Differences In Frequency Content Research Articles

Strength‐reduction factors for the design of light nonstructural elements in buildings

SummaryStrength‐reduction factors that reduce ordinates of floor spectra acceleration due to nonlinearity in the secondary system are investigated. In exchange for permitting some inelastic deformation to occur in the secondary system or its supports, these strength reduction factors allow to design the nonstructural elements or their supports for lateral forces that are smaller than those that would be required to maintain them elastically during earthquakes. This paper presents the results of a statistical analysis on component strength‐reduction factors that were computed considering floor motions recorded on instrumented buildings in California during various earthquakes. The effect of yielding in the component or its anchorage/bracing in offering protection against excessive component acceleration demands is investigated. It is shown that strength‐reduction factors computed from floor motions are significantly different from those computed from ground motions recorded on rock or on firm soils. In particular, they exhibit much larger reductions for periods tuned or nearly tuned to the dominant modal periods of the building response. This is due to the large differences in frequency content of ground motions and floor motions, with the former typically characterized by wide‐band spectra whereas the latter are characterized by narrow‐band spectra near periods of dominant modes in the response of the building. Finally, the study provides approximate equations to estimate component strength‐reduction factors computed through nonlinear regression analyses.

Chatter Identification in End Milling Process Based on Cutting Force Signal Processing

During milling process, chatter is one of the major limitations of productivity, it has more negative effects on the surface finish, dimensional accuracy and tool life. It is thus necessary to detect and avoid chatter occurrence. In this study, a chatter detection approach based on cutting force signal is presented. The milling force signals were measured by cutting force sensor and then analyzed by using time-frequency analysis approaches such as short-time Fourier transform (STFT) and continuous wavelet transform (CWT) in order to identify chatter. The different sets of cutting conditions were utilized to recognize chatter presence. The spectrogram and scalogram results of the force signals represented a great difference in frequency content between stable and unstable cuttings. The analysis results were then validated by cutting force behavior in the time domain.

Ambient-noise tomography of Katla volcano, south Iceland

A shear-wave velocity model of subglacial Katla volcano, southern Iceland, has been developed using ambient seismic noise tomography based on data from a temporary network operating between May 2011 and August 2013 and permanent stations around the volcano. Phase-velocity dispersion curves were obtained using cross-correlations of vertical components of 136 station pairs and non-linearly inverted for phase-velocity maps between 1.7 and 7.5s. Local dispersion curves were inverted for shear-velocity variation with depth using a grid search imposing a fixed ice layer at the top. The resulting one-dimensional (1-D) velocity models were combined to obtain a pseudo three-dimensional (3-D) model with estimated lateral resolution of 8km and depth resolution varying from close to 1km near the surface to about 8km at 10km depth. Shear wave velocities are generally higher within the Katla central volcano than in its surroundings. The most striking feature of the model is a high-velocity anomaly beneath the caldera at >6km depth interpreted to be due to cumulates resulting from differentiation of shallower magma intrusions and remelting of subsiding upper crust. No shallow low-velocity anomaly is resolved beneath the central caldera, but a low-velocity region is found at 2–4km depth beneath the western half of the caldera. VP/VS ratios, estimated from average velocity-depth profiles from surface-wave data and higher frequency P-wave data, are anomalously high (>1.9) compared to average Icelandic crust, particularly in the top 2–3km. This is argued not to be an artifact due to lateral refraction or topography. Instead, this anomaly could be explained as an artifact caused by velocity dispersion due to attenuation and a difference in frequency content, and possibly to a degree by the compositional difference between the transalkalic Fe-Ti basalts of Katla and average tholeiitic Icelandic crust.

Amputee locomotion: Frequency content of prosthetic vs. intact limb vertical ground reaction forces during running and the effects of filter cut-off frequency

