Correlation Window Length Research Articles

Comparing Orientation Analysis Methods for a Shallow-Water Ocean-Bottom Seismometer Array in the Bohai Sea, China

ABSTRACT The horizontal orientation estimation of an ocean-bottom seismometer (OBS) is critical for providing reliable data for seismological studies. In this article, we applied three independent polarization analysis methods to estimate the absolute horizontal orientation of a pilot shallow-water OBS array in Bohai Sea, China. The OBS array was deployed in the autumn of 2018 and comprised 32 broadband seismometers lasting around 1 yr, aimed at investigating the geodynamics of North China craton and adjacent areas. The timings of the data were corrected through the correlation analysis of regional and teleseismic earthquake events, before the polarization analysis. Polarization analysis using P wave and Rayleigh wave, from both natural earthquakes and noise cross correlations, was performed. In total, 28 out of 29 stations obtained the effective estimates combining the three methods, of which 11 stations showed relatively robust results with variations well below 10° among the three methods. However, the superiority of one method over the others is not obvious. As there is a trade-off between the accepted final estimates and the number of qualified measurements defined by parameters such as the correlation coefficient threshold, window length, and filtering options, we investigated these effects using 15 different groups of parameters for the three methods, and the deviation statistics showed a distribution with the root mean square deviation of 9.2° for the whole array.

Ultrasound Elasticity Imaging Based Multilevel Estimation Using Radiofrequency Data

An ultrasound elastography introduced to differentiate hard tumor inclusion embedded in soft tissue background based on similarity measurement of before and after deformation. In this study, freehand elastography has considered to localize hard inclusion embedded in soft tissue of phantom breast, where deformation generated by applying gentile compression using probe physical surface of ultrasound machine. Radiofrequency data of before and after deformation acquired and then processed off-line. A non-ability of refinement operation to regularize displacement estimation outliers at correlation window length of 2λ is addressed, where a multilevel processing algorithm has proposed to reinforce refinement operation by producing smooth elastography. In the first level of the processing, displacement field has estimated at correlation window length of 3λ, where global stretching as re-correlation operation and refinement operation as spatial regulation are included. While at second level, production of displacement estimation outliers at correlation window length of 2λ are regularized based on replacement of estimated cells with that interpolated one at first level. Results show an ability of multilevel algorithm to cope the issues that encountered previously proposed algorithm of refinement on estimation outlier free displacement field at an axial resolution of 2λ, and produces differential strain field.

A New Method to Construct Strictly Optimal Frequency Hopping Sequences With New Parameters

In order to evaluate the goodness of frequency hopping (FH) sequence design, the periodic Hamming correlation function is used as an important measure. Usually, the length of correlation window is shorter than the period of the chosen FH sequence, so the study of the partial Hamming correlation of FH sequence is particularly important. If an FH sequence or an FH sequence set has an optimal partial Hamming correlation with respect to the partial Hamming correlation bound for all length of correlation window, then the FH sequence or the FH sequence set is said to be strictly optimal. In this paper, we first prove that there is no strictly optimal FH sequence set of family size $M$ and sequence length $N$ over a frequency slot set of size $q$ with respect to the partial Hamming correlation bound derived by Niu et al. when $N>{q^{2}}/{M}$ and $q\geq 2$ , and that by Cai et al. when $N>{q^{2}}/{M}$ and $q\geq {2N}/({N-2})$ . Furthermore, we define a special partition-type difference packing (DP) called $[N,\nabla,H_{a}^{l}]$ PDP and give several classes of $[N,\nabla,H_{a}^{l}]$ PDPs. Then, we present a new construction of strictly optimal FH sequences. By choosing different PDPs, the FH sequences constructed can give new and flexible parameters. By utilizing this construction method recursively, we can obtain new $[N,\nabla,H_{a}^{l}]$ PDPs, which lead to infinitely many classes of strictly optimal FH sequences with new parameters. Moreover, based upon an $[N,\nabla,H_{a}^{l}]$ PDP, we present a construction of strictly optimal FH sequence sets. By preceding construction method and recursive construction, we can also obtain infinite classes of strictly optimal FH sequence sets which can give new and flexible parameters.

