Propagation Path Length Research Articles

Propagation of transient waves in a random medium

A theoretical analysis of the propagation of transient scalar waves in a one‐dimensional random medium is presented. The index of refraction of the medium is assumed to deviate only slightly from unity, which allows the analysis to be carried out with the aid of a perturbation method. The specific approach adopted here combines a renormalization technique with a travel‐time‐corrected averaging procedure called asynchronous ensemble averaging. A general expression, valid for an arbitrary initial disturbance, is obtained for the variance of the wave. From that result, an expression for the variance is derived for the special case in which the initial disturbance has the form of a ramp function with arbitrary slope. These results show that the variance of the wave is directly proportional to the variance of the refractive index of the medium, but is only weakly dependent on the propagation path length. It is also found that, as the slope of the ramp function decreases, the wave variance decreases as well. The presentation concludes with some observations on the relevance of these results to the problem of sonic‐boom propagation in the atmosphere. [Research supported by NASA.]

Heard Island Feasibility Test: Long-range sound transmission from Heard Island to Krylov underwater mountain

The Russian research vessel Akademik Nikolai Andreyev participated in the HIFT experiment while anchored above the Krylov Seamount (17.5° N, 30° W). The propagation path length from Heard Island to Krylov was 12.5 Mm, and was located just between the Ascension station (9 Mm) and the more distant American and Canadian stations (16 to 17 Mm). All 35 successful transmissions were received by two omnidirectional hydrophones and a 30-m-long array. Receptions were sampled at 228 Hz and processed in both time and frequency domains. The main result of the processing was quite unexpected: the signal exhibited strong amplitude variability (fading as deep as 20 dB in less than 5 min) and simultaneously exhibited an incredible phase stability. All the phase variance up to the accuracy of positioning was due to the mutual motion of the transmit and receive ships. The minimal propagation loss for cw transmissions was 120 dB. M-sequence processing indicated an 18- to 20-s arrival spread estimate. However, the arrivals were very unstable with a lifetime of about 5 min.

Remote sensing of ocean flows by spatial filtering of acoustic scintillations: Theory

Space-time acoustic scintillation analysis has proved to be a valuable technique for probing ocean flows over short (≲2 km) acoustic paths. Measurements of the amplitude and phase perturbations in a distant receiving plane are used to infer the intervening fine-scale variability and transverse current. Observations made using one transmitter and two receivers yield path-integrated measurements that are almost uniformly weighted along the propagation path. Higher resolution measurements can be obtained using multiple sources and receivers. By combining the signals from each transmitter–receiver pair in different ways, a number of different path positions can be probed and profiles of the fine-scale variability and transverse current along the propagation path retrieved. A theory describing the performance characteristics of such a system is presented. The case of linear transmitting and receiving arrays of equally spaced elements is considered in detail. The theory predicts a potential path resolution of up to L/[(N′t+Nr)/2], where N′t≫1 and Nr≫1 are the number of transmitters and receivers, respectively, and L is the propagation path length. The specific case of four-element transmitting and receiving arrays is also considered, and some simulations of profile retrievals are presented. A future paper [D. M. Farmer and G. B. Crawford, J. Acoust. Soc. Am. (in preparation)] will present results of an experiment to test such a system.

超音波速度測定によるクリープキャビティの評価

An ultrasonic techique for the evaluation of creep cavities in steel for high temperature use is proposed. By using samples taken from crept or ruptured specimens, longitudinal wave velocities in the parallel and normal propagation directions to the stress axis (VLP and VLN) were measured. Then the shear wave velocities both in the parallel propagation direction to the stress axis (VSP) and in the normal propagation direction for parallel and normal polarizations to the stress axis (VSNP and VSNN, respectively) were measured. These results showed that all of the ultrasonic wave velocities decrease linearly with increasing amount of creep cavities. Wave velocities were also sensitive to the directions of the propagation and the polarization. This sensitivity suggests the usefulness of VLP/VSP, VLN/VSNN and VSNP/VSNN as new parameters. The values of these three parameters were found to decrease linearly with an increase of the amount of creep cavities, and the comparison among these parameters showed that the ratio VLP/VSP was most sensitive to the amount of creep cavities. The evaluation method of the amount of creep cavities using the parameters of ultrasonic wave velocity may be useful for practical purposes because it does not require the propagation path length.

