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Global Seismicity: Results from Systematic Waveform Analyses, 1976–2012
4.18 Global Seismicity: Results from Systematic Waveform Analyses, 1976–2012 G Ekstr€om, Columbia University, Palisades, NY, USA ã 2015 Elsevier B.V. All rights reserved.
4.18.1 Introduction 4.18.2 The CMT Method 4.18.3 Aspects of Global Seismicity 4.18.4 Recent Discoveries and Future Directions Acknowledgments References
4.18.1
Introduction
Our knowledge of the geographic patterns of earthquake activity away from populated areas evolved with the global installation of seismographic stations during the first half of the twentieth century. In their classic 1941 paper, Seismicity of the Earth, and their 1949 book, Gutenberg and Richter (1941, 1949) documented the then-current understanding of seismic zones around the world, and some 25 years later, the spatial features of earthquake activity they described were given a comprehensive explanation in the context of plate tectonics. Integral to this explanation were the development of a kinematic model of the earthquake source in terms of fault motion and techniques of inferring the geometry of faulting from features in seismic recordings, initially from the first motions of P waves. While the fundamental aspects of global seismicity are well understood, the determination of source characteristics for individual earthquakes (i.e., location, magnitude, and source mechanism) remains important. The details of the seismicity of different regions are highly variable, and neither seismicity patterns nor focal mechanisms can be predicted with much precision from a simple characterization in terms of convergent, divergent, or transcurrent plate motion. Higher-order descriptions of the deformation field are needed, and these are best constrained by comprehensive investigations of the patterns of earthquake activity and strain release. Through the 1970s, the dominant mode of seismic recording was analog, and the determination of a single earthquake focal mechanism required a significant research effort. Access to the seismograms was the initial challenge, and any quantitative analysis required manual digitization of the seismograms. The low dynamic range of the analog recordings also generally restricted the analysis for teleseismic distances to earthquakes with magnitudes >6. The development and deployment of digital instruments with low noise in the mid-1970s provided the initial conditions for a more comprehensive and quantitative analysis of global seismicity. Concurrent with technical progress in the high-fidelity recording of seismic waves, theoretical and computational advances in the calculation of theoretical waveforms made possible new methods of source analysis, in particular those based on the direct comparison and correlation of observed and predicted long-period waveforms. A very successful approach was
Treatise on Geophysics, Second Edition
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that developed by Adam M. Dziewonski and his colleagues at Harvard University, who in 1981 (Dziewonski et al., 1981) published the Centroid-Moment-Tensor (CMT) algorithm for the systematic analysis of global and regional seismicity. The ongoing systematic application of the CMT method to data from the Global Seismographic Network (GSN) in the Global CMT Project (website www.globalcmt.org) has led to the accumulation of the most comprehensive catalog of global earthquake focal mechanisms available, spanning the years 1976 to the present. This chapter reviews this systematic analysis effort and some key characteristics of global seismicity as reflected in the CMT catalog. The review is not comprehensive, and I have limited the references to those directly associated with the evolution of the CMT Project. Section 4.18.2 provides a brief summary of the basic principles of the CMT method, as well as a description of how the algorithm has evolved since 1981. Section 4.18.3 presents a few representative maps and diagrams illustrating some of the primary characteristics of global seismicity. Section 4.18.4 describes recent discoveries of previously undetected earthquakes and suggests some possible future directions for the monitoring and study of global seismicity.
4.18.2
The CMT Method
The CMT method (Dziewonski et al., 1981) is based on the linear relationship that exists between the six independent elements of the zeroth-order moment tensor describing the earthquake source and the elastic vibrations of the Earth generated by the earthquake. This relationship holds as long as the earthquake source dimension is small relative to the wavelength of the seismic wave considered and the duration of the source is small relative to the period of the seismic wave. An additional component of the CMT algorithm is the consideration and estimation of the source centroid, which represents the spatial and temporal center of moment of the earthquake. The CMT concept is general and can in principle be used with any recorded seismogram, given that the point-source approximation holds. A necessary condition is, of course, that synthetic waveforms corresponding to the observed seismograms can be generated with sufficient fidelity to allow a quantitative comparison. In the CMT algorithm, complete seismograms are compared in a least squares sense, requiring
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Global Seismicity: Results from Systematic Waveform Analyses, 1976–2012
that the phase and amplitude of the waveforms can be matched very well. In their original paper, Dziewonski et al. (1981) used normal-mode summation for a spherical Earth to generate the synthetic seismograms necessary to retrieve the moment-tensor elements and the earthquake centroid. They found that the body-wave portion of long-period (T > 45 s) seismograms could be fit well using spherical-Earth synthetic waveforms, but that surface waves, which are significantly distorted by propagation through Earth’s laterally heterogeneous shallow structure, could not be fit well. In a follow-up paper, Dziewonski and Woodhouse (1983) extended the CMT method to consider very long-period (T > 135 s) surface waves in the inversion for the moment tensor. Following the development of tomographic models of the Earth’s upper mantle, the calculation of synthetic seismograms in the CMT processing was modified to include corrections for laterally varying Earth structure (Dziewonski et al., 1984; Woodhouse and Dziewonski, 1984). These corrections were particularly useful for improving the phase alignment of observed and synthetic waveforms and resulted in improved moment-tensor determinations. Even with better tomographic models of the upper mantle, the prediction of intermediate-period (35–150 s) surface waves was not sufficiently good to allow direct comparison of observed and synthetic surface-wave phases at regional or teleseismic distances. However, following the development of global phase-velocity maps for Love and Rayleigh waves in this period range (e.g., Ekstr€ om et al., 1997), Arvidsson and Ekstr€ om (1998) extended the CMT algorithm to include intermediate-period surface waves in the inversion for source parameters. This development, in turn, allowed the CMT algorithm to be applied to earthquakes of a smaller magnitude. Since 2004, the routine CMT analysis has included the fitting of intermediate-period surface-wave seismograms in the analysis, significantly increasing the number of earthquakes that can be successfully analyzed each year (Ekstr€ om et al., 2012).