Compared to intact limbs, running-specific prostheses have high resonance non-biologic materials and lack active tissues to damp high frequencies. These differences may lead to ground reaction forces (GRFs) with high frequency content. If so, ubiquitously applying low-pass filters to prosthetic and intact limb GRFs may attenuate veridical high frequency content and mask important and ecologically valid data from prostheses. To explore differences in frequency content between prosthetic and intact limbs we divided signal power from transtibial unilateral amputees and controls running at 2.5, 3.0, and 3.5m/s into Low (<10Hz), High (10–25Hz), and Non-biologic (>25Hz) frequency bandwidths. Faster speeds tended to reduce the proportion of signal power in the Low bandwidth while increasing it in the High and Non-biologic bandwidths. Further, prostheses had lower proportions of signal power at the High frequency bandwidth but greater proportions at the Non-biologic bandwidth. To evaluate whether these differences in frequency content interact with filter cut-offs and alter results, we filtered GRFs with cut-offs from 1 to 100Hz and calculated vertical impact peak (VIP). Changing cut-off had inconsistent effects on VIP across speeds and limbs: Faster speeds had significantly larger changes in VIP per change in cut-off while, compared to controls, prosthetic limbs had significantly smaller changes in VIP per change in cut-off. These findings reveal differences in GRF frequency content between prosthetic and intact limbs and suggest that a cut-off frequency that is appropriate for one limb or speed may be inappropriate for another.

Mid-European seismic attenuation anomaly

Macroseismic studies of various historical earthquakes with epicenters in the Eastern Alps region have shown a significant elongation of isoseismals in the North-West direction. Such an anomalous attenuation of seismic waves in Central Europe is investigated on the basis of instrumental records of two moderate-size earthquakes in the Vienna Basin, which occurred in September and October 2013. It has been found that for both earthquakes the peak amplitudes of both velocity and acceleration are considerably higher to the North-West of the epicenters compared to the other directions. The peak ground velocity amplitudes at comparable epicentral distances but different azimuths may vary by as much as one order of magnitude. The inspection of individual seismograms suggests that the phenomenon is associated mainly with the propagation of S waves. Significant differences in frequency content of the seismic waves radiated to different azimuths are also demonstrated. The maximum predominant frequency was not observed at stations closest to the epicenters but about 250km away, in the Bohemian Massif. The possible causes of these observations are briefly discussed on the basis of an elementary data analysis but further research and in-depth analysis is required to elucidate the causes of these phenomena.

A study of changes in apparent ionospheric reflection height within individual lightning flashes

Ionospheric reflection heights estimated using the zero-to-zero and peak-to-peak methods to measure skywave delay relative to the ground wave were compared for 108 first and 124 subsequent strokes at distances greater than 100km. For either metric there was a considerable decrease in average reflection height for subsequent strokes relative to first strokes. We showed that the observed difference cannot be explained by the difference in frequency content of first and subsequent return-stroke currents. Apparent changes in reflection height (estimated using the peak-to-peak method) within individual flashes for 54 daytime and 11 nighttime events at distances ranging from 50km to 330km were compared, and significant differences were found. For daytime conditions, the majority of the flashes showed either decrease (57%) or non-monotonic variation (39%) in reflection height with respect to the immediately preceding stroke. With respect to the first stroke, 91% of the flashes showed monotonic decrease in height. For nighttime flashes, patterns in reflection height changes with respect to the immediately preceding stroke were as follows: 46% no change, 27% monotonic decrease, and 27% non-monotonic variation. When changes were measured with respect to the first stroke, 54% of nighttime flashes showed monotonic decrease and 46% no change. Ionospheric reflection height tends to increase with return-stroke peak current. The observed daytime effects can be explained by (a) the dependence of EMP penetration depth on source intensity, which decreases with stroke order, (b) additional ionization associated with elves, or (c) combination of (a) and (b) above.

The open ocean energy decay of three recent trans‐Pacific tsunamis

The 2009 Samoa (Mw 8.1), 2010 Chile (8.8), and 2011 Tohoku (9.0) earthquakes generated destructive tsunamis recorded by a large number of DART stations in the Pacific Ocean. High‐resolution (15 s) DART records yield mean energy decay times for these events of 17.3, 24.7, and 24.6 h, respectively. We attribute these differences to the frequency content of the tsunamis. Specifically, the Samoa tsunami was a “high‐frequency” event with periods of 2–30 min whereas the Chile and Tohoku tsunamis were “broad‐band” events with periods of 2–180 min. Differences in frequency content are linked to differences in the source parameters: Samoa was a relatively small deep‐water earthquake while Chile and Tohoku were extensive shallow‐water earthquakes. Frequency‐dependent analysis of the Chile and Tohoku tsunamis indicates that shorter period waves attenuate much faster than longer‐period waves (decay times range from 15 h for 2–6 min waves to 29 h for 60–180 min waves).

