Warped Signal Research Articles

Simplified Automatic Seismic to Well Tying Using Smooth Dynamic Time Warping Technique in R

Seismic well tying is a crucial part of the interpretation phase in exploration seismology. Tying wells usually involves forward modeling a synthetic seismogram from sonic and density logs and then matching the obtained synthetic seismogram to the seismic reflection data. A huge amount of time is required to deal with it, yet the outcome signal may not be satisfying and may be suffering a low cross correlation between the seismic signal and the synthetic one; it also requires a high quality synthetic trace. Another problem with the so-called manual tying is that the tying process is not repeatable, indicating that one can rarely obtain the same stretched and squeezed signal if the tying procedure is repeated. In recent years, some researchers have used the dynamic time warping (DTW) method to address well tying problems. They have obtained good results according to the correlation between the seismic signal and the warped synthetic signal. This research demonstrates that the result will be better if filtering is applied before tying, and then the warped signal is smoothed. We also propose a simpler algorithm for extracting a warped signal from the warping curve and the original synthetic trace, which gives rise to better performance for well tying.

Warped Variational Mode Decomposition With Application to Vibration Signals of Varying-Speed Rotating Machineries

Recently, a powerful signal processing technique called variational mode decomposition (VMD) has drawn a great interest in various applications. The VMD assumes that the signal components are narrowly banded and separated in the frequency domain. Therefore, it cannot analyze wideband nonstationary signals with spectrum-overlapped components. To address this issue, a novel scheme called warped VMD (WVMD) is proposed in this paper. The WVMD includes the following steps. First, the phase function of a certain signal component is accurately estimated by optimizing a spectrum concentration index. Next, the time-warping principle is used to transform the original signal to a warped one in the phase coordinate where the spectrums of the components are well separated. Then, the conventional VMD can be used to effectively decompose the warped signal. Finally, the obtained signal components (of the warped signal) can be taken back to the time coordinate by the inverse warping operation. The WVMD works well in noisy environments and can even decompose signals with very close components. The effectiveness of the WVMD is validated by some simulated signals, a bat echolocation signal, and applications to real-life vibration signals of a rotor test rig and a hydroturbine.

A passive range method of underwater source based on single hydrophone

Aiming at the passive impulse wideband source range problem in shallow water waveguides, a passive source range method with single hydrophone which is applied to the shallow water waveguide with a bottom of liquid semi-infinite space is presented in this paper by combining the group delay theory and warping transformation. The receive signal is composed of several normal modes, and each mode represents many characteristics of the waveguide environment. Warping transformation is a good tool which can achieve the separation and extraction of normal modes from the received signal, and it is also an unitary and reversible transformation, so the warped signal of each normal mode can be recovered completely. The dispersion curves of normal modes can be extracted by warping transformation, and the relation between arrival time and frequency of each order normal mode can also be calculated, and then the time delay of arriving hydrophone between arbitrary two different normal modes is obtained. According to the group delay theory, different order normal mode has different arrival time at the same frequency, and the arrival time of normal mode is determined at its group speed when the distance between the source and hydrophone is certain. So the propagation range can be estimated when the time delay and the slow group speed difference between two different normal modes are known. When the waveguide environmental parameters are known, the slow group speed difference of arbitrary two normal modes can be calculated by KRAKEN. However, when the bottom parameters are unknown, the bottom reflection phase shift parameter is an important parameter describing the acoustic parameters of the bottom, and it contains nearly all the bottom information, what is more, the bottom reflection phase shift parameter is also a parameter that can be extracted by some experimental data easily. When the depth and the average sound speed of the water column are known, the slow group speed difference between two order normal modes can be represented by the seafloor phase shift parameter. Therefore, the source range can be represented by the bottom reflection phase shift parameter, the sea depth and the mean sound speed in the waveguide, and under this condition, the source location can be estimated by one single hydrophone. The effectiveness and accuracy of the method are proved by the numerical simulation results and sea experimental data processing, in which the signals are both received by a single hydrophone. The sea experimental data contain linear frequency modulation impulse source signal and explosion sound source signal, and the mean relative error of range estimation is less than 10%.

A far distance wideband geoacoustic parameter inversion method based on a modal dispersion curve

Acoustic propagation in shallow water is greatly influenced by the properties of the sea bottom. The dispersion characteristics of modes are relatively sensitive to the bottom parameters and have been used to invert the bottom parameters. Since the inversion error using a single wideband sound source increases with increasing range, a far distance inversion method based on the modal dispersion curve using a single hydrophone with two wideband sound sources is presented in this paper, in which a warping transform is applied so that it can accurately extract the modal dispersion curve from the warped signal spectrum. Experimental data used for the inversion are acquired using a hydrophone of vertical array in the South Sea of China during the Autumn in 2012. The transmitted signals are explosive signals, and the bottom sound speed and density are inverted by matching the theoretical arrival time differences of various modes and frequencies with those calculated using the experimental data. The attenuation coefficient is deduced using the transmission loss data recorded in the experiment. A genetic algorithm (GA) is used for optimization search for the parameter bounds. Inversion results demonstrate that the arrival time difference when using the bottom sound speed and density show a high consistency with those obtained using the experimental data. Moreover, the attenuation coefficient is nonlinear over the frequency band from 100 to 315 Hz. The validity of inverted parameters is evaluated by the posteriori probability distributions, and the numerical results of arrival time differences calculated using the inverted sound speed and density are in good agreement with those extracted from the other two wideband explosive signals at different distances. In addition, the theoretical transmission loss calculated using the inverted attenuation coefficient matches the experiment data very well. It is shown that the inversion scheme can provide a valid and stable environmental estimation.