The routine determination of moment tensors has benefited from the increasing number of broadband seismographic stations deployed globally. The earliest year for which the CMT method has been applied systematically is 1976 (Ekstr€ om and Nettles, 1997). In that year, the experimental high-gain long-period (HGLP) seismographic network was operating, as were a small number of Standard Research Observatory (SRO) and International Deployment of Accelerometer (IDA) stations. In total, fewer than a dozen stations were available for any single event. With the development first of the Global Digital Seismographic Network (GDSN) operated by the US Geological Survey (USGS) and subsequently the GSN of the Incorporated Research Institutions for Seismology (IRIS) and the USGS, both the number of stations and the quality of the data have improved. These improvements have, in turn, led to better and more robust moment-tensor determinations. In our current CMT analysis, seismograms from more than 100 stations are routinely analyzed for each earthquake (Ekstr€ om et al., 2012).
4.18.3
Aspects of Global Seismicity
Figure 1 shows a map of focal mechanisms for shallow earthquakes in the CMT catalog for the period 1976–2012. While many focal mechanisms are obscured by focal mechanisms of later, nearby earthquakes, the map conveys key aspects of the pattern of global seismicity. The plate boundaries are clearly delineated by earthquake activity, except in areas of very slow plate motion, or near fast-spreading ridges, where the lithosphere is too weak to support earthquakes of significant magnitude. The consistency of focal mechanisms along the plate boundaries is also evident, particularly in subduction zones and along oceanic transforms. While some portions of the continents are devoid of M > 5 earthquakes, it is evident that over the 37-year period shown, many continental intraplate regions have experienced significant seismicity. The regional
90 N
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Figure 1 Map showing focal mechanisms for shallow earthquakes (h < 70 km) in the CMT catalog, 1976–2012. The earthquakes are shown in lower-hemisphere projection, and the diameter of the symbols increases linearly with the moment magnitude. Plate boundaries are shown but are nearly entirely covered by focal mechanisms.
Global Seismicity: Results from Systematic Waveform Analyses, 1976–2012
variability of seismicity patterns (in terms of both frequency and the style of faulting) within oceanic plates is also striking. Seismically active plate boundaries involving at least one oceanic plate are normally characterized by a relatively narrow zone of tectonic deformation, reflected in a narrow zone of earthquakes. Figure 2 shows focal mechanisms from the Alaska–Aleutian Island subduction zone, an area of very active seismicity and the site of several M > 7.5 earthquakes since 1976. The vast majority of the earthquakes are consistent with the shallow underthrusting of the Pacific Plate beneath the North American Plate. In the western portion of the subduction zone, the greater predominance of strike-slip focal mechanisms reflects the increasing obliquity of plate motion toward the west. In the eastern portion of the subduction zone, the pattern of seismicity is more distributed, with earthquakes
469
associated with the plate collision occurring both in the interior of Alaska and within the Pacific Plate. The most dramatic example of geographically distributed seismicity occurring in response to plate convergence is that associated with the collision of India and Eurasia. Figure 3 shows focal mechanisms for shallow earthquakes in this zone. The geographic association of earthquakes with topography is evident, and the zone of activity extends more than 1000 km north from the Himalayan front. Within the Tibetan Plateau, earthquake focal mechanisms primarily represent not the relative plate motion, but rather the strains associated with the gravity-controlled dynamics of the elevated plateau. The vast majority of focal mechanisms indicate strike-slip and normal faulting consistent with east–west extension.
60 N
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Figure 2 Map showing the Alaska–Aleutian subduction zone, with focal mechanisms for shallow earthquakes from the CMT catalog for the period 1976–2012. While seismic activity along the central and western part of the subduction zone is focused on the plate boundary, several intraplate earthquakes in the eastern zone indicate deformation within both the North American and the Pacific Plates.
40 N
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70 E
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Figure 3 Map showing the India–Eurasia collision zone, with focal mechanisms for shallow earthquakes from the CMT catalog for the period 1976–2012. While earthquakes at the northern and southern edges of the Tibetan Plateau show mainly reverse motion associated with north–south compression, most of the earthquakes on the plateau reflect east–west extension.
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Figure 4 shows the cumulative global moment of earthquakes since 1976. As is well known, most of the seismic moment (and corresponding strain) in a region occurs in the largest earthquakes, while small earthquakes, individually and collectively, account for only a small fraction of the cumulative moment. This division of cumulative seismic moment is illustrated by the contribution provided by earthquakes with M < 6.5 to the total, represented by the area shaded green in Figure 4. Over the 37-year period of the CMT catalog, 29 earthquakes have moment magnitudes of 8.0 or above. The largest earthquake to occur during the last 40 years is the 2004
Sumatra earthquake, which is easily identified in Figure 4 as the largest step in cumulative moment. In the figure, I have used the extended-source magnitude of 9.3, which was obtained in a CMT analysis that considered the spatial and temporal extent of the source (Tsai et al., 2005). The secondlargest earthquake is the 2011 Japan earthquake. With a moment magnitude of 9.1 (Nettles et al., 2011), this event is also clearly identifiable as a step in cumulative moment in Figure 4. Figure 5 shows the cumulative number of earthquakes in the CMT catalog since 1976. The main trend in this figure is the
3.0
1023 N − m
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2.0
1.0
1980
1985
1990
1995
2000
2005
2010
Figure 4 Cumulative moment of all earthquakes in the CMT catalog. Red stars indicate the times of earthquakes with moment magnitude M 8.0. The field shaded yellow reflects the cumulative moment of earthquakes with M 6.5. The green field reflects cumulative moment of earthquakes with 5.3 M 6.5, and orange (barely visible) reflects earthquakes with M 5.3. The contributions of the December 2004 Sumatra (M ¼ 9.3) and March 2011 Japan (M ¼ 9.1) earthquakes to the total cumulative moment are seen as the largest steps in the curve.
35 000 30 000
# events
25 000 20 000 15 000 10 000 5000
1980
1985
1990
1995
2000
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2010
Figure 5 Cumulative number of earthquakes in the CMT catalog since 1976. Groups of earthquakes of different magnitudes are color-coded as in Figure 4 (orange, M 5.3; green, 5.3 M 6.5; and yellow, M 6.5). An increase in the number of earthquakes in the catalog is seen for events with M 5.3, especially since 2004 when intermediate-period surface waves were first included in the analysis.
