Numerical Waveforms Research Articles

Performance Limits in DS-CDMA Timing Acquisition

This paper addresses timing acquisition aspects in direct-sequence code division multiple access (DS-CDMA) systems. Various chip waveform shaping schemes are considered, including both one-chip long full-response pulses, and partial-response ones occupying several chip periods. Different figures of merits are considered in a comparative analysis that seeks to establish performance limits in terms of correct timing detection capability, false alarm rate, bandwidth occupancy, multiple-access interference (MAI), and inter-chip interference (ICI). A waveform design algorithm is formulated to optimize system performance in terms of signal-to-interference-ratio (SIR) subject to other signalling constraints, and a solution based on the use of prolate spheroidal wave functions (PSWF) is derived. Numerous waveform design examples are then constructed to illustrate acquisition detection capability versus system load for both faded and unfaded cases. A comparative assessment of the performance of conventional signalling waveforms against the optimized ones is also presented. In particular, the numerical results show that the half-sine pulse used in minimum shift keying (MSK) is quasi-optimal within the full-response category, while root-raised cosine (RRC) Nyquist filtering with 22% rolloff (used in third generation CDMA standards) is also close to optimal when considering many-chip-long pulses.

Mining information from binary black hole mergers: A comparison of estimation methods for complex exponentials in noise

The ringdown phase following a binary black hole merger is usually assumed to be well described by a linear superposition of complex exponentials (quasinormal modes). In the strong-field conditions typical of a binary black hole merger, nonlinear effects may produce mode coupling. Artificial mode coupling can also be induced by the black hole's rotation, if the radiation field is expanded in terms of spin-weighted spherical harmonics (rather than spin-weighted spheroidal harmonics). Observing deviations from the predictions of linear black hole perturbation theory requires optimal fitting techniques to extract ringdown parameters from numerical waveforms, which are inevitably affected by numerical error. So far, nonlinear least-squares fitting methods have been used as the standard workhorse to extract frequencies from ringdown waveforms. These methods are known not to be optimal for estimating parameters of complex exponentials. Furthermore, different fitting methods have different performance in the presence of noise. The main purpose of this paper is to introduce the gravitational wave community to modern variations of a linear parameter estimation technique first devised in 1795 by Prony: the Kumaresan-Tufts and matrix pencil methods. Using ``test'' damped sinusoidal signals in Gaussian white noise we illustrate the advantages of these methods, showing that they have variance and bias at least comparable to standard nonlinear least-squares techniques. Then we compare the performance of different methods on unequal-mass binary black hole merger waveforms. The methods we discuss should be useful both theoretically (to monitor errors and search for nonlinearities in numerical relativity simulations) and experimentally (for parameter estimation from ringdown signals after a gravitational wave detection).

How far away is far enough for extracting numerical waveforms, and how much do they depend on the extraction method?

We present a method for extracting gravitational waves from numerical spacetimes which generalizes and refines one of the standard methods based on the Regge–Wheeler–Zerilli perturbation formalism. At the analytical level, this generalization allows a much more general class of slicing conditions for the background geometry, and is thus not restricted to Schwarzschild-like coordinates. At the numerical level, our approach uses high-order multi-block methods, which improve both the accuracy of our simulations and of our extraction procedure. In particular, the latter is simplified since there is no need for interpolation, and we can afford to extract accurate waves at large radii with only little additional computational effort. We then present fully nonlinear three-dimensional numerical evolutions of a distorted Schwarzschild black hole in Kerr–Schild coordinates with an odd parity perturbation and analyse the improvement that we gain from our generalized wave extraction, comparing our new method to the standard one. In particular, we analyse in detail the quasinormal frequencies of the extracted waves, using both methods. We do so by comparing the extracted waves with one-dimensional high resolution solutions of the corresponding generalized Regge–Wheeler equation. We explicitly see that the errors in the waveforms extracted with the standard method at fixed, finite extraction radii do not converge to zero with increasing resolution. We find that even with observers as far out as R = 80M—which is larger than what is commonly used in state-of-the-art simulations—the assumption in the standard method that the background is close to having Schwarzschild-like coordinates increases the error in the extracted waves considerably. Furthermore, those errors are dominated by the extraction method itself and not by the accuracy of our simulations. For extraction radii between 20M and 80M and for the resolutions that we use in this paper, our new method decreases the errors in the extracted waves, compared to the standard method, by between one and three orders of magnitude. In a general scenario, for example a collision of compact objects, there is no precise definition of gravitational radiation at a finite distance, and gravitational wave extraction methods at such distances are thus inherently approximate. The results of this paper bring up the possibility that different choices in the wave extraction procedure at a fixed and finite distance may result in relative differences in the waveforms which are actually larger than the numerical errors in the solution.

