Elsevier

Computers & Geosciences

Volume 44, July 2012, Pages 60-69
Computers & Geosciences

Simultaneous seismic wave clustering and registration

https://doi.org/10.1016/j.cageo.2012.02.017Get rights and content

Abstract

In this paper we introduce a simple procedure to identify clusters of multivariate waveforms based on a simultaneous assignation and alignment procedure. This approach is aimed at the identification of clusters of earthquakes, assuming that similarities between seismic events with respect to hypocentral parameters and focal mechanism correspond to similarities between waveforms of events. Therefore we define a distance measure between seismic curves in Rdd1, in order to interpret and better understand the main features of the generating seismic process.

Highlights

► A procedure to identify clusters of multivariate waveforms is defined. ► Simultaneous assignation and alignment is carried out. ► Similar earthquakes with respect to hypocentral parameters and focal mechanism correspond to similar waveforms. ► Multiplets with very high mean correlation are identified.

Introduction

Earthquakes are usually generated by fracture processes that occur in the Earth's crust. The discontinuous fields of permanent deformation associated with earthquakes are largely compatible with rock dislocation along faults. Dislocation causes a partial release of the elastic strain energy stored by tectonic processes and the released energy is partially propagated away from its source as a wave-field. The location and time at which fractures originate define the earthquake hypocenter, while parameters related to fault orientation and the mean-slip vector define the focal mechanism of earthquakes. Both hypocenter and focal mechanism are determined by the analysis of the waveforms represented by seismograms, that are a spatial sampling of the wave-field and recorded by a seismic network. Seismic networks often record signals relative to earthquakes that occur in clusters: individual events of a seismic cluster have hypocenters densely distributed in space-time volumes, whose sizes grow with the magnitude of main events. Within seismic clusters, seismic networks sometimes record groups of earthquakes characterized by similar signals in each station (multiplets). Multiplets have been interpreted as stress release on fault asperities or clusters of asperities (Geller and Mueller, 1980, Aster and Scott, 1993, Maurer and Deichmann, 1995, Aster et al., 1996). Based on the similarity between complete seismograms of micro-earthquakes which occurred on the San Andreas Fault, Geller and Mueller (1980) deduced that their hypocenters could not have been distant from each other by more than a quarter of the dominant wavelength.

Tsujiura, 1983a, Tsujiura, 1983b suggested that such families of events are characteristic of earthquake swarms due to repeated slips on the same fault plane, whereas sequences of foreshocks–mainshock–aftershocks, characterized by different waveforms, represent ruptures in a complex fault zone. The occurrence of multiplets has been associated with both tectonic (Poupinet et al., 1984, Ito, 1985, Scherbaum and Wendler, 1986, Console and Di Giovambattista, 1987), volcanic seismic activity (Frémont and Malone, 1987; Got et al., 1994) and induced micro-seismicity in geothermal field (Moriya et al., 2002, Moriya et al., 2003, Asanuma et al., 2005, Asanuma et al., 2007). Multiplets have also been used to evaluate with high accuracy temporal variations of subsoil mechanical parameters (Frémont, 1984, Fréchet, 1985, Poupinet et al., 1984) and to reconstruct the shape of small tectonic structures (Deichmann and García-Fernandez, 1992, Moriya et al., 2002, Moriya et al., 2003).

The geometric features of seismic networks not specifically designed, the limited representativeness of velocity models, usually optimized at a regional scale and, the uncertainties in phases picking used by the most common inversion codes, makes the differences between estimates of hypocentral positions and focal mechanisms of events generated in small seismogenic volumes, that are not sufficiently reliable to characterize the tectonic of the source regions.

For this reason many relative hypocenter location methods, based on the inversion of experimental data vectors containing many differential travel times, were proposed. In some experimental conditions, these techniques allow a determination of the relative hypocenter locations of earthquakes with a precision of about ten meters (Poupinet et al., 1984, Fréchet, 1985).

To determine differential arrival times with high accuracy, techniques exploiting waveform similarities have been proposed (Ito, 1985, Scherbaum and Wendler, 1986, Deichmann and García-Fernandez, 1992). Assuming that waveform similarity implies the similarity of focal mechanisms, the analysis of signal subsets, characterized by very similar shapes, can be used to stabilize the estimate of the polarity of the P phase onsets, by means of low-noise seismograms of each set (Got et al., 1994, Shearer et al., 2003, Carmona et al., 2009, Shelly et al., 2009, Myhill et al., 2011). Methods to calculate precise relative locations have also been proposed for volcano-tectonic earthquake multiplets (Carmona et al., 2010, Hensch et al., 2008) and to delineate the structure of geothermal reservoirs (Asanuma et al., 2005).

Adelfio et al. (2011) combined the aim of finding clusters from a set of seismograms with the functional nature of data, applying a variant of a k-means algorithm based on the principal component rotation of data.

Waveform correlation techniques have been introduced to characterize the degree of event similarity (Mezcua and Rueda, 1994, Menke, 1999) and in facilitating more accurate relative locations within similar event clusters by providing more precise timing for P and S arrivals (Gillard et al., 1996, Phillips et al., 1997). Clustering methods based on cross-correlation and/or cross-spectral techniques are effective in forming subsets of similar events only if earthquakes included in each set are very close in space, magnitude and focal parameter domains and if the recorded signals have a good signal to noise ratio. Indeed, small variations in hypocenter position, magnitude, or any focal parameter, may change the waveform at a recording point enough to make small any cross-correlation measure between signals, while some information contained in the seismic signals (like polarity and phase travel time) tends to vary poorly for small changes in hypocenter position and are practically independent from earthquake magnitude.

