ESTIMATION OF DOWN-DIP LIMIT OF THE TONGA ...

ESTIMATION OF DOWN-DIP LIMIT OF THE TONGA SEISMOGENIC ZONE FROM OCEAN BOTTOM SEISMOGRAPH DATA by Suresh Dande B.Sc., Acharya Nagarjuna University, 2005 M.Sc. (Tech.), Andhra University, 2009

A Thesis Submitted in Partial Fulfillment of the Requirements for the Masters in Science Degree.

Department of Geology In the Graduate School Southern Illinois University Carbondale August 2013

THESIS APPROVAL ESTIMATION OF DOWN-DIP LIMIT OF THE TONGA SEISMOGENIC ZONE FROM OCEAN BOTTOM SEISMOGRAPH DATA

By Suresh Dande

A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science in the field of Geology

Approved by: Dr. James Conder, Chair Dr. John Sexton Dr. Liliana Lefticariu

Graduate School Southern Illinois University Carbondale May 24, 2013

AN ABSTRACT OF THE THESIS OF Suresh Dande, for the Master of Science degree in GEOLOGY, presented on May 24, 2013 at Southern Illinois University Carbondale. TITLE: ESTIMATION OF DOWN-DIP LIMIT OF THE TONGA SEISMOGENIC ZONE FROM OCEAN BOTTOM SEISMOGRAPH DATA MAJOR PROFESSOR: Dr. James A. Conder The largest earthquakes occur along the subduction thrust interface known as the seismogenic zone. Until recently, erosive margins like Tonga and Honshu have been thought to be unable to support earthquakes with magnitudes higher than 8.5. However, M 9, 2011 Tohoku-oki earthquake in Honshu requires a reevaluation of w

this notion. The seismic potential of Tonga is likely affected by the vertical spatial extent of the up-dip and down-dip limits, which confines the seismogenic zone. The larger the area of the seismogenic zone, the higher the potential for larger earthquakes. Some models suggest that down-dip limit coincides with the fore-arc Moho while others suggest that they are coincident with thermally controlled mineralogical phase changes during slab descent. Tonga is an ideal place to discriminate between these possibilities, as the incoming Pacific plate is cold and thick with rapid convergence, extending cool isotherms deep into the system. In contrast, the fore-arc Moho is only ~16 km deep. This study tests the hypothesis that the down-dip limit of the Tonga seismogenic zone coincides with the fore-arc Moho and thus ceases the seismicity by initiating a stable sliding between the mantle and the subducting crust. We determine the depth of the down-dip limit in Tonga by mapping the distribution of earthquakes recorded for a sixmonth period from January 1, 2010 to June 30, 2010 by a deployment of ocean bottom seismographs above the Tonga subduction zone. The earthquakes are located by a

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combination of grid-search method and least-square inversion of the observed arrival times. We identified a down-dip limit at a minimum depth of about 40 km below the sea level suggesting that the hypothesis is failed. Therefore, the commonly held idea that down-dip limit is coincides with the fore-arc Moho is not true in the Tonga case. It is likely controlled by the degree of serpentinization in the mantle wedge controlling the transition from stick-slip to stable sliding.

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DEDICATION I would like to dedicate my Thesis to my parents, especially my father, who passed away summer of 2012. They supported me through my educational journey, and for that I thank them.

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ACKNOWLEDGMENTS I would like to thank my advisor Prof. James Conder for his continuous guidance and support for the last two years. I would also like to thank my committee members Prof. John Sexton and Prof.. Liliana Lefticariu for their revisions and help. Thanks to the consortium of institutes for the Ocean Bottom Seismograph data. I would also like to thank all geology graduate students for their support during the last two years.

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TABLE OF CONTENTS CHAPTER

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ABSTRACT ....................................................................................................................... i DEDICATION ................................................................................................................. iii ACKNOWLEDGMENTS ................................................................................................. iv LIST OF FIGURES ......................................................................................................... vii CHAPTERS CHAPTER 1 – Introduction.................................................................................... 1 1.1 Hypothesis…………………………………………………………………….3 CHAPTER 2 – Background ................................................................................... 4 2.1 Tectonic Setting and Seismicity of Tonga Plate .................................... 4 2.2 Seismogenic Zone ................................................................................. 9 2.3 Down-Dip Controlling Factors.............................................................. 11 2.3.1 Thermal Down-dip Limit.............................................................. 11 2.3.2 Moho Down-dip Limit ................................................................. 12 2.4 Magnitude of Earthquakes................................................................... 15 CHAPTER 3 –Data and Methodology ................................................................. 17 3.1 Arrival Times........................................................................................ 17 3.2 Velocity Models ................................................................................... 19 3.3 Grid Search ......................................................................................... 21 3.4 Least-Squares Inversion...................................................................... 22 3.5 Error Analysis ...................................................................................... 29

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CHAPTER 4 – Results......................................................................................... 31 CHAPTER 5 – Discussion ................................................................................... 39 CHAPTER 6 – Conclusions ................................................................................. 46

REFERENCES ............................................................................................................... 47 APPENDICES Appendix A – Grid search method algorithm ....................................................... 53 Appendix B – Inversion method algorithm .......................................................... 56 Appendix C – Copy right permissions ................................................................ 65 VITA ............................................................................................................................. 72

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LIST OF FIGURES FIGURE

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Figure 1.1 – Cartoon of subduction zone ......................................................................... 2 Figure 1.2 – Seismogenic zone ........................................................................................ 3 Figure 2.1 – Tonga subduction zone ................................................................................ 5 Figure 2.2 – Seismicity of the Tonga ................................................................................ 6 Figure 2.3 – Historic large earthquakes in Tonga ............................................................ 7 Figure 2.4 – Distribution of erosional and accretionary margins ...................................... 8 Figure 2.5 – Thermally controlled seismogenic zone ..................................................... 12 Figure 2.6 – Moho controlled seismogenic zone ............................................................ 14 Figure 3.1 – Study area and OBS array ......................................................................... 18 Figure 3.2 – Example seismogram................................................................................. 19 Figure 3.3 – Velocity models .......................................................................................... 20 Figure 3.4 – Choosing a velocity model ......................................................................... 17 Figure 3.5 – Flow chart for Grid search algorithm .......................................................... 27 Figure 3.6 – Flow chart for Inversion algorithm .............................................................. 28 Figure 4.1 – Total earthquakes map .............................................................................. 32 Figure 4.2 – Hypocenters along the slab at locations A-E ............................................. 33 Figure 4.3 – Combined events from all the slab locations.............................................. 38 Figure 5.1 – Histogram of earthquakes with depth......................................................... 42