Anomalous Propagation of Long-Period Ground Motions Recorded in Tokyo during the 23 October 2004 Mw 6.6 Niigata-ken Chuetsu, Japan, Earthquake

Unusually large (5 cm) and prolonged shaking associated with long- period ground motions at periods of about 7 sec were observed in central Tokyo during the Mw 6.6 Niigata-ken Chuetsu earthquake of 23 October 2004. The long- period ground motions caused significant resonance in high-rise buildings of about 70 floors in height. Thus, it is an urgent matter to understand the development and amplification properties of long-period ground motions in Tokyo associated with large earthquakes. In this study, we use numerous waveform records from 585 stations in a nationwide accelerometer network (K-NET, KiK-net) and 495 intensity meters in the area around Tokyo. The data reveal that the long-period ground motion is characterized in most part by a surface, Rayleigh wave generated at the northern edge of Kanto basin, and the surface wave is developed as propagating through a thick cover of sediments (3000-4000 m) that overlies rigid bedrock. To complement the observational data, we conducted a large-scale computer simu- lation of seismic-wave propagation by employing the Earth Simulator supercomputer with a detailed source-slip model and a high-resolution 3D sedimentary structural model of central Japan. The results of the computer simulation demonstrate that the anomalously prolonged ground shaking of the long-period signal recorded in the center of Tokyo occurred because of the stagnation of seismic energy resulting from the multipathing and focusing of Rayleigh waves toward the bottom of the Kanto basin from surrounding mountain regions with interaction to the 3D basin structure.

Pulse wave propagation in a model human arterial network: Assessment of 1-D numerical simulations against in vitro measurements

A numerical model based on the nonlinear, one-dimensional (1-D) equations of pressure and flow wave propagation in conduit arteries is tested against a well-defined experimental 1:1 replica of the human arterial tree. The tree consists of 37 silicone branches representing the largest central systemic arteries in the human, including the aorta, carotid arteries and arteries that perfuse the upper and lower limbs and the main abdominal organs. The set-up is mounted horizontally and connected to a pulsatile pump delivering a periodic output similar to the aortic flow. Terminal branches end in simple resistance models, consisting of stiff capillary tubes leading to an overflow reservoir that reflects a constant venous pressure. The parameters required by the numerical algorithm are directly measured in the in vitro set-up and no data fitting is involved. Comparison of experimental and numerical pressure and flow waveforms shows the ability of the 1-D time-domain formulation to capture the main features of pulse wave propagation measured throughout the system test. As a consequence of the simple resistive boundary conditions used to reduce the uncertainty of the parameters involved in the simulation, the experimental set-up generates waveforms at terminal branches with additional non-physiological oscillations. The frequencies of these oscillations are well captured by the 1-D model, even though amplitudes are overestimated. Adding energy losses in bifurcations and including fluid inertia and compliance to the purely resistive terminal models does not reduce the underdamped effect, suggesting that wall visco-elasticity might play an important role in the experimental results. Nevertheless, average relative root-mean-square errors between simulations and experimental waveforms are smaller than 4% for pressure and 19% for the flow at all 70 locations studied.

Nondestructive Dynamic Evaluation of a Concrete Reaction Wall—Numerical and Experimental Studies

Proper identification of the modes of vibration of a structure is crucial in order to avoid the condition of resonance under dynamic loading conditions. A combination of numerical simulation, physical experimentation, and waveform analysis was employed in order to obtain a dynamic evaluation of the reaction wall for the Network for Earthquake Engineering Simulation (NEES) large scale testing laboratory at Cornell University. The first four modes of vibration of the structure were identified, and this information is now available to researchers who design experiments that utilize the NEES facility. This paper presents the numerical (finite element) studies and a description of the impact test procedure used to excite and record the response of this massive, posttensioned, reinforced concrete structure. It also illustrates how numerical modeling aided in the design of experiments and how waveform analysis proved essential for the proper characterization of the dynamic behavior of this unusual structure.