Global Seismicity: Results from Systematic Waveform Analyses, 1976–2012 gradual increase in the number of earthquakes with M < 5.3 that we have been able to analyze as a result of improvements in global station coverage and the CMT algorithm. In particular, the consideration of intermediate-period surface waves, which was initiated with earthquakes in 2004, nearly doubled the number of earthquakes that can be analyzed. Noticeable small increases in the seismicity rate can be observed associated with the many aftershocks that occurred in the months following the 2004 Sumatra and 2011 Japan earthquakes. Most earthquakes occur along plate boundaries at shallow depths, and this is also where a maximum in cumulative seismic moment is observed. Figure 6 shows the depth distribution of cumulative seismic moment for the period 1976–2012. A distinct minimum in moment occurs around 350 km depth, and a local maximum is evident at the bottom of the upper mantle, around 600 km depth. While all deep earthquakes can be associated with current subduction or the likely location of recently subducted lithosphere, though not always unambiguously, the nature of seismic faulting at depth and its relationship to the physical state, stress, and strain of the mantle rock is not resolved. Figure 7 shows an interesting example of seismic activity in the subducted slab beneath Chile and Argentina. The top panel of Figure 7 shows, in map view, the distribution of earthquakes along the plate interface and in the subducted Nazca slab. One of the deepest earthquakes is located to the east of the adjacent earthquakes, and in cross section (Figure 7, bottom), it is clear that a spatial separation exists between the main group of deep events and this ‘outlier earthquake.’ The outlier also exhibits a compression axis with a different orientation than the adjacent events, which have focal mechanisms consistent with downdip compression. The significance of outliers such as this one is hard to assess. If deep earthquakes are markers of subducted lithosphere, we must invoke some contortion of the subducting slab, or the existence of a second slab or slab fragment, in order to explain the existence of outlying earthquakes.
log M0 (N − m)
23
22
21
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100
300 Depth (km)
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Figure 6 Graph showing the cumulative moment of earthquakes in the CMT catalog, 1976–2012, for different depths. The earthquakes have been binned in 40 km thick layers. Most of the cumulative moment is located in the top 40 km. A minimum occurs in the depth range 320–360 km. A local maximum occurs at the bottom of the upper mantle, in the range 560–680 km.
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A further illustration of the complexity of deep seismicity is provided by the earthquakes beneath Fiji and Tonga, the world’s most productive zone of deep seismicity. The top panel of Figure 8 shows the earthquakes in this region in map view; the bottom panel shows the seismicity projected onto a vertical plane with a strike close to that of the deep seismicity. In this view, it is clear that the earthquakes show complex spatial patterns, including both lineations in the seismicity and large volumes without significant seismicity. The deepest earthquakes, toward the south, are surrounded by a large area lacking significant earthquakes during the last 30 years. Although most of the compression axes shown in the bottom panel of Figure 8 are consistent with downdip compression, there are several clear and systematic deviations from this basic pattern, which require more detailed explanations in terms of the stresses and deformation in the subducted lithosphere.
4.18.4
Recent Discoveries and Future Directions
The study of global seismicity depends on the initial detection and location of seismic events. Several agencies are responsible for the monitoring of seismic activity on a global scale, in particular the National Earthquake Information Service (NEIS) of the USGS, the International Seismological Centre (ISC), and the International Monitoring System (IMS) in Vienna. All of these organizations rely primarily on highfrequency seismic signals for the detection of seismic events, leaving open the possibility that earthquakes deficient in radiated short-period energy may escape detection. In recent work, we have applied a new method of array processing of continuous long-period vertical data from the GSN (Ekstr€ om, 2006; Ekstr€ om et al., 2003) to search for sources of long-period Rayleigh waves. The algorithm was applied to data filtered in the period range 40–150 s, in which seismic noise is low and knowledge of Earth’s structure is sufficiently good to allow accurate deconvolution of surfacewave dispersion effects for arbitrary ray paths. In the initial application of the detection and location algorithm to data for the period 1993–2003, we found nearly 25 000 seismic sources with magnitudes M > 4.5, where the magnitude M is a good estimate of the moment magnitude. The vast majority of these events are standard earthquakes that are also found in the event catalogs of the NEIC, ISC, and the IMS. Approximately 5% of the events are, however, not listed in any of these catalogs and are therefore considered ‘new.’ Figure 9 shows the locations of new earthquakes for the period 1993–2012. Most of the events occur in the southern hemisphere along the ridge-transform plate boundaries. Very few events are located in subduction zones. The events near plate boundaries may be earthquakes that have unusual rupture characteristics, or they may have gone undetected for other reasons (e.g., high microseismic noise or nodal radiation to many stations). Several other events are located in areas where earthquakes of this magnitude (M > 4.5) are unexpected or where they should have been detected if they represent standard earthquake sources. Most prominent in this category are the events on Greenland, which we have identified with a new phenomenon called ‘glacial earthquakes’ (Ekstr€ om et al., 2003, 2006), and
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Global Seismicity: Results from Systematic Waveform Analyses, 1976–2012
20S
60W
70W
600 km
400 km
200 km
0 km
200 km
50W
400 km
600 km
0km 100km
200km 300km 400km 500km 600km 700km Figure 7 (Top) Compression axes of CMT moment tensors in the western part of South America, projected into the horizontal plane. The earthquakes are color-coded with respect to depth, with white symbols for shallow earthquakes and red symbols indicating the deepest events. The red box indicates the area shown in cross section in the bottom panel. The viewing direction is shown by the thin red line in the center of the box. (Bottom) Vertical cross section aligned with a viewing direction in the plane of the earthquakes associated with the subduction of the Nazca Plate beneath South America. Compression axes of CMT focal mechanisms are shown, projected into the plane of the cross section. At the bottom of the subduction zone, one outlying event has a compression axis that is rotated by 70 with respect to the downdip slab direction suggested by the main seismicity at this depth. This event is also displaced horizontally by nearly 200 km from the inferred location of the subducted slab.