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1 CHAPTER 1 INTRODUCTION

Subduction zones generate Earth’s largest and most devastating earthquakes and tsunamis. These earthquakes and subsequent tsunamis can impact densely populated coastal areas, causing large number of fatalities. For example, the December 26, 2004 Sumatra tsunami earthquake left more than 200,000 people killed or missing [http://earthquake.usgs.gov/earthquakes/eqinthenews/2004/us2004slav/#summary] and the recent March 11, 2011 Tohoku-oki tsunami earthquake in Japan left more than 15,000 dead and thousands missing [www.ngdc.noaa.gov/hazard/tsunami/pdf/2011_0311.pdf]. Subduction zones are characterized by a dipping and relatively narrow (~100-200 m width) and shallow (8) and great (M>9) earthquakes [Dixon and Timothy, 2007]. The dipping surface is an interface between subducting and overriding plates and often termed the seismogenic zone (Figure 1.1). The seismogenic zone is the ruptured subduction thrust interface and is bounded by up-dip and down-dip limits. The vertical spatial extent of these limits is controlled thermally and/or mineralogically limiting the maximum vertical spatial extent of the rupture. The maximum observed magnitude of subduction thrust earthquakes is variable among subduction zones and may be related to the seismogenic width, W (Figure 1.2) or to the physical characteristics and stress on the fault [Dixon and Timothy, 2007]. It is important to know the extent of the down-dip limit for disaster mitigation because the areas with severe damage and crustal deformation are delimited by downdip rupture limit of earthquake faults [Seno, 2005].

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Seismogenic zone

Figure 1.1. A cartoon of subduction zone and processes (modified from Wikipedia.org).

The down-dip limit has been defined using different seismic characteristics of the subduction thrust faults: (1) the down-dip rupture limit of great earthquakes as determined by waveform modeling, (2) the down-dip limit of great earthquake aftershocks [Husen et al., 1999], (3) small thrust earthquakes occurring between great events, and (5) geodetic data that provides constraints on the down-dip limit of the interseismic locked zone [Dixon and Timothy, 2007]. It has been proposed that the down-dip limit of the seismogenic zone is determined either by the brittle-ductile transition around ~350-450oC of the crustal material at the plate interface [e.g., Wiens et al., 2007] or the Moho of the forearc of the upper plate [e.g., Tichelaar and Ruff, 1993]. The former corresponds to the transition in mechanical or frictional properties from brittle to plastic, and the latter is due to the serpentinization of the forearc mantle

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wedge above the subducting plate, which makes the thrust zone to slide smoothly [Seno, 2005].

Figure 1.2. Seismogenic zone and its geometrical parameters. U and D are the up-dip and down-dip limits of the seismogenic zone respectively. [Ux; Uz] and [Dx; Dz] are their respective coordinates of distance-to-trench axis and depth. Wx and Wz are the horizontal and vertical extents of the seismogenic zone. W and θ are the down-dip width and dip of the subduction interface. Stars represent earthquakes in seismogenic zone [modified from Heuret et al., 2011]. 1.1 HYPOTHESIS We hypothesize that the down-dip limit of the Tonga seismogenic zone coincides with the Moho, which is 16 km [Contreras-Reyes et al., 2011] under the Tonga fore arc, that means the down-dip limit of the subduction thrust earthquakes is limited by hydrous serpentine minerals that form in the fore-arc mantle wedge. Such a shallow depth will limit the size of the largest possible plate boundary earthquakes in Tonga.

4 CHAPTER 2 BACKGROUND

2.1 TECTONIC SETTING AND SEISMICITY OF TONGA PLATE The study area is located in the southwestern Pacific Ocean roughly between longitudes 176o W – 172o W and latitudes 15o S – 23o S (Figure 2.1). The Tonga subduction zone formed when the Pacific plate subducted under the Tonga plate. Above the subduction zone are the Tonga forearc ridge and the Tofua volcanic arc. These bound the Lau basin on the East, where the Lau ridge remnant arc divides the basin from the rest of the Australian plate to the West (Figure 2.1). The back-arc opening in the Lau basin creates a divergent boundary between the Australian and Tonga plates (Figure 2.1). The back-arc spreading rates are 159±10 mm/yr. at 16oS and decreases to 91± 4 mm/yr. at 21oS as determined from GPS observations [Bevis et al., 1995]. The convergence rate between the Tonga and Pacific plate is 164±5 mm/yr near Tongatapu and 240±11 mm/yr. at northern end of the Tonga trench [Bevis et al., 1995], which is the fastest plate velocity recorded on Earth. These differences in spreading and convergence rate across the Tonga and the Lau causes a V-shaped Lau basin (Figure 2.1). The fast convergent rates are result of a combination of Tonga and Pacific convergence and Tonga and Australian plate divergence. This unusually fast convergence rate causes considerable seismic activity, which is demonstrated by the earthquake activity recorded for six months (Figure 2.2).

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Figure 2.1. Bathymetry and topography of the Tonga plate (enclosed in solid white line) and Lau basin (V-shaped shown between Lau ridge and Tonga ridge)(http://www.geomapapp.org, Smith and Sandwell v9.1). Dashed red square denotes the location of OBS array; dashed white line indicates Lau Spreading Center (LSC), and double arrows with different lengths indicate variation of the backarcspreading rate. Different lengths of single arrows indicate variation in convergence rate of the Tonga and Pacific plates. Red triangles within the Tonga plate indicate active Tofua volcanic arc. The Tonga subduction zone has experienced several earthquakes larger than magnitude 7 and a couple of small tsunamis in the last 100 years. Some examples of significant earthquakes include the June 26, 1917 earthquake (Ms 8.4); September 8, 1948 earthquake (Ms 7.8); May 3, 2006 earthquake (Ms 8.0); March 19, 2009

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earthquake (Ms 7.6); and several other earthquakes with magnitudes greater than 7 (Figure 2.3) [Pacheco et al., 1992].

Figure 2.2. Earthquakes that occurred during a six-month period from November 1, 2008, through April 30, 2009, (USGS PDE database). These earthquakes demonstrate the high seismicity of the Tonga subduction zone in a relatively short time frame.

Tsunamis recorded in Tonga include the April 30, 1919 earthquake with magnitude 8.3, which lasted 2 ½ minutes and generated a tsunami with a maximum water height of 2.5 meters [Soloviev and Go, 1975]. The recent July 6, 2011 Kermadec earthquake with Mw 7.6 near the Louisville ridge generated a tsunami with a maximum water height of 10m [http://nctr.pmel.noaa.gov/kermadec20110706/], and the September 29, 2009 Samoa earthquake with Mw 8.1, which generated a killer tsunami with a water height of over 22 meters in Samoa [http://earthquake.usgs.gov/earthquakes/recenteqsww/Quakes/us2009mdbi.php#detail]

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(Figure 2.3). However, the 2009 and 2011 events are interplate outer rise events and did not originate in the seismogenic zone (Figure 2.3). Similar and possibly large future earthquakes may pose a significant seismic and tsunami hazard to the Tonga and the surrounding islands.

