Scattered Wave Energy Research Articles

制御震源地震探査データの共通散乱点重合法解析による北部フォッサマグナ地域の散乱体分布

Seismic waves are refracted, reflected, or scattered by heterogeneities in the Earth's crust. Small-scale structures less than wave-lengths are difficult to be observed by conventional refraction and/or reflection methods although scattered wave energy is observed as coda waves. In March 1997, a seismic reflection survey was conducted to reveal the active tectonics in the Japan arc across the Northern Fossa Magna in Japan. The profiling revealed a strongly deformed thick sedimentary layer. At the same time, we carried out a seismic array observation using off-line seismic recorders in the same area to image crustal structure. We used four large vibrators as seismic sources with a spacing of 200m. The array consisted of 39 seismometers distributed two dimensionally with a spacing of 100m. We applied the CSP (common scatterer point) stacking method for all the combination of sources and receivers. We assumed 3-D grid points with a spacing of 100m in a studied area. We calculated a travel time field for the 3-D structure by a finite difference method. To investigate whether a scattered energy was really originated from a particular grid point or not, we calculated cross-correlation coefficients between the CSP stacked waveforms and a source waveform. We interpret that the correlation coefficients represent a distribution of point scatterers. The scatterers are distributed near the Earth's surface and at depths of 800m and 1600m. Compared with the reflection profile, scatterers are distributed in severely deformed strata. Since our method strongly depends on the background velocity structure, it is important to use a realistic background velocity structure to estimate scatterer distributions accurately.

クラックによる散乱波動エネルギーの解析

クラックによる散乱波動エネルギーの解析

Qβ estimates from spectral ratios and multiple lapse time window Analysis: Results from an underground research laboratory in granite

An experiment to measure quality factor (Q) in‐situ was carried out at the Underground Research Laboratory in Manitoba, Canada using the Spectral Ratio technique and a form of the Mulitple Lapse Time Window Analysis technique. The volume of rock examined measures approximately 30 × 30 × 30 m at a depth of 420 m in Lac Du Bonnet Granite. The site encompases 16 triaxial accelerometers grouted in the bottom of boreholes drilled from access tunnel walls. The source for the seismic pulses was a mechanical hammer placed at the bottom of specially located boreholes. Results from the Spectral Ratio experiment gave S‐wave quality factor (Qβ) of 114 ± 18. Based upon the short duration of the first arrival pulses and low scattered wave energy in the signal coda, we conclude that the Spectral Ratio technique measured the intrinsic attenuation of the rock mass. Further analysis using the more recently developed Multiple Lapse Time Window Analysis gave results for intrinsic Qβ (Qi) of between 85 and 100. Conversely, values for scattering Qβ (Qs) were greater than 800. The high correlation for Qi values between the two methods help to confirm the nature and absolute values of the attenuation, and also support the use of the later technique where spectral ratios cannot be applied.

On the propagation of water waves along a porous-walled channel

The propagation of linear water waves in regions bounded by porous media is examined analytically. Two cases are considered: a single porous medium and a channel with porous sidewalls. For the first case, a porous medium boundary condition is developed for use in numerical parabolic models that allows for scattered wave energy to leave the computational domain without reflection.

Comment on “Compact solutions for multiple scattered wave energy in time domain” by Yuehua Zeng

Comment on “Compact solutions for multiple scattered wave energy in time domain” by Yuehua Zeng

Compact solutions for multiple scattered wave energy in time domain

Compact solutions for multiple scattered wave energy in time domain

Scattering wave energy propagation in a random isotropic scattering medium: 1. Theory

In this paper we provide a complete formulation of scattered wave energy propagation in a random isotropic scattering medium. First, we formulate the scattered wave energy equation by extending the stationary energy transport theory studied by Wu (1985) to the time dependent case. The iterative solution of this equation gives us a general expression of temporal variation of scattered energy density at arbitrary source and receiver locations as a Neumann series expansion characterized by powers of the scattering coefficient. The first term of this series leads to the first‐order scattering formula obtained by Sato (1977). For the source and receiver coincident case, our solution gives the corrected version of high‐order formulas obtained by Gao et al. (1983b). Solving the scattered wave energy equation using a Fourier transform technique, we obtain a compact integral solution for the temporal decay of scattered wave energy which includes all multiple scattering contributions and can be easily computed numerically. Examples of this solution are presented and compared with that of the single scattering, energy flux, and diffusion models. We then discuss the energy conservation for our system by starting with our fundamental scattered wave energy equation and then demonstrating that our formulas satisfy the energy conservation when the contributions from all orders of scattering are summed up. We also generalize our scattered wave energy equations to the case of nonuniformly distributed isotropic scattering and absorption coefficients. To solve these equations, feasible numerical procedures, such as a Monte Carlo simulation scheme, are suggested. Our Monte Carlo approach to solve the wave energy equation is different from previous works (Gusev and Abubakirov, 1987; Hoshiba, 1990) based on the ray theoretical approach.