we now understand to be the seismic expression of massive iceberg calving (Nettles et al., 2008). These events radiate surface waves with polarities and amplitudes consistent with a mass-sliding source, rather than with tectonic stress release. Figure 10 shows an example of a teleseismic record section from one of the glacial earthquakes, clearly demonstrating that signals for these events are large and can easily be identified at long periods. Several events in the Himalayas and in Alaska
have been identified as catastrophic landslides (Ekstr€ om and Stark, 2013), and the events off the east coast of the United States may represent submarine landslides or slumps. Other groups of new events are spatially associated with volcanoes, and yet others lack, at this time, an obvious association or explanation. These findings, and other recent discoveries of new events and processes that generate seismic radiation, indicate that the
Global Seismicity: Results from Systematic Waveform Analyses, 1976–2012
473
15S
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North
South 600 km
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0 km
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600 km 0 km
100 km 200 km 300 km 400 km 500 km 600 km 700 km Figure 8 (Top) Map view of deep seismicity beneath Fiji–Tonga. The red box indicates the area viewed in cross section in the bottom panel. (Bottom) Vertical cross section aligned with a viewing direction perpendicular to the strike of the deep seismicity associated with the Tonga subduction zone. The compression axes of the focal mechanism are projected onto the vertical plane and show a very complex pattern of internal deformation in the plane of the slab. Some spatial trends in the locations and stress axes can be followed for hundreds of kilometers along the slab.
spectrum of seismic sources is richer than we had previously realized. These new events may be important for our understanding not only of lithospheric tectonics but potentially also of other phenomena such as magma motion and subaerial and submarine mass wasting. With the aid of the powerful infrastructure provided by the GSN, and by many new regional broadband seismographic networks, it seems likely that a focused effort to investigate the global seismic wave field in the period range 20–40 s for seismic events would be fruitful. Events with M > 4.0 routinely generate large surface waves in this period range, and it seems possible that, with recent advances in the characterization of crustal structure and shallow upper-mantle elastic and anelastic structure, these waves could be properly migrated and stacked for array processing and event detection.
Acknowledgments I thank Adam Dziewonski, the founder and for many years the leader of the CMT Project, and Meredith Nettles, the current coleader with the author of the Global CMT Project. The seismic waveforms used in the CMT Project come primarily from stations of the Global Seismographic Network operated by IRIS and the USGS; the waveforms are distributed by the IRIS Data Management Center. Additional waveforms come from several other networks, including the Geoscope, Mednet, GEOFON, and the US and Canadian national seismic networks. We are grateful to everyone involved in the collection and distribution of data from these networks. The CMT catalog and associated results are accessible at the website www.globalcmt.org. The CMT Project has been continuously funded by the National
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Global Seismicity: Results from Systematic Waveform Analyses, 1976–2012
90N
45N
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0
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180E
135E
90W
90S
45W
Figure 9 Map showing the locations of 3157 previously undetected earthquakes for the period 1993–2012 located using the surface-wave algorithm of Ekstr€om (2006). The smallest earthquake has an estimated magnitude of M ¼ 4.6 and the largest M ¼ 5.9. The quality of detection is indicated by the color of the symbol, with red indicating the best quality, green very good quality, and yellow good quality.
E200109031301A
Event: 2001/09/03, 13:01:12.0, EASTERN GREENLAND Hypocenter (SWEB): Lat = 68.50, Lon = 34.50, h = 10.0, mb = 0.0, MS = 4.9 Filter: VEL 75.0 60.0 35.0 25.0, Component: 1
3.6 km s−1
30⬚
0⬚ −10
0
10
20
30
40
50
60
Minutes Figure 10 Record section for a glacial earthquake, showing the long-period Rayleigh wave arrivals at global stations out to a distance of 45 . Approximately 30 min after the main Rayleigh wave arrivals (which triggered the detection), a second arrival is seen with the same moveout, suggesting that a second, smaller event occurred in the same location.
Science Foundation since its inception, most recently by award EAR-1249167.
References Arvidsson R and Ekstr€om G (1998) Global CMT analysis of moderate earthquakes, MW 4.5, using intermediate period surface waves. The Bulletin of the Seismological Society of America 88: 1003–1013. Dziewonski AM, Chou T-A, and Woodhouse JH (1981) Determination of earthquake source parameters from waveform data for studies of global and regional seismicity. Journal of Geophysical Research 86: 2825–2853.
Dziewonski AM, Franzen JE, and Woodhouse JH (1984) Centroid-moment tensor solutions for July-September 1983. Physics of the Earth and Planetary Interiors 34: 1–8. Dziewonski AM and Woodhouse JH (1983) An experiment in the systematic study of global seismicity: Centroid-moment tensor solutions for 201 moderate and large earthquakes of 1981. Journal of Geophysical Research 88: 3247–3271. Ekstr€om G (2006) Global detection and location of seismic sources by using surface waves. The Bulletin of the Seismological Society of America 96: 1201–1212. Ekstr€om G and Nettles M (1997) Calibration of the HGLP seismograph network and centroid-moment tensor analysis of significant earthquakes of 1976. Physics of the Earth and Planetary Interiors 101: 219–243. Ekstr€om G, Nettles M, and Abers GA (2003) Glacial earthquakes. Science 302: 622–624.
Global Seismicity: Results from Systematic Waveform Analyses, 1976–2012 Ekstr€om G, Nettles M, and Dziewonski AM (2012) The Global CMT Project 2004–2010: Centroid-moment tensors for 13,017 earthquakes. Physics of the Earth and Planetary Interiors 200–201: 1–9. Ekstr€om G, Nettles M, and Tsai VC (2006) Seasonality and increasing frequency of Greenland glacial earthquakes. Science 311: 1756–1758. Ekstr€om G and Stark CP (2013) Simple scaling of catastrophic landslide dynamics. Science 339: 1416–1419. Ekstr€om G, Tromp J, and Larson EWF (1997) Measurements and global models of surface wave propagation. Journal of Geophysical Research 102: 8137–8157. Gutenberg B and Richter CF (1941) Seismicity of the earth. Geological Society of America Special Papers 34: 131. Gutenberg B and Richter CF (1949) Seismicity of the Earth. Princeton: Princeton University Press.
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Nettles M, Ekstr€om G, and Koss HC (2011) Centroid-moment tensor analysis of the 2011 off the Pacific coast of Tohoku earthquake and its larger foreshocks and aftershocks. Earth, Planets and Space 63: 519–523. Nettles M, Larsen TB, Elo´segui P, et al. (2008) Step-wise changes in glacier speed coincide with calving and glacial earthquakes at Helheim Glacier, Greenland. Geophysical Research Letters 35: L24503. http://dx.doi.org/ 10.1029/2008GL036127. Tsai VC, Nettles M, Ekstr€om G, and Dziewonski AM (2005) Multiple CMT source analysis of the 2004 Sumatra earthquake. Geophysical Research Letters 32: L17304. http://dx.doi.org/10.1029/2005GL023813. Woodhouse JH and Dziewonski AM (1984) Mapping the upper mantle: Three dimensional modelling of earth structure by inversion of seismic waveforms. Journal of Geophysical Research 89: 5953–5986.
