Approximations of zero and first orders with an optimized seismic signal estimation complicated by regular and irregular interference of complex structure
We have proposed a new least-squares method for signal estimation with a complicated and therefore more realistic mathematical model of the multichannel seismic record containing random noise and an arbitrary number of coherent noise wavetrains. It is supposed that the signal and all the coherent no...
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| Datum: | 2010 |
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S. Subbotin Institute of Geophysics of the NAS of Ukraine
2010
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| Назва журналу: | Geofizicheskiy Zhurnal |
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Geofizicheskiy Zhurnal| _version_ | 1856543357744971776 |
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| author | Tyapkin, Yu. K. Silinskaya, E. A. |
| author_facet | Tyapkin, Yu. K. Silinskaya, E. A. |
| author_sort | Tyapkin, Yu. K. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2020-10-07T10:57:50Z |
| description | We have proposed a new least-squares method for signal estimation with a complicated and therefore more realistic mathematical model of the multichannel seismic record containing random noise and an arbitrary number of coherent noise wavetrains. It is supposed that the signal and all the coherent noise wavetrains bear individual trace-independent waveforms being mutually uncorrelated in time stationary stochastic processes. The amplitudes and arrival times of these record components vary from trace to trace in an arbitrary manner. Random noise is assumed to be a stationary stochastic process uncorrelated with the signal and all the coherent noise wavetrains and from trace to trace as well. Its spectral (autocorrelation) function is trace independent to within a scale factor, the variance. Under certain conditions, the method may be reduced to two successive stages, namely preliminary subtraction of estimates of all the coherent noise wavetrains and final estimation of the signal from the residual record. On both stages, optimum weighted stacking is used with reference to the variances of random noise and to the amplitudes and arrival times of the corresponding coherent component. A simplified scheme and an advanced scheme for subtracting coherent noise are proposed, which are called the zeroorder and first-order approximations, respectively. The first of them is the generalization of a conventional approach for subtracting coherent noise to the complicated data model adopted in this paper. The second scheme has an obvious advantage over the first scheme, since it allows the distortions that appear when estimating and subsequently subtracting the coherent noise wavetrains to be compensated. A simulation on synthetic data shows the efficiency of the firstorder approximation, and it provides a qualitative and quantitative comparison of those results with the results given by the zero-order approximation. |
| first_indexed | 2025-07-17T11:09:21Z |
| format | Article |
| id | journalsuranua-geofizicheskiy-article-117573 |
| institution | Geofizicheskiy Zhurnal |
| language | Russian |
| last_indexed | 2025-07-17T11:09:21Z |
| publishDate | 2010 |
| publisher | S. Subbotin Institute of Geophysics of the NAS of Ukraine |
| record_format | ojs |
| spelling | journalsuranua-geofizicheskiy-article-1175732020-10-07T10:57:50Z Approximations of zero and first orders with an optimized seismic signal estimation complicated by regular and irregular interference of complex structure Tyapkin, Yu. K. Silinskaya, E. A. We have proposed a new least-squares method for signal estimation with a complicated and therefore more realistic mathematical model of the multichannel seismic record containing random noise and an arbitrary number of coherent noise wavetrains. It is supposed that the signal and all the coherent noise wavetrains bear individual trace-independent waveforms being mutually uncorrelated in time stationary stochastic processes. The amplitudes and arrival times of these record components vary from trace to trace in an arbitrary manner. Random noise is assumed to be a stationary stochastic process uncorrelated with the signal and all the coherent noise wavetrains and from trace to trace as well. Its spectral (autocorrelation) function is trace independent to within a scale factor, the variance. Under certain conditions, the method may be reduced to two successive stages, namely preliminary subtraction of estimates of all the coherent noise wavetrains and final estimation of the signal from the residual record. On both stages, optimum weighted stacking is used with reference to the variances of random noise and to the amplitudes and arrival times of the corresponding coherent component. A simplified scheme and an advanced scheme for subtracting coherent noise are proposed, which are called the zeroorder and first-order approximations, respectively. The first of them is the generalization of a conventional approach for subtracting coherent noise to the complicated data model adopted in this paper. The second scheme has an obvious advantage over the first scheme, since it allows the distortions that appear when estimating and subsequently subtracting the coherent noise wavetrains to be compensated. A simulation on synthetic data shows the efficiency of the firstorder approximation, and it provides a qualitative and quantitative comparison of those results with the results given by the zero-order approximation. S. Subbotin Institute of Geophysics of the NAS of Ukraine 2010-02-01 Article Article application/pdf https://journals.uran.ua/geofizicheskiy/article/view/117573 10.24028/gzh.0203-3100.v32i1.2010.117573 Geofizicheskiy Zhurnal; Vol. 32 No. 1 (2010); 107-121 Геофизический журнал; Том 32 № 1 (2010); 107-121 Геофізичний журнал; Том 32 № 1 (2010); 107-121 2524-1052 0203-3100 ru https://journals.uran.ua/geofizicheskiy/article/view/117573/111615 Copyright (c) 2020 Geofizicheskiy Zhurnal https://creativecommons.org/licenses/by/4.0 |
| spellingShingle | Tyapkin, Yu. K. Silinskaya, E. A. Approximations of zero and first orders with an optimized seismic signal estimation complicated by regular and irregular interference of complex structure |
| title | Approximations of zero and first orders with an optimized seismic signal estimation complicated by regular and irregular interference of complex structure |
| title_full | Approximations of zero and first orders with an optimized seismic signal estimation complicated by regular and irregular interference of complex structure |
| title_fullStr | Approximations of zero and first orders with an optimized seismic signal estimation complicated by regular and irregular interference of complex structure |
| title_full_unstemmed | Approximations of zero and first orders with an optimized seismic signal estimation complicated by regular and irregular interference of complex structure |
| title_short | Approximations of zero and first orders with an optimized seismic signal estimation complicated by regular and irregular interference of complex structure |
| title_sort | approximations of zero and first orders with an optimized seismic signal estimation complicated by regular and irregular interference of complex structure |
| url | https://journals.uran.ua/geofizicheskiy/article/view/117573 |
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