Acoustic field excited by a pulsed laser line source in a cylinder

The excitation and propagation of the acoustic waves in an elastic cylinder are studied by laser ultrasonics both theoretically and experimentally. The theoretical analysis of the two-dimensional acoustic field excited by a pulsed laser line source impacting on the generatrix of an elastic cylinder is presented. The dispersive properties for both cylindrical Rayleigh wave and the higher modes – whispering gallery (WG) modes are analyzed in detail. The numerical transient displacement waveforms for a detecting point located another terminal of the cylinder diameter opposite the source are calculated. The experimental excitation and detection of the acoustic waves in an aluminum cylinder are carried out on a laser ultrasonic system, which mainly consists of a Q-switched Nd:YAG laser and a laser interferometer. The wave components of bulk waves and surface waves (cylindrical Rayleigh waves and WG modes) are analyzed by comparing the numerical and experimental waveforms. The results are in good agreement.

Detecting gravitational waves from test-mass bodies orbiting a Kerr black hole with P-approximant templates

In this study, we apply post-Newtonian (T-approximants) and resummed post-Newtonian (P-approximants) to the case of a test particle in equatorial orbit around a Kerr black hole. We compare the two approximants by measuring their effectualness (i.e., larger overlaps with the exact signal) and faithfulness (i.e., smaller biases while measuring the parameters of the signal) with the exact (numerical) waveforms. We find that in the case of prograde orbits, T-approximant templates obtain an effectualness of ∼0.99 for spins q ⩽ 0.75. For 0.75 < q < 0.95, the effectualness drops to about 0.82. The P-approximants achieve effectualness of >0.99 for all spins up to q = 0.95. The bias in the estimation of parameters is much lower in the case of P-approximants than T-approximants. We find that P-approximants are both effectual and faithful and should be more effective than T-approximants as a detection template family when q > 0. For q < 0, both T- and P-approximants perform equally well so that either of them could be used as a detection template family. However, for parameter estimation, the P-approximant templates still outperform the T-approximants.

Simultaneous inversion of shear wave splitting observations from seismic arrays

Seismic waveforms recorded at high‐density receiver arrays facilitate the application of new inversion techniques, which take advantage of the coherent nature of the observations. We use measurements of shear wave splitting parameters from observed SKS waveforms along a dense receiver profile and compare them with splitting parameters obtained from numerical waveform modeling through anisotropic Earth models. We use two different iterative approaches for the inversion of the observed splitting parameters (1) a local optimization technique (the downhill simplex method) and (2) a global genetic algorithm search. In our forward modeling, we calculate SKS waveforms by a finite difference (FD) method solving the anisotropic wave equation, instead of deriving individual anisotropic models for each station and combining them into one model. By the comparison of FD modeling and observations we avoid a direct interpretation of the splitting parameters in terms of medium properties. We apply these techniques to the analysis of SKS phases recorded along a 100‐km profile located at the Dead Sea transform fault. The measured splitting parameters show gradual short‐scale variations along the profile which depend on frequency. Lateral and vertical variations of anisotropy are accounted for by two‐dimensional block structures. For the simplex method the complexity of the models (the number of anisotropic blocks) is increased gradually, whereas the number of anisotropic blocks is kept fixed for the genetic algorithm search. The anisotropic structures of the best fitting models derived from the two inversion approaches agree well. The results support earlier interpretations of the observations in terms of a narrow, approximately 20 km wide, vertical decoupling zone in the mantle that accommodates the transform motion between the African and Arabian plates.

Improved gravitational waveforms from spinning black hole binaries

The standard post-Newtonian approximation to gravitational waveforms, called T-approximants, from non-spinning black hole binaries are known not to be sufficiently accurate close to the last stable orbit of the system. A new approximation, called P-approximants, is believed to improve the accuracy of the waveforms rendering them applicable up to the last stable orbit. In this study we apply P-approximants to the case of a test-particle in equatorial orbit around a Kerr black hole parameterized by a spin parameter q that takes values between -1 and 1. In order to assess the performance of the two approximants we measure their effectualness (i.e. larger overlaps with the exact signal), and faithfulness (i.e. smaller biases while measuring the parameters of the signal) with the exact (numerical) waveforms. We find that in the case of prograde orbits, that is orbits whose angular momentum is in the same sense as the spin angular momentum of the black hole, T-approximant templates obtain an effectualness of ~ 0.99 for spins q < 0.75. For 0.75 < q < 0.95, the effectualness drops to about 0.82. The P-approximants achieve effectualness of > 0.99 for all spins up to q = 0.95. The bias in the estimation of parameters is much lower in the case of P-approximants than T-approximants. We find that P-approximants are both effectual and faithful and should be more effective than T-approximants as a detection template family when q>0. For q<0 both T- and P-approximants perform equally well so that either of them could be used as a detection template family.