4.18.1 Introduction 4.18.2 The CMT Method 4.18.3 Aspects of Global Seismicity 4.18.4 Recent Discoveries and Future Directions Acknowledgments References
4.18.1
Introduction
Our knowledge of the geographic patterns of earthquake activity away from populated areas evolved with the global installation of seismographic stations during the first half of the twentieth century. In their classic 1941 paper, Seismicity of the Earth, and their 1949 book, Gutenberg and Richter (1941, 1949) documented the then-current understanding of seismic zones around the world, and some 25 years later, the spatial features of earthquake activity they described were given a comprehensive explanation in the context of plate tectonics. Integral to this explanation were the development of a kinematic model of the earthquake source in terms of fault motion and techniques of inferring the geometry of faulting from features in seismic recordings, initially from the first motions of P waves. While the fundamental aspects of global seismicity are well understood, the determination of source characteristics for individual earthquakes (i.e., location, magnitude, and source mechanism) remains important. The details of the seismicity of different regions are highly variable, and neither seismicity patterns nor focal mechanisms can be predicted with much precision from a simple characterization in terms of convergent, divergent, or transcurrent plate motion. Higher-order descriptions of the deformation field are needed, and these are best constrained by comprehensive investigations of the patterns of earthquake activity and strain release. Through the 1970s, the dominant mode of seismic recording was analog, and the determination of a single earthquake focal mechanism required a significant research effort. Access to the seismograms was the initial challenge, and any quantitative analysis required manual digitization of the seismograms. The low dynamic range of the analog recordings also generally restricted the analysis for teleseismic distances to earthquakes with magnitudes >6. The development and deployment of digital instruments with low noise in the mid-1970s provided the initial conditions for a more comprehensive and quantitative analysis of global seismicity. Concurrent with technical progress in the high-fidelity recording of seismic waves, theoretical and computational advances in the calculation of theoretical waveforms made possible new methods of source analysis, in particular those based on the direct comparison and correlation of observed and predicted long-period waveforms. A very successful approach was
Treatise on Geophysics, Second Edition
467 467 468 471 473 474
that developed by Adam M. Dziewonski and his colleagues at Harvard University, who in 1981 (Dziewonski et al., 1981) published the Centroid-Moment-Tensor (CMT) algorithm for the systematic analysis of global and regional seismicity. The ongoing systematic application of the CMT method to data from the Global Seismographic Network (GSN) in the Global CMT Project (website www.globalcmt.org) has led to the accumulation of the most comprehensive catalog of global earthquake focal mechanisms available, spanning the years 1976 to the present. This chapter reviews this systematic analysis effort and some key characteristics of global seismicity as reflected in the CMT catalog. The review is not comprehensive, and I have limited the references to those directly associated with the evolution of the CMT Project. Section 4.18.2 provides a brief summary of the basic principles of the CMT method, as well as a description of how the algorithm has evolved since 1981. Section 4.18.3 presents a few representative maps and diagrams illustrating some of the primary characteristics of global seismicity. Section 4.18.4 describes recent discoveries of previously undetected earthquakes and suggests some possible future directions for the monitoring and study of global seismicity.
4.18.2
The CMT Method
The CMT method (Dziewonski et al., 1981) is based on the linear relationship that exists between the six independent elements of the zeroth-order moment tensor describing the earthquake source and the elastic vibrations of the Earth generated by the earthquake. This relationship holds as long as the earthquake source dimension is small relative to the wavelength of the seismic wave considered and the duration of the source is small relative to the period of the seismic wave. An additional component of the CMT algorithm is the consideration and estimation of the source centroid, which represents the spatial and temporal center of moment of the earthquake. The CMT concept is general and can in principle be used with any recorded seismogram, given that the point-source approximation holds. A necessary condition is, of course, that synthetic waveforms corresponding to the observed seismograms can be generated with sufficient fidelity to allow a quantitative comparison. In the CMT algorithm, complete seismograms are compared in a least squares sense, requiring
http://dx.doi.org/10.1016/B978-0-444-53802-4.00085-3
467
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Global Seismicity: Results from Systematic Waveform Analyses, 1976–2012
that the phase and amplitude of the waveforms can be matched very well. In their original paper, Dziewonski et al. (1981) used normal-mode summation for a spherical Earth to generate the synthetic seismograms necessary to retrieve the moment-tensor elements and the earthquake centroid. They found that the body-wave portion of long-period (T > 45 s) seismograms could be fit well using spherical-Earth synthetic waveforms, but that surface waves, which are significantly distorted by propagation through Earth’s laterally heterogeneous shallow structure, could not be fit well. In a follow-up paper, Dziewonski and Woodhouse (1983) extended the CMT method to consider very long-period (T > 135 s) surface waves in the inversion for the moment tensor. Following the development of tomographic models of the Earth’s upper mantle, the calculation of synthetic seismograms in the CMT processing was modified to include corrections for laterally varying Earth structure (Dziewonski et al., 1984; Woodhouse and Dziewonski, 1984). These corrections were particularly useful for improving the phase alignment of observed and synthetic waveforms and resulted in improved moment-tensor determinations. Even with better tomographic models of the upper mantle, the prediction of intermediate-period (35–150 s) surface waves was not sufficiently good to allow direct comparison of observed and synthetic surface-wave phases at regional or teleseismic distances. However, following the development of global phase-velocity maps for Love and Rayleigh waves in this period range (e.g., Ekstr€ om et al., 1997), Arvidsson and Ekstr€ om (1998) extended the CMT algorithm to include intermediate-period surface waves in the inversion for source parameters. This development, in turn, allowed the CMT algorithm to be applied to earthquakes of a smaller magnitude. Since 2004, the routine CMT analysis has included the fitting of intermediate-period surface-wave seismograms in the analysis, significantly increasing the number of earthquakes that can be successfully analyzed each year (Ekstr€ om et al., 2012).