EMG analysis tuned for determining the timing and level of activation in different motor units

Recruitment patterns and activation dynamics of different motor units greatly influence the temporal pattern and magnitude of muscle force development, yet these features are not often considered in muscle models. The purpose of this study was to characterize the recruitment and activation dynamics of slow and fast motor units from electromyographic (EMG) recordings and twitch force profiles recorded directly from animal muscles. EMG and force data from the gastrocnemius muscles of seven goats were recorded during in vivo tendon-tap reflex and in situ nerve stimulation experiments. These experiments elicited EMG signals with significant differences in frequency content ( p < 0.001). The frequency content was characterized using wavelet and principal components analysis, and optimized wavelets with centre frequencies, 149.94 Hz and 323.13 Hz, were obtained. The optimized wavelets were used to calculate the EMG intensities and, with the reconstructed twitch force profiles, to derive transfer functions for slow and fast motor units that estimate the activation state of the muscle from the EMG signal. The resulting activation–deactivation time constants gave r values of 0.98–0.99 between the activation state and the force profiles. This work establishes a framework for developing improved muscle models that consider the intrinsic properties of slow and fast fibres within a mixed muscle, and that can more accurately predict muscle force output from EMG.

How to make robust splitting measurements for single-station analysis and three-dimensional imaging of seismic anisotropy

SUMMARY We quantify errors on splitting intensity measurements produced by incoherent noise on horizontal components through a detailed analysis of synthetic seismograms and of SKS and SKKS waves recorded by four permanent broad-band stations. We find that these errors are quite significant, even on high-quality records, because the measurement procedure involves the comparison of radial and transverse components, which are both contaminated by noise. To decrease the level of noise in the data, it is thus recommended to average splitting intensities from waves coming from the same backazimuth. Alternatively, one can analyse stacked radial and transverse components after applying a Wiener filter, which standardizes the waveforms. This is found to be equivalent because the measure of splitting intensity is a linear process. The utilization of Wiener filters reduces variations of apparent splitting resulting from differences in frequency content of the waveforms. It is possible to determine splitting parameters (splitting delays and fast directions) from azimuthal variations of splitting intensity at a particular station. Tests on synthetic seismograms demonstrate that this approach gives unbiased and robust estimates of splitting parameters, in contrast to the Silver and Chan method, which only works on the rare records that have very large signals on their transverse components. The Wolfe and Silver method does not suffer from this limitation and gives the same results as the multichannel splitting intensity method. Analysis of splitting intensities at stations BDFB, BGCA, CAN and ERM gives fast directions that are generally in excellent agreement with those determined with the Wolfe and Silver method. However, at some stations, azimuthal variations of splitting intensities reveal features that are not well captured by the sinusoidal variation representing the average anisotropy beneath the station. This suggests that smallscale lateral variations of anisotropy are present in the subcontinental mantle, which remain to be imaged in detail.

Imaging laterally varying regional heterogeneities from seismic coda using a source-array analysis

Seismic coda is composed of scattered waves originated from various kinds of heterogeneities, whose locations are not confined in the great-circle ray-path direction between the source and receiver. We devise a technique to image laterally varying regional heterogeneities using single-station seismograms for clustered events. We analyze regional seismic records of the Borovoye seismic station for the Balapan nuclear explosions in Kazakhstan. Scattered waves that arrive coherently over the source arrays, are extracted by directional beamformings. The locations of scatterers responsible for the scattered waves are mapped from the beamforming direction, travel time and slowness (equivalently, phase velocity). The illuminated locations of heterogeneities are highly correlated with the structural variations in surface topography, crustal thickness and sedimentary thickness. The influence of the structural variations on seismic waves is quantified in terms of scattering intensity and quality factor. The scattering properties are observed to vary with phase due to the difference in frequency content and phase velocity. The proposed technique appears to be useful for a study of active tectonic regions with limited monitoring stations.

Land Seismic Acquisition Repeatability for Time-Lapse Monitoring of CO2 Sequestration

