A test of ray theory and scattering theory based on a laboratory experiment using ultrasonic waves and numerical simulation by finite-difference method

Spetzler, Jesper; Sivaji, Chadaram; Nishizawa, Osamu; Fukushima, Yo

doi:10.1046/j.1365-246x.2002.01001.x

Cited by 15 publications

(14 citation statements)

References 42 publications

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“…However, if the breakdown of ray theory for finite-frequency waves is significant in a weakly perturbed velocity field, this complication will certainly be important in heterogeneous media with a larger strength of velocity perturbations. Examples of finitefrequency transmission experiments using a more complex velocity perturbation field with a strength of 10% compared to the reference medium are shown in Spetzler et al (2002), Spetzler (2003), and in the next sections.…”

Section: Ray Theory and Finite-frequency Wave Theory Regime Examplementioning

confidence: 99%

The Fresnel volume and transmitted waves

2004

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In seismic imaging experiments, it is common to use a geometric ray theory that is an asymptotic solution of the wave equation in the high‐frequency limit. Consequently, it is assumed that waves propagate along infinitely narrow lines through space, called rays, that join the source and receiver. In reality, recorded waves have a finite‐frequency content. The band limitation of waves implies that the propagation of waves is extended to a finite volume of space around the geometrical ray path. This volume is called the Fresnel volume. In this tutorial, we introduce the physics of the Fresnel volume and we present a solution of the wave equation that accounts for the band limitation of waves. The finite‐frequency wave theory specifies sensitivity kernels that linearly relate the traveltime and amplitude of band‐limited transmitted and reflected waves to slowness variations in the earth. The Fresnel zone and the finite‐frequency sensitivity kernels are closely connected through the concept of constructive interference of waves. The finite‐frequency wave theory leads to the counterintuitive result that a pointlike velocity perturbation placed on the geometric ray in three dimensions does not cause a perturbation of the phase of the wavefield. Also, it turns out that Fermat's theorem in the context of geometric ray theory is a special case of the finite‐frequency wave theory in the limit of infinite frequency. Last, we address the misconception that the width of the Fresnel volume limits the resolution in imaging experiments.

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Section: Ray Theory and Finite-frequency Wave Theory Regime Examplementioning

confidence: 99%

The Fresnel volume and transmitted waves

2004

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“…Statistical character of random heterogeneity is described by the autocorrelation function (ACF) or the power spectral density function (PSDF) (Aki and Richards, 1980;Sato and Fehler, 1998). Spetzler et al (2002) and Sivaji et al (2001Sivaji et al ( , 2002 investigated the ACF and PSDF of the compressional-wave velocity fluctuations in granitic rocks on the basis of microstructure analysis. In their analysis, the velocity fluctuations were obtained by substituting the appropriate velocity values to the distributed mineral grains.…”

Section: Statistical Characterization Of Rock Heterogeneitiesmentioning

confidence: 99%

Laboratory Study on Scattering Characteristics of Shear Waves in Rock Samples

Fukushima¹,

Nishizawa

Sato³

et al. 2003

Bulletin of the Seismological Society of America

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To understand the scattering characteristics of seismic shear waves in the Earth, a laboratory physical model experiment in ultrasonic frequency range was performed. By analyzing waveform envelopes and particle motions of shear waves in media with different correlation distance and fluctuation intensity, we studied the strength of scattered wave excitation and the distortion of shear-wave polarization as a function of ka (wavenumber times the correlation distance). We used gabbro and granite as media having different small-scale random heterogeneities. The granite we used contained preferred-oriented thin microcracks. The correlation distance a and the standard deviation of the fractional fluctuation of the shear-wave velocity e were estimated by fitting exponential-type autocorrelation functions. The estimated values were a ‫ס‬ 0.84 mm and e ‫ס‬ 8.1% for the gabbro, and a ‫ס‬ 0.39 mm and e ‫ס‬ 17.0% for the granite. Waveform measurements were performed in the frequency range 0.25-1 MHz, which roughly corresponds to ka as 0.25-1. Envelope broadening appeared when ka exceeds 0.4 for the granite and 1.4 for the gabbro. Shear-wave polarizations were distorted by scattering when ka exceeds 0.2 for the granite and 0.7 for the gabbro. The results on envelope broadening suggest the importance of large-angle scattering due to small-scale random heterogeneities and cracks in the envelope broadening, in addition to diffraction effects due to large-scale heterogeneities. The effect of aligned microcracks on scattering was also examined. It was found that scattering was prominent when shear wave propagates perpendicular to the aligned crack plane.

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“…The photo scan method uses a scanner to take a picture of the polished flat surface of a small rock sample (e.g. Sivaji et al, 2002;Spetzler et al, 2002;Fukushima et al, 2003). For the case of a granite sample, they classified color images on a straight line into three types of mineral grains; quartz, plagioclase and biotite.…”

Section: Photo Scan Of the Rock Surfacementioning

confidence: 99%

Power Spectra of Random Heterogeneities of the Solid Earth

Sato¹

2018

Preprint

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Abstract. Recent seismological observations focusing on the collapse of an impulsive wavelet revealed the existence of small-scale random heterogeneities in the earth medium. The radiative transfer theory (RTT) is often used for the study of the propagation and scattering of wavelet intensities, the mean square amplitude envelopes. For the statistical characterization of the power spectral density function (PSDF) of the random fractional fluctuation of velocity inhomogeneities in a 3D space, we use von Karman type with three parameters: the root mean square (RMS) fractional velocity fluctuation, the characteristic length, and the order of the modified Bessel function of the second kind, which leads to the power-law decay of PSDF at wavenumbers higher than the corner. We compile reported statistical parameters of the lithosphere and the mantle based on various types of measurements for a wide range of wavenumbers: photo scan data of rock samples, acoustic well log data, and envelope analyses of cross-hole experiment seismograms, regional seismograms and tele-seismic waves based on the RTT. Reported exponents of wavenumber are distributed between −3 and −4, where many of them are close to −3. Reported RMS fractional fluctuations are of the order of 0.01 ~ 0.1 in the crust and the upper mantle. Reported characteristic lengths distribute very widely, however, each one seems to be restricted by the dimension of the measurement system or the sample length. In order to grasp the spectral characteristics, eliminating strong heterogeneity data and the lower mantle data, we have plotted all the reported PSDFs of the crust and the upper mantle against wavenumber for a wide range 10−3 ∼ 108 km−1. We find that the envelope of those PSDFs is well approximated by the −3rd power of wavenumber. It suggests that the earth medium randomness has a broad spectrum. In theory, we need to re-examine the applicable range of the Born approximation in the RTT when the wavenumber of a wavelet is much higher than the corner. In observation, we will have to measure carefully the PSDF on both sides of the corner. We may consider the obtained power-law decay spectral envelope as a reference for studying the regional differences. It is interesting to study what kinds of geophysical processes created the observed power-law spectral envelope in different scales and in different portions of the solid earth medium.

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A test of ray theory and scattering theory based on a laboratory experiment using ultrasonic waves and numerical simulation by finite-difference method

Cited by 15 publications

References 42 publications

The Fresnel volume and transmitted waves

The Fresnel volume and transmitted waves

Laboratory Study on Scattering Characteristics of Shear Waves in Rock Samples

Power Spectra of Random Heterogeneities of the Solid Earth

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