Wavelet-Radon domain dealiasing and interpolation of seismic data

Geophysics ◽  
2007 ◽  
Vol 72 (2) ◽  
pp. V41-V49 ◽  
Author(s):  
Zhou Yu ◽  
John Ferguson ◽  
George McMechan ◽  
Phil Anno
Keyword(s):  
Time Series ◽  
Radon Transform ◽  
Seismic Data ◽  
High Frequency ◽  
Transform Domain ◽  
Original Time Series ◽  
Spatial Aliasing ◽  
Multichannel Data ◽  
And Migration ◽  
Original Time

Spatial aliasing is unavoidable in some seismic data and has serious effects on the performance of multichannel data processing and migration. Antialias filtering produces distortion of the signal through the removal of high-frequency information. In contrast, dealiasing produces an unaliased estimate of the signal at all frequencies present in the original time series. A new dealiasing algorithm is developed by exploiting the properties of seismic wavefields in the wavelet-Radon transform domain, specifically the overlap of information between wavelet scales at the same frequency. The effectiveness of the wavelet-Radon dealiasing algorithm is demonstrated through the processing of both synthetic and field seismic data.

scholarly journals Superiority of Hybrid Soft Computing Models in Daily Suspended Sediment Estimation in Highly Dynamic Rivers

2021 ◽  
Vol 13 (2) ◽  
pp. 542
Author(s):  
Tarate Suryakant Bajirao ◽  
Pravendra Kumar ◽  
Manish Kumar ◽  
Ahmed Elbeltagi ◽  
Alban Kuriqi
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Suspended Sediment ◽  
River Basin ◽  
Time Series Data ◽  
Series Data ◽  
Discrete Wavelet ◽  
Original Time Series ◽  
Inference System ◽  
Original Time

Estimating sediment flow rate from a drainage area plays an essential role in better watershed planning and management. In this study, the validity of simple and wavelet-coupled Artificial Intelligence (AI) models was analyzed for daily Suspended Sediment (SSC) estimation of highly dynamic Koyna River basin of India. Simple AI models such as the Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) were developed by supplying the original time series data as an input without pre-processing through a Wavelet (W) transform. The hybrid wavelet-coupled W-ANN and W-ANFIS models were developed by supplying the decomposed time series sub-signals using Discrete Wavelet Transform (DWT). In total, three mother wavelets, namely Haar, Daubechies, and Coiflets were employed to decompose original time series data into different multi-frequency sub-signals at an appropriate decomposition level. Quantitative and qualitative performance evaluation criteria were used to select the best model for daily SSC estimation. The reliability of the developed models was also assessed using uncertainty analysis. Finally, it was revealed that the data pre-processing using wavelet transform improves the model’s predictive efficiency and reliability significantly. In this study, it was observed that the performance of the Coiflet wavelet-coupled ANFIS model is superior to other models and can be applied for daily SSC estimation of the highly dynamic rivers. As per sensitivity analysis, previous one-day SSC (St-1) is the most crucial input variable for daily SSC estimation of the Koyna River basin.

scholarly journals The Systematic Bias of Entropy Calculation in the Multi-Scale Entropy Algorithm

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 659
Author(s):  
Jue Lu ◽  
Ze Wang
Keyword(s):  
Time Series ◽  
Standard Deviation ◽  
Coarse Graining ◽  
Sample Entropy ◽  
Systematic Bias ◽  
Original Time Series ◽  
Multi Scale ◽  
Calculation Results ◽  
Surrogate Measure ◽  
Original Time

Entropy indicates irregularity or randomness of a dynamic system. Over the decades, entropy calculated at different scales of the system through subsampling or coarse graining has been used as a surrogate measure of system complexity. One popular multi-scale entropy analysis is the multi-scale sample entropy (MSE), which calculates entropy through the sample entropy (SampEn) formula at each time scale. SampEn is defined by the “logarithmic likelihood” that a small section (within a window of a length m) of the data “matches” with other sections will still “match” the others if the section window length increases by one. “Match” is defined by a threshold of r times standard deviation of the entire time series. A problem of current MSE algorithm is that SampEn calculations at different scales are based on the same matching threshold defined by the original time series but data standard deviation actually changes with the subsampling scales. Using a fixed threshold will automatically introduce systematic bias to the calculation results. The purpose of this paper is to mathematically present this systematic bias and to provide methods for correcting it. Our work will help the large MSE user community avoiding introducing the bias to their multi-scale SampEn calculation results.

