Abstract
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 through random
media. For the statistical characterization of the power spectral density function (PSDF)
of the random fractional fluctuation of velocity inhomogeneities in a 3-D space, we use
an isotropic von Kármán-type function characterized by 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 the 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
teleseismic 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 on 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 spectral
envelope of those PSDFs is well approximated by the inverse cube 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 carefully measure 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 at different scales and in different
geological environments in the solid earth medium.
Subject
Paleontology,Stratigraphy,Earth-Surface Processes,Geochemistry and Petrology,Geology,Geophysics,Soil Science
Cited by
20 articles.
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