Catalog cluster identification using Single Link Cluster analysis

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Sound source temporal properties

A sound may be transient, of relatively short duration, having an obvious start and end, or it may be continuous. Transient underwater sounds include impulsive sounds from explosions, airguns, sonars, and earthquakes. An explosion produces a single transient sound, but airguns, pile drivers, earthquake sequences and many sonars produce repeated transient sounds. However, the distinction between transient and continuous sounds is not absolute. Sound emitted from a ship underway is continuous, but it is transient insofar as a stationary receiver is concerned. Also many sounds are not purely transient or purely continuous even at the source.


In describing a transient sound it is useful to present the peak level as well as some description of how the sound varies with time (its waveform). The peak level may be described as being either a particular pressure or a mean square pressure averaged over a relatively short time interval. The terms phase, phase difference, relative phase and phase angle can be used in comparing two periodic waveforms with the same period. For example, sound components from one source that arrive at a given point via two different propagation paths may differ in phase. Phase refers to the difference in time, or the offset between two waveforms. If the difference equals the period, or any integer multiple of period, the two waveforms look the same and the phase difference is zero. Thus, it is possible to describe phase as an angle in the range +/- 180◦. For example, if phase difference is 1/4 of the period, phase angle is +/-90◦. The sign depends on whether the waveform of interest leads or lags the reference waveform. For continuous waveforms that are random or non periodic, the phase concept generalizes to one of time delay, describing the time offset of a waveform and its replica.

Source level

Source Level is defined as the pressure level that would be measured at a standard reference distance from an ideal point source radiating the same amount of sound as the actual source being measured (Ross, 1976). This concept is necessary because sound measurements near large, distributed sources like seismic phases converted into T-phase depend strongly on source size and measurement location, and are difficult to relate to levels measured far away. This concept of source level introduces the dimension of distance into the description of sound. To compare different sound sources, it is necessary to adopt a standardized reference distance at which source levels will be determined. For underwater sounds, a reference distance of 1 m is usually used. Source level is estimated by adjusting the measured level to allow for transmission loss between a standard reference range and the range where the sound was measured. The standard units for source levels of underwater sound are dB re 1µP a at 1m.

Sound propagation

Discussions on sound propagation include two equivalent terms: transmission loss and prop-agation loss. Conceptually, a sound wave traveling from point A to point B diminishes in am-plitude, or intensity, as it spreads out in space, is reflected, and is absorbed. If the source level is at 1m 160dB re 1µP a at 1m, the received level at range 1 km may be only 100dB re 1µP a at 1m; in this case transmission loss is 60 dB. Transmission loss is generally expressed in dB, representing a ratio of powers, intensities or energies of a sound wave at two distances from the source. The distance at which the denominator measurement is taken is the reference distance for transmission loss. log(P/P0) = log(P ) − log(P0) (2.3).
Because dB scales are logarithmic, transmission loss can be expressed as the difference, in dB, between the levels at the two distances.
In a uniform medium with no nearby boundaries and no absorption loss, sound from an om-nidirectional source spreads uniformly outward with a spherical wavefront. Sound pressure de- creases as the area of the wavefront expands. At distances that are large compared with the source dimensions (far field), sound pressure is inversely proportional to distance. Thus, transmission loss due to the spherical spreading is given by: T Lspherical (dB) = 20logR (2.4) With spherical spreading, sound levels diminish by 6 dB when distance is doubled, and by 20 dB when distance increases by a factor of 10.

Land based arrays and OBS arrays

AuH distributions complement the poor magnitude and spatial covering of the international land based seismic networks for most parts of the world’s oceans. It provides long term and more precise event locations and can be seen as a way to complement the still shorter autonomy of seismic seafloor experiments. Nevertheless, the special characteristics of T-phases oblige any interpretation made using AuH data to be done while keeping in mind the differences from more classical seismic data.

Teleseismic data

At the slow-spreading MAR the largest magnitude earthquakes (with a sufficient size to be detected by land-based seismic stations) are associated with the axis. A seismic moment deficiency has been observed teleseismically along oceanic transform faults (Engeln et al., 1986; Abercrombie and Ekström, 2001). Other zones are seismically inactive, and might correspond either to areas where deformation is accommodated through low magnitude seismicity (lower than the detection limit of the land-based array), or to areas where deformation occurs aseismically, or to quiescent areas in which stress is accumulated and not released (Behn et al., 2002b).
The larger earthquakes occur preferentially in areas with a deeper median valley (Huang and Solomon, 1988), and are likely to be tectonic in origin. Bergman and Solomon (1990) concluded that volcanic earthquakes on the MAR probably fall below the magnitude threshold for teleseismic detection using global seismic networks. They observed a number of teleseismic swarms on the MAR, and determined that they were due to tectonic extension. However the results of these studies have been limited in their capacity to provide a representative account of general seismicity at the MAR, because they do not include the lower magnitude tectonic and volcanic events. Despite the fact that the pattern of seismically active/inactive areas observed in the AuH data can be recognized in the longer term teleseismic record, it is not as clearly defined. This lack of definition may be due to the lower number of events (Figure 3.9), or to the much larger error ellipses associated with teleseismic locations. The similarities suggest that the patterns of seismicity along the axis can be persistent at timescales of one year to several decades (Smith et al., 2003).

