Wavefront Arrival Research Articles

Determination of elastic constants of a concrete specimen using transient elastic waves

This paper presents the results of measuring the Rayleigh wave as well as longitudinal wave velocities in a concrete specimen using transient elastic waves. The Rayleigh surface wave generated by a steel ball impact on a concrete material is studied in detail and then a method for the determination of Rayleigh surface wave velocity based on the cross-correlation method is proposed. The longitudinal wave velocity of a concrete specimen is determined by measuring the wavefront arrival of a longitudinal wave. A special triggering device for the accurate determination of the impact time origin is utilized. The measured velocities of both the Rayleigh wave and the longitudinal wave in the concrete specimen are in good agreement with those measured by utilizing the conventional ultrasonic method. It is noted that with the Rayleigh wave and the longitudinal wave velocities measured, the Young’s modulus as well as the shear modulus of a concrete specimen can be obtained in a straightforward way.

PERFORMANCE STUDY OF A MINIMAX ROBUST MATCHED FIELD PROCESSOR

In both conventional array processing, where wave front arrivals are assumed planar, and matched field processing, where full field propagation models are used to predict the signal field at the array, detection and localization are carried out by looking for large values of the beamformer response. This approach does not generally model the statistical uncertainty in the signal wave front arrival structure that results from fundamentally stochastic ocean environmental phenomena. The realization that, inevitably, the true environment differs from that used to generate the predicted signal field has motivated interest in robust matched field processors. In a recent paper, we showed how one may adapt the minimax solution to the uncertain communication channel equalization problem to derive robust matched field processors. In this paper we discuss some of the acoustic and computational issues associated with these robust matched field processors and describe the results obtained upon applying these processors to the Acoustic Models in Signal Processing (AMSP) Workshop test data sets.

Measurements of ultrasonic pulse arrival time and energy level variations produced by propagation through abdominal wall

Ultrasonic pulse arrival time and energy level variations introduced by propagation through human abdominal wall specimens have been measured. A hemispheric transducer transmitted an ultrasonic pulse that was detected by a linear array transducer after propagation through an abdominal wall section. The array was translated in the elevation direction to collect data over a two-dimensional aperture. Differences in arrival time and energy level between the measured waveforms and calculated references that account for geometric delay and spreading were found. Plots of waveforms compensated for geometric path, maps of time delay differences and energy level fluctuations, and statistics derived from these for water paths and tissue paths characterize the measurement system and describe the time delay differences and energy level fluctuations caused by 14 different human abdominal wall specimens. Repeated measurements using the same specimens show that individual tissue path measurements are reproducible, the results depend on specimen position, and frozen storage of a specimen for three months does not appear to alter the time delay differences and energy level fluctuations produced by the specimen. Comparison of measurements at room and body temperature indicates that appreciably higher time delay differences occur at body temperature while energy level fluctuations and time delay difference patterns are less affected. For the 14 different abdominal wall specimens, the rms time delay differences and energy level fluctuations have average values of 43.0 ns and 3.30 dB, respectively, and the associated correlation lengths of the time delay differences and energy level fluctuations are 7.90 and 2.28 mm, respectively. The spatial patterns of time delay difference and energy level fluctuation in the reception plane appear largely uncorrelated, although some background variations in energy level fluctuation are similar to features in time delay difference maps. The results provide important new information about the variety and range of ultrasonic wave front arrival and energy variations caused by transmission through abdominal wall.

Fundamental elastodynamic solutions for anisotropic media with ellipsoidal slowness surfaces

When the slowness surface S of an anisotropic elastic medium consists of three concentric ellipsoids, solutions of the displacement equations of motion can be generated from functions satisfying scalar wave equations and the problem of constructing the fundamental, or Green’s, tensor G for an infinite region becomes tractable. This paper has two aims: first, to find all the conditions on the linear elastic moduli under which S is ellipsoidal (that is the union of concentric ellipsoids), and, second, to determine G for each case in which S simplifies in this way. The two stages of the investigation have a key idea in common. The ellipsoidal form of S requires the eigenvalues of the acoustical tensor Q ( n ) to be quadratic forms in the unit vector argument n : at least two of the associated eigenvectors are either constant or linear in n and the squared moduli of the linear eigenvectors are divisors of eigenvalue differences. These algebraic properties provide a classification of media with ellipsoidal slowness surfaces and aid in characterizing the membership of each class. The first stage culminates in four sets of conditions, labelled A, B, C(i) and C(ii): case C(i) is a restriction of transverse isotropy and the others are specializations of orthorhombic symmetry. At the second stage n is replaced by the gradient ∂ with respect to spatial position and polynomials in n become differential operators. The construction of G involves two canonical problems of classical type, an initial-value problem for a scalar wave equation and a potential problem for a pair of ‘ charged ’ ellipsoids. The divisibility property indicated above implies that the ellipsoids are confocals carrying equal and opposite charges and these characteristics render the fundamental solution causal in the sense that the entire disturbance excited by the point impulse begins with the first and ends with the last of the wavefront arrivals. The structures of the fundamental solutions in cases A, B, C(i) and C(ii) are described and the latter solution is shown to reduce to a standard result of Stokes in the degenerate case of isotropy. Mention is also made of a specialization of case B, appropriate to a transversely isotropic medium which is inextensible in the direction of the symmetry axis.