scholarly journals Technical Note: Long-term memory effect in the atmospheric CO<sub>2</sub> concentration at Mauna Loa

2006 ◽  
Vol 6 (6) ◽  
pp. 11957-11970 ◽  
Author(s):  
C. Varotsos ◽  
M.-N. Assimakopoulos ◽  
M. Efstathiou
Keyword(s):  
Carbon Dioxide ◽  
Time Series ◽  
Power Law ◽  
Carbon Dioxide Concentration ◽  
Global Climate Models ◽  
Fluctuation Analysis ◽  
Original Time Series ◽  
Mauna Loa ◽  
Carbon Dioxide Concentrations ◽  
Original Time

Abstract. The monthly mean values of the atmospheric carbon dioxide concentration derived from in-situ air samples collected at Mauna Loa Observatory, Hawaii, during 1958–2004 (the longest continuous record available in the world) are analyzed by employing the detrended fluctuation analysis to detect scaling behavior in this time series. The main result is that the fluctuations of carbon dioxide concentrations exhibit long-range power-law correlations (long memory) with lag times ranging from four months to eleven years, which correspond to 1/f noise. This result indicates that random perturbations in the carbon dioxide concentrations give rise to noise, characterized by a frequency spectrum following a power-law with exponent that approaches to one; the latter shows that the correlation times grow strongly. This feature is pointing out that a correctly rescaled subset of the original time series of the carbon dioxide concentrations resembles the original time series. Finally, the power-law relationship derived from the real measurements of the carbon dioxide concentrations could also serve as a tool to improve the confidence of the atmospheric chemistry-transport and global climate models.

Precipitation Forecast Based on WA-SVM Theory

2012 ◽  
Vol 518-523 ◽  
pp. 4039-4042
Author(s):  
Zhen Min Zhou
Keyword(s):  
Time Series ◽  
Support Vector Machine ◽  
Wavelet Analysis ◽  
Precipitation Forecast ◽  
Support Vector ◽  
Estimation Model ◽  
Original Time Series ◽  
Set Up ◽  
Original Time

In order to improve the precision of medium-long term rainfall forecast, the rainfall estimation model was set up based on wavelet analysis and support vector machine (WA-SVM). It decomposed the original rainfall series to different layers through wavelet analysis, forecasted each layer by means of SVM, and finally obtained the forecast results of the original time series by composition. The model was used to estimate the monthly rainfall sequence in the watershed. Comparing with other method which only uses support vector machine(SVM), it indicates that the estimated accuracy was improved obviously.

Aliasing in the tau-p transform and the removal of spatially aliased coherent noise

Geophysics ◽  
1990 ◽  
Vol 55 (11) ◽  
pp. 1496-1503 ◽  
Author(s):  
Greg Turner
Keyword(s):  
Time Series ◽  
Radon Transform ◽  
Seismic Data ◽  
Graphical Method ◽  
Temporal Frequency ◽  
Coherent Noise ◽  
P Values ◽  
One Dimensional ◽  
Noise Rejection ◽  
P Domain

The tau-p transform is a discretized Radon transform. The choice of discretization parameters is a very important part of performing the transform. Insufficient sampling in the tau direction leads to aliasing problems equivalent to those encountered in any one‐dimensional time series. A simple graphical method illustrates that too coarse sampling in the p direction results in reconstructions containing data duplicated incorrectly at different spatial positions. The spacing of these duplications is dependent on the temporal frequency of the data. Insufficient spatial sampling of the original seismic data causes events to plot at multiple p values in tau-p domain, again dependent on temporal frequency. Therefore, to velocity filter spatially aliased noise efficiently, multiple p values must be filtered. The use of appropriate filters in the p-f domain can substantially improve the noise rejection capabilities of velocity filters on spatially aliased noise while having little effect on desired reflection signals.