Figure 2.3 Map of historic large earthquakes and tsunamis. Size of the circles indicates earthquake magnitude. All earthquakes plotted are greater than magnitude 7 and above 60km depth recorded from 1903 through 2011. Red circles are earthquakes and yellow circles are tsunamis. Numbers within the circles are magnitudes. Color bar indicates the depth of the sea floor. Earthquakes from Pacheco et al., [1992] and base map from http://www.geomapapp.org and Ryan et al., [2009].

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Figure 2.4. Distribution of erosional and accretionary margins [modified from Bilek, 2010]. Tonga subduction zone is an erosional margin and may trigger a tsunami earthquake in the future. Subduction zones are divided into erosional and accretionary type margins. Along the accretionary margins, materials are actively added to the overriding plate, whereas along the erosional margins materials are removed from the base of the overriding plate. The up-dip edge of the seismogenic zone, thrust fault setting, and area of the rupture are expected to play an important role in tsunamigenesis. Tsunami earthquakes, those events that produce large tsunamis relative to their seismic moment (Mo) and have an unusually long rupture time, arise from slip in the shallowest portion (up-dip) of the subduction zones (e.g., Ammon et al., 2006). These tsunami earthquakes are primarily located in erosive margins because of the geometry and frictional behavior of erosional margins relative to accretionary margins [Bilek, 2010]. Earthquakes with magnitude greater than 9 occur predominantly along accretionary margins (Figure 2.4) possibly because of frictional behavior that allows for slip to extend seaward than in

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erosive margins, thus allowing for wider areas for co-seismic rupture and leading to much larger magnitude earthquakes [Bilek, 2010]. Prior to the 2011 Tohoku-oki earthquake, it was widely thought that despite tsunami earthquakes occurring at erosional margins, the largest events only occurred at accretionary margins and not erosive ones like Tonga [e.g., Bilek, 2010]. However, with the advent of the magnitude 9 Tohoku-oki event, reassessment of erosional margin seismogenic zones like Tonga is warranted. 2.2 SEISMOGENIC ZONE The seismogenic zone is a narrow subduction interface bounded by up-dip and down-dip limits (Figure 1) [Oleskevich et al., 1999; Tichelaar and Ruff, 1993]. The updip limit represents the aseismic to seismic zone transition and affects the likelihood of tsunami generation [Schotlz, 1990]. The down-dip limit represents the seismic to aseismic zone transitions and determines the extent of the rupture zone, which is one of the useful parameters for predicting the possibility of largest earthquakes triggered by the subduction thrust fault [Oleskevich et al., 1999]. The total down-dip width (W) of the seismogenic zone as well as the horizontal extent (Figure 1) is important in limiting the size of the earthquakes because magnitude is closely related to rupture area (equation 1). Mapping the distribution of shallow subduction zone earthquakes allows for determination of the vertical spatial extent of the seismogenic zone [Fischer et al., 1991]. For most subduction zones on Earth, the up-dip limit has been found between 210 km depth where the subduction thrust temperatures are between 100 - 150oC [e.g., Oleskevich et al., 1999; Moore and Saffer, 2001]. The location of a down-dip limit may

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involve complex structural and thermal phase changes. Numerical models suggest that the down-dip limit on thrust zones occurs either where the temperature reaches 350oC or at Moho depth, whichever is shallower [Oleskevich et al., 1999]. However, seismic observations in the Mariana Trench suggest that the down-dip limit can sometimes extend well below the Moho – to depths of 50 km in places where the Moho is 20 km deep [Wiens et al., 2007]. Global studies based on teleseismic datasets from various subduction zones [Pacheco et al., 1993; Tichelaar and Ruff, 1993] found the seismogenic zone down-dip depths ranging from 35-70 km. The maximum depth of down-dip transition for the Tonga subduction is near the shallower end of the global range at 40 km depth [Pacheco et al., 1993 and Hayes et al., 2012]. The depth limits of the Tonga seismogenic zone have thus far only been determined from teleseismic observations as the geographical setting of the Tonga Islands (Figure 2.1) limits the coverage of local land based seismic arrays. The Tonga plate is mostly underwater except for a few islands, which are aligned parallel to the trench axis (Figure 2.1). Even with seismometers on the Tonga islands, the linear trend of these islands makes it difficult to precisely locate earthquakes because of the one dimensionality of the station locations. Most of the past research focused on deeper parts of the Tonga slab or used teleseismic data to infer the depth limits of the seismogenic zone [e.g., Fischer et al., 1991; Bonnardot et al., 2009; Contreras-Reyes et al., 2011]. The study proposed herein uses part of the local earthquake data recorded between November 2009 and November 2010 by an OBS (Ocean Bottom Seismograph) array, which was deployed on the seafloor above the subducting Pacific

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plate. Local array data can better constrain the depth of earthquakes than teleseismic data because of smaller epicentral distances relative to depth. 2.3 DOWN-DIP LIMIT CONTROLLING FACTORS 2.3.1 Thermal Down-Dip Limit Much debate has been centered on the thermal properties of the materials along the plate interface, which control the depth of the down-dip limit. The cessation of earthquakes below the down-dip limit demonstrates that there must be a significant change in the properties of the contact zone [Ruff and Kanamori, 1983]. For young subduction zones, the down-dip limit may be controlled by temperature of the subduction interface [Hyndman and Wang, 1993, Tichelaar and Ruff, 1993] suggesting a temperature limit corresponds approximately to the onset of quartz plasticity and is believed to be the transition from brittle to semi-brittle behavior of continental crustal rocks, which may cause to cease the seismicity [Scholtz, 1990]. This idea of thermally controlled down-dip limit has been tested in northern Cascadia margin, where the thermally determined down-dip limit is in agreement with the down-dip limit estimated from geodetic modeling of interseismic deformation [Hyndman and Wang, 1993; Dragert et al., 1994]. Laboratory tests on quartzofelspathic crustal rocks also indicate that the critical temperature for this transition is 350oC, and the critical temperature for mafic composition in island arcs, may be slightly higher than 350oC [Blanpied et al., 1991, 1995]. If the down-dip limit is temperature controlled, the seismogenic width, W, depends on the rate of increase in temperature on the thrust fault. So, thrust faults with shallow dips have wider seismogenic zones than with the steeper dips [Hyndman et al., 1995]. The main factors that control the thrust temperature are the thickness of the

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sediments on the incoming plate, the plate age and thus heat flow, convergence rate, and the plate dip [Hyndman and Wang 1993; Wang et al., 1995]. In addition to the 350oC temperature, there has been identified another maximum temperature limit for the rupture of earthquakes initiated at less than 350oC may extend to 450oC. This temperature limit has been observed as the limiting temperature of down-dip slip of two great earthquakes in Southwest Japan [Hyndman et al., 1995]. Scholtz, [1990] defined the region between 350oC – 450oC as a region of conditional stability. Figure 2.5 shows a schematic diagram illustrating these temperature limits and thermally controlled seismogenic zone in a young subduction interface.