The radio time delay in the double quasar 0957 + 561

Gravitational lens models for the double quasar 0957+561 predict that there should be a time delay of roughly 1 year between the arrival of wave fronts from the two images. In order to measure this delay, the flux densities were monotored at λ = 6 cm of 0957+561A and 0957+561B since 1979. The flux curves of the two images constructed from the VLA data are presented, which are accurate to 2% of the image flux densities. The VLA data are best fitted by a time delay of 1.40 ± 0.1 yr (513 ± 40 days, A leading), with a magnification ratio (B/A) of 0.697 ± 0.003. The error estimates were obtained through Mont Carlo methods, and include 68% of the simulated solutions

The constrained total least squares technique and its applications to harmonic superresolution

The constrained total least squares (CTLS) method is a natural extension of TLS to the case when the noise components of the coefficients are algebraically related. The CTLS technique is developed, and some of its applications to superresolution harmonic analysis are presented. The CTLS problem is reduced to an unconstrained minimization problem over a small set of variables. A perturbation analysis of the CTLS solution is derived, and from it the root mean-square error (RMSE) of the CTLS solution, which is valid for small noise levels, is obtained in closed form. The complex version of the Newton method is derived and applied to determine the CTLS solution. It is also shown that the CTLS problem is equivalent to a constrained parameter maximum-likelihood problem. The CTLS technique is applied to estimate the frequencies of sinusoids in white noise and the angle of arrival of narrowband wavefronts at a linear uniform array. In both cases the CTLS method shows superior or similar accuracy to other advanced techniques. >

Experimental analysis of reservoir release wave routing in upland boulder bed rivers

AbstractReservoir release wave routing during 33 controlled reservoir releases, along 15 upland boulder bed river channel reaches, on five different regulated rivers were monitored to assess the importance of river channel roughness and reservoir release magnitude on reservoir release wave speeds. Wave speeds varied between 0.52 and 3.01 m s−1. Reservoir release wave translation, steepening, and attenuation occurred. With high channel roughness values reservoir release wave arrival speed is retarded in comparison to peak stage and wave steepening occurs, but with a reduction in channel roughness reservoir release wave front arrival is accelerated producing attentuation. The threshold between reservoir release wave front attenuation and steepening occurs at a pre‐release discharge/channel width of approximately 0.1, an index of channel roughness.The paper also demonstrates, via comparison of observed and calculated reservoir release wave speeds on the River Washburn, Yorkshire, the difficulty of accurately predicting flood wave movement in upland boulder bed channels using existing prediction equations. The calculated values, however, revealed systematic error with pre‐release discharge and reservoir release magnitude. Apparently the equations fail to account for the effects of high channel roughness together with pressure gradient forces, induced by rapid rates of stage change on the rising limb of reservoir releases. In order to accurately predict reservoir release wave movement in regulated rivers, this paper demonstrates that hydraulic studies need to be undertaken and pre‐release discharges prescribed to determine desired reservoir release wave routing behaviour. Manipulation of the reservoir release pattern at the dam alone, cannot dictate reservoir release wave front form downstream or wave speed.

Interference-tolerant time-difference-of-arrival estimation for modulated signals

A method for estimation of the difference in the times of arrival of wavefronts of two separate sensors is introduced. The method, called SPECCORR, exploits the spectral correlation property, called spectral coherence, that essentially all modulated signals exhibit to obtain estimates that are highly tolerant to severely corruptive noise and interference. This tolerance is explained theoretically and demonstrated with simulations. >

Traveling wave and SEM representations for transient scattering by a circular cylinder

When observed over long observation times, scattered returns from targets illuminated by broadband acoustic signals reveal distinctive features in the early and late time regimes. The features can be explained in terms of the different wave phenomena, progressive and oscillatory, that are dominant during these respective intervals. The former represent wave front arrivals, and the latter full body resonances. A hybrid theory, recently developed by Heyman and Felsen [IEEE Trans. Antennas Propag. AP-31, 426–437 (1983)], has formalized the connection between them and has provided new interpretations that have not emerged from more conventional treatments. These interpretations can clarify issues which have arisen within the resonance expansion procedure, in particular, the adequacy of the expansion at early times. In this paper, the canonical problem of scattering by a circular cylinder serves as a rigorous test for general observations made elsewhere [E. Heyman and L. B. Felsen, IEEE Trans. Antennas Propag. AP-31, 706–718 (1985)], concerning the traveling wave interpretation of the resonance series, and especially the role of the entire function in the complex frequency plane that is included to repair resonance series deficiencies of the Singularity Expansion Method (SEM). The resonance series of damped global oscillatory wave fields corresponding to the complex resonant frequencies represents, collectively, the multiple effects of diffracted (creeping) waves traveling around the cylinder in the positive and negative directions, but it cannot incorporate the specularly reflected field in the lit region, which has not sampled the obstacle surface as a whole. This contribution remains as a free term that can be identified in the complex frequency plane as an intrinsic (nonremovable) entire function. The analysis also shows how delaying the turn-on time of the resonance series, by retaining some early creeping wave front arrivals intact, can generate, in addition, a nonintrinsic (i.e., removable) entire function. These considerations, having rigorous foundation and appealing physical content, aid in the understanding of wave phenomena associated with broadband scattering from targets observed over early and late time periods.