The routine determination of moment tensors has benefited from the increasing number of broadband seismographic stations deployed globally. The earliest year for which the CMT method has been applied systematically is 1976 (Ekstr€ om and Nettles, 1997). In that year, the experimental high-gain long-period (HGLP) seismographic network was operating, as were a small number of Standard Research Observatory (SRO) and International Deployment of Accelerometer (IDA) stations. In total, fewer than a dozen stations were available for any single event. With the development first of the Global Digital Seismographic Network (GDSN) operated by the US Geological Survey (USGS) and subsequently the GSN of the Incorporated Research Institutions for Seismology (IRIS) and the USGS, both the number of stations and the quality of the data have improved. These improvements have, in turn, led to better and more robust moment-tensor determinations. In our current CMT analysis, seismograms from more than 100 stations are routinely analyzed for each earthquake (Ekstr€ om et al., 2012).
4.18.3
Aspects of Global Seismicity
Figure 1 shows a map of focal mechanisms for shallow earthquakes in the CMT catalog for the period 1976–2012. While many focal mechanisms are obscured by focal mechanisms of later, nearby earthquakes, the map conveys key aspects of the pattern of global seismicity. The plate boundaries are clearly delineated by earthquake activity, except in areas of very slow plate motion, or near fast-spreading ridges, where the lithosphere is too weak to support earthquakes of significant magnitude. The consistency of focal mechanisms along the plate boundaries is also evident, particularly in subduction zones and along oceanic transforms. While some portions of the continents are devoid of M > 5 earthquakes, it is evident that over the 37-year period shown, many continental intraplate regions have experienced significant seismicity. The regional
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Figure 1 Map showing focal mechanisms for shallow earthquakes (h < 70 km) in the CMT catalog, 1976–2012. The earthquakes are shown in lower-hemisphere projection, and the diameter of the symbols increases linearly with the moment magnitude. Plate boundaries are shown but are nearly entirely covered by focal mechanisms.
Global Seismicity: Results from Systematic Waveform Analyses, 1976–2012
variability of seismicity patterns (in terms of both frequency and the style of faulting) within oceanic plates is also striking. Seismically active plate boundaries involving at least one oceanic plate are normally characterized by a relatively narrow zone of tectonic deformation, reflected in a narrow zone of earthquakes. Figure 2 shows focal mechanisms from the Alaska–Aleutian Island subduction zone, an area of very active seismicity and the site of several M > 7.5 earthquakes since 1976. The vast majority of the earthquakes are consistent with the shallow underthrusting of the Pacific Plate beneath the North American Plate. In the western portion of the subduction zone, the greater predominance of strike-slip focal mechanisms reflects the increasing obliquity of plate motion toward the west. In the eastern portion of the subduction zone, the pattern of seismicity is more distributed, with earthquakes
469
associated with the plate collision occurring both in the interior of Alaska and within the Pacific Plate. The most dramatic example of geographically distributed seismicity occurring in response to plate convergence is that associated with the collision of India and Eurasia. Figure 3 shows focal mechanisms for shallow earthquakes in this zone. The geographic association of earthquakes with topography is evident, and the zone of activity extends more than 1000 km north from the Himalayan front. Within the Tibetan Plateau, earthquake focal mechanisms primarily represent not the relative plate motion, but rather the strains associated with the gravity-controlled dynamics of the elevated plateau. The vast majority of focal mechanisms indicate strike-slip and normal faulting consistent with east–west extension.
60 N
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Figure 2 Map showing the Alaska–Aleutian subduction zone, with focal mechanisms for shallow earthquakes from the CMT catalog for the period 1976–2012. While seismic activity along the central and western part of the subduction zone is focused on the plate boundary, several intraplate earthquakes in the eastern zone indicate deformation within both the North American and the Pacific Plates.
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Figure 3 Map showing the India–Eurasia collision zone, with focal mechanisms for shallow earthquakes from the CMT catalog for the period 1976–2012. While earthquakes at the northern and southern edges of the Tibetan Plateau show mainly reverse motion associated with north–south compression, most of the earthquakes on the plateau reflect east–west extension.
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Global Seismicity: Results from Systematic Waveform Analyses, 1976–2012
Figure 4 shows the cumulative global moment of earthquakes since 1976. As is well known, most of the seismic moment (and corresponding strain) in a region occurs in the largest earthquakes, while small earthquakes, individually and collectively, account for only a small fraction of the cumulative moment. This division of cumulative seismic moment is illustrated by the contribution provided by earthquakes with M < 6.5 to the total, represented by the area shaded green in Figure 4. Over the 37-year period of the CMT catalog, 29 earthquakes have moment magnitudes of 8.0 or above. The largest earthquake to occur during the last 40 years is the 2004
Sumatra earthquake, which is easily identified in Figure 4 as the largest step in cumulative moment. In the figure, I have used the extended-source magnitude of 9.3, which was obtained in a CMT analysis that considered the spatial and temporal extent of the source (Tsai et al., 2005). The secondlargest earthquake is the 2011 Japan earthquake. With a moment magnitude of 9.1 (Nettles et al., 2011), this event is also clearly identifiable as a step in cumulative moment in Figure 4. Figure 5 shows the cumulative number of earthquakes in the CMT catalog since 1976. The main trend in this figure is the
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Figure 4 Cumulative moment of all earthquakes in the CMT catalog. Red stars indicate the times of earthquakes with moment magnitude M 8.0. The field shaded yellow reflects the cumulative moment of earthquakes with M 6.5. The green field reflects cumulative moment of earthquakes with 5.3 M 6.5, and orange (barely visible) reflects earthquakes with M 5.3. The contributions of the December 2004 Sumatra (M ¼ 9.3) and March 2011 Japan (M ¼ 9.1) earthquakes to the total cumulative moment are seen as the largest steps in the curve.
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Figure 5 Cumulative number of earthquakes in the CMT catalog since 1976. Groups of earthquakes of different magnitudes are color-coded as in Figure 4 (orange, M 5.3; green, 5.3 M 6.5; and yellow, M 6.5). An increase in the number of earthquakes in the catalog is seen for events with M 5.3, especially since 2004 when intermediate-period surface waves were first included in the analysis.