A Combinatorial Construction for Strictly Optimal Frequency-Hopping Sequences

Frequency-hopping sequences (FHSs) with favorable partial Hamming correlation properties have important applications in many synchronization and multiple-access systems. Strictly optimal FHSs are those FHSs with optimal partial Hamming autocorrelation irrespective of the correlation window length. In this paper, strictly optimal FHSs are investigated from a combinatorial approach. A generic connection between strictly optimal FHSs and disjoint cyclic perfect Mendelsohn difference families is established. By virtue of this connection, new strictly optimal FHSs are generated from some disjoint CPMDFs. These strictly optimal FHSs have new parameters not covered in the literature.

How much averaging is necessary to cancel out cross-terms in noise correlation studies?

Abstract We present an analytical approach to jointly estimate the correlation window length and number of correlograms to stack in ambient noise correlation studies to statistically ensure that noise cross-terms cancel out to within a chosen threshold. These estimates provide the minimum amount of data necessary to extract coherent signals in ambient noise studies using noise sequences filtered in a given frequency bandwidth. The inputs for the estimation process are (1) the variance of the cross-correlation energy density calculated over an elementary time length equal to the largest period present in the filtered data and (2) the threshold below which the noise cross-terms will be in the final stacked correlograms. The presented theory explains how to adjust the required correlation window length and number of stacks when changing from one frequency bandwidth to another. In addition, this theory provides a simple way to monitor stationarity in the noise. The validity of the deduced expressions have been confirmed with numerical cross-correlation tests using both synthetic and field data.

Low-hit-zone frequency hopping sequence sets with optimal partial Hamming correlation properties

In order to evaluate the goodness of frequency hopping sequence (FHS) design, the periodic Hamming correlation function is used as an important measure. Usually, the length of correlation window is shorter than the period of the chosen FHS, so the study of the partial Hamming correlation of FHS is particularly important. In this paper, a class of low-hit-zone (LHZ) FHS sets with good partial Hamming correlation properties which has not yet been reported previously is constructed based on interleaving techniques. It is shown that new FHS sets are optimal with respect to the partial Hamming correlation bound of FHSs with LHZ.

Frequency/time hopping sequence sets with optimal partial Hamming correlation properties

Frequency hopping/time hopping(FH/TH) sequences have found wide applications in various modern FH/TH spread spectrum communications, such as digital cellular mobile communication, short-range wireless communication, personal communication, and multi-user radar, sonar systems. In order to evaluate the goodness of FH/TH sequences design, the periodic Hamming correlation function is used as an important measure. Usually, the length of correlation window is shorter than the period of the chosen FH/TH sequence, so the study of the partial Hamming correlation of FH/TH sequence is particularly important. In this paper, a new class of FH/TH sequence sets with good partial Hamming correlation properties is proposed and investigated. The construction of new FH/TH sequence sets is based upon the generalized m-sequence and generalized Gordon-Mills-Welch sequence over a polynomial residue class ring. It is shown that new FH/TH sequence sets are optimal with respect to the partial Hamming correlation bound.

Lower Bounds on the Maximum Partial Correlations of Frequency Hopping Sequence Set with Low Hit Zone

In order to evaluate the goodness of frequency hopping sequence design, the periodic Hamming correlation function is used as an important measure. Usually, the length of correlation window is shorter than the period of the chosen frequency hopping sequence, so the study of the partial Hamming correlation of frequency hopping sequence is particularly important. In this paper, the maximum partial Hamming correlation lower bounds of frequency hopping sequences with low hit zone, with respect to the size of the frequency slot set, the length of correlation window, the family size, the low hit zone, the maximum partial Hamming autocorrelation and the maximum partial Hamming crosscorrelation are established. It is shown that the new bounds include the known Lempel-Greenberger bound, Peng-Fan bounds, Eun-Jin-Hong-Song bound and Peng-Fan-Lee bounds as special cases.