Figure 2.5. Schematic diagram of a subduction interface showing a thermally controlled seismogenic zone [modified from Hyndman et al., 1997]. 2.3.2 Moho Down-Dip Limit Serpentinization is believed to play an important role in controlling the geological processes in mantle wedge and along the subduction interface [Ji et al., 2013], and may

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influence the location of the down-dip limit. Serpentinization often begins with the intersection of the subducting plate with the fore-arc Moho of the upper plate. The down-dip rupture limit of large thrust earthquakes is often thought to coincide with the fore-arc Moho [Tichelaar and Ruff, 1993] because the occurrence of stable sliding serpentinite in the mantle wedge ceases the rupture below the Moho [Oleskevich et al., 1999]. A fore-arc mantle wedge initially rich in dry, strong olivine and pyroxene ultramafic rocks can potentially be hydrated by the large amount of water carried down through the subducting crust and the downgoing sediments [Fyfe and McBirney, 1975]. At certain critical pressures and temperatures, these dry mantle minerals alter into weak, hydrous mineral assemblages consisting of serpentine minerals, talc, and brucite. Peacock and Hyndman, [1999] proposed that the formation of serpentine + brucite rocks in the mantle wedge and metasomatic talc at the slab-mantle interface controls the down-dip limit of the subduction earthquakes, because these rocks cause stable sliding of the subduction interface, and thus cause seismic rupture to cease. The much lower flow strengths of serpentine results in strong localization of strain into weak, narrow shear zones with low flow stress, and cold thermal structures [Uchida et al., 2009]. It is found that serpentine acts as a lubricant in lithospheric faults and it affects the frictional stability at the down-dip edge. Thus, the presence or absence of serpentine is believed to control the transition between stick-slip to stable-sliding behavior [Moore and Lockner, 2007]. The distribution of serpentine thus may control the seismicity of oceanic subduction zones [Seno 2005].

14 In some Island arc subduction systems, a deep second seismogenic zone

(Figure 2.6) has been suggested at depths of 40-50 km. Pacheco et al., (1993) found this second seismogenic zone in the Kermadec, Solomon, and Kamchatka arc subduction zones. The reasons for this seismogenic zone are not well explained, however, few possible reasons are given. One possibility is that the hydrated mantle minerals serpentine, talc and brucite that are responsible for the aseismic zone between depths of 20-40 km are dehydrated by the higher temperatures (550-750 oC) at greater depths, again allowing the thrust earthquakes [Hyndman et al., 1997].

Figure 2.6. Schematic diagram illustrating the affect of serpentinized mantle on seismicity in an oceanic subduction. Note that this figure shows a second possible deep seismogenic zone because of dehydrated minerals in the mantle at depth [modified from Hyndman et al., 1997]. Other things that affect the down-dip limit are the geometrical parameters of the seismogenic zone (Figure 1.2), which correlate with plate parameters such as

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convergence rate, plate age, and dip. One of the correlations is that as the convergent velocity increases, the down-dip depth (Dz) of the seismogenic zone and the dip (θ) of the subduction interface increases [Heuret et al., 2011]; therefore, the Tonga seismogenic zone may have a deeper down-dip limit on the northern end of the trench and a more shallow down-dip on the southern end of the trench because the convergent velocity increases from South to North (refer to section 2.1 for velocities). 2.4 MAGNITUDE OF EARTHQUAKES The area of the ruptured portion (A) and the amount of the slip (D) along the thrust fault are primary parameters that determine the moment and magnitude of an earthquake (equation 1) [Wells and Coppersmith, 1994].

Moment of an earthquake Mo = µAD Moment magnitude Mw =

(1)

2 log(Mo ) − 6.0 3

Where

µ is the shear modulus used to measure the rigidity of the earth (dyne/cm 2 ) A is the area (cm 2 ) of the rupture along the fault D is the average displacement or slip (cm) along the fault area A The area (A) of rupture depends on the down-dip depth (Dz) (Figure 1.2) and

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length along the strike of the subduction thrust fault. Therefore, the deeper the down-dip limit and the longer the length along strike, the greater the area of potential rupture and the greater the possibility of triggering large earthquakes. Large earthquakes occur frequently at subduction zones with fast convergence rates. The tectonic convergent rate (ν) of a thrust fault, moment of an earthquake (Mo), and down-dip width (W) are primary parameters that determine the recurrence interval

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of large earthquakes. The relationship between these three parameters and the recurrence interval is explained through equation (2) [Molnar, 1979].

Recurrence intervel T(Mo ) =

β β M1− m Mo (1− β )µLWν

(2)

Where

ν is the tectonic convergent rate(velocity) W is the down -dip width L is the thrust fault length µ is the rigidity Mm is the maximum moment of an earthquake Mo is the moment of an earthquake

β is a constant depends on moment -magnitude According to equation (2) the recurrence interval for an earthquake of a given

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size varies inversely with the convergence rate and the down-dip width. Therefore, faster convergent boundaries with greater widths tend to produce earthquakes more frequently with high moment because faster convergent rates result in shorter recurrence intervals (McCaffrey, 1994). However, the Tonga subduction zone, which is the fastest convergent boundary on Earth with a rate of 240±11 mm/yr at the northern end of the Tonga trench [Bevis et al., 1995], has experienced only one earthquake near magnitude 8.5 in the past 100 years occurring in 1917 with Ms 8.4 [Pacheco and Skyes, 1992]. This suggests that the seismogenic zone in Tonga might not support earthquakes larger than magnitude 8.5 because of the other parameters such as width, fault length, and rigidity in (2). Therefore, constraining limits helps illuminate both size and frequency of largest potential earthquakes.