Estimation of time differences of arrival by pole decomposition

Time differences of arrival (TDOA's) of emitter wave fronts to a spatially distributed array of sensors can be used to determine the source location. In this paper, we suggest a new method of TDOA estimation for multiple unknown autoregressive moving average (ARMA) sources and additive noise that may be correlated between the sensors. We derive a theoretical formula that only uses the receiver cross spectra and the source poles for the TDOA determination. The poles are estimated by a least squares technique, and two methods are suggested for the estimation of the cross spectra which allow tradeoffs between computational complexity and accuracy. A new time delay model is derived and used to show the applicability of the methods for noninteger TDOA's. Results from simulations illustrate the performance of the algorithm by Monte Carlo trials and compare it to the Cramer-Rao bound.

Creeping waves and resonances in transient scattering by smooth convex objects

Scattering by smooth convex objects, excited by a transient field with broad spectral content, has been analyzed either by ray formulations, which are useful at observation times descriptive of the early arrivals, or by the complex resonances of the singularity expansion method (SEM), which are most appropriate at intermediate and late observation times. Within the framework of SEM, efforts have recently been made to show that in a grouping of the resonances along "layers," rather than along the conventional "arcs" based on an angular harmonic field representation, the higher order resonances behave collectively like a wave traveling circumferentially around the object. This observation has provided the stimulus for the present investigation in which the relation between the wavefront arrivals (creeping waves) and the SEM resonances is placed on a rigorous basis. Using a perfectly conducting circular cylinder as a canonical model, this is done by direct application of the theory of characteristic Green's functions to construct alternative field solutions, and by collective summation of groups of wavefront arrivals or groups of resonances. The connection between creeping waves and resonances thus having been established, hybrid formulations are developed which combine the creeping waves and the SEM resonances within a single rigorous framework so as to maximize the utility of each over the entire range of observation times. These results are then generalized to smooth cylindrical objects with noncircular convex shape.

Pulse generation in an elastic half space by normal pressure

The generation of pulse in an elastic half space by impulsive normal pressure over a circular area on the surface has been investigated by Cagniard De-Hoop technique. The approximate representations of the displacement field near the times of arrival of various wave fronts have been derived by a limiting process.

Pulse generation in an elastic half-space by the uniform normal loading of a circular surface segment

In this paper we consider the generation of an elastic pulse in a semi-infinite, homogeneous, isotropic elastic solid by the application of a uniform time-dependent normal pressure over a circular portion of the surface of the half-space. Formal expressions are presented for the Laplace transforms of the displacement components which describe the axisymmetrical poloidal pulse. The pattern of wavefronts which develops consists of a direct wavefront, edge dilatational and rotational wavefronts, and head wavefronts. The discontinuous behaviour associated with the arrival of the various wavefronts is examined with the aid of approximate representations of the displacement field.

Transient Wavefronts on Lossy Transmission Lines-Effect of Source Resistance

Approximations are derived for current and voltage produced on a skin-effect lossy line by a step-function voltage source with a series lumped resistance. Differences among computed normalized voltages corresponding to different values of source resistance increase with distance from the source and with time after wavefront arrival.

Analysis of a Computer Simulation of a DIMUS System

In the usual shift-register/delay-line arrangement, as detailed by Anderson (1960, 1961) and Rudnick (1960), geometry of the array, in conjunction with sound velocity in the medium, establishes a time delay for each wavefront arrival at a particular phone. The pressure waveform is then stored in each shift register, and is then clocked at a rate sufficiently above the Nyquist frequency, such that degradation of zero crossover information is avoided. Sampling the shift-register matrix, at points appropriate to the array geometry, will result in a gain for the signal emanating from a given direction. One characteristic feature of the DIMUS system is an amplitude normalization, which devolves from the binary nature of quantization. Thus, from the maximum signal-to-noise ratio to the minimum, from +∞ to −∞ dB, a response ratio corresponding to the directivity index is achieved. For 100 hydrophones, this range would be 20 dB (re power); for 10 phones, 10 dB, etc. The levels are thus predictable, regardless of pressure level of the source as seen at the array. The paper discusses the analytic and computer simulation aspects of these phenomena. Correlation functions are derived analytically and compared with simulation results for several cases.