State Space Reconstruction of Nonstationary Time-Series

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Hong-Guang Ma ◽  
Chun-Liang Zhang ◽  
Fu Li
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
State Space ◽  
Phase Angle ◽  
Analytical Form ◽  
Nonstationary Time Series ◽  
Original Time Series ◽  
State Space Reconstruction ◽  
Original Time ◽  
The Hilbert Transform

In this paper, a new method of state space reconstruction is proposed for the nonstationary time-series. The nonstationary time-series is first converted into its analytical form via the Hilbert transform, which retains both the nonstationarity and the nonlinear dynamics of the original time-series. The instantaneous phase angle θ is then extracted from the time-series. The first- and second-order derivatives θ˙, θ¨ of phase angle θ are calculated. It is mathematically proved that the vector field [θ,θ˙,θ¨] is the state space of the original time-series. The proposed method does not rely on the stationarity of the time-series, and it is available for both the stationary and nonstationary time-series. The simulation tests have been conducted on the stationary and nonstationary chaotic time-series, and a powerful tool, i.e., the scale-dependent Lyapunov exponent (SDLE), is introduced for the identification of nonstationarity and chaotic motion embedded in the time-series. The effectiveness of the proposed method is validated.

Amplitude preservation of Radon-based multiple-removal filters

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. V123-V126 ◽  
Author(s):  
Ethan J. Nowak ◽  
Matthias G. Imhof
Keyword(s):  
Radon Transform ◽  
Seismic Data ◽  
Transform Domain ◽  
Multiple Reflections ◽  
Avo Analysis ◽  
Amplitude Versus Offset ◽  
Amplitude Preservation ◽  
Amplitude Versus

This study examines the effect of filtering in the Radon transform domain on reflection amplitudes. Radon filters are often used for removal of multiple reflections from normal moveout-corrected seismic data. The unweighted solution to the Radon transform reduces reflection amplitudes at both near and far offsets due to a truncation effect. However, the weighted solutions to the transform produce localized events in the transform domain, which minimizes this truncation effect. Synthetic examples suggest that filters designed in the Radon domain based on a weighted solution to the linear, parabolic, or hyperbolic transforms preserve the near- and far-offset reflection amplitudes while removing the multiples; whereas the unweighted solutions diminish reflection amplitudes which may distort subsequent amplitude-versus-offset (AVO) analysis.

scholarly journals Piecewise Trend Approximation: A Ratio-Based Time Series Representation

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Jingpei Dan ◽  
Weiren Shi ◽  
Fangyan Dong ◽  
Kaoru Hirota
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Series Representation ◽  
Feature Space ◽  
Original Data ◽  
Series Data ◽  
High Dimensional ◽  
Original Time Series ◽  
Data Space ◽  
Original Time

A time series representation, piecewise trend approximation (PTA), is proposed to improve efficiency of time series data mining in high dimensional large databases. PTA represents time series in concise form while retaining main trends in original time series; the dimensionality of original data is therefore reduced, and the key features are maintained. Different from the representations that based on original data space, PTA transforms original data space into the feature space of ratio between any two consecutive data points in original time series, of which sign and magnitude indicate changing direction and degree of local trend, respectively. Based on the ratio-based feature space, segmentation is performed such that each two conjoint segments have different trends, and then the piecewise segments are approximated by the ratios between the first and last points within the segments. To validate the proposed PTA, it is compared with classical time series representations PAA and APCA on two classical datasets by applying the commonly used K-NN classification algorithm. For ControlChart dataset, PTA outperforms them by 3.55% and 2.33% higher classification accuracy and 8.94% and 7.07% higher for Mixed-BagShapes dataset, respectively. It is indicated that the proposed PTA is effective for high dimensional time series data mining.

INTERPRETATION OF SINGULAR SPECTRUM ANALYSIS AS COMPLETE EIGENFILTER DECOMPOSITION

2012 ◽  
Vol 04 (04) ◽  
pp. 1250023 ◽  
Author(s):  
KENJI KUME
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Singular Value ◽  
Original Time Series ◽  
Singular Vectors ◽  
Singular Spectrum ◽  
Original Time ◽  
Value Decomposition ◽  
Insight Into

Singular spectrum analysis is a nonparametric and adaptive spectral decomposition of a time series. This method consists of the singular value decomposition for the trajectory matrix constructed from the original time series, followed with the subsequent reconstruction of the decomposed series. In the present paper, we show that these procedures can be viewed simply as complete eigenfilter decomposition of the time series. The eigenfilters are constructed from the singular vectors of the trajectory matrix and the completeness of the singular vectors ensure the completeness of the eigenfilters. The present interpretation gives new insight into the singular spectrum analysis.

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