M. Nettles's research while affiliated with Columbia University and other places

Publications (94)

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The flow speed of the Greenland Ice Sheet changes dramatically in inland regions when surface meltwater drains to the bed. But ice-sheet discharge to the ocean is dominated by fast-flowing outlet glaciers, where the effect of increasing surface melt on annual discharge is unknown. Observations of a supraglacial lake drainage at Helheim Glacier, and...
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We present a new, three-dimensional model of seismic velocity and anisotropy in the Pacific upper mantle, PAC13E. We invert a dataset of single-station surface-wave phase-anomaly measurements sensitive only to Pacific structure for the full set of thirteen anisotropic parameters that describe surface-wave anisotropy. Realistic scaling relationships...
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The number of gigaton‐sized iceberg‐calving events occurring annually at Greenland glaciers is increasing, part of a larger trend of accelerating mass loss from the Greenland Ice Sheet. Though visual observation of large calving events is rare, ∼60 glacial earthquakes generated by these calving events are currently recorded each year by regional an...
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The influence of surface melt on the flow of Greenland's largest outlet glaciers remains poorly known and in situ observations are few. We use field observations to link surface meltwater forcing to glacier-wide diurnal velocity variations on East Greenland's Helheim Glacier over two summer melt seasons. We observe diurnal variations in glacier spe...
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The Helheim glacier, located in southeast Greenland, has more than ten campaign-type Global Positioning System (GPS) sites; data processing led to the observation of a very rapid change in the ionospheric delay. To identify the cause of these sporadic disturbances, we analyzed the slant total electron content (STEC), single-differenced STEC (SD-STE...
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We develop a procedure to improve estimates of relative earthquake locations using Rayleigh and Love wave arrivals for multiple earthquakes recorded at common stations. We fit predicted differential traveltimes to those measured using a cross-correlation technique, and correct the phases of the cross-correlation functions for phase delays that resu...
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Many large calving events at Greenland's marine‐terminating glaciers generate globally detectable glacial earthquakes. We perform a cross‐correlation analysis using regional seismic data to identify events below the teleseismic detection threshold, focusing on the 24 hr surrounding known glacial earthquakes at Greenland's three largest glaciers. We...
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In December, 2009, a rare sequence of earthquakes initiated within the weakly extended Western Rift of the East African Rift system in the Karonga province of northern Malawi, providing a unique opportunity to characterize active deformation associated with intrabasinal faults in an early-stage rift. We combine teleseismic and regional seismic reco...
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We present new anisotropic phase-velocity maps of the Pacific basin for Rayleigh and Love waves between 25 and 250 s. The isotropic and anisotropic phase-velocity maps are obtained by inversion of a data set of single-station surface-wave phase-anomaly measurements recorded for paths crossing the Pacific basin. We develop an age-dependent gradient-...
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We use an empirical approach to assess the amplitude calibration and sensor orientation of 1857 seismographic stations for the full duration of the USArray deployment across the conterminous United States. Long-period seismograms recorded at each operating station during the 10-year period 2006–2015 are compared with synthetic waveforms for more th...
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We study the spectral amplitudes of the first two Earth radial modes, 0S0 and 1S0, excited by the Sea of Okhotsk earthquake of 24 May 2013, the largest deep event ever recorded, in the search for an isotropic component to its source. In contrast to the case of the 1994 Bolivian earthquake, we detect an implosive component MI=-1.1×1027 dyn*cm, equiv...
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Glacial earthquakes are caused by large iceberg calving events, which are an important mechanism for mass loss from the Greenland ice sheet. The number of glacial earthquakes in Greenland has increased sixfold over the past two decades. We use teleseismic surface waves to analyze the 145 glacial earthquakes that occurred in Greenland from 2011 thro...
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Glacial earthquakes are slow earthquakes of magnitude M ~5 associated with major calving events at near-grounded marine-terminating glaciers. These globally detectable earthquakes provide information on the grounding state of outlet glaciers and the timing of large calving events. Seismic source modeling of glacial earthquakes provides information...
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Using a new biaxial friction apparatus, we conducted experiments of ice-on-rock friction in order to better understand basal sliding of glaciers and ice streams. A series of velocity-stepping and slide–hold–slide tests were conducted to measure friction and healing at temperatures between −20°C and melting. Experimental conditions in this study are...