Frequency invariability of acoustic field and passive source range estimation in shallow water

The frequency invariability of the warped modal signal and the warped signal autocorrelation function in shallow water is discussed. A method is proposed for passive source-range estimation based on the frequency invariability and warping transform of signal autocorrelation function received by a single hydrophone in a range-independent or weak range-dependent shallow water environment. In the method, a guided source with a known range is employed to provide the crucial and relative invariant scaled features. The experimental data in shallow water with an iso-speed profile and a fluctuated thermocline are used to verify this approach. The relative errors of the source range estimation are basically less than 10%.

Vandermonde Factorization of Toeplitz Matrices and Applications in Filtering and Warping

By deriving a factorization of Toeplitz matrices into the product of Vandermonde matrices, we demonstrate that the Euclidean norm of a filtered signal is equivalent with the Euclidean norm of the appropriately frequency-warped and scaled signal. In effect, we obtain an equivalence between the energy of frequency-warped and filtered signals. While the result does not provide tools for warping per se, it does show that the energy of the warped signal can be evaluated efficiently, without explicit and complex computation of the warped transform. The main result is closely related to the Vandermonde factorization of Hankel matrices.

Inversion of seabed attenuation using time-warping of close range data

An inversion scheme based on time-warping is presented for estimating seabed sound attenuation from modal dispersion of close-range single-hydrophone data. The dispersion information is extracted directly from the warped signal spectrum. Seabed sound speed and density are inverted from the modal group velocity curves, and the attenuation is inverted from the normalized modal amplitudes. The method is applied to experimental data collected in the Yellow Sea of China during the winter of 2002. The inverted sound speed and density are consistent with the sand-silt-clay sediment at the site, and the attenuation is nonlinear over the frequency band from 125-500 Hz.

Bubble Pulse Cancelation in the Time-Frequency Domain Using Warping Operators

The received shock waves produced by explosive charges are often polluted by bubble pulses in underwater acoustic experiments. A method based on warping operators is proposed to cancel the bubble pulses in the time-frequency domain. This is applied to the explosive data collected during the Yellow Sea experiment in November 2000. The original received signal is first transformed into a warped signal by warping operators. Then, the warped signal is analyzed in the time-frequency domain. Due to the different features between the shock waves and the bubble pulses in the time-frequency domain for the warped signal, the bubble pulses can be easily filtered out. Furthermore, the shock waves in the original time domain can be retrieved by the inverse warping transformation. The autocorrelation functions and the time-frequency representation show that the bubble pulses can be canceled effectively.

A dispersion compensation procedure to extend pulse-echo defects location to irregular waveguides

Abstract A time–frequency signal processing procedure aimed at extending pulse-echo defect detection methods based on guided waves to irregular waveguides is proposed. In particular, the procedure returns the distance traveled by a guided wave that has propagated along a waveguide composed by segments with different dispersive properties by processing the detected echo signal. To such aim, the acquired signal is processed by means of a two-step procedure. First, a warped frequency transform (WFT) is used to compensate the dispersion of the guided wave due to the traveled distance in a portion of the waveguide that is assumed as reference. Next, a further compensation is applied to remove from the warped signal the group delay introduced by the remaining irregular portion of the waveguide. Thanks to this processing strategy, the actual distance traveled by the wave in the regular portion of the irregular waveguide is revealed. Thus, the proposed procedure is suitable for automatically locate defect-induced reflections in irregular waveguides and can be easily implemented in real applications for structural health monitoring purposes. The potential of the procedure is demonstrated and validated numerically by simulating and processing Lamb waves propagating in waveguides made up of different uniform, tapered and curved segments.

SAGA: A novel signal alignment method based on genetic algorithm

Signal alignment is one of the most commonly used strategies in analyzing a group of time series in order to learn the variations or common patterns across individual signals. A pairwise alignment algorithm aligns two signals by warping the time axis of the first signal so that the warped signal is “near” to the second. The majority of alignment algorithms are focused on extracting features like the locations of significant peaks or peak widths, and using those features in aligning the signals instead of raw signal. Although this approach allows fast alignments, it suffers from the risk of missing important features, leading to inaccurate alignments. In this paper, a novel Signal Alignment method based on Genetic Algorithm (SAGA) is proposed to align raw signals by first modeling the warping function with an ODE model. The parameters of the warping function are then optimized by using a genetic algorithm. The SAGA does not require feature extraction and it preserves the smoothness of the signals. The performance of the proposed method is evaluated on two sets of synthetic and real world datasets and compared to the well-known alignment algorithms. The results show that SAGA is a powerful algorithm that can compete with the others.

Analysis and application of digital spectral warping in analog and mixed-signal testing

Spectral warping is a digital signal processing transform which shifts the frequencies contained within a signal along the frequency axis. The Fourier transform coefficients of a warped signal correspond to frequency-domain 'samples' of the original signal which are unevenly spaced along the frequency axis. This property allows the technique to be efficiently used for DSP-based analog and mixed-signal testing. The analysis and application of spectral warping for test signal generation, response analysis, filter design, frequency response evaluation, etc. are discussed in this paper along with examples of the software and hardware implementation.