Maximum likelihood spectrum estimation method and its application in seismo-magnetic relation

Abstract

For abstracting the periodical spectra of geophysical parameters, there are normally three options, i.e. the periodograms or window spectra method (FFT or BT method), the maximum entropy spectrum estimation method (MEM) and the maximum likelihood spectrum estimation method (MLM). According to the comparison of three kinds of methods of spectral estimation and their application to geophysical study, we come to the conclusion that the MLM is better than MEM in frequency resolution, power estimation, extracting signals from the background with strong noise. Furthermore, it is more efficient in working out numerical values by MLM than by MEM, especially when accurate spectral estimation is made, for example, estimation of the parameters in a system. Among these three methods, MEM shows the highest resolution in frequency, hut the lowest precision in power estimation. In the geomagnetic deep sounding (GDS), power estimation is emphasized. So, the application of MLM to the geomagnetism and earthquake prediction has been examined in this paper and the results are satisfied. The results of analysis with FFT method of a total number of 1460 Ax indices for 1967"~ 1969 at the Beijing Geomagnetic Observatory show that few of the spectral lines can pass the significant test, especially for those lines with period of 27 days near to that of the solar rotation. On the contrary, MLM analysis of the same data MLM shows the most striking peak of the power at a period of near 27.5 days (Figure 1). This is a typical example showing that when strong noise background exist, the MLM is much more efficient than the FFT method.