In this paper, to overcome the limitation of the cross-correlation technique, we introduce a new approach for simultaneous clustering and the alignment of sets of varying curves observed over time, such as seismic signals. Looking for curve similarity could be a complex issue characterized by subjective choices related to the continuous transformation of observed discrete data (Chiodi, 1989). Here, the alignment problem is handled with the introduction of a new, simple and efficient procedure, based on a similarity measure between curves.

In Section 2 we introduce some notation relative to functional data, looking at the functional nature of waveforms and related continuous transformation of curves. The proposed method that aligns and assigns curves to clusters of waveforms, according to an EM (Estimation Maximization)-type procedure is introduced in Section 3. In Section 4, this technique is applied to four-component signals relative to 159 seismic events which occurred in the South Tyrrhenian Sea recorded only by one OBS/H (Ocean Bottom Seismometer with Hydrophone). Section 5 is devoted to a discussion of results and some general conclusions.

Section snippets

Seismic waves as functional data

Usually, we refer to data observed as functions of time (such as seismic waveforms, financial time series, temperatures recorded by a central source, etc.) as functional data. Since realizations of continuous time series are available as observations of a process recorded in discrete time intervals in many statistical applications, one crucial point is to convert discrete data to continuous functions, that is, from vectors to curves or more generally functions x in Rd,d1. When we talk about

Clustering of waveforms

Waveform clustering may be considered as an issue of clustering of functional data; more generally it could be defined within the wider framework of partition type cluster analysis. Let {x1,,xN} be N multivariate curves, where xi are functions in Rd,d1, defined in Section 2. For example, xi(·) can be a 4-dimensional seismic wave observed as a parametric curve in R4 and depending on a real parameter t. We seek a partition P={G1,G2,,Gk} of the N curves in k exhaustive clusters with strong

Application

Despite the fact that the northern Sicily coastline is one of the most seismically active areas of the Italian territory, because of its position with respect to the INGV national seismic network, the minimum magnitude of completeness, which is defined as the lowest magnitude of events that a seismic network is able to detect, in its central-western sector is about ML=2 (D'Alessandro et al., 2011).

On September 6, 2002 at 01:21 GMT a shallow earthquake with MW=5.9 occurred near Palermo (Sicily);

Discussion and conclusion

In this paper we have presented a simple procedure to identify, in the seismic activity of a complex seismogenetic area, group of earthquakes with similar hypocentral parameters and focal mechanisms. The proposed procedure is based on the reasonable assumption that seismic events, which are similar with respect to the mentioned parameters, generate similar wave fields and then similar seismic signals in each station of a monitoring network. This procedure, introduced to overcome the limitations

Acknowledgments

This paper and the related work have been supported by the Scientific Research funds 2007, of the University of Palermo, entitled: “Development of estimation and diagnostic methods in space-time point processes”.

References (57)

  • H. Asanuma et al.

    Analysis of microseismic events from a stimulation at Basel, Switzerland

    GRC Transactions

    (2007)
  • R. Aster et al.

    Comprehensive characterization of waveform similarity in microearthquake data sets

    Bulletin of the Seismological Society of America

    (1993)
  • R.C. Aster et al.

    Differential analysis of coda Q using similar microearthquakes in seismic gaps. Part 1: techniques and application to seismograms recorded in the Anza seismic gap

    Bulletin of the Seismological Society of America

    (1996)
  • G.E.P. Box et al.

    Distribution of residual autocorrelations in autoregressive integrated moving average time series models

    Journal of the American Statistical Association

    (1970)
  • D.A. Brillinger

    Time Series, Data Analysis and Theory

    (1975)
  • T.M. Brocher

    Empirical relations between elastic wavespeeds and density in the Earth's crust

    Bulletin of the Seismological Society of America

    (2005)
  • M.A. Cameron

    The prediction variance and related statistics for stationary time series

    Biometrika

    (1978)
  • E. Carmona et al.

    Multiplet focal mechanisms from polarities and relative locations: the Izanjar swarm in Southern Spain

    Bulletin of the Seismological Society of America

    (2009)
  • E. Carmona et al.

    Characterization of fracture systems using precise array locations of earthquake multiplets: an example at Deception Island volcano, Antarctica

    Journal of Geophysical Research

    (2010)
  • M. Chiodi

    The clustering of longitudinal data when time series are short

    Multivariate Data Analysis

    (1989)
  • A. D'Alessandro et al.

    Seismic network evaluation through simulation: an application to the Italian national seismic network

    Bulletin of the Seismological Society of America

    (2011)
  • N. Deichmann et al.

    Rupture geometry from high-precision relative hypocenter locations of microearthquake clusters

    Geophysical Journal International

    (1992)
  • B. Everitt

    Cluster Analysis

    (1993)
  • E.A. Flinn

    Signal analysis using rectilinearity and direction of particle motion

    Proceedings of the IEEE

    (1965)
  • E.W. Forgy

    Cluster analysis of multivariate data: efficiency vs interpretability of classifications

    Biometrics

    (1965)
  • Fréchet, J., 1985. Sismogenese et doublets sismiques. PhD Thesis. University of...
  • Frémont, M.J., 1984. Mesure de variations temporelles des paramètres de la croute terrestre et d'effects de sources par...
  • M.J. Frémont et al.

    High precision relative locations of earthquakes at Mount St. Helens, Washington

    Journal of Geophysical Research

    (1987)
  • Cited by (0)

    View full text