System to recognize a geometry parameter of unknown object with continuous wave acoustic energy

An acoustic sensing system to measure a geometry parameter such as, for example, position, orientation and/or shape of an object. The system includes a transmitter for transmitting acoustic wave energy at a single frequency, which acoustic wave energy, in an operating system, interacts with the object in a sensing region to provide reflected or scattered wave energy. A sensor mechanism consisting of many acoustic transducers is positioned to receive the reflected or scattered wave energy, each transducer being operable to convert the received acoustic wave energy to an electrical signal. A processor is connected to receive the electrical signals from the plurality of acoustic transducers; the processor is operable to obtain amplitude and phase information with respect to the electrical signal from each of the transducers, the amplitude and phase information from each of the plurality of transducers being combined and analyzed to derive a geometric parameter of the object.

Unified approach to amplitude attenuation and coda excitation in the randomly inhomogeneous lithosphere

A unified model is proposed for explaining the frequency dependent amplitude attenuation and the coda wave excitation on the basis of the single scattering process in the randomly inhomogeneous lithosphere. Adopting Birch's law and a direct proportion between density and wave velocity, we statistically describe the inhomogeneous medium by one random function characterized by the von Karman autocorrelation function. We calculate the amplitude attenuation from the solid angle integral of scattered wave energy on the basis of the Born approxiimation after subtracting the travel-time fluctuation effect caused by slowly varying velocity inhomogeneities. This subtraction is equivalent to neglect energy loss by scattering within a cone around the forward direction. The random inhomogeneity of the von Karman autocorrelation function of order 0.35 with the mean square fractional fluctuation of 7.2×10−3 ≈1.3×10−2 and the correlation distance of 2.1≈5.1 km well explains observed backward scattering coefficientgπ and the ratioQP−1/QS−1, and observed and partially conjecturedQS−1for frequencies between 0.5 Hz and 30 Hz.

Scattering of Shelf Waves by Islands

Abstract The domain exterior to an island in a channel with topography is not simply connected and so the circulation about the island is indeterminate. Rhines shows that, in a rotating flow with a rigid lid, requiring the pressure to be continuous forces the circulation to be constant in time. It is shown here that the constant-circulation continuous-pressure solution also conserves energy and, moreover, the circulation associated with scattering of incident shelf waves is identically zero. The scattering problem is then well posed and a method is given for constructing the scattered field at arbitrary frequencies. The problem simplifies greatly in the low frequency limit and an explicit solution for waves scattered by a thin barrier follows by decomposing the motion into propagating modes and a geostrophic current following Hsieh and Buchwald. Explicit values are given for the round-island flux and the distribution of scattered wave energy for a long, thin island in the center of a channel. It is shown ...

Acoustic scattering from an arbitrarily rough surface

A method is described for dealing with acoustic scattering from a time-independent pressure-release surface. As in work by previous authors, the problem is formulated as an integral equation on the surface. This formulation takes account of arbitrarily large surface roughness and multiple scattering phenomena at the surface. The problem may be considered naturally in two stages. The first part of the problem is to invert the integral equation to find the pressure gradient on the surface. The eigenfunction expansion method used by Holford [J. Acoust. Soc. Am. 70, 1116–1128 (1981)] for periodic surfaces is extended to deal with more general aperiodic surfaces. It is then shown that this approach is almost exactly equivalent to a direct collocation method. The second part of the problem is to evaluate the scattered pressure away from the surface. The method used here is to calculate the reflection coefficients from the Fourier transform of the pressure gradient on the surface. The reflection coefficients give a convenient representation of the distribution of scattered wave energy with angle and can be used to find the scattered pressure directly. Results are presented showing the growth of fluctuations in the nearfield of the surface and demonstrating the qualitative as well as quantitative differences between a surface with a Gaussian correlation function and a more realistic surface with a modified Pierson–Moskowitz spectrum. From a study of the cases dealt with here, it appears that the Kirchhoff approximation is more successful with randomly modulated surfaces than it is with simple periodic surfaces.