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Functional linear models for the analysis of similarity of waveforms.
Last modified: 2018-05-18
Abstract
In seismology methods based on waveform similarity analysis are adopted
to identify sequences of events characterized by similar fault mechanism and propagation pattern. Seismic waves can be considered as spatially interdependent three dimensional curves depending on time and the waveform similarity analysis can be configured as a functional clustering approach, on the basis of which the membership is assessed by the shape of the temporal patterns. For providing qualitative extraction of the most important information from the recorded signals we propose an
integration of the metadata, related to the waves, as explicative variables of a functional linear models. The temporal patterns of this effects, as well as the residual component, are investigated in order to detect a cluster structure. The implemented clustering techniques are based on functional data depth.
to identify sequences of events characterized by similar fault mechanism and propagation pattern. Seismic waves can be considered as spatially interdependent three dimensional curves depending on time and the waveform similarity analysis can be configured as a functional clustering approach, on the basis of which the membership is assessed by the shape of the temporal patterns. For providing qualitative extraction of the most important information from the recorded signals we propose an
integration of the metadata, related to the waves, as explicative variables of a functional linear models. The temporal patterns of this effects, as well as the residual component, are investigated in order to detect a cluster structure. The implemented clustering techniques are based on functional data depth.
References
1.Adelfio, G., Chiodi, M., D’Alessandro, A. and Luzio, D., D’Anna, G., Mangano, G. Simulta-
neous seismic wave clustering and registration. Computers Geosciences, 8(44), 6069 (2012)
2. Adelfio G., Di Salvo F., Sottile G. Depth-based methods for clustering of functional data TIES
2017 Conference, Bergamo, Italy, July 24th 26th, (2017).
3. Barani, S. Ferretti, G., Massa, M., Spallarossa D. : The waveform similarity approach
to identify dependent events in instrumental seismic catalogues , Geophys. J. Int. doi:
10.1111/j.1365-246X.2006.03207.x (2006)
4. Di Salvo, F., Rotondi, R., Lanzano, G.: Detecting clusters in spatially correlated waveforms,
GNGTS conference, Trieste, November 13th - 16th (2017)
5. Hao-kun, D., Jun-xing, C.,Ya-juan, X., Xing-jian, W., Seismic facies analysis based on self-
organizing map and empirical mode decomposition, Journal of Applied Geophysics, 112,
5261 (2015)
6. Jagla, E. A., Kolton A. B.: A mechanism for spatial and temporal earthquake clustering, J.
Geophys. Res. doi:10.1029/2009JB006974 (2010)
7. Lopez-Pintado, S., Romo, J., : Depth-based inference for functional data, Computational
Statistics and Data Analysis 51 (10), 4957-4968, (2007).
8. Reasenberg, P. : Second-order moment of Central California seismicity, 1969 - 1982, J. geo-
phys. Res., 90, 54785495 (1985)
9. Silvestrov, I., Tcheverda V.:SVD analysis in application to full waveform inversion of
multicomponent seismic data,Journal of Physics: Conference Series 290 doi:10.1088/1742-
6596/290/1/012014 (2011)
10. Shou, H., Zipunnikov, V., Crainiceanu, C. M., Greven, S. : Structured Functional Principal
Component Analysis, Biometrics, 71(1), 247257 doi.org/10.1111/biom.12236, (2015)
11. Suk, H. W., Hwang, H. : Functional Generalized Structured Component Analysis. Psychome-
trika, 81(4), 940968. doi.org/10.1007/s11336-016-9521-1, (2016)
12. Tucker, D.J., Wu, W. , Srivastava, A., Generative models for functional data using phase and
amplitude separation, Computational Statistics and Data Analysis, 61, 5066, (2013)
neous seismic wave clustering and registration. Computers Geosciences, 8(44), 6069 (2012)
2. Adelfio G., Di Salvo F., Sottile G. Depth-based methods for clustering of functional data TIES
2017 Conference, Bergamo, Italy, July 24th 26th, (2017).
3. Barani, S. Ferretti, G., Massa, M., Spallarossa D. : The waveform similarity approach
to identify dependent events in instrumental seismic catalogues , Geophys. J. Int. doi:
10.1111/j.1365-246X.2006.03207.x (2006)
4. Di Salvo, F., Rotondi, R., Lanzano, G.: Detecting clusters in spatially correlated waveforms,
GNGTS conference, Trieste, November 13th - 16th (2017)
5. Hao-kun, D., Jun-xing, C.,Ya-juan, X., Xing-jian, W., Seismic facies analysis based on self-
organizing map and empirical mode decomposition, Journal of Applied Geophysics, 112,
5261 (2015)
6. Jagla, E. A., Kolton A. B.: A mechanism for spatial and temporal earthquake clustering, J.
Geophys. Res. doi:10.1029/2009JB006974 (2010)
7. Lopez-Pintado, S., Romo, J., : Depth-based inference for functional data, Computational
Statistics and Data Analysis 51 (10), 4957-4968, (2007).
8. Reasenberg, P. : Second-order moment of Central California seismicity, 1969 - 1982, J. geo-
phys. Res., 90, 54785495 (1985)
9. Silvestrov, I., Tcheverda V.:SVD analysis in application to full waveform inversion of
multicomponent seismic data,Journal of Physics: Conference Series 290 doi:10.1088/1742-
6596/290/1/012014 (2011)
10. Shou, H., Zipunnikov, V., Crainiceanu, C. M., Greven, S. : Structured Functional Principal
Component Analysis, Biometrics, 71(1), 247257 doi.org/10.1111/biom.12236, (2015)
11. Suk, H. W., Hwang, H. : Functional Generalized Structured Component Analysis. Psychome-
trika, 81(4), 940968. doi.org/10.1007/s11336-016-9521-1, (2016)
12. Tucker, D.J., Wu, W. , Srivastava, A., Generative models for functional data using phase and
amplitude separation, Computational Statistics and Data Analysis, 61, 5066, (2013)
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