Seismological Studies at Parkfield IX: Fault-Zone Imaging Using Guided Wave Attenuation

Numerical modeling studies and a growing number of observations have argued for the propagation of fault-zone guided waves (FZGWs) within a San Andreas Fault (SAF) zone that is 100-200 m wide at seismogenic depths and with 20%-40% lower shear-wave velocity than the adjacent unfaulted rock. Thousands of microearthquakes have been recorded since 1987 by the borehole High-Resolution Seismic Network at Parkfield, California, and they provide a comprehensive data set for characterizing wave propagation in the SAF zone. Using microearthquakes we confirm that FZGWs at Parkfield are generated within the fault zone (FZ) and that they are most prominent late in the coda of S . Numerical waveform modeling and guided-wave amplitude tomographic inversion show clearly that FZGWs are significantly less attenuated in a well-defined region of the FZ. This region plunges to the northwest along the northwest boundary of the region of highest moment release and separates locked and slipping sections of the SAF at depth, as determined independently from geodesy, seismicity, and the recurrence rates of characteristically repeating microearthquakes. We interpret this localized zone of strong FZGW propagation to be the northwest edge of the M 6 asperity at Parkfield. The mechanism for low FZGW attenuation in the zone is possibly due to dewatering by fracture closure and/or fault-normal compression or changes in fracture orientation due to a complex stress or strain field at the boundary between creeping and locked zones of the SAF. Manuscript received 23 April 2002.

Non-linear flexural waves in thin layers

Non-linear flexural waves in thin plates or layers have been analyzed in this paper. The equation of motion of the plate is derived assuming that the motion is antisymmetric about the mid-plane of the plate and that the plate is thin. The plate is considered to be elastic. The Von Karman non-linear strains and Landau elastic constants have been used to model geometric and material non-linearities, respectively. An asymptotic analysis of wave motion is presented using the method of multiple scales. Evolution equations are derived for small amplitude traveling flexural elastic waves. Numerical results show waveform distortion, amplitude amplification, and harmonic generation.

A New Metaphor to Display Critical Pulmonary Events during Anesthesia

The anesthesiologist is faced with a fire-hose of information in the operating room. Data from the patient monitors include numerical data, waveforms, control settings, and alarm conditions. During an unexpected event, the anesthesiologist must quickly assess available information in order to diagnose and treat the patient before the patient is injured. However, human error is associated with more than 80% of critical anesthesia incidents and more than 50% of anesthetic deaths.1 In a recent study at the University of Washington, Department of Anesthesiology, 32% of the reported human error incidents were related …

Radiation digital signal processing using smoothing spline

The noise component in digitized signal data greatly affects the result of numerical waveform processings. The effectiveness of the smoothing spline method has been examined by obtaining the distributions of calculated rise-time value. During the comparison of the distributions with the Savitzky–Golay method, the better suppression of the noise component was observed by applying the smoothing spline method.

Numerical waveform control for rotational single sheet testers

Rotational single sheet testers are imposed as measuring systems for a complete, in plane. characterisation of magnetic materials. The numerical waveform control that drives the RSST is, despite its slow speed. more precise and versatile than the analogic version. Its adaptability to almost every induction waveform in a large frequency range makes it suitable for completely automated test procedures. The actual hardware implementations is reported. The existence of a variable coupling between the two principal axes imposes a simultaneous correction with respect to the flux waveform of the perpendicular axis. The magnetic circuit with airgaps hinders a-simple direct relation between circuit and field equations. whence the difficulty of estimating the first correction steps. The electromagnetic model and the electrical equations are discussed in order to determine solutions that improve numerical convergence.

Comparison of 2-D numerical viscoelastic waveform modeling with ultrasonic physical modeling

The objective of the study is to test the validity of theoretical models of wave attenuation by comparing their predictions of attenuation against physical model results. The study is confined to a 2-D geometry, and the viscoelastic materials used in physical modeling are those commonly used in the experiment. The physical modeling data of homogeneous media are compared with the numerical results in the frequency domain. The time‐domain comparisons between numerical modeling and physical modeling are also shown by three examples. The theoretical viscoelastic models used in the numerical study are the Kelvin‐Voigt model, the standard linear solid model, and the standard linear solid model with a continuous spectrum of relaxation time. On the comparison of a single model, all the models simulate the physical model fairly well, but the standard linear solid model gives the best result among them. The Kelvin‐Voigt model is easy to use as a quick first‐order simulation of the viscoelastic materials because it has fewer viscosity parameters than the other two models. The disadvantage of the Kelvin‐Voigt model is that it predicts too much attenuation of the high‐frequency components. It is also shown that neglecting the viscosity of some materials like polyvinylcloride plastic (PVC), which has high viscosity, will produce incorrect results in synthetic seismograms.