Earthquake Cluster: What Can We Learn from Waveform Similarity?

Abstract The seismograms of earthquakes, which have closely spaced hypocenters, tend to be similar due to the similarity of the Green’s functions characterizing the source-receiver paths. Based on the λ /4 criterion, it is frequently argued that similar earthquakes may represent repeated slip of the same patch of a fault. Because of the phenomenological nature of waveform similarity, such interpretations are strongly dependent on seismic signal characteristics and on the way, the waveform similarity is defined. In this article, we use two-dimensional synthetic wave-field simulations in lateral heterogeneous media to investigate how the waveform similarity of closely spaced hypocenters changes with interevent separation. We analyze the influence of correlation window length, signal frequency bandwidth, and source-receiver geometry on the waveform similarity and discuss under which conditions the λ /4 criterion can be applied to the synthetic data set. With the correlation window length defined as 2.8 times the travel-time difference between the S - and P -phase onsets, we find a correlation threshold value of 0.95 independent of the signal frequency bandwidth. We use the same threshold value for two field data examples that are similar to the synthetic data in frequency content and waveform complexity, and we discuss the implications of the λ /4 criterion. For three microearthquakes occurring during a fluid-injection experiment at the German deep drilling site (Kontinentale Tiefbohrung [KTB]), the interevent separation constrained by the λ /4 criterion is sufficient to identify these events as a sequence of repeating earthquakes in the sense that at least a fraction of the source area experienced repeated slip. For a second data example of four natural (micro-) earthquakes occurring near the island of Crete, the λ /4 criterion does not sufficiently constrain the hypocenter location to identify these events as repeating earthquakes due to the lack of high-frequency information.

Signal-to-noise ratio, contrast-to-noise ratio and their trade-offs with resolution in axial-shear strain elastography

In axial-shear strain elastography, the local axial-shear strain resulting from the application of quasi-static axial compression to an inhomogeneous material is imaged. In this paper, we investigated the image quality of the axial-shear strain estimates in terms of the signal-to-noise ratio (SNRasse) and contrast-to-noise ratio (CNRasse) using simulations and experiments. Specifically, we investigated the influence of the system parameters (beamwidth, transducer element pitch and bandwidth), signal processing parameters (correlation window length and axial window shift) and mechanical parameters (Young's modulus contrast, applied axial strain) on the SNRasse and CNRasse. The results of the study show that the CNRasse (SNRasse) is maximum for axial-shear strain values in the range of 0.005–0.03. For the inclusion/background modulus contrast range considered in this study (<10), the CNRasse (SNRasse) is maximum for applied axial compressive strain values in the range of 0.005%–0.03%. This suggests that the RF data acquired during axial elastography can be used to obtain axial-shear strain elastograms, since this range is typically used in axial elastography as well. The CNRasse (SNRasse) remains almost constant with an increase in the beamwidth while it increases as the pitch increases. As expected, the axial shift had only a weak influence on the CNRasse (SNRasse) of the axial-shear strain estimates. We observed that the differential estimates of the axial-shear strain involve a trade-off between the CNRasse (SNRasse) and the spatial resolution only with respect to pitch and not with respect to signal processing parameters. Simulation studies were performed to confirm such an observation. The results demonstrate a trade-off between CNRasse and the resolution with respect to pitch.

Resolution of axial shear strain elastography

The technique of mapping the local axial component of the shear strain due to quasi-static axial compression is defined as axial shear strain elastography. In this paper, the spatial resolution of axial shear strain elastography is investigated through simulations, using an elastically stiff cylindrical lesion embedded in a homogeneously softer background. Resolution was defined as the smallest size of the inclusion for which the strain value at the inclusion/background interface was greater than the average of the axial shear strain values at the interface and inside the inclusion. The resolution was measured from the axial shear strain profile oriented at 45° to the axis of beam propagation, due to the absence of axial shear strain along the normal directions. The effects of the ultrasound system parameters such as bandwidth, beamwidth and transducer element pitch along with signal processing parameters such as correlation window length (W) and axial shift (ΔW) on the estimated resolution were investigated. The results show that the resolution (at 45° orientation) is determined by the bandwidth and the beamwidth. However, the upper bound on the resolution is limited by the larger of the beamwidth and the window length, which is scaled inversely to the bandwidth. The results also show that the resolution is proportional to the pitch and not significantly affected by the axial window shift.