Time-lapse surface and borehole seismic surveys are planned for monitoring the injection of CO2 in the CO2CRC Otway Basin Pilot Project in Victoria. Critical to the success of this is to ensure optimum repeatability of acquisition parameters and ground conditions. In order to assess the relative influences of source types and environmental conditions, a series of repeated test surveys have been undertaken. The study utilised repeated high-resolution seismic surveys along the same 2D line. The first test line was acquired with mini-vibroseis (6000 lb) in wet conditions when the top soil and the weathered layers were fully saturated. The line was subsequently re-recorded in dry conditions where we utilised the same mini-vibrator, but in addition repeated the line using a free-fall weight drop. Both sources have similar total energy output but a vibrator is a controlled frequency source while a weight drop is not. Despite differences in the frequency content and phase of the signal generated by these two sources, and positioning differences for source and receiver locations of up to 1m, almost identical stacked sections were obtained after phase matching and scaling of the two datasets. Far greater differences in total energy, frequency content and phase of the signal were observed between the two vibroseis lines recorded at different times of the year (wet and dry periods). Our results clearly demonstrate that near surface conditions has a first order effect on repeatability of land seismic surveys. A common belief that deployment of the same seismic source and positioning errors are crucial for successful time-lapse seismic needs to be reexamined in light of our results, which show that these factors are of secondary importance when it comes to land seismic surveys.

Sediment Thicknesses and Qs vs. Qp Relations in the Kachchh Rift Basin, Gujarat, India Using Sp Converted Phases

Delineation of the top sedimentary structure and its Qs vs. Qp relationship using the travel-time difference of direct S and converted Sp phase is key to understanding the seismic hazard of any sedimentary basin area. We constructed filtered displacement waveforms from local ETNA Episensor acceleration recordings as well as local velocity recordings of aftershocks of the 2001 Bhuj earthquake recorded by the Kachchh seismological network of the National Geophysical Research Institute (NGRI), Hyderabad, India during 2001–2004. Stations are within 15–70km of epicenters, and the resulting displacement waveforms are generally simple, displaying prominent P, Sp, and S wave pulses. Particle motion of P and S waves suggest near-vertical raypaths consistent with preliminary depth estimates. The direct S wave on the horizontal component is characterized by lower frequency content than the converted Sp phase on the vertical component. This difference in frequency content between S and Sp phases can be explained in terms of different attenuation effects for P and S waves in the unconsolidated sediments. The Sp phase is generated by S-to-P phase conversion at the base of Mesozoic sediments of the Kachchh basin. Travel-time inversion (VELEST) of 2565 P and 2380 S arrivals from 658 well located aftershocks recorded at 8–14 three-component local seismic stations led to 1 D velocity models indicated very slow sediments in the upper 0–2 km depth range (Vp: 2.92 km/s and Vs: 0.90 km/s) and an increasing trend of velocities with depth at 2–40 km depth. The estimated sediment thicknesses beneath 12 accelerograph and 6 seismograph sites from the estimated velocity model and the travel-time difference between S and converted Sp phases reaches a maximum of (1.534 ± 0.117) km beneath Bandri (near the location of 2001 Bhuj mainshock) and attains a minimum sediment thickness of (0.858 ± 0.104) km beneath Ramvav and Burudia. The spectral ratios between Sp and S from 159 three-component accelerograms have been used to study seismic wave attenuation in the Kachchh rift basin. The estimated Qs vs. Qp relations for 12 accelerograph sites vary from Qs = 0.184 Qp (at Chobari) to Qs = 0.505 Qp (at Dudhai). For stations Chobari, Chopdwa, Jahawarnagar, Vondh and Tapar, the spectral ratio slopes and hence the calculated Qs vs. Qp relations are effectively the same, and the correlation coefficients are quite high (0.91–0.93). Stations Adhoi, Manfara, New Dudhai, Dudhai and Sikara have similar Qs vs. Qp relationships to each other and also have high correlation coefficients (0.78–0.87). The spectral ratios for stations Anjar and Ramvav are small and poorly constrained, resulting in less reliable Qs vs. Qp relations. This could be due to noisy data, fewer available waveforms, or scattering due to velocity heterogeneities and/or interface irregularities.

Sliding response of gravity dams including vertical seismic accelerations

Seismic safety assessment of gravity dams has become a major concern in many regions of the world while the effects of vertical seismic accelerations on the response of structures remain poorly understood. This paper first investigates the effect of including vertical accelerations in the sliding response analysis of gravity dams subjected to a range of historical ground motion records separated in two groups according to their source-to-site distance. Analyses showed that the incidence of vertical accelerations on the sliding response of gravity dams is significantly higher for near-source records than for far-source records. The pseudo-static 30% load combination rule, commonly used in practice to account for the non-simultaneous occurrence of the peak horizontal and vertical accelerations, yielded good approximations of the minimum safety factors against sliding computed from time-history analyses. A method for empirically estimating the vertical response spectra based on horizontal spectra, accounting for the difference in frequency content and amplitudes between the two components is investigated. Results from analyses using spectrum compatible horizontal and vertical synthetic records also approximated well the sliding response of a gravity dam subjected to series of simultaneous horizontal and vertical historical earthquake records.

