Index of content:
Volume 103, Issue 6, June 1998
- GENERAL LINEAR ACOUSTICS 
103(1998); http://dx.doi.org/10.1121/1.423074View Description Hide Description
Many geophysical applications of the array sonic measurements require the knowledge of the true source-time function. Recovery of the source-time function from the borehole sonic P head waves is different from the source inversion problem in explorationseismology. The difficulty in the inversion of borehole sonic measurements arises due to the inexact knowledge of the impulse response, e.g., the inability to model the whole problem including the tool body and transducers. The random noise often encountered in seismic signals is not the key obstacle here. The inverse source problem is ill posed due to the interference of P head-wave multiples. Using waveforms from a laboratory scale model we have applied two deconvolution methods, one using a Wiener filter and the other the time-domain least-squares method. As expected, without constraints on the solutions, one cannot recover a satisfactory source-time function. An unconventional smoothness constraint is applied in the source spectrum (instead of the usual smoothness in the time-domain signals), which corresponds to a finite-duration pulse in the time domain (instead of the usual band-limited spectrum). This technique is thus called the “duration-limited” inversion. The inverted results, obtained by Wiener filtering combined with this “duration limiting” process and multichannel stacking, agree well with an independent free-field measurement. Furthermore, reconstructed receiver waveforms using the inverted source function match the measured ones. The inversion procedure is robust and potentially useful for field measurements.
103(1998); http://dx.doi.org/10.1121/1.423033View Description Hide Description
A procedure for the measurement of intrinsic scattering object properties is presented and used to obtain illustrative results. The procedure is based on the measurement of the scattered acoustic field as a function of scattering angle and frequency. Measurements are normalized using analytically determined expressions for emitter and detector beams resulting from a combination of unfocused linear elements arranged in a circular configuration. The spatialeffects of finite emitter pulse length and detector gate length are represented by a convolution formula valid for narrow-band transmitted signals and long receiver gates. The normalization includes correction for target absorption as well as measurement of the directly transmitted acoustic power in the free field and yields the average differential scattering cross section per unit volume. Under the Born approximation, this quantity is directly proportional to the spatial-frequency spectrum of the scattering medium inhomogeneities. Measured results are reported for two phantoms consisting of glass microspheres embedded in a weakly absorbing agar background medium. For the phantoms employed, scatteringeffects, rather than increased absorption, are shown to account for most of the difference in transmission loss between pure agar and agar with glass spheres. The measured differential scattering cross sections are compared with theoretical cross sections for distributions of glass spheres measured experimentally. The measured values show good relative agreement with theory for varying angle, frequency, and phantom properties. The results are interpreted in terms of wave space resolution and the potential for tissue characterization using similar fixed transducer configurations.
103(1998); http://dx.doi.org/10.1121/1.423034View Description Hide Description
When waves propagate through a medium with smooth velocity perturbations the propagation of wavefronts is determined by the eikonal equation. Here the propagation of wavefronts through a medium with small-scale velocity perturbations is analyzed using the method of strained coordinates. A partial differential equation for the first-order perturbation of wavefronts is derived that includes frequency-dependent wave propagation effects. It is shown that for the special case of the scalar Helmholtz equation with a homogeneous reference medium this leads to the same perturbation of wavefronts as obtained from the Rytov approximation. However, the method presented here can possibly be generalized to more complex wave propagation problems where the Rytov approximation cannot be used, such as the propagation of vector waves.
Various loss factors of a master harmonic oscillator coupled to a number of satellite harmonic oscillators103(1998); http://dx.doi.org/10.1121/1.423035View Description Hide Description
Three loss factors are defined for a master harmonic oscillator (HO); the I-loss factor, the U-loss factor, and the effective loss factor. A conductance (β) is conventionally defined as the ratio of the power imparted to a dynamic system by an external drive to the stored energy that this input power generates. The conductance (β) is related to the loss factor (η) by the frequency (ω); In light of this definition, it is shown that all three loss factors are identical for an isolated master HO at resonance. Differences arise among these loss factors when the master HO is coupled to satellite harmonic oscillators (HO’s). The first two loss factors retain their definitive format in the sense that the stored energy is reckoned only in the master HO; the energy stored in the coupled satellite HO’s and in the couplings is discounted. The effective loss factor, on the other hand, is defined by accounting for the total stored energy that the external drive applied to the master HO generates in the complex. The complex here is composed of the master HO, the satellite HO’s, and the in situ couplings. In those situations in which the portion of the total energy stored in the satellite HO’s and in the couplings substantially exceeds the stored energy in the master HO, the I-loss factor and the U-loss factor may substantially exaggerate the true loss factor of the coupled master HO. Situations of this type are illustrated by data obtained in computational experiments, and it is argued that the true loss factor of the master HO in the complex as a whole is the effective loss factor.