S U M M A R YWe present a detailed description of a new method of spectral analysis named 'Sompi'. The basic idea of this method originates in the physical concept of the characteristic property of the linear dynamic system that is described by a linear differential equation. The time series modelling in the Sompi method consists essentially of estimating the governing differential equation of the hypothetical linear dynamic system that has yielded the given time series data. Due to the equivalence of a linear differential equation and a linear difference equation [or an autoregressive (AR) equation], this method takes the form of the familiar AR method. However, our basic concept of the AR model and the exact formulation based on the maximum likelihood principle have led to a model estimation algorithm different from previous AR methods, and further, to spectral estimation with higher resolution and reliability. By the Sompi method, a time series is deconvoluted into a linear combination of coherent oscillations with amplitudes decaying (or growing) exponentially with time, and additional noise. In other words, it yields a line-shaped spectrum in complex frequency space, unlike the traditional harmonic decomposition in real frequency space, and is powerful for the analysis of the decaying characteristics, as well as the periods, of the oscillations. Also, the variances of the spectral estimates by the Sompi method can be given in simple formulae unlike most modern parametric methods. Although some practical problems still remain unresolved, the theory presented here will provide the theoretical prototype for a new discipline of physical spectral analysis.
A high velocity passage of a meteoroid through the atmosphere generates a shock wave with a conical front. When the shock front arrives at the surface, it causes high frequency ground motions that are registered on the seismograms. We can use seismological data to determine the trajectory of the meteoroid in the atmosphere. A strong shock wave from the 1998 Miyako fireball is recorded by more than 20 stations in a dense array of seismographs installed in the northeastern region of Honshu Island, Japan. We determine the velocity and the trajectory of the fireball in the upper atmosphere using the arrival times of the shock wave at the stations.
[1] A continuous observation of shear wave splitting for 17 years reveals a unique temporal variation in seismic anisotropy in the shallow crust induced by a larger earthquake (M W 5.7) beneath the Tokai region, Japan. The delay time between the fast and slow wavelets coseismically increased and then decreased back to the pre-event value. The duration of the decreasing stage is about two years. The decrease may indicate crack healing in the upper 10 km of the crust. We approximate the temporal variation in the delay time as a function of logarithm of time, which is concordant with healing phenomena of cracks reported by laboratory experiments. The observation indicates that healing of cracks in crustal rocks is complete in approximately two years.
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