17 CHAPTER 3 DATA AND METHODOLOGY

In 2009, a consortium of institutions, including Southern Illinois University

Carbondale (SIUC), University of Hawaii, Lamont-Doherty Earth Observatory, and Scripps Institute of Oceanography, and led by Washington University in St. Louis, deployed an array of ocean bottom seismographs (OBS) extending ~400 km across the Eastern Lau Spreading Center, the Tonga arc and trench, with variable station spacing. The local OBS stations were deployed between longitudes 176.5o W – 174o W and latitudes 20.5o S – 22.5o S for one year from November 2009 – November 2010. This study uses six months of that one-year data from nine OBS stations that were deployed along the Tonga arc and in the back arc region, and one OBS deployed on the fore arc of the Tonga subduction zone (Figure 3.1). Tonga is a highly seismically active region. For comparison 322 events with a magnitude between 3 and 8.4 (PDE catalog of USGS) (Figure 2.2) were recorded in the six months period from November 1, 2008, and April 30, 2009. This high rate of seismicity suggests that six months of OBS data is likely sufficient to detect a large number of events and determine an accurate down-dip limit. 3.1. ARRIVAL TIMES We picked 16,670 P and S first arrivals from six months of data recorded at ten stations. An example seismogram is shown in figure 3.2. A first pass auto-picking algorithm filters the raw data by applying a band pass filter (0.8 - 8 Hz) to window the frequency content of earthquakes coming from the seismogenic zone and picks P- and S-wave arrival times based on the LTA/STA ratio. STA is the average amplitude of a

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seismic signal in a short-time window of 3 sec. LTA is the average amplitude of a seismic signal in a long-term time window of 12 sec next to the STA window. If the LTA/STA ratio is equal to or greater than a threshold of 8, then algorithm picks the first arrivals. Some times the algorithm picks wrong arrivals when the data contain more noise. Therefore, every auto-picked seismogram has been carefully inspected to refine or remove wrong picks. To determine the effect of filtering, we find the S–P time of an event from both the raw and filtered data and found that the difference in S–P time is minimal.

Figure 3.1 Geographical setting of the Tonga Islands and an array of local OBS stations (blue solid squares). Red triangles show volcanic arc. The arrival time t at a station i is the sum of travel time and origin time (equation 3). The travel time T is a function of station and hypocenter parameters, and the velocity of the medium through which seismic waves traveled. Here, velocity models are derived

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from seismic refraction data collected in the central Lau basin [Crawford et al., 2003]. The travel times are determined using 1D teleseismic travel times algorithm written in Matlab [Knapmeyer, 2004]. t i = T(x i , y i ,z i , x 0 , y 0 ,z 0 ) + t 0

(3)

Where t i is the arrival time at station i T is the travel time as a function of the location of station x i , y i ,z i and the hypocenter x 0 , y 0 ,z 0 t 0 is the origin time of an earthquake

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Figure 3.2. Waveforms of an earthquake recorded at 5 stations located in the study area (Figure 3.1) showing P and S wave arrivals. Each station’s recording consist of three traces, from top to bottom, the east (1), north (2) and vertical (z) components of ground motion. 3.2 VELOCITY MODELS Four different velocity models (Figure 3.3) are used to build travel time lookup tables. A travel time lookup table is an array of pre-computed travel times used to estimate the travel time from any depth point to receiver through linear interpolation. The look up table replaces the runtime computation of travel times with a simpler array

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indexing operation. This saves significant processing time, since it is faster to retrieve a value from memory rather than continuously executing extensive computations. Grid search and least squares inversion methods both use the look up tables to find the predicted arrival times.

Figure 3.3. Velocity models of the Tonga and adjacent regions used for event location [Crawford et al., 2003 and Contreras-Reyes et al., 2011]. Because of the complex structure of the crust in the Tonga and surrounding area, we divided it into four geological zones: Eastern Lau basin, Tonga ridge, Tonga forearc, and Pacific plate (Figure 3.4) to choose appropriate velocity models. The Tonga ridge has a very thick crust of ~20 km in contrast to the ~16 km of Tonga forearc and 6 km thick crust on the Pacific plate (Figure 3.3). The Eastern Lau backarc velocity model has somewhat thinner crust (~6.5 km), but an overall slower velocity mantle than the Tonga fore-arc mantle. Selection of a particular velocity model depends on the locations of both the earthquake and the station. For example, if an earthquake is located under the

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Tonga forearc and it is recorded at a station located on Tonga ridge, then we take the average of the travel times for the two models to find travel time from that earthquake location to the station. If the station and earthquake locations are in the same region, we take a single velocity model of that region. In the first case, the average is not weighted based on the path length in each region.

Figure 3.4. The study area is divided into four regions based on tectonic setting and geology of the subsurface. Straight parallel black lines indicate the separation between regions. Blue line is the Tonga trench. 3.3 GRID SEARCH A simple method to locate earthquakes in a volume thought to have earthquakes is to execute a grid search over that volume to find the location most compatible with

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observed arrival times. This method successively performs finer, systematic gridsearches within a spatial x, y, z volume to obtain a misfit function and an optimal hypocenter to use as an initial hypocenter in the least-squares inversion program. The common approach to find a minimum misfit between observed and calculated arrival times of each observation is to find a minimum of the sum of the squared residuals (chi square) (equation 4) from n observations. n

χ 2 = ∑ (t obs − t a )2 i =1

(4)

Where t obs is the observed arrival time Tcal is the calculated travel time t 0 cal is the calculated origin time t a = Tcal + t 0 cal is the calculated arrival time The Matlab algorithm of the grid search method is given in the appendix (A) and the

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flow chart of that is shown in figure 3.5. 3.4 LEAST-SQUARES INVERSION Before discussing the inverse modeling, it is worth mentioning forward modeling to better understand the inversion. Assuming an earthquake location in the subsurface called hypocenter mj = (xj, yj, zj, tj) we can find the arrival time (ti) at different stations (i) as function of origin time tj and travel time Ti between the source and the station as defined by (3). If the velocity structure is known, we can set up a forward problem using the following formulation ti = Gmj

(5)

23

where Gij =

∂t i is a matrix of partial derivatives of travel times in space. So, we can ∂m j

compute arrival times at any station with an assumed model parameters mj = (xj, yj, zj, tj).

€

Least-squares inversion is an opposite of forward modeling. Given the observed arrival times, we need to find the model parameters that best fit them. So, the first step in the inversion is to make a guess to the starting model parameters

m j0 = (x j0 , y j0 ,z j0 ,t j0 ), which is estimated from the grid search method and we hope is close to the solution we seek. Using this starting model we find the arrival time, which is

€

called the calculated arrival time at station i, ti0 = Gmj0. The OBS stations (xi, yi, zi) on the surface detect the earthquake at arrival time called the observed arrival time tiobs. The travel time residual ri = tiobs – ti0 is the difference between the observed and the calculated arrival time. The residual is due to the error in the starting model. Therefore to minimize the error we change the starting model by δmj = ( dx j, dy j, dz j, dt j) from its original location. Therefore, the new model parameters that will make the calculated data closer to those observed data are m j = m j 0 + δm j .

€

€

€

€ (6)

In general, the data do not depend linearly on the model, so we linearize the problem by approximating the travel time function by a Taylor series about the starting model mj0 and using only the first term. Then the observed arrival time can now be written as follows:

t iobs = t i0 + ∑ j

∂t i δm j . ∂m j

This can be written as travel time residual equation

€

(7)

24

δri = t iobs - t i0 = ∑ j

∂t i δm j = ∑ Gij δm j j ∂m j

(8)

we can write this in matrix form as

€

δri = Gij * δm j where Gij =

(9)

∂t i ∂m j

for simplicity we can write equation (9) as

δr = G * δm.