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OBS data

Micro earthquake studies help constrain the interpretation of AuH recorded events patterns due to the more detailed view of the seismicity distribution given by ocean bottom seismometers. Unfortunately these experiments are not concurrent in time with the AuH experiments and are conducted on a limited number of MAR sites. Five OBS experiments were conducted on four different segments on the MAR spanning across 20 years. Experiments were conducted on segments 15 (22.23N – 22.67N), 24 (25.92N – 26.25N), 32 (28.84N – 29.41N) and 45 (34.50N – 35.27N) (Smith et al., 2003).
Microearthquake distribution seem to be quite consistent along these segments. Predominantly, earthquakes occur at segment extremities, generally linked to inside corners, and/or segment centers (Barclay et al., 2001; de Martin et al., 2007; Kong et al., 1992; Wolfe et al., 1995). Segment 15 revealed numerous miroearthquakes recorded extending from the northern end of the segment to near the center (Toomey et al., 1985, 1988). Seismic distribution plots with bathymetry, reveal that much of the seismic activity has a strong tectonic signature (Barclay et al., 2001; de Martin et al., 2007; Kong et al., 1992; Toomey et al., 1985, 1988; Wolfe et al., 1995) suggesting that spreading has been mainly accommodated by faulting during the last few tens of millions of years on these segments. AuH recorded earthquake distribution are generally consistent with the OBS recorded ones (Smith et al., 2003). Differences between the two kinds of distribution seem to be explained by the magnitude level of the microearthquakes and the detection threshold of the AuH arrays. In some of the cases AuH seismic distributions also seem to be shifted when they are close to shallow topography (Smith et al., 2003). For the segment 15, AuH data revealed that the entire length of the segment was active during the years of monitoring (Smith et al., 2003).

Table of contents :

Résumé étendu
1 Introduction 
2 Sound in the Ocean, T-phase and AuH 
2.1 Sound measurements
2.1.1 Sound spectra
2.1.2 Sound source temporal properties
2.1.3 Waveform
2.1.4 Source level
2.1.5 Sound propagation
2.1.6 Ambient noise
2.2 T-phases
2.2.1 The down-slope conversion model
2.2.2 T-waves in the mode formalism
2.2.3 Scattering of T-waves in the mode formalism
2.2.4 T-phase waveform
2.3 Hydrophone Technology
2.3.1 Hydrophone and Mooring
2.3.2 Hydrophone servicing at sea
2.4 Data processing
2.4.1 Event location and source level
2.4.2 Location error analysis
2.5 Autonomous Hydrophone arrays
2.5.1 AuH detection thresholds and location accuracy
2.5.2 AuH and teleseismic data correlations
2.6 Conclusions
3 Mid Oceanic ridges and AuH data 
3.1 Ridge segmentation and Morphology
3.2 Ridge Faulting
3.2.1 Detachment Faulting
3.3 Magmatic contribution Faulting and Morphology
3.4 Oceanic ridges seismic patterns
3.5 Land based arrays and OBS arrays
3.5.1 Teleseismic data
3.5.2 OBS data
3.6 Conclusions
4 MAR AuH seismicity analysis 
4.1 Introduction
4.2 AuH array error field
4.3 MAR AuH Data
4.3.1 Time Distance Plots
4.3.2 Detection thresholds analysis
4.3.3 Mean error as a function of number of stations
4.4 Mantle Bouguer Anomaly
4.5 Analysis of the seismicity
4.5.1 Cluster analysis
4.5.2 Analysis of the seismicity at broad wavelength
4.5.3 Principal Component Analysis of the MAR Seismicity
4.6 Conclusions
5 Analysis of MAR AuH seismic clusters 
5.1 Introduction
5.2 Catalog cluster identification using Single Link Cluster analysis
5.3 Mainshock-aftershock sequences
5.3.1 Modified Omori Law
5.3.2 Size-frequency relationship
5.4 Miami Parabolic Equation model
5.5 Previous analyses of seismic sequences along the MAR
5.6 Mantle Bouguer anomaly inversion and MAR segmentation
5.7 Mid-Atlantic Ridge seismic sequences
5.8 Transmission Loss analyses
5.9 Size Frequency analyses
5.10 MOL analysis
5.11 Conclusions
6 General Conclusions 


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