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Nearly half of Greenland's mass loss occurs through iceberg calving, but the physical mechanisms operating during calving are poorly known and in situ observations are sparse. We show that calving at Greenland's Helheim Glacier causes a minutes-long reversal of the glacier's horizontal flow and a downward deflection of its terminus. The reverse mot...
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During summer 2013 we installed a network of 19 GPS nodes at the ungrounded margin of Helheim Glacier in southeast Greenland together with three cameras to study iceberg calving mechanisms. The network collected data at rates up to every 7 s and was designed to be robust to loss of nodes as the glacier calved. Data collection covered 55 days, and m...
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We have used tide-gauge data from near Helheim Glacier, East Greenland, and GPS data acquired on the glacier to investigate the spectra of tidal forcing and flow response. For both the tidegauge and GPS time series, we calculated amplitudes and phases for a harmonic expansion using a limited set of harmonic constituents. We find that the semidiurna...
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We examine the effect of overtone interference on fundamental-mode Love-wave phase measurements made using single-station and array-based techniques at 25-100 s periods. For single-station teleseismic measurements on USArray Transportable Array data, the contamination effects are small, less than 1% of the path-averaged phase velocity, consistent w...
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We analyze the first ever GPS observations of static surface deformation from a deep earthquake: the 24 May 2013 MW 8.3 Sea of Okhotsk event. Previous studies of deep earthquake sources relied on seismology, and might have missed evidence for slow slip in the rupture. We observed coseismic static offsets on a GPS network of 20 stations over the Sea...
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We calculate two-station phase measurements using single-station measurements made on USArray Transportable Array data for surface waves at periods from 25 to 100 s. The phase measurements are inverted for baseline Love and Rayleigh wave phase velocity maps on a 0.5° × 0.5° grid. We make estimates of the arrival angle for each event at each station...
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Some of the most dramatic effects of climate change have been observed in the Earth's polar regions. In Greenland, ice loss from the Greenland ice sheet has accelerated in recent years [Shepherd et al., 2012]. Outlet glaciers are changing their behavior rapidly, with many thinning, retreating, and accelerating [Joughin et al., 2004]. The loss of ic...
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Calving glaciers have been identified as having a crucial role in the mass balance of the Greenland Ice Sheet, with acceleration and retreat of these glaciers resulting in major mass loss from the ice sheet interior, leading to a corresponding sea level rise. The ability to reproduce observed glacier behaviour in calving models is very desirable, b...
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Many volcanic earthquakes large enough to be detected globally have anomalous focal mechanisms and frequency content. In a previous study, we examined the relationship between active volcanism and the occurrence of a specific type of shallow, non-double-couple earthquake. We identified 101 earthquakes with vertical compensated-linear-vector-dipole...
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Glacial earthquakes are anomalous earthquakes associated with large ice-loss events occurring at marine-terminating glaciers, primarily in Greenland. They are detectable teleseismically, and a proper understanding of the source mechanism may provide a remote-sensing tool to complement glaciological observations of these large outlet glaciers. We mo...
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Earthquake moment tensors reflecting seven years of global seismic activity (2004–2010) are presented. The results are the product of the global centroid-moment-tensor (GCMT) project, which maintains and extends a catalog of global seismic moment tensors beginning with earthquakes in 1976. Starting with earthquakes in 2004, the GCMT analysis takes...
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Seismogenic rumblings from the large Greenland outlet glacier Helheim Glacier have a characteristic frequency content, distinctively different from both tectonic earthquakes and the background noise. The glacier emits energy containing both high- and low-frequency waves with typical event duration between 15 and 30 minutes. Teleseismically detected...
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In November 2010, one of the largest swarms of earthquakes ever recorded in an extensional oceanic setting took place in the western Gulf of Aden. Within a 24-hour period, over 100 earthquakes were detected teleseismically on an ~80-km section of the east-west trending Aden Ridge. In this area, northeastward motion of the Arabian plate relative to...
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Observations of fundamental-mode Love- and Rayleigh-wave dispersion provide some of the strongest constraints on the elastic structure of the upper mantle including lateral variations in radial anisotropy. However, estimates of the phase speed of fundamental-mode Love waves can easily be contaminated by the presence of overtones with similar group...
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The flow speed of Greenland outlet glaciers is governed by several factors, the relative importance of which is poorly understood. The delivery of surface-generated meltwater to the bed of alpine glaciers has been shown to influence glacier flow speed when the volume of water is sufficient to increase basal fluid pressure and hence basal lubricatio...