Quantum theory of Rabi sideband generation by forward four-wave mixing.

The predictions of a quantum-mechanical theory of forward four-wave mixing in a homogeneously broadened system of two-level atoms are presented. In the limit of a very short interaction region, the predictions of this theory reproduce those of well-known theories for the spontaneous-emission spectrum of an atom in the presence of an intense laser field. More generally, the theory predicts how the emission spectrum is modified due to propagation effects for a medium of arbitrary length. For long propagation path lengths, the emitted radiation can be quite intense and has a spectrum that is strongly peaked at the Rabi sidebands of the incident laser frequency. The theory shows that Rabi sideband generation in the forward direction can be understood as parametric amplification of weak radiation emitted spontaneously at the Rabi sidebands. The quantum noise that initiates the four-wave-mixing process has contributions both from fluctuations in the incident vacuum radiation field and from fluctuations in the polarization of the atomic dipoles. Both contributions are important for the case of a radiatively broadened medium, although the material fluctuations make the dominant contribution for the case of a medium in which the broadening is largely collisional. Under certain conditions large amounts of squeezing in the radiated field are predicted.

Measurements of coda buildup and decay rates of western Pacific P, Po, and So phases and their relevance to lithospheric scattering

We use empirical functions to characterize the shape of band‐passed P, Po, and So coda envelopes of 93 earthquakes. The data sets consist of earthquake data from the western and northwestern Pacific recorded by arrays of several stations and include both hydrophone and geophone recordings on analog and digital instruments. Each earthquake was band‐passed into six octave‐wide frequency bands between 0.8 and 50 Hz. The empirical function (a Poisson function, Pn(γ,t) = A γn+1 tn e−γt /n!) has parameters A (a measure of energy), γ (falloff rate), and nç//γ (time of the maximum). The study showed that these parameters varied in systematic ways. Po/So area (A) ratios were found to be considerably higher for hydrophone data in the 20°–35° range than for geophone and hydrophone data in the 8°–20° range. The difference was significantly larger than between vertical and hydrophone data in the same range. In some instances a strong frequency dependence or “reverse dispersion” of the time of maximum amplitude (n/γ) was observed, with the lower (1–2 Hz) frequencies arriving up to 25s later than the higher (10–20 Hz) frequencies. P, Po, and So average falloff rates ã vary systematically with frequency, where the lowest frequencies most commonly have the minimum falloff rates and the middle frequencies have the maximum falloff rates. The variation in falloff between earthquakes is large, with the trends only becoming apparent upon averaging many measurements. A strong increase in falloff rates at about 3 Hz may be associated with a decrease in the amount of scatterers with scale lengths of about one half the wavelength of a 3‐Hz compressional wave, which is about 1.3 km. Falloff rates were seen to decrease with epicentral range, reflecting an increased scattering with length of propagation path. The scattering that produces the coda is thus not concentrated in the source region but distributed along the propagation path. Falloff rates were seen to decrease with increasing age of crust. The difference may be due to the different average age of the lithosphere in these two geographical areas. Earthquakes at a depth of 100–300 km have systematically lower Po falloff values than shallower events. This effect is clearly seen in trench earthquakes and indicates that significant scattering occurs within (or near) the deeper buried part of the subducting plate. The So/Po falloff ratio is a factor of 2 lower for the hydrophone data than for the geophone measurements. This difference is most likely due to conversion of shear waves at or below the seafloor. If we assume that the coda decay is controlled by intrinsic attenuation, then measurements of coda decay can be converted into estimates of the quality factor Q. At 10 Hz our falloff rates give QPo = 1250, which is a reasonable number for a compressional wave quality factor in the uppermost mantle, and QSo ≈ QPo/2 The low snear wave Q is in disagreement with inferences made by other observers. However, the fact that the falloff rates are fairly constant in the frequency range 5–30 Hz but vary with propagation distance suggests that attenuation cannot be the only phenomenon determining the decay of the coda. Other factors, such as reverberations in the water column, may play an important part in the coda formation as well and may bias these estimates Q.