(10)

where δr is the residual observed data vector, G is the matrix of partial derivatives, and €

δm is the model vector in location and origin time that needs to be determined by the €

€

€ is a vector of matrix representing a system of inversion of matrix G . Equation 9, which simultaneous linear equations with j columns ranges from 1 to 4 representing the model

€ parameters and i rows ranges from 1 to n representing the observed arrival time, is given by: ⎡δr1 ⎤ ⎡G11 G12 ⎢ ⎥ ⎢ ⎢δr2 ⎥ ⎢G21 G22 ⎢ . ⎥ ⎢ . . ⎢ ⎥ = ⎢ . ⎢ . ⎥ ⎢ . ⎢ . ⎥ ⎢ . . ⎢ ⎥ ⎢ ⎣δrn ⎦ ⎣Gn1 Gn 2

G13 G23 . . . Gn3

G14 ⎤ ⎥ G24 ⎥⎡ δm1 ⎤ ⎢ ⎥ . ⎥⎢δm 2 ⎥ ⎥ . ⎥⎢δm3 ⎥ ⎢ ⎥ . ⎥⎣δm 4 ⎦ ⎥ Gn 4 ⎦

(11)

Because each arrival time measurment represents one equation, and each model €

parameter provides one unknown, G has a number of rows equal to number of observed arrival times and columns equal to number of model parameters. So, there are more equations than unknowns and it represents an overdetermined problem. Such problems pose difficulties for inversion as it is not possible to invert a rectangular (non-

25

square) matrix. Thus, to make G a square matrix, which means to make the number of equations and the number of unkowns equal, we must pre multiply equation (10) with

€ transpose of G; G T on both sides. GT δr = GT G * δm € €

(12)

now multiply equation (12) with (G TG )−1 ,which is a square matrix and thus has an inverse, on both sides to solve for vector m (GT G)−1GT δr = (GT G)−1GT Gδm (GT G)−1GT G =€I is an identity matrix € therefore, (GT G)−1GT δr = I * δm

δm = (GT G)−1GT δr

(13)

which is the standard least squares solution for an overdetermined problem. Equation €

13 uses (GT G)−1GT is called generalized inverse and it acts on data to give model parameters for the corresponding calculated or predicted arrival time. It provides the

€ “best” possible solution in a least squares sense, because it gives the smallest squared misfit. The model parameters from the inversion may or may not best fit the obseved arrival times. In most of the cases we never get a unique model that best describes the obseved data because of errors in the observed arrival time data. The errors include reading arrival time errors, inaccuracies in the clocks at the stations, and misidentification of the first arrivals. In addition to these errors of measurement, there are systematic errors due to the fact that the model velocity structure is not perfectly known and is lateraly variable. Therefore, we seek a solution that best fits the data in a least squares sense. To do this, we treat the observations t iobs as having errors described by their standard deviation σ i and find the model that minimizes the misfit,

€

€

26 ⎞ 2 1 ⎛ χ = ∑ 2 ⎜δri − ∑ Gij δm j ⎟ , ⎠ i σ ⎝ j i 2

(14)

which is the error in the calculated arrival time. The misfit is the normalized sum of the €

squares of the difference between the observed and calculated arrival times. To minimize the misfit we weight the data by the reciprocal of their variances ( σ i2 ) so that most uncertain values have the least effect on the total misfit.

€ So, we start with an initial model m0 and using equations from 6 -13, we find the residual arrival time data vector δr, evaluate the matrix of partial derivatives, and finally calculate δm, the change in the starting model that gives a better fit to the data. If the misfit χ2 from the initial € model parameters is high, we seek changes in the model € parameters and set up a new model €

m 1 = m 0 + δm 0

(15)

to predict the data for forward modeling. This time the predicted data should be closer to

€

the observed data than the predictions from the starting model. We can test this by measuring the misfit value between observed and calculated arrival times. If the misfit is still high we have to change the model parameters again to set up a new model m2. This process is repeated until successive iterations produce only a small change in the model, and hence in the total misfit of the data [Stein and Wysession 2003]. The algorithm of the inversion is given in appendix (B) and the flow chart of that algorithm is shown in figure 3.6.

Figure 3.5. Flow chart for grid search procedure.

27

Figure 3.6. Flow chart for inversion procedure.

28

29

3.5 ERROR ANALYSIS As the arrival time data has errors, we expect uncertainties in the resultant model parameters. These uncertainties can to be determined from the variance-covariance matrix of the model parameters which is given by

σm2 = σ2 * (GT G)−1,

(16)

which depends on the variance ( σ2 ) of the data. We calculate the σ2 from the misfit

€

between observed and calculated data, € n 1 σ2 = ∑ (t obs − t ical )2 , n − k i =1 i

€

(17)

where t iobs are the observations t ical are the best fitted data from the inversion n is the number of observed data values k is the number of model parameters. The variance-covariance matrix ( σm2 ) shows how the model parameters are correlated. If

€

we look at the each element of the matrix (equation 18), we can draw the uncertainties

€ 2 in the model parameters. for example, if σ xy is nonzero then it gives the uncertainties in the x and y location together and those two parameters are correlated.

⎡σ2 ⎢ xx2 ⎢σ σm2 = ⎢ yx2 σ ⎢ zx2 ⎣σtx

2 xy 2 yy 2 zy 2 ty

σ σ σ σ

2 xz 2 yz 2 zz 2 tz

σ σ σ σ

2 xt 2 yt 2 zt 2 tt

σ σ σ σ

⎤ ⎥ ⎥ ⎥ ⎥ ⎦

€

(18)

To illustrate how the model parameters are correlated we often extract a 2 x 2

€

submatrix from equation 18 and diagonalize that by finding eigenvalues λ1 and λ2 and

€

€

30

their eigenvectors (x11,x21 ) and (x12 ,x22 ) , here superscripts indicates their corresponding

λ . For example if we want to find uncertanies in epicenter, we extract xy elements as a submatrix€which is

€

⎛σ2 ⎜⎜ xx 2 ⎝σyx

€

σxy2 ⎞ ⎟. σyy2 ⎟⎠

(19)

Here the uncertanity in the hypocenters can be visualized in the form of

€

confidence ellipses as shown in figure 4.2. The semi-major and semi-minor axes of the ellipses are the eigenvalues and their orientations are determined by the eigenvectors. The confidence ellipses represent that there is a 68% ( 1σ) chances for the location to lie within the ellipse. The shape and orientation of the ellipse depend on the (GTG) −1 matrix

€ and size depends on the variance of the data σ2 . € We also determined error estimates in depth for a few events shown as pluses in € figure 4.2 and 4.3 from grid search. For these events the inversion was able calculate the variance-covariance matrix for the x (easting) and y (northing) model parameters but not for z (depth) parameter. Therefore, we used grid spacing (used in grid search) as the depth uncertainty, which is within 15 km from the event location. The horizontal (easting) uncertainties for these events are determined from horizontal limits of the corresponding ellipses calculated from variance-covariance matrix.

