High-frequency S-wave seismogram envelopes of microearthquakes broaden with increasing travel distance,a phenomenon known as S-wave envelope broadening. Multiple forward scattering and diffraction for the random inhom...High-frequency S-wave seismogram envelopes of microearthquakes broaden with increasing travel distance,a phenomenon known as S-wave envelope broadening. Multiple forward scattering and diffraction for the random inhomogeneities along the seismic ray path are the main causes of S-wave envelope broadening,so the phenomenon of S-wave envelope broadening is used to study the inhomogeneity of the medium. The peak delay time of an S-wave,which is defined as the time lag from the direct S-wave onset to the maximum amplitude arrival of its envelope,is accepted to quantify S-wave envelope broadening. 204 small earthquake records in Changbaishan Tianchi volcano were analyzed by the S-wave envelope broadening algorithm. The results show that S-wave envelope broadening in the Changbaishan Tianchi volcano is obvious,and that the peak delay time of S-wave has a positive correlation with the hypocenter distance and frequency of the S-wave. The relationships between the S-wave peak delay time and the hypocenter distance for different frequency bands were obtained using the statistics method. The results are beneficial to the understanding of the S-wave envelope broadening phenomena and the quantitative research on the inhomogeneities of the crust medium in the Changbaishan Tianchi volcano region.展开更多
We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method. First, the time-delayed feedback bang-ba...We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method. First, the time-delayed feedback bang-bang control force is expressed approximately in terms of the system state variables without time delay. Then the averaged It6 stochastic differential equations for the system are derived using the stochastic averaging method. Finally, the response of the system is obtained by solving the Fokker-Plank-Kolmogorov （FPK） equation associated with the averaged lt6 equations. A Duffing oscillator with time-delayed feedback bang-bang control under combined harmonic and white noise excitations is taken as an example to illus- trate the proposed method. The analytical results are confirmed by digital simulation. We found that the time delay in feedback bang-bang control will deteriorate the control effectiveness and cause bifurcation of stochastic jump of Duffing oscillator.展开更多
基金sponsored by the National Key Technology R&D Program (2006BAC01B04)the Joint Earthquake Science Foundation (A08026,A07138),China
文摘High-frequency S-wave seismogram envelopes of microearthquakes broaden with increasing travel distance,a phenomenon known as S-wave envelope broadening. Multiple forward scattering and diffraction for the random inhomogeneities along the seismic ray path are the main causes of S-wave envelope broadening,so the phenomenon of S-wave envelope broadening is used to study the inhomogeneity of the medium. The peak delay time of an S-wave,which is defined as the time lag from the direct S-wave onset to the maximum amplitude arrival of its envelope,is accepted to quantify S-wave envelope broadening. 204 small earthquake records in Changbaishan Tianchi volcano were analyzed by the S-wave envelope broadening algorithm. The results show that S-wave envelope broadening in the Changbaishan Tianchi volcano is obvious,and that the peak delay time of S-wave has a positive correlation with the hypocenter distance and frequency of the S-wave. The relationships between the S-wave peak delay time and the hypocenter distance for different frequency bands were obtained using the statistics method. The results are beneficial to the understanding of the S-wave envelope broadening phenomena and the quantitative research on the inhomogeneities of the crust medium in the Changbaishan Tianchi volcano region.
基金Project supported by the National Natural Science Foundation of China(Nos.10772159 and 10802030)the Research Fund for Doctoral Program of Higher Education of China(No.20060335125)
文摘We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method. First, the time-delayed feedback bang-bang control force is expressed approximately in terms of the system state variables without time delay. Then the averaged It6 stochastic differential equations for the system are derived using the stochastic averaging method. Finally, the response of the system is obtained by solving the Fokker-Plank-Kolmogorov （FPK） equation associated with the averaged lt6 equations. A Duffing oscillator with time-delayed feedback bang-bang control under combined harmonic and white noise excitations is taken as an example to illus- trate the proposed method. The analytical results are confirmed by digital simulation. We found that the time delay in feedback bang-bang control will deteriorate the control effectiveness and cause bifurcation of stochastic jump of Duffing oscillator.
