Waveform Cross‐Correlation for Differential Time Measurement: Bias and Limitations

2019 ◽  
Author(s):  
Martin Bachura ◽  
Tomáš Fischer
Keyword(s):  
Cross Correlation ◽  
Double Difference ◽  
Correlation Technique ◽  
S Waves ◽  
Aftershock Sequences ◽  
Waveform Cross Correlation ◽  
West Bohemia ◽  
The Cross ◽  
Cross Correlation Technique ◽  
Magnitude Difference

ABSTRACT The waveform cross‐correlation technique is a popular tool for estimating the differential times of seismic phases in a fast and reliable manner. Differential times are used for a variety of methods, with the double‐difference relocation method HypoDD being the most popular. In this work, we analyzed the precision and possible error of cross‐correlated differential times by conducting a simple comparison with reference manual datasets. Our study was carried out on two well‐studied mainshock–aftershock datasets from the seismically active West Bohemia region (Czechia). We observed that the magnitude difference δML between two cross‐correlated earthquakes presents a significant bias, resulting in the over‐ or underestimation of the final differential time of both P and S waves. The earthquakes of differing magnitudes exhibit unequal first pulse durations in otherwise similar waveforms. As a result, the cross‐correlated differential time, which shifts seismograms to the position of maximum cross‐correlation, is different from the differential time between phase arrivals. Our test cases revealed that the resulting deviation from the true differential time depends on the actual δML and can reach values higher than 0.025 s when δML>2. Hence, in standard differential time datasets, the error has a greater impact on the data related to strong events—mainshocks. In HypoDD applications, the error leads to mislocations of mainshocks, and at the same time, the locations of the weak events are improved. We demonstrate the mislocation potential of the error on relocated hypocenters of mainshock–aftershock sequences and earthquake swarms from West Bohemia, as well as on synthetic tests. The error cannot be avoided by changing the cross‐correlated window length or filtration. We propose a few suggestions to suppress the consequences of the magnitude difference data bias. Nonetheless, the differential times error and its effects cannot currently be completely suppressed using the mentioned methods.

Pipeline system identification through cross-correlation analysis

2002 ◽  
Vol 216 (3) ◽  
pp. 133-142 ◽  
Author(s):  
S B M Beck ◽  
N J Williamson ◽  
N D Sims ◽  
R Stanway
Keyword(s):  
Correlation Analysis ◽  
Cross Correlation ◽  
Correlation Technique ◽  
Pipeline System ◽  
Pipe Network ◽  
Cross Correlation Analysis ◽  
Valve Position ◽  
Single Sensor ◽  
The Cross ◽  
Cross Correlation Technique

The pipeline systems used to carry liquids and gases for the ventilation of buildings, water distributions networks, and the oil and chemical industries are usually monitored by a multiplicity of pressure, flow, and valve position sensors. By comparing the input signal to a valve with the pressure reading from the network using cross-correlation analysis, the technique described in this paper enables a single sensor to be used for monitoring. Specifically, the offset and gradient change of the cross-correlation function show the time delay between the input wave and the acquired output signal. These reflections arise from junctions, valves, and terminations, which can be located effectively using the cross-correlation technique. Investigations using a T-shaped pipe network have been conducted with a valve inserted in the pipeline to introduce artificial water hammer-type perturbations into the system. Both computational and experimental data are presented and the results are compared with the actual pipe network geometry. It is shown that it is possible to identify the location of various features of the network from the reflections and thus to perform either system characterisation or condition monitoring.

scholarly journals Investigations on the Coregistration of Sentinel-1 TOPS with the Conventional Cross-Correlation Technique

2018 ◽  
Vol 10 (9) ◽  
pp. 1405 ◽  
Author(s):  
Yuxiao Qin ◽  
Daniele Perissin ◽  
Jing Bai
Keyword(s):  
Cross Correlation ◽  
Phase Error ◽  
Impulse Response Function ◽  
Correlation Method ◽  
Correlation Technique ◽  
Geometrical Approach ◽  
Rigid Transformation ◽  
Interferometric Phase ◽  
The Cross ◽  
Cross Correlation Technique

In Sentinel-1 TOPS mode, the antenna sweeps in the azimuth direction for the purpose of illuminating the targets with the entire azimuth antenna pattern (AAP). This azimuth sweeping introduces an extra high-frequency Doppler term into the impulse response function (IRF), which poses a more strict coregistration accuracy for the interferometric purpose. A 1/1000 pixel coregistration accuracy is required for the interferometric phase error to be negligible, and the enhanced spectral diversity (ESD) method is applied for achieving such accuracy. However, since ESD derives miscoregistration from cross-interferometric phase, and phase is always wrapped to [ − π , π ) , an initial coregistration method with enough accuracy is required to resolve the phase ambiguity in ESD. The mainstream for initial coregistration that meets this requirement is the geometrical approach, which accuracy mainly depends on the accuracy of orbits. In this article, the authors propose to investigate the feasibility of using the conventional coregistration approach, namely the cross-correlation-and-rigid-transformation, as the initial coregistration method. The aim is to quantify the coregistration accuracy for cross-correlation-and-rigid-transformation using the Cramér-Rao lower bound (CRLB) and determine whether this method could eventually help to resolve the phase ambiguities of ESD. In addition, we studied the feasibility and robustness of the cross-correlation plus ESD under different conditions. For validation, we checked whether the cross-correlation plus ESD approach could reach the same coregistration accuracy as geometrical plus ESD approach. In general, for large areas with enough coherence and little topography variance, the cross-correlation method could be used as an alternative to the geometrical approach. The interferogram from the two different approaches (with ESD applied afterward) shows a negligible difference under such circumstances.

scholarly journals Speckle Cross-Correlation Method in Measuring Fine Surface Displacements

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
M. Bahrawi ◽  
N. Farid ◽  
M. Abdel-Hady
Keyword(s):  
Cross Correlation ◽  
Correlation Method ◽  
Industrial Applications ◽  
Correlation Technique ◽  
Surface Displacements ◽  
Speckle Patterns ◽  
The Cross ◽  
And Performance ◽  
The Stability ◽  
Cross Correlation Technique

Industrial applications need regular testing for the lifetime, movement, strength, and performance of manufacturing machines during production process. Since speckle photography is a simple economic technique, it is used in investigating object response under mechanical and thermal effects depending on the movement of the speckle patterns with respect to the deformation strength and direction. In the present work, the cross-correlation technique is used to analyze the speckle patterns by iterative method to define both values and directions of rigid body translation and expansion. In order to check the accuracy of the cross-correlation technique, the results are compared with the displacement values given by analyzing the Young's interference fringes resulted from the Fourier transformation of the speckle patterns. This noncontact technique is found to be accurate and informative depending on the stability and sensitivity of the optical system. This method of measurement is an effective tool in studying the hard cases of objects and machines under various effects.

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