An Analog/Digital Baseband Processor Design of a UWB Channelized Receiver for Transmitted Reference Signals

The frequency channelized receiver enables the use of practical analog-to-digital converters (ADC) to digitize ultra-wideband (UWB) signals. The design issues of the analog and digital baseband processor for the channelized receiver in a UWB transmitted reference (TR) system are investigated. In the analog part, the receiver performance is shown to be weakly dependent on the analog filter bandwidth, the filter order, and the ADC oversampling ratio assuming white input noise. In the digital part, the coarse acquisition performance is shown to be significantly better in a channelized receiver than in a fullband receiver. The implementation issues for fine synchronization and correlation window length are also studied.

CORRELATION ANALYSIS OF BROKEN WIRE SIGNAL IN WIRE ROPE TESTING

Correlation analysis is an important method to recognize broken wire from testing the signal of steel wire rope. Based on character of testing signal, by means of correlation function of testing signal, cross-correlation between signal with broken wire and standard signal extracting from testing signal is performed by choosing best time-relay. The length of correlation window has significant influence on correlation coefficient, and reasonable resolution is presented. As a key index for gaining stable correlation character index, time-relay is researched. At last, testing signal is analyzed with correlation analysis method. Reliability of automotive recognition can be increased with correlation analysis method, cooperating with other recognition methods in time domain.

Emergence of the time domain Green’s function from ocean noise correlations

The time domain Green’s function (TDGF) between two receivers can be extracted from the time-averaged correlation of synchronized recordings of ocean noise [Roux et al., J. Acoust. Soc. Am. 113, 2218 (2003)]. The deterministic TDGF appears through spatial and temporal integration over the distributed random noise sources in the ocean and corresponds to the correlation of random noise passing through both receivers. We will present an analysis of the convergence time of this correlation process based on ultrasonic noise and high frequency ocean noise recordings. We will investigate how, for a given environment, the emergence of the TDGF depends on (1) the spatial and temporal noise distribution, (2) the correlation window length, and (3) the frequency bandwidth.

Estimation of the correlation amplitude of RF signals in small cutaneous vessels

Time domain correlation technique is a widely used method for blood flow velocity measurement. The time shift between a pair of windowed ultrasonic echoes is estimated by searching the temporal position of the maximum of the interpolated normalized correlation function. Between two consecutive echoes, the acoustical footprint of a group of scatterers, which are transported with the flow, moves and is deformed. This implies a decreasing of the amplitude of the normalized correlation coefficient. In the case of microcirculation (low flow rate, low SNR), the amplitude of the correlation peak can be used to detect the presence of blood flow and to discriminate false and true detections (reliability index). We have numerically evaluated the statistical performances of the cross-correlation algorithm used as a correlation peak amplitude estimator in severe conditions (short correlation window length, low SNR). These theoretical results have been compared with in vitro experimentation on a 100-/spl mu/m-diameter microcirculatory phantom and with in vivo experimentation on a 180-/spl mu/m-diameter vessel of a human leg carrying erysipelas.

Errors in time delay measurements

Simple delay and sum of sensors in a seismic array is an effective method for noise suppression. However, unless we have precise steering delays, much of the signal energy is lost during the beam forming process too. We have investigated possible error sources in time delay measurements, using a computerized cross-correlation procedure. Parameters perturbed are correlation window length and positioning, signal frequency content and signal to noise ratio (SNR). Our results indicate that relative low frequency waves and using the very first part of theP-signals give the most reliable and stable time delay values. High frequency bandpass filtering improves SNR, but signal correlation and the precision in beam steering corrections decrease. Significant loss of high frequency energy during beamforming seems to be unavoidable.