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Centroid moment tensors (CMTs) for the March 11, 2011, off the Pacific coast of Tohoku Earthquake and its larger foreshocks and aftershocks are presented. The CMTs are calculated using long-period data from the Global Seismographic Network retrieved in near-real time, and the inversion algorithm employed in the Global CMT Project. Owing to its larg...
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Understanding the behavior of large outlet glaciers draining the Greenland Ice Sheet is critical for assessing the impact of climate change on sea level rise. The flow of marine-terminating outlet glaciers is partly governed by calving-related processes taking place at the terminus but is also influenced by the drainage of surface runoff to the bed...
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The dynamic nature of fast-flowing outlet glaciers in Greenland poses a challenge to traditional methods of investigation, such as in situ GPS observations (limited spatial coverage) and satellite remote sensing (low temporal resolution). While we have applied both approaches with great success in our study of Helheim Glacier in East Greenland, the...
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Some of the largest and most anomalous volcanic earthquakes have non-double-couple focal mechanisms. Here, we investigate the link between volcanic unrest and the occurrence of non-double-couple earthquakes with dominant vertical tension or pressure axes, known as vertical compensated-linear-vector-dipole (vertical-CLVD) earthquakes. We determine f...
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We collected simultaneous high-rate GPS observations at several locations distributed along and across Helheim Glacier, East Greenland, for various periods of time during the summer seasons of 2006-2008. The fast temporal sampling rate and high precision of our GPS observations allow us to study details of the flow behavior of this large tidewater...
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The flow speed of Greenland outlet glaciers is governed by many factors, some of which are poorly understood. One such factor is surface-generated melt water, which has been shown to have a significant effect by enhancing basal lubrication. Previously, we have demonstrated a correlation between variations in glacier flow speed and meltwater input a...
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The GreenLand Ice Sheet monitoring Network (GLISN) is an international, broadband seismic capability for Greenland, being installed and implemented through the collaboration of Denmark, Canada, Germany, Italy, Japan, Norway, Poland, Switzerland, and USA. GLISN is a real-time sensor array of seismic stations to enhance and upgrade the performance of...
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Previous analyses of geological and geodetic data suggest that the obliquely compressive relative motion across the Caribbean–North America plate boundary in Hispaniola is accommodated through strain partitioning between near-vertical transcurrent faults on land and low-angle thrust faults offshore. In the Dominican Republic, earthquake focal-mecha...
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Large calving events at Greenland's largest outlet glaciers are associated with glacial earthquakes and near-instantaneous increases in glacier flow speed. At some glaciers and ice streams, flow is also modulated in a regular way by ocean tidal forcing at the terminus. At Helheim Glacier, analysis of geodetic data shows decimeter-level periodic pos...
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Glacial earthquakes are a new class of seismic events, first discovered as signals in long-period seismograms recorded on the Global Seismographic Network. Most of these events occur along the coasts of Greenland, where they are spatially related to large outlet glaciers. Glacial earthquakes show a strong seasonality, with most events occurring dur...
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Velocity fields of Greenland's outlet glaciers are widely studied because outlet glaciers are large, fast moving, and involved in controlling the mass balance of the ice sheet. Helheim Glacier is among the most studied Greenland glaciers, yet relatively little is known about the parameters that describe its surface velocity field. We have developed...
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When estimating sea level rise, understanding the behavior of the large, fast-flowing outlet glaciers in Greenland is crucial. Based on measurements from an automatic weather station (AWS) on the surface of Helheim Glacier, we have developed a distributed energy balance model for the Helheim catchment, allowing us to estimate the melt volume spatia...
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Ice-mass fluctuations on a large scale are known to influence the occurrence of tectonic earthquakes, primarily as a result of loading and unloading of the Earth's lithosphere. Smaller-scale ice-mass fluctuations, in the form of large calving events at marine-terminating outlet glaciers, are now also known to generate seismic signals directly, in t...
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Evidence obtained by several workers during the past few years has shown that the major outlet glaciers in Greenland can both accelerate and decelerate more rapidly than previously appreciated. Some abrupt accelerations at the largest outlet glaciers, including Jakobshavn Isbrae and Helheim and Kangerdlugssuaq Glaciers, have been linked to large-sc...
