{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:36:15Z","timestamp":1760232975664,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2022,12,8]],"date-time":"2022-12-08T00:00:00Z","timestamp":1670457600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004913","name":"University of Palermo","doi-asserted-by":"publisher","award":["FFR 2021 GIADA ADELFIO"],"award-info":[{"award-number":["FFR 2021 GIADA ADELFIO"]}],"id":[{"id":"10.13039\/501100004913","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, we propose a new approach based on the fitting of a generalized linear regression model in order to detect points of change in the variance of a multivariate-covariance Gaussian variable, where the variance function is piecewise constant. By applying this new approach to multivariate waveforms, our method provides simultaneous detection of change points in functional time series. The proposed approach can be used as a new picking algorithm in order to automatically identify the arrival times of P- and S-waves in different seismograms that are recording the same seismic event. A seismogram is a record of ground motion at a measuring station as a function of time, and it typically records motions along three orthogonal axes (X, Y, and Z), with the Z-axis being perpendicular to the Earth\u2019s surface and the X- and Y-axes being parallel to the surface and generally oriented in North\u2013South and East\u2013West directions, respectively. The proposed method was tested on a dataset of simulated waveforms in order to capture changes in the performance according to the waveform characteristics. In an application to real seismic data, our results demonstrated the ability of the multivariate algorithm to pick the arrival times in quite noisy waveforms coming from seismic events with low magnitudes.<\/jats:p>","DOI":"10.3390\/s22249636","type":"journal-article","created":{"date-parts":[[2022,12,9]],"date-time":"2022-12-09T03:59:46Z","timestamp":1670558386000},"page":"9636","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Statistical Picking of Multivariate Waveforms"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8878-5986","authenticated-orcid":false,"given":"Nicoletta","family":"D\u2019Angelo","sequence":"first","affiliation":[{"name":"Dipartimento di Scienze Economiche, Aziendali e Statistiche, Universit\u00e0 degli Studi di Palermo, 90128 Palermo, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3194-4296","authenticated-orcid":false,"given":"Giada","family":"Adelfio","sequence":"additional","affiliation":[{"name":"Dipartimento di Scienze Economiche, Aziendali e Statistiche, Universit\u00e0 degli Studi di Palermo, 90128 Palermo, Italy"},{"name":"Osservatorio Nazionale Terremoti, Istituto Nazionale di Geofisica e Vulcanologia (INGV), 90146 Palermo, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0331-4078","authenticated-orcid":false,"given":"Marcello","family":"Chiodi","sequence":"additional","affiliation":[{"name":"Dipartimento di Scienze Economiche, Aziendali e Statistiche, Universit\u00e0 degli Studi di Palermo, 90128 Palermo, Italy"},{"name":"Osservatorio Nazionale Terremoti, Istituto Nazionale di Geofisica e Vulcanologia (INGV), 90146 Palermo, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0074-3125","authenticated-orcid":false,"given":"Antonino","family":"D\u2019Alessandro","sequence":"additional","affiliation":[{"name":"Osservatorio Nazionale Terremoti, Istituto Nazionale di Geofisica e Vulcanologia (INGV), 90146 Palermo, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1080\/03610918.2011.592248","article-title":"Change-point detection for variance piecewise constant models","volume":"41","author":"Adelfio","year":"2012","journal-title":"Commun. Stat. Simul. Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1785\/0119990070","article-title":"Automatic phase-detection and identification by full use of a single three-component broadband seismogram","volume":"90","author":"Bai","year":"2000","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_3","unstructured":"K\u00fcperkoch, L., Meier, T., and Diehl, T. (2012). Automated event and phase identification. New Manual of Seismological Observatory Practice 2 (NMSOP-2), Deutsches GeoForschungsZentrum GFZ."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/S0031-9201(99)00007-2","article-title":"Robust automatic P-phase picking: An on-line implementation in the analysis of broadband seismogram recordings","volume":"113","author":"Sleeman","year":"1999","journal-title":"Phys. Earth Planet. Inter."},{"key":"ref_5","unstructured":"Aldersons, F. (2004). Toward Three-Dimensional Crustal Structure of the Dead Sea Region from Local Earthquake Tomography. [Ph.D. Thesis, Senate of Tel-Aviv University]."},{"key":"ref_6","first-page":"1159","article-title":"Automated determination of P-phase arrival times at regional and local distances using higher order statistics","volume":"181","author":"Meier","year":"2010","journal-title":"Geophys. J. Int."