An asymptotic approach to the inversion of free oscillation data

Summary. A technique is suggested for the non-linearized inversion of subsets of free oscillation periods which are short enough that their asymptotic properties may be exploited. The general background of the method for monotonic and non-monotonic velocity distributions are described and applications to torsional and spheroidal free oscillation data are suggested. The advantages of joint analysis of travel times and free oscillation periods as a single data stream for non-linearized inversion are discussed.     

A numerical method to determine physical source parameters from free oscillation data

A method to determine physical source parameter using free oscillation data is presented. It is assumed that the geometry of the source is known, e.g. from P -wave data. The source is assumed to propagate in the horizontal direction, while unknown parameters to be determined are the azimuth and velocity of propagation, the distance over which the seismic source propagated and the source intensity as a function of propagation distance.
The method consists in the systematic search for the set of source parameters rendering phase corrections which maximize the spectral peak amplitudes within the excitation criterion scheme.
If there is no precursive motion, the average dislocation time function can be determined from the spectrum of the seismic moment and the space source intensity. The source intensity as a function of instantaneous source location is found independently of the P -wave origin time and source dislocation time function. The method does not require to correct the data for attenuation.     

The effect of data windows on the estimation of free oscillation parameters

Summary In seeking to estimate the frequencies, decay rates, amplitudes and phases of the free oscillations of the Earth using observed seismic spectra, data windows are required to reduce the effects of mode—mode interference. Formal expressions for the variances and covariances of these estimated parameters are derived here, for the case of a single isolated mode and an arbitrary data window. Explicit results are given for a Hann and Blackman—Harris minimum four-term window as well as for a boxcar. The optimum or minimum variance record length for measuring frequencies and decay rates using a Hann window is 1.1 Q -cycles, and that for determining amplitudes and phases is 0.5 Q -cycles.     

The inverse eigenvalue problems of free oscillation data inversion: the Backus—Gilbert conjecture for angular-order spectra

Summary. In their fundamental paper of 1967, Backus & Gilbert made the following conjecture (p. 265): '… that if we seek uniquely to determine v of the functions ρ, k, μ (with ν = 1, 2, 3) from the mass, moment, and eigen-frequencies of the normal modes, we need 2ν different infinite sequences of eigenfrequencies, each sequence consisting either of all toroìdal modes of a given angular order or all spheroidal modes of a given angular order…' . We show that, at least if attention is not restricted to geophysically realistic solutions, the conjecture is false. The question of its validity remains open when attention is restricted to geophysically realistic solutions. However, as the present result indicates, the fact cannot now be ignored that, even in a quite appropriate geophysical context, an examination of angular-order spectra is not sufficient to determine ρ, k and μ.     

基于多源遥感数据的1970—2020年巴尔喀什湖动态监测

利用ICESat-1、CryoSat-2测高数据与水文站实测数据,分析了1970—2020年巴尔喀什湖水位变化特征,结合MOD09A1数据及相关资料分析了巴尔喀什湖长时间序列面积和水量变化状况,并利用巴尔喀什湖流域灌溉数据及Climatic Research Unit(CRU)气象数据,简要探究了气候变化及人类活动对湖...     

The coupling and attenuation of nearly resonant multiplets in the Earth's free oscillation spectrum

Summary. The effect of attenuation on the coupling of nearly resonant multiplets in the Earth's free oscillation spectrum is investigated and numerical results are presented for several of the most strongly coupled low frequency multiplet pairs. The coupling influences considered are those of the Coriolis forces due to rotation and of the Earth's hydrostatic ellipticity of figure. It is found that the effects of attenuation (in particular the difference in Q ⁻¹ for the two multiplets) can significantly change the splitting diagrams and the degree to which coupling takes place. The Q values for the coupled singlets are, in general, all different and lie between the two Q values of the uncoupled multiplet pair. In addition it is shown that the diagonal sum rule may be readily extended to sets of coupled multiplets.