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Recent work has suggested that CLVD earthquakes with vertical P or T axes occurring near active volcanoes may be associated with slip on pre-existing ring-fault structures. In this study, we perform a systematic global search for moderate-sized, vertical-CLVD earthquakes located within approximately 100 kilometers of volcanoes that have erupted sin...
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Observations at high spatial and temporal resolution are key for improving our understanding of the physical processes that govern outlet-glacier flow variations. We collected simultaneous high-rate GPS observations at several locations distributed along and across Helheim Glacier, East Greenland, during the three Arctic summers of 2006-2008, along...
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1] Geodetic observations show several large, sudden increases in flow speed at Helheim Glacier, one of Greenland's largest outlet glaciers, during summer, 2007. These step-like accelerations, detected along the length of the glacier, coincide with teleseismically detected glacial earthquakes and major iceberg calving events. No coseismic offset in...
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Our study of Helheim glacier was initiated in 2006 primarily to investigate the source of glacial earthquakes. Glacial earthquakes appear to be sensitive to climate parameters and could potentially serve as an "early warning" for changes in the dynamics of the Arctic glaciers. However, glacial earthquakes are only useful for this purpose if we unde...
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We present a distributed surface energy balance model of Helheim Glacier based on data collected by Automatic Weather Stations (AWSs) in the summer of 2008. Measurements were made at two sites in the ablation zone, at different elevations, overlapping in operation period. Using a digital elevation model we quantify the melt over the entire glacier...
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At the junction between ice sheets, oceans, and atmosphere, fast-moving outlet glaciers can respond to environmental changes operating over a wide range of timescales, thus providing critical insight into the state of those systems. We have developed a high-accuracy, low-cost, L1-only GPS receiving system that enables determination of glacier flow...
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GPS data acquired on Helheim glacier, East Greenland, in the Arctic summer 2007 demonstrate significant temporal variations in glacier flow during glacial earthquakes. There is no coseismic offset in GPS position time series, but there is a significant change in the velocity of the glacier near the time of the earthquake. It would be useful to use...
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Satellite observations during the last decade have shown dramatic changes in flow speed at Greenland's outlet glaciers, often accompanied by retreats of several km in calving-front location and increasing numbers of glacial earthquakes. Geodetic, seismological, and oceanographic data collected as part of a multidisciplinary field experiment at Helh...
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Observations that are high resolution in both space and time at outlet glaciers are key for improving our understanding of the physical processes that govern glacier flow variations. We collected high-rate GPS observations simultaneously at several locations distributed along and across Helheim Glacier, East Greenland, during three Arctic summers b...
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Helheim Glacier in East Greenland is the focus of coordinated studies aimed at understanding tidewater outlet-glacier dynamics and kinematics, and their link to glacial earthquakes. As part of this effort, we installed three time-lapse cameras overlooking the calving terminus of the glacier during the Arctic summer of 2008. Images were captured eve...
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A surface wave dispersion data set of unprecedented size is used to obtain a variable-resolution model of the radially anisotropic shear wave velocity structure of the upper mantle beneath North America and globally. Love and Rayleigh wave phase velocities for periods in the range 35–150 s constrain a three-dimensional model of velocity variations...
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We used satellite images to examine the calving behavior of Helheim and Kangerdlugssuaq Glaciers, Greenland, from 2001 to 2006, a period in which they retreated and sped up. These data show that many large iceberg-calving episodes coincided with teleseismically detected glacial earthquakes, suggesting that calving-related processes are the source o...
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The harsh environment on the highly crevassed surfaces of fast-flowing tidewater glaciers makes the acquisition of in situ geodetic measurements, such as GPS, extremely difficult. These measurements, however, provide key information pertaining to glacier dynamics, including glacial earthquakes, and help improve our understanding of the complex inte...
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Glacial earthquakes occur primarily in Greenland, in connection with major outlet glaciers. They were first discovered by Ekstrom et al in 2003 using teleseismic data and a global detection algorithm based on surface waves. Seismograms recorded in Greenland reveal a much richer frequency content in the glacial earthquakes than observed in the teles...
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We have obtained a suite of detailed geophysical observations, spanning two summer seasons, at Helheim Glacier, East Greenland. This interdisciplinary dataset includes geodetic, seismic, radar, and lidar observations, in addition to tidal, weather, and satellite remote-sensing data. Continuous high-rate GPS observations from a period of 50 days in...
