Mathematical model of seismic signal, as a flow of physically non realizable single seismic waves
The new conception of seismic data analysis is proposed. It is based on preliminary studying of seismic background. Its characteristics are a base for using mathematical models of non realizable seismic signals. The specific mathematical model of the seismic signal is proposed as well. The peculiari...
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| Дата: | 2016 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Subbotin Institute of Geophysics of the NAS of Ukraine
2016
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| Онлайн доступ: | https://journals.uran.ua/geofizicheskiy/article/view/107830 |
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| Назва журналу: | Geofizicheskiy Zhurnal |
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journalsuranua-geofizicheskiy-article-1078302020-10-07T11:19:44Z Mathematical model of seismic signal, as a flow of physically non realizable single seismic waves Mostovoy, V. S. Mostovyi, S. V. seismic signal stochastic flow a posterior probability seismic background noise mathematical model The new conception of seismic data analysis is proposed. It is based on preliminary studying of seismic background. Its characteristics are a base for using mathematical models of non realizable seismic signals. The specific mathematical model of the seismic signal is proposed as well. The peculiarity of the model is that it allows you to simulate the flow of seismic waves of different classes each of them appears in the stream with specific time delay. This process takes place against the micro-seismic background noise. It is natural to model the flow of signals by the physically realizable signal. It means those signals which do not have a trace in prehistory. But this representation of the signal is unacceptable for two reasons. The first one is related to the smoothness of the signal at the time of its appearance on the seismic record. The second one is related to the fact that the fade of the signal in the noise does not allow us to determine the time of its appearance on the record accurately. The latter circumstance does not leave us the possibility to simulate the time of the signal occurrence by using the determined value. Therefore, the time of occurrence of the signal is simulated by random variable with variance depending on the level of micro-seismic background. We introduce the notion of generalized seismic signal as a function of time and of the vector of parameters, which determine its shape, the energy, the place in flow of the other signals, spectral characteristics, and in general behavior in the entire history of its existence. Any widely spread seismic signal models used in practice are a particular case of this one. Or in a more rigorous approach to the definition the different particular cases of the signals classes are transformed into the different hyper-planes into space of parameters. Subbotin Institute of Geophysics of the NAS of Ukraine 2016-08-01 Article Article application/pdf https://journals.uran.ua/geofizicheskiy/article/view/107830 10.24028/gzh.0203-3100.v38i5.2016.107830 Geofizicheskiy Zhurnal; Vol. 38 No. 5 (2016); 164-169 Геофизический журнал; Том 38 № 5 (2016); 164-169 Геофізичний журнал; Том 38 № 5 (2016); 164-169 2524-1052 0203-3100 en https://journals.uran.ua/geofizicheskiy/article/view/107830/102779 Copyright (c) 2020 Geofizicheskiy Zhurnal https://creativecommons.org/licenses/by/4.0 |
| institution |
Geofizicheskiy Zhurnal |
| collection |
OJS |
| language |
English |
| topic |
seismic signal stochastic flow a posterior probability seismic background noise mathematical model |
| spellingShingle |
seismic signal stochastic flow a posterior probability seismic background noise mathematical model Mostovoy, V. S. Mostovyi, S. V. Mathematical model of seismic signal, as a flow of physically non realizable single seismic waves |
| topic_facet |
seismic signal stochastic flow a posterior probability seismic background noise mathematical model |
| format |
Article |
| author |
Mostovoy, V. S. Mostovyi, S. V. |
| author_facet |
Mostovoy, V. S. Mostovyi, S. V. |
| author_sort |
Mostovoy, V. S. |
| title |
Mathematical model of seismic signal, as a flow of physically non realizable single seismic waves |
| title_short |
Mathematical model of seismic signal, as a flow of physically non realizable single seismic waves |
| title_full |
Mathematical model of seismic signal, as a flow of physically non realizable single seismic waves |
| title_fullStr |
Mathematical model of seismic signal, as a flow of physically non realizable single seismic waves |
| title_full_unstemmed |
Mathematical model of seismic signal, as a flow of physically non realizable single seismic waves |
| title_sort |
mathematical model of seismic signal, as a flow of physically non realizable single seismic waves |
| description |
The new conception of seismic data analysis is proposed. It is based on preliminary studying of seismic background. Its characteristics are a base for using mathematical models of non realizable seismic signals. The specific mathematical model of the seismic signal is proposed as well. The peculiarity of the model is that it allows you to simulate the flow of seismic waves of different classes each of them appears in the stream with specific time delay. This process takes place against the micro-seismic background noise. It is natural to model the flow of signals by the physically realizable signal. It means those signals which do not have a trace in prehistory. But this representation of the signal is unacceptable for two reasons. The first one is related to the smoothness of the signal at the time of its appearance on the seismic record. The second one is related to the fact that the fade of the signal in the noise does not allow us to determine the time of its appearance on the record accurately. The latter circumstance does not leave us the possibility to simulate the time of the signal occurrence by using the determined value. Therefore, the time of occurrence of the signal is simulated by random variable with variance depending on the level of micro-seismic background. We introduce the notion of generalized seismic signal as a function of time and of the vector of parameters, which determine its shape, the energy, the place in flow of the other signals, spectral characteristics, and in general behavior in the entire history of its existence. Any widely spread seismic signal models used in practice are a particular case of this one. Or in a more rigorous approach to the definition the different particular cases of the signals classes are transformed into the different hyper-planes into space of parameters. |
| publisher |
Subbotin Institute of Geophysics of the NAS of Ukraine |
| publishDate |
2016 |
| url |
https://journals.uran.ua/geofizicheskiy/article/view/107830 |
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2024-04-21T19:39:55Z |
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