An asymptotically optimal algorithm for approximating bounded analytic functions

1997 ◽  
Vol 75 (3) ◽  
pp. 397-404
Author(s):  
Klaus Wilderotter
Keyword(s):  
Analytic Functions ◽  
Optimal Algorithm ◽  
Bounded Analytic Functions ◽  
Asymptotically Optimal ◽  
Asymptotically Optimal Algorithm

Detection and estimation of the Slichter mode based on the data of the IGETS superconducting gravimeters network using the asymptotically optimal algorithm

2020 ◽  
Author(s):  
Vadim Milyukov ◽  
Mikhail Vinogradov ◽  
Alexey Mironov ◽  
Andrey Myasnikov
Keyword(s):  
Optimal Algorithm ◽  
Signal To Noise Ratio ◽  
Likelihood Method ◽  
Maximum Efficiency ◽  
Signal To Noise ◽  
Asymptotically Optimal ◽  
Asymptotically Optimal Algorithm ◽  
Superconducting Gravimeters ◽  
Noise Ratio ◽  
Slichter Mode

<p>Traditionally, searching the Slichter mode (the longest-period mode of the Earth's free oscillations <sub>1</sub>S<sub>1</sub>) is based on the data of the superconducting gravimeters of the international GGP network. Currently this network is included in the International Geodynamics and Earth Tide Service (IGETS).</p><p>The sensitivity limit of the best superconducting gravimeters is about 1 nGal and not sufficient for direct observation of the Slichter mode even after the significant earthquakes. To reduce the detection threshold, the researchers used the “stacking” procedure — an joint data processing of the several instruments, but the different sensitivity level of the gravimeters prevents the achievement of maximum efficiency.</p><p>We have developed an asymptotically optimal algorithm based on the maximum likelihood method that takes into account the features of the Slichter mode and seismic noise. An important feature of the algorithm is its ability to evaluate the splitting parameter b which determines the distance between the side singlets of the triplet, simultaneously with the mode period T. The use of a non-linear inertial converter allows to take into account the non-Gaussian noise of real data. The use of the Neumann-Pearson criterion makes also possible to determine confidence level of detection: the false alarm probability and the correct detection probability, depending on the signal-to-noise ratio).</p><p>The algorithm was tested on synthetic data. A computer experiment has shown that the algorithm can detect the Slichter mode for a signal-to-noise ratio of 10<sup>-4</sup>. The algorithm was used to search the Slichter mode after the largest earthquakes based on the data of the IGETS network.</p><p>The results of the analysis are reported.</p><p>This work is supported by the Russian Foundation for Basic Research under Grant No Grant No 19-05-00341.</p>

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