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Boundary conditions at the frontal margins of tidewater glaciers provide important constraints on the balance of forces affecting ice flow and iceberg calving. For many large outlet glaciers in Greenland, the type of boundary condition (floating vs grounded ice) is not well known, owing to limited knowledge of ice thickness and fjord bathymetry. He...
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Three years ago we reported on the discovery of glacial earthquakes, a new class of earthquakes associated with fast-moving glaciers. These seismic events generate long-period (25--100 sec) Rayleigh and Love waves that in amplitude are equivalent to those generated by a traditional magnitude-5 earthquake, but which produce little high-frequency ene...
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Some glaciers and ice streams periodically lurch forward with sufficient force to generate emissions of elastic waves that are recorded on seismometers worldwide. Such glacial earthquakes on Greenland show a strong seasonality as well as a doubling of their rate of occurrence over the past 5 years. These temporal patterns suggest a link to the hydr...
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We present evidence for significant deviations of the true instrument gain from that reported for several modern broadband permanent seismograph stations. Our result derives from a systematic comparison of observed and synthetic long-period seismograms for approximately 600 large earthquakes. Seismograms were collected from globally distributed sta...
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The two largest earthquakes of the past 40 years ruptured a 1600-kilometer-long portion of the fault boundary between the Indo-Australian and southeastern Eurasian plates on 26 December 2004 [seismic moment magnitude (M_w) = 9.1 to 9.3] and 28 March 2005 (M_w = 8.6). The first event generated a tsunami that caused more than 283,000 deaths. Fault sl...
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The inverse problem for the determination of density structure from perturbations in the gravity field is highly nonunique. The combination of gravity data and other observables can, however, be used to make inferences about the Earth's density structure in three dimensions. We use the three-dimensional shear-wave velocity model of Nettles and Dzie...
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1] While it is agreed that the great Sumatra earthquake of December 26, 2004 was among the largest earthquakes of the past century, there has been disagreement on how large it was, which part of the fault ruptured, and how the rupture took place. We present a centroid-moment-tensor (CMT) analysis of the earthquake in which multiple point sources ar...
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The two largest earthquakes of the past 40 years ruptured a 1600-kilometer-long portion of the fault boundary between the Indo-Australian and southeastern Eurasian plates on 26 December 2004 [seismic moment magnitude (Mw) = 9.1 to 9.3] and 28 March 2005 (Mw = 8.6). The first event generated a tsunami that caused more than 283,000 deaths. Fault slip...
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Rapid centroid-moment-tensor (CMT) analysis of the December 26, 2004, Sumatra earthquake in the period range 300--500~s gave a seismic scalar moment of 4×1029~dyne-cm (MW~9.0). The strike, dip, and rake of the presumed fault plane were found to be 329°, 8°, and 110°, respectively. The centroid location was determined to be 3.1°N, 94.3°E, and the ce...
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Centroid–moment-tensor solutions are presented for 1034 earthquakes that occurred during 2002. The solutions are obtained using the method of Dziewonski et al. [Dziewonski, A.M., Chou, T.-A., Woodhouse, J.H., 1981. Determination of earthquake source parameters from waveform data for studies of global and regional seismicity. J. Geophys. Res. 86, 28...
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Centroid–moment-tensor (CMT) solutions are presented for 1087 earthquakes that occurred during 2003. The solutions are obtained using the method of Dziewonski et al. [Dziewonski, A.M., Chou, T.-A., Woodward, J.H., 1981. Determination of earthquake source parameters from waveform data for studies of global and regional seismicity. J. Geophys. Res. 8...
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The Global Seismographic Network (GSN) is the primary source of data for studies of global earthquake activity. The growth of the network to more than 100 well-distributed stations has dramatically increased our ability to detect, locate, and investigate earthquakes anywhere on Earth. The Harvard centroid-moment-tensor (CMT) project was started mor...
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The velocity structure of the upper mantle under North America is of great interest as the USArray project's deployment of a dense grid of broadband seismographs begins. The data from the stations of \linebreak USArray will provide a regional-scale complement to the large volume of high-quality seismic data now available from the Global Seismograph...
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With more than 100 well-distributed stations, the Global Seismographic Network (GSN) provides a continuous record of broadband ground motion of the Earth's surface. Data from many GSN stations are routinely used for traditional high-frequency detection and location of earthquakes, but research using GSN data has until recently been focused almost e...
