Travel Time Fluctuations Research Articles

Amplitude attenuation of impulsive waves in random media based on travel time corrected mean wave formalism

Waves gradually collapse with propagation through media with random velocity fluctuation; however, impulsive waves propagate without large attenuation when the wavelength is shorter than the correlation distance. The Q−1 value predicted from the usual mean wave formalism monotonously increases with frequency even in the high-frequency limit, due to taking a mean over waves with large travel time fluctuations caused by the long scale velocity fluctuation compared with the wavelength studied. We propose a new statistical averaging method appropriate for the amplitude attenuation measurement of impulsive waves, in which the mean wave is defined after the correction of travel time fluctuations. We investigate impulsive scalar waves propagation in three-dimensional media with homogeneous and isotropic random fractional velocity fluctuation, based on the binary interaction approximation in this improved mean wave formalism. We successfully derive the Q−1 value that has a peak of the order of the mean square fractional velocity fluctuation around the frequency corresponding to the correlation distance and decreases with frequency in the high-frequency limit, when the random media is characterized by the von Karman autocorrelation function. The correction of travel time fluctuation is shown to be equivalent to the neglect of energy scattering around the forward direction.

Tidal effects on long‐range sound transmission

Time series of acoustic travel times over long distances have significant tidal components. We discuss three experiments: First, for a 900 km westward transmission from a moored source southwest of Bermuda, the M2 constituent (apart from mooring motion) of 8 ms can be accounted for by a variable propagation with and against the 2 cm/s barotropic tidal current. The situation is different for the K1 and S2 constituents (which have a significant solar component), particularly for rays with shallow turning points, suggesting an effect from a minute daily variation in the temperature of the upper 100 m. Second, for a 500 km transmission from the Bahamas northward and parallel to the continental margin, the measured M2 constituent is not in phase with the computed effect of the barotropic tidal current, unlike the westward transmission mentioned above. Here the mode conversion from barotropic to baroclinic tides plays a crucial role: the principal cause of the travel time oscillations in quadrature with the tidal current is a vertical oscillation by several meters (and attendant temperature and sound speed fluctuations) associated with the baroclinic tide just seaward of the continental margin, in the near‐zone of mode conversion. Third, for 300 km transmissions from a moored source northwest of Bermuda to both a moored receiver and a landbased receiver, the tidal components in the travel time are dominated by tidally induced mooring motions. The tidal amplitude varies in time as the tidal mooring motion is modulated by the variable current (because of the nonlinear drag), and the current can be so estimated. An important part, possibly a predominant part, of the (nontidal) travel time variation of 0.7 s is evidently associated with the mean mooring motion.—The interpretation of the tidal fluctuations in travel time is varied and complex.

DETERMINATION OF LATERAL INHOMOGENEITIES IN REFLECTION SEISMICS BY INVERSION OF TRAVELTIME RESIDUALS*

AbstractLateral inhomogeneities generate fluctuations in the traveltime of seismic waves. By evaluation of these traveltime fluctuations from different source and receiver positions, lateral inhomogeneities can be located using a pseudo inverse matrix method (Aki, Christoffersson and Husebye 1977). The formulation of the problem is possible for transmitted waves as well as for reflected and refracted waves. In reflection seismics this method is of importance, if no reflections from the inhomogeneities themselves, but only reflections from lower boundaries can be observed.The basic assumptions for the mathematical formulation are (1) the average velocities and depths of the reflecting horizons are known already from standard processing methods, and (2) the traveltime residuals are due to lateral velocity changes between different reflectors or between reflectors and the surface. The area of the earth to be considered is divided into layers and the layers into rectangular blocks. The parallel displacement of a ray after passing a disturbed block is neglected, only the traveltime residual is taken into account.In this paper the method and its application to data obtained with two‐dimensional models are described.

Ocean Acoustic Tomography: Can It Work?

We consider the mapping of meso‐scale ocean eddies from fluctuations of acoustic travel times between sources and receivers at separations of the order of 1000 km. The procedure for, “inverting” these measurements to form the best linear estimate of the interior eddy field is discussed. The effectiveness of such a system depends on the distribution of the sources and receivers and the precision of the travel time measurements. We do not know whether the system can be made to work.

Sound-velocity perturbations due to low-frequency motions in the ocean

The properties of low- and intermediate-frequency external and internal waves in the open ocean, and the nature of the acoustic velocity perturbations they produce, are examined. The basic principles are illustrated with theoretical calculations based on representative oceanic cases. Such calculations provide a rational estimate for the vertical and horizontal dependence of the perturbation of the acoustic velocity field due to external and internal waves. External waves can cause travel-time fluctuations by their horizontal velocity fluctuations (or fluctuations in the total sound velocity). Internal waves can cause acoustic travel-time fluctuations both by their vertical displacement of isotherms (or isolines of sound speed) and by their velocity fluctuations (or fluctuations in total sound velocity). Both external and internal waves can have horizontal wavelengths ranging from a fraction of a kilometer to hundreds of kilometers. The longer waves can be effective in producing travel-time fluctuations over long propagation paths; the shorter waves are probably most influential in the scattering of acoustic energy. Subject Classification: 30.20.

Travel-time errors in the laterally inhomogeneous earth

abstract Travel times from earthquakes or explosions contain both positive and negative systematic errors. Positive skews in travel-time residuals due to epicenter mislocation, and negative skews due to lateral inhomogeneity in the Earth, are analyzed. Methods for travel-time estimation are critically reviewed. Recent travel-time tables, including the J-B tables, are within the range of root-mean-square travel-time fluctuations; the J-B tables are systematically late but cannot be reliably improved by least-square methods. Effects of lateral inhomogeneity at teleseismic distances can be estimated by chronoidal methods independently of standard tables, but the available explosion data are insufficiently well-distributed in azimuth and distance for this purpose.

Experimental Prediction of Acoustic Path Stability from Thermistor-Chain Data

The propagation time stability of an acoustic path traveling from the ocean surface to the bottom is predicted by a ray-path analysis. The sound-velocity profile as a function of horizontal distance is derived from towed thermistor-chain data, with a representative stable structure assumed between the thermistor-chain data and the bottom. The fluctuations of travel time at various points along the ship track due to sound-velocity profile variations are predicted by calculating the ray path travel time. The spectrum of these fluctuations shows a slope of K−3, where K is the spatial wavenumber, for K in the region of 2×10−4<K <2×10−3. Measurement noise due to the 0.05°C resolution of the thermistor-chain data exceeds the predicted travel-time fluctuation for K>2×10−3.

Effect of Rough Surfaces on the Resolution of Acoustic Rays in the Ocean

In the frequency region below 1 kc, the effect of velocity inhomogeneities on acoustic propagation in the ocean will be negligible. In this frequency region, fluctuations in travel time and ray direction will be caused by scattering from rough boundaries. In this paper, the effect of boundary scattering on the resolution of ray paths is investigated. Using a simplified model of the process, a rough estimate of the spatial line broadening of a low-frequency ray in the ocean is obtained.