PROPAGATION PATH OF LOW-FREQUENCY SKY-WAVE SIGNALS

The propagation path of the sky-wave signals are studied in detail and some problems and errors occurring in the relevant work in the past are analysed. In the consideration of the refraction effect of the atmosphere, the radio apparent range, the length of the propagation path of the low-frequency sky-wave, the launching angle and the incidence angle with their influence on the time delay and the field strength of the LF sky-wave signals are deduced and calculated. The predictions on the D-layer of ionosphere and the time delay and field strength of the LF sky-wave signals are studied and the results show that the difference between the predicted values and the measured values are within ±1.5μs and ±2.5 dB for the time delay and the field strength respectively and that the accuracy of the timing via LF sky-wave can be raised to ±1.2μs and ±2.8 μs st daytime and at night respectively.

Comparison of scintillation methods for measuring the inner scale of turbulence

One method of inner scale measurement uses the irradiance variance of a diverging monochromatic wave (the irradiance being obtained through a small aperture at the receiver position) and the irradiance variance of a large-aperture C(2)(n) scintillometer. The ratio of these two variances depends on the inner scale of turbulence l(0) but not on the refractive-index structure parameter C(2)(n). Another method uses the bichromatic correlation of irradiances from waves having two different wavelengths, transmitted through a common small aperture (the irradiance being obtained through a small aperture at the receiver position) and the two corresponding monochromatic irradiance variances. The ratio of the bichromatic correlation to the geometric mean of the two monochromatic variances depends on l(0) but not on C(2)(n). A third method is to obtain the ratio of the two monochromatic variances without using the bichromatic correlation. These methods are compared graphically using calculations based on an accurate atmospheric refractive-index spectrum. A scaling analysis is performed to determine the minimum number of parameters needed to describe the methods. It is suggested that systematic errors, rather than signal-to-noise limitations, determine the accuracy with which inner scale is measured. The effects of refractive-index dispersion between the two wavelengths must be taken into account. The results indicate that the bichromatic method has advantages when l(0) less, similar0.6 radicalL/k, whereas the method using small and large apertures has the advantage when l(0) greater, similar0.6 radicalL/k were L is the propagation path length and k is the optical wave number.

Displacement measurement by SAW delay-line oscillator consisting of two LiNbO3 plates with IDT

A displacement sensor can be made by constructing a surface acoustic wave (SAW) delay-line oscillator, in which two LiNbO <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> plates with an interdigital transducer (IDT) on the surface of each plate are conjoined by attaching a part of the propagation surface of one plate to a part of the propagation surface of the other one. In the SAW sensor, the oscillation frequency depends upon propagation path length of the SAW element, which is changed by moving one of two LiNbO <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> plates of the oscillator. It is shown that SAW displacement sensors with high sensitivity, 300 Hz/μm and 1.0 kHz/ μm, were achieved by making IDT's of 6.5 pairs with 0.55-mm pitch and those of 5 pairs with 0.4-mm pitch on the surfaces of Y-X LiNbO <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> plates, respectively. The mode transition of the SAW delay-line oscillator, which occurred at certain propagation path lengths, was observed by using a spectrum analyzer.

Methods of metallic loose parts location and impact energy estimation from information on reference impact sounds

Reference impacts were employed to achieve accurate location and energy estimation of metallic loose parts in inhomogeneous systems such as nuclear reactor vessels. Impact positions are determined using distances from reference impacts and pattern recognition technique. To confirm the method, experiments were carried out using a cylindrical steel tank (diameter = 2m, height = 5m, thickness = 2m). The reference impacts were arranged on lattice points, separated by 1 meter, on the tank wall. The signal amplitudes of various impacts positions with a uniform impact energy and the same propagation path length exhibited deviations of around one order of magnitude. This fact would seem to limit the posibility of achieving accurate location and energy estimations from the amplitude data. However, the results were surprisingly good. Using amplitude data, the impact positions on the tank were located within an error of 13cm and impact energies were estimated within an error of 25%.