Global Seismicity: Results from Systematic Waveform Analyses, 1976–2012 gradual increase in the number of earthquakes with M < 5.3 that we have been able to analyze as a result of improvements in global station coverage and the CMT algorithm. In particular, the consideration of intermediate-period surface waves, which was initiated with earthquakes in 2004, nearly doubled the number of earthquakes that can be analyzed. Noticeable small increases in the seismicity rate can be observed associated with the many aftershocks that occurred in the months following the 2004 Sumatra and 2011 Japan earthquakes. Most earthquakes occur along plate boundaries at shallow depths, and this is also where a maximum in cumulative seismic moment is observed. Figure 6 shows the depth distribution of cumulative seismic moment for the period 1976–2012. A distinct minimum in moment occurs around 350 km depth, and a local maximum is evident at the bottom of the upper mantle, around 600 km depth. While all deep earthquakes can be associated with current subduction or the likely location of recently subducted lithosphere, though not always unambiguously, the nature of seismic faulting at depth and its relationship to the physical state, stress, and strain of the mantle rock is not resolved. Figure 7 shows an interesting example of seismic activity in the subducted slab beneath Chile and Argentina. The top panel of Figure 7 shows, in map view, the distribution of earthquakes along the plate interface and in the subducted Nazca slab. One of the deepest earthquakes is located to the east of the adjacent earthquakes, and in cross section (Figure 7, bottom), it is clear that a spatial separation exists between the main group of deep events and this ‘outlier earthquake.’ The outlier also exhibits a compression axis with a different orientation than the adjacent events, which have focal mechanisms consistent with downdip compression. The significance of outliers such as this one is hard to assess. If deep earthquakes are markers of subducted lithosphere, we must invoke some contortion of the subducting slab, or the existence of a second slab or slab fragment, in order to explain the existence of outlying earthquakes.
log M0 (N − m)
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Figure 6 Graph showing the cumulative moment of earthquakes in the CMT catalog, 1976–2012, for different depths. The earthquakes have been binned in 40 km thick layers. Most of the cumulative moment is located in the top 40 km. A minimum occurs in the depth range 320–360 km. A local maximum occurs at the bottom of the upper mantle, in the range 560–680 km.
471
A further illustration of the complexity of deep seismicity is provided by the earthquakes beneath Fiji and Tonga, the world’s most productive zone of deep seismicity. The top panel of Figure 8 shows the earthquakes in this region in map view; the bottom panel shows the seismicity projected onto a vertical plane with a strike close to that of the deep seismicity. In this view, it is clear that the earthquakes show complex spatial patterns, including both lineations in the seismicity and large volumes without significant seismicity. The deepest earthquakes, toward the south, are surrounded by a large area lacking significant earthquakes during the last 30 years. Although most of the compression axes shown in the bottom panel of Figure 8 are consistent with downdip compression, there are several clear and systematic deviations from this basic pattern, which require more detailed explanations in terms of the stresses and deformation in the subducted lithosphere.
4.18.4
Recent Discoveries and Future Directions
The study of global seismicity depends on the initial detection and location of seismic events. Several agencies are responsible for the monitoring of seismic activity on a global scale, in particular the National Earthquake Information Service (NEIS) of the USGS, the International Seismological Centre (ISC), and the International Monitoring System (IMS) in Vienna. All of these organizations rely primarily on highfrequency seismic signals for the detection of seismic events, leaving open the possibility that earthquakes deficient in radiated short-period energy may escape detection. In recent work, we have applied a new method of array processing of continuous long-period vertical data from the GSN (Ekstr€ om, 2006; Ekstr€ om et al., 2003) to search for sources of long-period Rayleigh waves. The algorithm was applied to data filtered in the period range 40–150 s, in which seismic noise is low and knowledge of Earth’s structure is sufficiently good to allow accurate deconvolution of surfacewave dispersion effects for arbitrary ray paths. In the initial application of the detection and location algorithm to data for the period 1993–2003, we found nearly 25 000 seismic sources with magnitudes M > 4.5, where the magnitude M is a good estimate of the moment magnitude. The vast majority of these events are standard earthquakes that are also found in the event catalogs of the NEIC, ISC, and the IMS. Approximately 5% of the events are, however, not listed in any of these catalogs and are therefore considered ‘new.’ Figure 9 shows the locations of new earthquakes for the period 1993–2012. Most of the events occur in the southern hemisphere along the ridge-transform plate boundaries. Very few events are located in subduction zones. The events near plate boundaries may be earthquakes that have unusual rupture characteristics, or they may have gone undetected for other reasons (e.g., high microseismic noise or nodal radiation to many stations). Several other events are located in areas where earthquakes of this magnitude (M > 4.5) are unexpected or where they should have been detected if they represent standard earthquake sources. Most prominent in this category are the events on Greenland, which we have identified with a new phenomenon called ‘glacial earthquakes’ (Ekstr€ om et al., 2003, 2006), and
472
Global Seismicity: Results from Systematic Waveform Analyses, 1976–2012
20S
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200km 300km 400km 500km 600km 700km Figure 7 (Top) Compression axes of CMT moment tensors in the western part of South America, projected into the horizontal plane. The earthquakes are color-coded with respect to depth, with white symbols for shallow earthquakes and red symbols indicating the deepest events. The red box indicates the area shown in cross section in the bottom panel. The viewing direction is shown by the thin red line in the center of the box. (Bottom) Vertical cross section aligned with a viewing direction in the plane of the earthquakes associated with the subduction of the Nazca Plate beneath South America. Compression axes of CMT focal mechanisms are shown, projected into the plane of the cross section. At the bottom of the subduction zone, one outlying event has a compression axis that is rotated by 70 with respect to the downdip slab direction suggested by the main seismicity at this depth. This event is also displaced horizontally by nearly 200 km from the inferred location of the subducted slab.
we now understand to be the seismic expression of massive iceberg calving (Nettles et al., 2008). These events radiate surface waves with polarities and amplitudes consistent with a mass-sliding source, rather than with tectonic stress release. Figure 10 shows an example of a teleseismic record section from one of the glacial earthquakes, clearly demonstrating that signals for these events are large and can easily be identified at long periods. Several events in the Himalayas and in Alaska
have been identified as catastrophic landslides (Ekstr€ om and Stark, 2013), and the events off the east coast of the United States may represent submarine landslides or slumps. Other groups of new events are spatially associated with volcanoes, and yet others lack, at this time, an obvious association or explanation. These findings, and other recent discoveries of new events and processes that generate seismic radiation, indicate that the
Global Seismicity: Results from Systematic Waveform Analyses, 1976–2012
473
15S
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100 km 200 km 300 km 400 km 500 km 600 km 700 km Figure 8 (Top) Map view of deep seismicity beneath Fiji–Tonga. The red box indicates the area viewed in cross section in the bottom panel. (Bottom) Vertical cross section aligned with a viewing direction perpendicular to the strike of the deep seismicity associated with the Tonga subduction zone. The compression axes of the focal mechanism are projected onto the vertical plane and show a very complex pattern of internal deformation in the plane of the slab. Some spatial trends in the locations and stress axes can be followed for hundreds of kilometers along the slab.