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1521","DOI":"10.1785\/BSSA0680051521","article-title":"Automatic earthquake recognition and timing from single traces","volume":"68","author":"Allen","year":"1978","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"S225","DOI":"10.1785\/BSSA07206B0225","article-title":"Automatic phase pickers: Their present use and future prospects","volume":"72","author":"Allen","year":"1982","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1437","DOI":"10.1785\/BSSA0770041437","article-title":"An automatic phase picker for local and teleseismic events","volume":"77","author":"Baer","year":"1987","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_10","unstructured":"Hartung, J., Elpelt, B., and Kl\u00f6sener, K.H. (2014). Statistik: Lehr-und Handbuch der Angewandten Statistik, Oldenbourg Verlag."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Akaike, H. (1998). Autoregressive model fitting for control. Selected Papers of Hirotugu Akaike, Springer.","DOI":"10.1007\/978-1-4612-1694-0_12"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1137\/0313010","article-title":"Markovian representation of stochastic processes by canonical variables","volume":"13","author":"Akaike","year":"1975","journal-title":"SIAM J. Control."},{"key":"ref_13","first-page":"281","article-title":"Automatic detection of onset time of seismic waves and its con-fidence interval using the autoregressive model fitting","volume":"37","author":"Morita","year":"1984","journal-title":"Earthquake"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"267","DOI":"10.4294\/jpe1952.36.267","article-title":"A new efficient procedure for the estimation of onset times of seismic waves","volume":"36","author":"Takanami","year":"1988","journal-title":"J. Phys. Earth"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"D\u2019Angelo, N., Adelfio, G., D\u2019Alessandro, A., and Chiodi, M. (2020, January 1\u20134). A Fast and Efficient Picking Algorithm for Earthquake Early Warning Application Based on the Variance Piecewise Constant Models. Proceedings of the International Conference on Computational Science and Its Applications, Cagliari, Italy.","DOI":"10.1007\/978-3-030-58820-5_65"},{"key":"ref_16","unstructured":"D\u2019Angelo, N., Adelfio, G., D\u2019Alessandro, A., and Chiodi, M. (2021). Evaluating the performance of a new picking algorithm based on the variance piecewise constant models. Book of Short Papers\u2014SIS 2021, Pearson."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2101","DOI":"10.1007\/s00477-022-02218-x","article-title":"A new picking algorithm based on the variance piecewise constant models","volume":"36","author":"Adelfio","year":"2022","journal-title":"Stoch. Environ. Res. Risk Assess."},{"key":"ref_18","unstructured":"R Core Team (2019). R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1093\/bioinformatics\/btq647","article-title":"Efficient change point detection for genomic sequences of continuous measurements","volume":"27","author":"Muggeo","year":"2011","journal-title":"Bioinformatics"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1080\/03610929808832115","article-title":"A multivariate generalization of the power exponential family of distributions","volume":"27","year":"1998","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1177\/1471082X0100100301","article-title":"Exact and approximate REML for heteroscedastic regression","volume":"1","author":"Smyth","year":"2001","journal-title":"Stat. Model."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/10618600.2016.1154063","article-title":"Regression Models for Multivariate Count Data","volume":"26","author":"Zhang","year":"2017","journal-title":"J. Comput. Graph. Stat."},{"key":"ref_23","unstructured":"Zhang, Y., and Zhou, H. MGLM: Multivariate Response Generalized Linear Models, R Package Version 0.2.0."},{"key":"ref_24","first-page":"50","article-title":"Estimating the number of changepoints in segmented regression models: Comparative study and application","volume":"4","author":"Priulla","year":"2020","journal-title":"d\/Seas Work. Pap."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Mourhatch, R., and Krishnan, S. (2020). Simulation of Broadband Ground Motion by Superposing High-Frequency Empirical Green\u2019s Function Synthetics on Low-Frequency Spectral-Element Synthetics. Geosciences, 10.","DOI":"10.3390\/geosciences10090339"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3811","DOI":"10.1093\/bioinformatics\/bti646","article-title":"Detection of DNA copy number alterations using penalized least squares regression","volume":"21","author":"Huang","year":"2005","journal-title":"Bioinformatics"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1093\/biostatistics\/kxm013","article-title":"Spatial smoothing and hot spot detection for CGH data using the fused lasso","volume":"9","author":"Tibshirani","year":"2008","journal-title":"Biostatistics"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/24\/9636\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:36:48Z","timestamp":1760146608000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/24\/9636"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,8]]},"references-count":27,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["s22249636"],"URL":"https:\/\/doi.org\/10.3390\/s22249636","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,12,8]]}}}