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The development of the Global Seismographic Network (GSN) has been critical for advances in seismic tomographic imaging of the Earth's interior. Tomographic models need no longer rely on travel-time data alone nor on hand-digitized records from a few large earthquakes. The high-quality digital data recorded by the GSN allow information to be extrac...
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The 1975 Kalapana, Hawaii, earthquake occurred under the highly mobile south flank of Kilauea Volcano. It has been interpreted variously as a normal-faulting earthquake, a thrust-faulting earthquake, and a landslide. Primary evidence for the landslide model has been the failure of previous faulting models to explain the observed Love-wave radiation...
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1] High precision relocation of earthquakes recorded by the Hawaiian Volcano Observatory (HVO) seismic network provides new information on the characteristics of seismic faulting at this oceanic hot spot. Using waveform cross correlation, we have measured correlation coefficients and travel time differences for a set of 14,605 deep (!13 km) earthqu...
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We have detected dozens of previously unknown, moderate earthquakes beneath large glaciers. The seismic radiation from these earthquakes is depleted at high frequencies, explaining their nondetection by traditional methods. Inverse modeling of the long-period seismic waveforms from the best-recorded earthquake, in southern Alaska, shows that the se...
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Centroid-moment tensor (CMT) solutions are presented for 961 earthquakes occurring during 2001. The solutions are obtained using corrections for aspherical Earth structure represented by the whole-mantle shear-velocity model SH8/U4L8 of Dziewonski and Woodward [A.M. Dziewonski, R.L. Woodward, Acoustic imaging at the planetary scale, in: H. Emert, H...
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A large amount of digital seismic data recorded at stations in North America is now available, and the Earthscope project will, over the next decade, increase the amount of data available dramatically. This large amount of high-quality data makes it possible to constrain the three-dimensional velocity structure of the North American upper mantle wi...
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Quantitative comparisons between the three-dimensional velocity structure of the upper mantle and relevant geological, geochemical, and geophysical data are required in order to achieve a better and more detailed understanding of the relationship between the crust, the lithospheric and tectospheric mantle, and the convecting mantle. With the large...
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1] Through combination of surface wave and body wave constraints we derive a three-dimensional (3-D) crustal S velocity model and Moho map for Iceland. It reveals a vast plumbing system feeding mantle plume melt into upper crustal magma chambers where crustal formation takes place. The method is based on the partitioned waveform inversion to which...
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Centroid moment tensor solutions are presented for 76 intermediate-depth earthquakes (with reported depths between 130 and 300km) covering the years 1962–1975. These solutions are obtained by applying the algorithm used for modern events to restricted datasets of analog (WWSSN) and digital (HGLP) seismograms.
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New heat flow measurements and relocated hypocenters that constrain the subduction geometry of the Pacific plate at the Kermadec trench yield an estimate of shear stress on the thrust fault. With the exception of a few relatively high values (>60 mW m-2) on the upper forearc region near the active volcanic ridge, most of the 64 heat flow values alo...
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The MW=8.4 Peru earthquake of June 23, 2001 is, as of this writing, the largest earthquake to have occurred during the era of widespread digital seismogram recording ( ~1976--present), and it is the largest earthquake reported in the Harvard centroid-moment tensor (CMT) catalog. CMT analysis of the Peru earthquake using a short-period cutoff of 200...
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The March 25, 1998, Antarctic plate earthquake (Mw=8.1) occurred ∼250 km from the nearest plate boundary, in oceanic lithosphere with an age of 35–55 my. Analysis of aftershock patterns shows that the earthquake ruptured a fault, or series of strike-slip fault segments, nearly 300 km long. The strike of the fault(s) is nearly perpendicular to the n...
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The source characteristics of 10 shallow earthquakes of moderate size (M>5) beneath Bárdarbunga Volcano in Iceland are investigated using long-period and broadband teleseismic data. The highly non-double-couple nature of the focal mechanisms for several of the events previously reported in the Harvard centroid moment tensor (CMT) catalog is confirm...
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A methodology is developed for determining accurate instrument response functions for seismographs of the High-Gain Long-Period (HGLP) Network. Recordings of daily transient calibration pulses provide a detailed history of the time-varying responses of the HGLP stations. When the instrument displacement transfer function is available, knowledge of...