Wavelet ◽  
Wavelet Coefficients ◽  
Kirchhoff Migration ◽  
Individual Scale ◽  
The Individual

We propose a Kirchhoff‐style algorithm that migrates coefficients obtained by wavelet decomposition of seismic traces over time. Wavelet‐based prestack multiscale Kirchhoff migration involves four steps: wavelet decomposition of the seismic data, thresholding of the resulting wavelet coefficients, multiscale Kirchhoff migration, and image reconstruction from the multiscale images. The migration procedure applied to each wavelet scale is the same as conventional Kirchhoff migration but operates on wavelet coefficients. Since only the wavelet coefficients are migrated, the cost of wavelet‐based migration is reduced compared to that of conventional Kirchhoff migration. Kirchhoff migration of wavelet‐decomposed data, followed by wavelet reconstruction, is kinematically equivalent to and yields similar migrated signal shapes and amplitudes as conventional Kirchhoff migration when data at all wavelet scales are included. The decimation in the conventional discrete pyramid wavelet decomposition introduces a translation‐variant phase distortion in the wavelet domain. This phase distortion is overcome by using a stationary wavelet‐transform rather than the conventional discrete wavelet‐transform of the data to be migrated. A wavelet reconstruction operator produces a single composite broadband migrated space‐domain image from multiscale images. Multiscale images correspond to responses in different frequency windows, and migrating the data at each scale has a different cost. Migrating some, or only one, of the individual scale data sets considerably reduces the computational cost of the migration. Successful 2D tests are shown for migrations of synthetic data for a point‐diffractor model, a multilayer model, and the Marmousi model.

Denoising of aeromagnetic data via the wavelet transform

Geophysics ◽  
2001 ◽  
Vol 66 (6) ◽  
pp. 1793-1804 ◽  
Author(s):  
George E. Leblanc ◽  
William A. Morris
Keyword(s):  
Wavelet Transform ◽  
High Frequency ◽  
Random Noise ◽  
Synthetic Data ◽  
Analysis Procedure ◽  
Data Sets ◽  
Aeromagnetic Data ◽  
Wavelet Method ◽  
Southern Alberta ◽  
Geologic Data

Noise has traditionally been suppressed or eliminated in aeromagnetic data sets by the use of Fourier analysis filters and, to a lesser degree, nonlinear statistical filters. Although these methods are quite useful under specific conditions, they produce undesirable effects when denoising features of moderate to large amplitude and spatial extent. In this study, a new wavelet analysis procedure is presented that substantially reduces the contribution from high‐frequency random noise and noise that is user defined. Applications to both synthetic data and aeromagnetic data from southern Alberta, Canada, show that the wavelet method eliminates the noise portion of the signal more efficiently and retains a greater amount of geologic data than other methods.

scholarly journals Eliminated aliasing effect on wavelet transform based multiresolution analysis

2016 ◽  
Vol 55 (3) ◽  
Author(s):  
Ernesto González-Flores ◽  
José Oscar Campos-Enríquez ◽  
Erick Camacho-Ramírez ◽  
David Ernesto Rivera-Recillas
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Multiresolution Analysis ◽  
Synthetic Data ◽  
Seismic Signal ◽  
Discrete Wavelet ◽  
Frequency Bands ◽  
Analysis Technique ◽  
The Time Domain ◽  
Seismic Signal Processing

Multiresolution analysis, based on the discrete wavelet transform, is here incorporated in seismic signal processing. This analysis technique enables decomposing a seismic signal, in different frequency bands, and thus to analyze the information contained in these frequency bands. Multiresolution analysis allows visualizing in the time domain the information contained in the frequency bands. Wavelets commonly used in the discrete wavelet transform present an overlay between scales, this constitutes an aliasing effect that gives rise to spurious effects. Vaidyanathan wavelet minimizes the overlay between scales. We applied this wavelet to synthetic data and to a 3D seismic cube. Accordingly, spurious effects from aliasing generated by overlay between scales are minimized with the Vaidyanathan wavelet.

Non-invasive fetal ECG extraction using discrete wavelet transform recursive inverse adaptive algorithm

2020 ◽  
Vol 28 (5) ◽  
pp. 507-520
Author(s):  
Bahaa Al-Sheikh ◽  
Mohammad Shukri Salman ◽  
Alaa Eleyan ◽  
Shadi Alboon
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Adaptive Filtering ◽  
Synthetic Data ◽  
Recursive Least Squares ◽  
Discrete Wavelet ◽  
Significant Information ◽  
Filtering Algorithms ◽  
Filtering Algorithm ◽  
Fetal Ecg

BACKGROUND: Fetal heart activity adds significant information about the status of the fetus health. Early diagnosis of issues in the heart before delivery allows early intervention and significantly improves the treatment. OBJECTIVE: This paper presents a new adaptive filtering algorithm for fetal electrocardiogram (FECG) extraction from the maternal abdominal signal, known in literature as abdominal electrocardiogram (AECG) signal. Fetal QRS complex waves will be identified and extracted accurately for fetal health care and monitoring purposes. METHODS: We use discrete wavelet transform recursive inverse (DWT-RI) adaptive filtering algorithm for this objective. Thoracic maternal electrocardiogram (MECG) is used as a reference in the proposed algorithm and FECG components are extracted from AECG signal after suppressing the MECG projections. The proposed algorithm is compared to other typical adaptive filtering algorithms, least mean squares (LMS), recursive least squares (RLS), and recursive inverse (RI). RESULTS: Fetal QRS waveforms successful identification and extraction from AECG signal is evaluated objectively and visually and compared to other algorithms. We validated the proposed algorithm using both synthetic data and real clinical data. CONCLUSIONS: The proposed algorithm is capable of extracting fetal QRS waveforms successfully from AECG and outperforms other adaptive filtering algorithms in terms of accuracy and positive predictivity.

Sign in / Sign up

Export Citation Format

Share Document