Delta function excitation of waves in the earth's ionosphere

Excitation of the earth's ionosphere by delta function current sheets is considered, and the temporal and spatial evolution of wave packets is analyzed for a two‐component collisional F2 layer. Approximations of an inverse Fourier‐Laplace transform via saddle point methods provide plots of typical wave packets. These illustrate cold plasma wave theory and may be used as a diagnostic tool since it is possible to relate specific features, e.g., the frequency of a modulation envelope, to plasma parameters such as the electron cyclotron frequency. It is also possible to deduce the propagation path length and orientation of a remote radio beacon.

Signal compression method applied for a measurement of sound attenuation by a barrier under wind effects.

Signal compression method was applied for a measurement of wind effects to a sound attenuation by a barrier. This method uses special computer generated test signal, which can be compressed to a pulse like signal by a numerical phase shift filter. External noise can be reduced and effects of reflected sounds can be eliminated by this method, so it is suitable for a measurement of sound attenuation in noisy air flow conditions. Experiments were performed in rather small test room for short propagation path length. Obtained signals and computer processed waveforms are illustrated with the results of attenuation characteristics for five wind conditions.

K distributions in atmospheric propagation of laser light

Experimental results are presented which suggest that the probability distribution of fluctuations in the intensity of laser light propagating through atmospheric turbulence are reasonably well described by K distributions in the intermediate range of propagation path lengths, L ≃ 600 m, β0≃1–2, where the mean square fluctuation 〈I2〉 /〈I〉2 can be as high as five.

On the ground‐borne noise propagation from a subway

A prediction method of noise in the house caused by subway was studied by means of hypothetical theory and measurement. This procedure was done by two steps. (1) Supposing that waves propagate through the various impedance soil layers from the imaginary vibration line source placed under the subway construction to the ground surface. Coefficients in the formula are decided experimentally with measured values. (2) The relation between the noise in the house and ground vibration led by field measurements. The acceleration level (Lv) on the ground is expressed as follows: Lv = Lo − 10 log ( ∑ i ri) − ∑ i αiri + ∑ i Ki, where Lo is the imaginary source level; ri, the propagation path length in the i'th soil layer; αi, the damping factor of i'th layer; and Ki, correction terms. The relation of ground vibration (Lv) and noise (LA) in the house is expressed as LA = 0.88 Lv − 17. These relations may be available in the case of comparatively shallow tunnel construction. [Works supported by Teito Rapid Transit Authority and Yokohama City.]

On the Renormalization Method in Random Wave Propagation

In this work it is shown that the diagrams that correspond to the first renormalization equation for the coherent field, in a statistically homogeneous and isotropic medium, are the dominant diagrams. To study the cumulative effect of the omitted diagrams, which increase in number with each power of the expansion parameter ∈, we sum the next largest omitted diagrams. This sum is proportional to the propagation path length times the usual first renormalization solution. The above analysis and a more compact one that utilizes the full Dyson equation both yield a validity criterion that is basically distance independent. The derivation of the validity criterion is primarily based on two observations that are not used by other authors. First we note and account for the fact that the solution of the first renormalition integral equation is always approximated. Secondly, we utilize the simple observation that phase accumulation and rate of decay are unimportant if the amplitude of the wave is already insignificant. We obtain the same criterion as other authors for kol ≫ 1, where ko is the free space wave number and l is the correlation length of the dielectric fluctuations; for kol ≪ 1 the criterion is new. Finally, a relatively simple method of solving the first renormalization integral equation for the correlation function of the field is presented for the case kol ≫ 1 and some justification for the validity of this equation is given.