Evidence for fault lubrication during the 1999 Chi‐Chi, Taiwan, earthquake (Mw7.6)

The ground motion data of the 1999 Chi‐Chi, Taiwan, earthquake exhibit a striking difference in frequency content between the north and south portions of the rupture zone. In the north, the ground motion is dominated by large low‐frequency displacements with relatively small high‐frequency accelerations. The pattern is opposite in the south, with smaller displacements and larger accelerations. We analyze the fault dynamics in light of a fault lubrication mechanism using near‐field seismograms and a detailed rupture model. The fault zone contains viscous material (e.g., gouge), in which pressure increases following the Reynolds lubrication equation. When the displacement exceeds a threshold, lubrication pressure becomes high enough to widen the gap, thereby reducing the area of asperity contact. With less asperity contact, the fault slips more smoothly, suppressing high‐frequency radiation.

Frequency-domain analysis of the QRS complex after treatment of childhood cancer with anthracycline cytostatics.

Long-term cardiac complications, occurring several years after completion of anticancer treatment, may develop from subclinical myocardial damage induced during cardiotoxic therapy. The aim of this study was to evaluate the usefulness of frequency-domain signal-averaged ECG analysis of the QRS complex for assessing the cardiotoxicity of anthracycline cytostatics. Altogether, 172 signal-averaged electrocardiography (SAECG) registrations were performed in 50 repeatedly evaluated oncologic patients. These registrations were performed 0.2-15 years after completion of anthracycline therapy for childhood cancer. The control group consisted of 120 healthy children and young volunteers; in 20 of these controls, SAECGs were performed repeatedly. Using gliding window fast Fourier transformation within the QRS complex, values area ratio (AR) 60-120 Hz/0-120 Hz were calculated in X, Y, and Z lead. Area ratio of patients after anthracycline therapy was significantly higher than those in control group in X lead. Differences in frequency content in the QRS complex between patients and controls might signal an initial stage of anthracycline-induced myocardial damage.

Ultrasonic characterization of tissues via backscatter frequency dependence

Phantom and patient studies were performed to assess the potential of backscatter frequency dependence as a useful parameter for tissue characterization. A commercial phased-array ultrasonic scanner was adapted to allow dignitization of the intermediate-frequency ultrasonic data. Studies of agar phantoms containing polystyrene microspheres with 3.5 and 5 MHz transducers indicated the ability for robust differentiation of phantoms having different scatterer size and frequency dependence, based on calculated differences in mean frequencies of backscattered spectra. Using a 3.5-MHz probe, significantly lower mean frequency of ultrasound backscattered from cirrhotic, compared to normal, liver tissue was noted. Studies of benign and malignant liver tumors (hemangiomas and metastases, respectively) indicated differences in frequency content of these tumors, compared to the adjacent normal liver, that were statistically significant for 3.5-MHz data.

Sound Pressure Gradients Across the Head of Fetal Sheep in Utero During Vibroacoustic Stimulation

This study was undertaken to determine if sound pressures reaching the right and left ears of the sheep fetus are equal during vibroacoustic stimulation using an electronic artificial larynx (EAL). Three ewes (one carrying twins) were sacrificed as part of other experiments. Two miniature hydrophones were fixed to skin in the left and right temporal areas of the exteriorized fetal heads. The fetal head was replaced in the uterus and aligned such that the two hydrophones were in line with the axis of stimulation and at right angles to the abdominal surface. Intrauterine sound pressure levels (SPL) from both hydrophones were compared during extraabdominal stimulation with an electronic artificial larynx. SPL at the proximal hydrophone ranged from 138-145 dB (re: 20 μPa), and were on average 17 dB greater than SPL from the distal hydrophone. One-third octave band analyses of the two hydrophone outputs revealed marked differences in frequency content. For example, differences in SPL were 19 dB at 100 Hz. 25 dB at 2,000 Hz, 34 dB at 5,000 Hz and 15 dB at 20,000 Hz. During vibroacoustic stimulation using an EAL, a significant differential in sound pressure level and frequency content reaching the right and left fetal ears may occur.