High‐frequency precursors to P wave arrivals in New Zealand: Implications for slab structure

This report revisits the very early high‐frequency slab phases from earthquakes in the Kermadec slab (between −25°S and −37°S) that arrive as a precursor to the P wave onset at stations in New Zealand. The analysis of short‐period digital records for station SNZO (South Karori New Zealand) for the time period between 1980 and 1986 involved 4 times as many data as in previous studies. We confirm most of the earlier observations, in particular the relationship between source region and observed waveform. Numerical waveform modeling using two‐dimensional slab models confirm that the high‐frequency precursor can be explained by P wave propagation in a thin (8–10 km) high‐velocity layer (HVL). The sensitivity of the high‐frequency phase to source position in the slab is investigated, and we demonstrate that the slab phase does not survive interruptions or strong lateral variations of the HVL. Assuming the shape of the slab from tomographic images and continuity of the HVL, we infer that the large negative travel time residuals can be explained if P wave propagation is 4 to 5% faster than in the ambient mantle for depths to 300 km and about 2% faster for depths between 300 and 600 km. Rather than resorting to regional differences in structure and composition of the HVL, we argue that specific source‐receiver configurations and the shape of the slab explain the observed regional variation in the character of the high‐frequency slab phases.

Machine scoring of somatosensory evoked potentials

A machine-scoring algorithm was developed for automatic identification and measurement of the positive and negative peaks of short-latency somatosensory evoked potentials (SEPs). The algorithm enables objective and consistent identification and naming of specific components with minimal operator involvement, avoiding inaccuracies and variability resulting from differences in the criteria used by different operators, or by the same operator at different times. The algorithm is based on finite impulse response filtering of wave forms from 4 conventional recording channels at a bandpass of 90–240 Hz. The bandpass was based on the major lobe in power spectra of multiple records and was verified as effective by application to numerous wave forms. Peak identification is based on identifying the peak at its optimal channel and verifying its consistency with corresponding peaks in the other channels. The machine-scoring algorithm was validated on SEPs from 120 subjects. The machine-scored peak latencies obtained with this procedure were significantly correlated with their manually measured counterparts.

QUANTITATIVE EVALUATION OF DEFECTS BY NEURAL NETWORK

Abstract A neural network is applied to a quantitative evaluation of defects. The training data for learning of neural network are prepared from a numerical analysis based on an elastic wave theory. The question posed here is to. evaluate the depth of surface-breaking cracks in a structural component. The numerical analysis is carried oui for ten cracks ranging from 0.6 mm to 2.4 mm separated by 0.2 mm in depth. Waveforms in the time and frequency domains are calculated by the use of the boundary element method for these ten types of crack depth. The neural network used here is the three layered network of perception type. Each layer is called input, association, and output layer, respectively. In this type of network, we can use a learning algorithm called back error-propagation and the network deduces the waveform characteristics from the training data and induces the evaluation criteria. After the network training by the use of numerical waveforms, the network is used to evaluate the measured data obta...

Multipole sources in boreholes penetrating anisotropic formations: Numerical and experimental results

A 2.5-D velocity-stress finite-difference code is described that models acoustic propagation in a borehole penetrating a generally anisotropic formation. The excitation may be a dilatation (monopole), or a point force (dipole) in an arbitrary direction. The anisotropic formation is homogeneous along the axis of the borehole but may be inhomogeneous in the transverse plane. The borehole cross section and location of the source in the borehole are arbitrary. Synthetic time-domain waveforms are displayed for arrays of monopole and dipole receivers deployed along the borehole axis in both fast and slow anisotropic formations. The specific anisotropy model employed for the numerical results is a transversely isotropic (TI) formation with its axis of symmetry inclined with respect to the borehole axis by an arbitrary angle. Flexural/shear and Stoneley wave slowness and attenuation estimates are extracted from the synthetic waveforms using a variant of Prony’s method for a range of borehole inclinations relative to the formation axis of symmetry. In a fast formation, with borehole and formation symmetry axes perpendicular, flexural mode dispersion curves for quasi-SV and SH polarizations separate only at low frequency where moderate attenuation is also observed. In a slow formation, distinct dispersion curves are obtained for quasi-SV and SH polarizations over the entire frequency range. Moderate attenuation is again observed at low frequency. Scaled laboratory experiments confirm the numerical procedure. Experimental and numerical waveforms for monopole and several polarizations of dipole excitation in a transversely isotropic model formation overlay with excellent agreement.