spectrum of seismic sources is richer than we had previously realized. These new events may be important for our understanding not only of lithospheric tectonics but potentially also of other phenomena such as magma motion and subaerial and submarine mass wasting. With the aid of the powerful infrastructure provided by the GSN, and by many new regional broadband seismographic networks, it seems likely that a focused effort to investigate the global seismic wave field in the period range 20–40 s for seismic events would be fruitful. Events with M > 4.0 routinely generate large surface waves in this period range, and it seems possible that, with recent advances in the characterization of crustal structure and shallow upper-mantle elastic and anelastic structure, these waves could be properly migrated and stacked for array processing and event detection.
Acknowledgments I thank Adam Dziewonski, the founder and for many years the leader of the CMT Project, and Meredith Nettles, the current coleader with the author of the Global CMT Project. The seismic waveforms used in the CMT Project come primarily from stations of the Global Seismographic Network operated by IRIS and the USGS; the waveforms are distributed by the IRIS Data Management Center. Additional waveforms come from several other networks, including the Geoscope, Mednet, GEOFON, and the US and Canadian national seismic networks. We are grateful to everyone involved in the collection and distribution of data from these networks. The CMT catalog and associated results are accessible at the website www.globalcmt.org. The CMT Project has been continuously funded by the National
474
Global Seismicity: Results from Systematic Waveform Analyses, 1976–2012
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Figure 9 Map showing the locations of 3157 previously undetected earthquakes for the period 1993–2012 located using the surface-wave algorithm of Ekstr€om (2006). The smallest earthquake has an estimated magnitude of M ¼ 4.6 and the largest M ¼ 5.9. The quality of detection is indicated by the color of the symbol, with red indicating the best quality, green very good quality, and yellow good quality.
E200109031301A
Event: 2001/09/03, 13:01:12.0, EASTERN GREENLAND Hypocenter (SWEB): Lat = 68.50, Lon = 34.50, h = 10.0, mb = 0.0, MS = 4.9 Filter: VEL 75.0 60.0 35.0 25.0, Component: 1
3.6 km s−1
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0⬚ −10
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Minutes Figure 10 Record section for a glacial earthquake, showing the long-period Rayleigh wave arrivals at global stations out to a distance of 45 . Approximately 30 min after the main Rayleigh wave arrivals (which triggered the detection), a second arrival is seen with the same moveout, suggesting that a second, smaller event occurred in the same location.
Science Foundation since its inception, most recently by award EAR-1249167.
References Arvidsson R and Ekstr€om G (1998) Global CMT analysis of moderate earthquakes, MW 4.5, using intermediate period surface waves. The Bulletin of the Seismological Society of America 88: 1003–1013. Dziewonski AM, Chou T-A, and Woodhouse JH (1981) Determination of earthquake source parameters from waveform data for studies of global and regional seismicity. Journal of Geophysical Research 86: 2825–2853.
Dziewonski AM, Franzen JE, and Woodhouse JH (1984) Centroid-moment tensor solutions for July-September 1983. Physics of the Earth and Planetary Interiors 34: 1–8. Dziewonski AM and Woodhouse JH (1983) An experiment in the systematic study of global seismicity: Centroid-moment tensor solutions for 201 moderate and large earthquakes of 1981. Journal of Geophysical Research 88: 3247–3271. Ekstr€om G (2006) Global detection and location of seismic sources by using surface waves. The Bulletin of the Seismological Society of America 96: 1201–1212. Ekstr€om G and Nettles M (1997) Calibration of the HGLP seismograph network and centroid-moment tensor analysis of significant earthquakes of 1976. Physics of the Earth and Planetary Interiors 101: 219–243. Ekstr€om G, Nettles M, and Abers GA (2003) Glacial earthquakes. Science 302: 622–624.
Global Seismicity: Results from Systematic Waveform Analyses, 1976–2012 Ekstr€om G, Nettles M, and Dziewonski AM (2012) The Global CMT Project 2004–2010: Centroid-moment tensors for 13,017 earthquakes. Physics of the Earth and Planetary Interiors 200–201: 1–9. Ekstr€om G, Nettles M, and Tsai VC (2006) Seasonality and increasing frequency of Greenland glacial earthquakes. Science 311: 1756–1758. Ekstr€om G and Stark CP (2013) Simple scaling of catastrophic landslide dynamics. Science 339: 1416–1419. Ekstr€om G, Tromp J, and Larson EWF (1997) Measurements and global models of surface wave propagation. Journal of Geophysical Research 102: 8137–8157. Gutenberg B and Richter CF (1941) Seismicity of the earth. Geological Society of America Special Papers 34: 131. Gutenberg B and Richter CF (1949) Seismicity of the Earth. Princeton: Princeton University Press.
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Nettles M, Ekstr€om G, and Koss HC (2011) Centroid-moment tensor analysis of the 2011 off the Pacific coast of Tohoku earthquake and its larger foreshocks and aftershocks. Earth, Planets and Space 63: 519–523. Nettles M, Larsen TB, Elo´segui P, et al. (2008) Step-wise changes in glacier speed coincide with calving and glacial earthquakes at Helheim Glacier, Greenland. Geophysical Research Letters 35: L24503. http://dx.doi.org/ 10.1029/2008GL036127. Tsai VC, Nettles M, Ekstr€om G, and Dziewonski AM (2005) Multiple CMT source analysis of the 2004 Sumatra earthquake. Geophysical Research Letters 32: L17304. http://dx.doi.org/10.1029/2005GL023813. Woodhouse JH and Dziewonski AM (1984) Mapping the upper mantle: Three dimensional modelling of earth structure by inversion of seismic waveforms. Journal of Geophysical Research 89: 5953–5986.