Evidence for severe microwave signal fading in the atmosphere of Venus due to turbulence

Atmospheric turbulence, inducing dielectric permittivity fluctuations with variance ∈², will cause signal fading (more severely at higher frequencies). Earth’s turbulence yields ∈∼10−6, which is too weak for significant effects on line of sight propagation at radio frequencies. Recent evidence indicates that the USSR probe Venera 4 sent signals through the atmosphere of Venus to earth that showed mild fading. The Russian analysis yields ∈>10−5 on Venus, but it is contingent upon an ad hoc estimate of the macroscale of turbulence Lo, and it appears to utilize improper statistics and incorrect propagation pathlength. We will reanalyze their measurements, show that the observed fading rate yields values of Lo, and apply turbulence theory to obtain ∈²>10−7 at 25 km above the surface of Venus. The Mariner 5 situation data will be discussed. We will also show that severe fading at 5 GHz and higher is the result of such values of ∈ on Venus.

Relation between ultrasound propagation velocity and path length in solid concrete

In ultrasonic tests of concrete quality in thick-walled structures (more than 0.5 m thick) and in massive blocks in hydraulic structures, it is necessary to take into account change in the amplitude-frequency spectra of ultrasound pulses with the path length in the concrete, which is a regular phenomenon associated with the normal absorbing properties of the concrete. This must be distinguished from the changes indicating quality deterioration or structural defects in the concrete. The quantitative decrease in the velocity of propagation of ultrasound along a ray in the direction of each sounding depends on the physicomechanical properties of the concrete, its composition, its age, and the natural frequency of the ultrasound-pulse emitter-transducer; for measurement bases between 1 and 6 m, it lies in the range 1–12%. Correction coefficients δ for assessing the effect of this factor can be found with sufficient accuracy for practical purposes from the measured acoustic characteristics of the concrete, in conjunction with the theoretical relation (13) or the graphs in Fig. 6.

Comments on the communication and data problems associated with a Mars trip during a conjunction phase

The analysis and comments presented in this paper are meant to establish the general communication parameters associated with Martian flyby probes and with lander and manned vehicles. Fundamental data transfer problems are reviewed to define comparisons and trends of tradeoffs for future studies. Selected focal points are based upon the long propagation path length, with inherent time delays, and the high noise produced by the sun. These problems are magnified because large quantities of data must be obtained to satisfy the needs of the scientific community and the curiosity of an interested public. A comparison of two communication systems is provided: the microwave spectrum and the optical spectrum, as represented by the microwaves at 2.3 GHz and the laser at 6328 Å. A method of cost effectiveness or value received from space missions (a criterion of power input for data quantity received) is also presented.

Stress relaxation behind elastic shock waves in rocks

The amplitude of elastic shock waves in Arkansas novaculite is observed to decrease at a rate of ≈3.3 kb/mm for shock propagation path lengths of 6 to 12 mm. The amplitude of the final shock state in the experiments is held near the 155-kb pressure level. A total variation of elastic shock wave amplitude (Hugoniot elastic limit) of ≈40 kb (from 110 to 70 kb) is observed in ≈1 cm of shock travel. The intrinsic attenuation term in a constitutive equation for a stress-relaxing elastoplastic material is found to account for ≈90% of the observed peak pressure attenuation of the elastic shock, as compared with the ≈10% which is predicted from the instantaneous elastic shock profile. The Hugoniot elastic limits of Sioux and Eureka quartzites, which were not as intensively studied as the Arkansas novaculite, are also found to decrease with shock propagation path length.

Auditory discrimination of seismic signals from earthquakes and explosions

Abstract Magnetic tape recordings of short-period seismic signals from approximately 200 earthquakes and explosions were time-compressed by a factor of up to 512 to shift seismic frequencies to the audible range. These seismic data include the inhomogeneities introduced by substantial variations in the locations of sources and receivers (world-wide), propagation path length (32 to 7000 km), and source magnitude (M = 0.5 to M = 6.5). Subjects were trained with a representative set of the “seismic sounds.” Auditory experiments were conducted to determine the ability of the human auditory system to distinguish between seismic signals from earthquakes and explosions. The results of the experiments suggest that a trained listener can identify approximately two-thirds of the seismic sounds presented, where one half corresponds to chance performance.