Qp-Qs relations in the sedimentary basin of the upper Mississippi Embayment using converted phases

AbstractThree-component digital seismograms recorded by the 40 PANDA (Portable Array for Numerical Data Acquisition) stations in the New Madrid seismic zone were analyzed to study seismic wave attenuation in the sedimentary basin using the spectral ratio method. A prominent S-to-P (Sp) converted phase was generated at the boundary between the uppermost sedimentary basin and the underlying Paleozoic rocks. The direct S wave on the horizontal component is characterized by a lower-frequency content than that of the converted Sp wave on the vertical component. The differences in frequency content between the direct S and the Sp converted waves can be attributed to the different attenuation effects between P and S waves in the unconsolidated sediments. The spectral ratio between the low-frequency S wave and the high-frequency converted Sp wave from the bottom of the sediments can be used to yield a relationship between Qp and Qs in the sediments. Results from PANDA stations with well-constrained spectral ratios in the frequency range from 2 to 25 Hz give the Qp value ranging from 25 to 60 and Qs from 25 to 30 for the sedimentary basin in the upper Mississippi Embayment.

Broadband observations of upper-mantle seismic phases in northern Australia and the attenuation structure in the upper mantle

Abstract Sources in the earthquake belt through Indonesia and New Guinea, recorded at a broadband Guralp CMG3 seismometer at the Warramunga array in the Northern Territory of Australia, give good coverage of propagation through the upper part of the mantle. The midpoints of the propagation paths lie along the northern margin of the Australian continent. Beyond 18° there is a significant difference in the frequency content of P and S waves. The P waves remain high frequency, but the S waves returned from the transition zone and below are of intermediate period (0.1–0.5 Hz), which would be difficult to record without a broadband instrument and a quiet site. The later branches associated with the 410 and 660 km discontinuities are clearly seen in individual seismograms. The S waves recorded on the radial (SV) and tangential (SH) components are of comparable quality, because the hard-rock recording site minimizes the influence of coupling to P on the radial component. We interpret the observed difference in frequency content of P and S waves at transition-zone distances as the effect of a layer under the seismically fast lid which possesses a large degree of shear dissipation. We quantify the observation in terms of the decay rate of the spectral ratio of S and P waves. That quantity can be interpreted in terms of path integrals of the difference in inverse Q for S waves and P waves, t s * − t p * . We analyse 22 seismograms from the WRA broadband instrument and a further four from portable broadband instruments deployed near Warramunga. The measured slope of the S/P spectral ratio is consistently small out to 18° epicentral distance, where it increases dramatically. Assuming that shear dissipation dominates over bulk dissipation, these measurements are consistent with an average quality factor for S waves in the lid of the order of Q s = 1400 (Q p = 2800) on top of a highly attenuative asthenosphere of 200 km thickness with Q s = 100 (Q p = 200) , which is underlain by a transition zone with Q s = 600 (Q p = 1200) . The low- Q zone in the asthenosphere can equally well be modelled with a thinner layer with a lower Q, e.g. a layer of 100 km thickness with Q s = 60 . Frequency dependence of Q may render the above estimates of Q about 25% too large. These results compare fairly well with published results from 0.3 Hz body-wave observations under the Eurasian shield. Notable exceptions are that we obtain a somewhat lower value for Q s in the asthenosphere and a much higher value in the lid. The lid under northern Australia is unusually

Aliasing and sampling criteria for higher-order correlations

While sampling data at a Nyquist frequency equal to the highest frequency present in the data (critical sampling) is sufficient to prevent aliasing in both the data and the discrete-time autocorrelation calculated from the data of a bandlimited energy signal, the sampling requirements for the avoidance of aliasing in higher-order correlations are not necessarily the same. They depend on whether one samples the continuous-time autobicorrelation or autotricorrelation directly, for which critical sampling is sufficient, or whether these quantities are calculated from sampled data, in which case it is not. For the latter, the sampling interval for the autobicorrelation must be no greater than two-thirds the interval associated with critical sampling, and no greater than one-half for the autotricorrelation. Numerical calculations of autobicorrelation and autotricorrelation zero-lag values corresponding to spectral area and volume, as well as bispectral contour plots, for example, bandlimited deterministic signals, are presented as illustrations. Spectral and convolutional masking filters which remove aliasing in higher-order correlations calculated from critically sampled data are presented. Differences in frequency content for rectified signals and in aliasing for autocorrelations sampled directly or calculated from sampled data are also discussed. [Work supported by ONR/NRL-SSC.]