31 CHAPTER 4 RESULTS We located 1243 events (Figure 4.1) beginning January 1, 2010, through to June

30, 2010 using 15,670 P and S arrivals. To illuminate certain areas along the subduction zone, we have taken depth profiles of the Tonga slab at 5 different locations labeled A, B, C, D, and E (Figure 4.1) extracted from the three dimensional depth contours of global subduction zone geometries determined by the linear interpolation of individual slabs along the earthquake distribution at various locations along the strike of the Tonga trench [Slab 1.0;Hayes et al., 2012]. The slab profiles are taken within the areal extent of the OBS array because earthquake locations are more constrained in that region. Considering these slab profiles, we extracted events within 10 km of each slab profile and within 10 km of the plate interface. Events further from the slab interface are less important for the question explored here. The interface events used for interpretation are further filtered based on size of confidence ellipses and error bars leaving the 112 best events shown as circles and pluses in figures 4.2a-b and 4.3. The uncertainties of the events shown as circles are derived from the size of the ellipses determined from the variance-covariance matrix in the inversion. The major radii of these ellipses range from 0.46 to 42.2 km. The depth uncertainties of the events shown as pluses are determined from the 15 km grid spacing (used in grid search method), meaning roughly ±10 km. The horizontal uncertainty, which is calculated from the horizontal variance in the inversion, ranges from 1.25 km to 67 km. We plotted all 112 events together to see the density of the earthquakes along the slab interface (Figure 4.2c). This density is determined with a 2D histogram using 25

32

equally spaced bins in both vertical and horizontal directions. The darker the region the higher the density of earthquakes. A rapid fading of the color at about 40 km indicates a rapid decrease in the number of earthquakes. We also plotted events from all the slab profiles together (Figure 4.3) to see if there are any variations in the results. We found a similar down-dip limit, to the results obtained from the individual slab profiles (Figure 4.2).

Figure 4.1. Map view of earthquakes located with the inversion of six months of OBS data. Lines labeled with A, B, C, D, and E are the locations of bathymetry and subduction slab profiles used in figure 4.2-3. The profiles are chosen only within the OBS array because events have lower error location compared to events outside of the OBS array.

33

Figure 4.2. (a). Hypocenters along the slab at locations A-E showed in figure 4.1. (b) Hypocenters with their confidence ellipses and error bars for the events showed in (a). (c) Density of earthquakes for all the events, here events showed as pluses in (a) and (b), are also plotted as circles.

Figure 4.2. (continued)

34


35


36


37

38

Figure 4.3. Events combined from all slab locations. (a) Hypocenters plotted in the depth cross-section (b) Hypocenters along with confidence ellipses and error bars for the events showed in (a). (c) Density of all earthquakes shown in (a) and (b). Partial to full coupling is shown only in this figure.

39 CHAPTER 5 DISCUSSION This study identified a depth of down-dip limit between 33 and 42.5 km below sea

level (Figure 4.2-3) for the Tonga seismogenic zone. This depth range is based on the termination of earthquakes along various slab profiles (Figure 4.2). Since the earthquake distribution along the most of the slab profiles terminates at about 40 km, we consider this depth as the minimum depth for the down-dip limit of the Tonga seismogenic zone. We graphically show the termination at about 40 km in a histogram of number of events versus depth (red line in figure 5.1). More over, the 40 km depth approximately coincides with the depth capturing 90% of the interface earthquakes (black dashed line in figure 5.1). The distribution of earthquakes down to a depth of 40 km may indicate a mechanical decoupling between the Tonga and the Pacific plate. There are a few events extending to depths down to 80 km, possibly indicating a partial coupling between the mantle and subducting Pacific plate in the depth range of 40-80 km or more likely could simply be interslab events. Studies on yield strength of oceanic lithosphere suggest that the effective elastic thickness and depth of the brittle-plastic transition increases with the age of the subducting plate [e.g., Watts 2001]. According to those studies, the transition is expected to occur at ~40 km for old and ~25 km for young lithospheric plates. Previous studies on Tonga subduction zone found a maximum depth of 40 km for the down-dip limit based on the centroid depths of moderate earthquakes (between 5.5 and 6.5) from Harvard’s CMT catalog from 1900 to 1990 [Pacheco et al., 1993 and Hayes et al., 2012]. In contrast, this study found a minimum depth of 33 km (Figure 4.2(v)) and it

40

extends to a depth of about 42.2 km (Figure 4.3). More over, the events determined from this local data are more depth constrained than the previous teleseismic studies. Tichelaar and Ruff, [1993] proposed that the down-dip transition that is aseismic to seismic coincides with the mineral property transitions from stick-slip to stable sliding. This is because the crustal rocks become plastic at ~350 – 450oC isotherms [Scholtz, 1990]. In contrast, the down-dip limit of the Tonga seismogenic zone is not controlled by the 350–450oC isotherms, which may be reached at a greater depth of about 80 km [Syracuse et al., 2010]. Moreover, the idea of thermally controlled down-dip limit is applicable to young subducting plates, which are relatively warm [Oleskevich et al., 1999] and may not be for old subducting plates such as Pacific plate. Another often stated controller of the down-dip limit is the fore-arc Moho or the mantle wedge. Hyndman et al., [1997] suggested that for cold subduction zones where the down-dip limit coincides with fore-arc Moho when the downgoing plate encounters it before temperatures reaches ~350 oC isotherms. This is because the mantle wedge contains serpentinite, a rock believed to cause stable sliding and thus ceases the seismicity. However, Hyndman’s idea is not valid for Tonga because the down-dip limit is found to be deeper than the Moho (16 km) (Figure 4.2-3). The down-dip limit deeper than Moho indicates that the mantle wedge may not be serpentinized up to a depth of 40 km. However, using active source seismic tomography, Contreras-Reyes et al., [2011] reported low mantle wedge velocities (~7.5 km/s) much lower than those typical of upper mantle peridotite (> 8.0 km/s). The low velocities suggest hydration of the forearc mantle wedge and likely a high degree of serpentinization (30%) [Christensen, 1996]. Other factors that also suggest vigorous mantle wedge hydration in Tonga are:

41

the fast convergence rate (~200 mm/a), relatively thin arc crust 15-20 km, and a highly hydrated subducting Pacific oceanic lithosphere [Contreras-Reyes et al., 2011]. Seno, [2005] suggests that stress state (compression or tension) in the mantle wedge controls the extent of the serpentinization. He observed variations in the depth of the down-dip limit regardless of Moho depth in subduction zones near Japan, where the Pacific and Philippine Sea plates are subducting. Seno, [2005] reported that in Kanto and Southern Kyushu where the Philippine Sea plate is subducting, the mantle wedge is not likely serpentinized. This is based on the located down-dip depth of 60-70 km, which is deeper than the Moho of the upper plate. In contrast, in the region off Iwate in Northern Honshu and in Bonin, where the old Pacific plate is subducting, the mantle wedge is serpentinized. This is because the down-dip limit is located at depth of 20–30 km in those regions, which is around the Moho of the upper plate. Seno, [2005] explains this contrast with the stress regime of the mantle wedge. The extent of serpentinization and thus the down-dip limit depend on the stress state of the mantle wedge providing the hydration of the mantle wedge is conducted through hydro-fracturing by water released from the dehydrating subducting crust. It is observed that in a reverse-fault type stress regime, hydro-fracturing is not favored and the wedge is not serpentinized. In contrast, in a normal-fault stress regime, hydro-fracturing is favored resulting in a serpentinized wedge. If the fore-arc is tensional such as Tonga, Bonin, and Mariana oceanic island arcs, the mantle wedge is serpentinized, and the seismogenic zone is limited. If the fore-arc is compressional such as Chile or Northern Honshu, the mantle wedge is not serpentinized, and the extent of the seismogenic zone may be larger. Although tomography studies [Contreras-Reyes et al., 2011] and the likely

42

tensional stress state of the Tonga fore-arc suggested a serpentinized mantle wedge, the seismicity from this study reveals a down-dip limit at 40 km which is deeper than the Moho. This paradox might be explained by considering the degree of serpentinization. The shallow part of the mantle wedge may not be sufficiently hydrated to create enough serpentinite for stable sliding until a depth of 40 km. Below 40 km; the mantle wedge may have been hydrated by more rapid dehydration of the subducting crust. More intense hydration may create enough serpentinite to cause stable sliding below 40 km and thus limiting the seismicity.

Figure 5.1. Depth distribution of seismogenic zone earthquakes. The number of events located within ±10 km of the slab interface is plotted versus depth using 20 equally spaced bins. Red line shows the inferred down-dip limit at about 40 km. Black dotted line shows the depth above which 90% of the total events occurred. Panels (a) through (e) correspond to slab profiles (A) through (E) respectively. Panel (f) combines all 112 earthquakes into one histogram. Green lines in (f) shows the down-dip limit at different slab locations based on the earthquake distribution.


43


44


45

46 CHAPTER 6 CONCLUSIONS From 1243 located earthquakes, we identified 112 best events along the slab interface for 5 selected slab profiles within the footprint of the Lau OBS array. This study identified the down-dip limit of the Tonga seismogenic zone at a minimum depth of 33 km at the slab location E (Figure 4.2(v)) and ~42 km at other locations (Figure 4.2(i)-(iv)). The apparent shallower limit at profile E may be due to the relatively fewer events located along that southernmost profile. If we were to consider a few sparely located events below ~35 km, the down-dip limit may be picked close to 40 km as well. Since the earthquake distribution at majority of the slab locations terminates at about 40 km, we propose 40 km as the minimum depth for the down-dip limit of the Tonga seismogenic zone. The reported down-dip limit contrasts well with the teleseismic study by Pacheco et al., [1993] which suggests 40 km as the maximum depth of down-dip limit. Therefore, this study provides a range of possible down-dip depth values using more depth constrained local data recorded for a period of six months compared to the previous tele-seismic studies. There may not be significant change in the depth of the down-dip limit with more data because; the additional number of events may fall above the reported seismogenic down-dip depth limit. Thus, the commonly held idea that the Moho controls the down-dip limit is not true in the Tonga case where the Moho is closer to 16 km. It is more likely controlled by the degree of serpentinization in the mantle wedge controlling the transition from stick-slip to stable sliding.

47 REFERENCES

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Ruff, L., H. Kanamori (1983), Seismic coupling and uncoupling at subduction zones, Tectonophysics, 99, 99-117. Scholtz, C.H. (1990), The mechanics of earthquakes and faulting, Cambridge University Press, New York. Soloviev, L., and N. Go, (1975), A catalogue of tsunamis on the eastern shore of the Pacific Ocean (1513-1968). Nauka Publishing House, Moscow, USSR, 204p. Can. Transl. Fish. Aquat. Sci., 5078, 1984. Seno, T. (2005), Variation of downdip limit of the seismogenic zone near the Japanese islands: Implications for the serpentinization mechanism of the forearc mantle wedge, Earth and Planetary Science Letteres, 231, 249-262. Stein S., and M. Wysession, (2003), Inverse problems, in An introduction to seismology, earthquakes, and earth structure, 415 – 442, Blackwell publishing, Singapore. Syracuse, M. E., P.E. van Keken, G. A. Abers (2010), The global range of subduction zone thermal models, Phys. Earth Planet. Inter. 183, 73-90. Tichelaar, B. W., and L.J. Ruff (1993), Depth of seismic coupling along subduction zones, J. Geophys. Res, 98(B2), 2017–2037. Uchida, N., J. Nakajima, A. Hasegawa, and T. Matsuzawa (2009), What controles interplate coupling? : Evidence for abrupt change in coupling across a boarder between two overlying plates in NE Japan subduction zone, Earth Planet. Sci. Lett., 283(1-4), 111-121.

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Wang, K., R.D. Hyndman, and M. Yamano (1995), Thermal regime of the southwest Japan subduction zone: Effects of age history of the subducting plate, Tectonophysics, 248, 53-69. Watts, A. B. (2001), Isostasy and Flexure of the Lithosphere,458 pp., Cambridge Univ. Press, New York Wells, D. L., and K. J. Coppersmith (1994), New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement, Bull. Seismol. Soc. Am., 84, 974-1002. Wiens, D. A., S. Pozgay, J. Conder, E. Emry, M. Barklage, H. Shiobara, and H. Sugioka, (2007), Seismogenic characteristics and seismic structure of the Mariana Arc System: Comparison with Central America, In: Workshop to Integrate Subduction Factory and Seismogenic Zone Studies in Central America, edited by Silver, E., T. Plank, K. Hoernle, M. Protti, G. Alvarado, and V. Gonza ́ lez, Heredia, Costa Rica, 121.

APPENDICES

APPENDIX A GRID SEARCH ALGORITHM

53

54

55

APPENDIX B LEAST SQUARES INVERSION ALGORITHM

56

57

58

59

60

61

62

63

64

FOR FIGURE 3.3

APPENDIX C COPY RIGHT PERMISSIONS

65

66 FOR FIGURE 3.3

67 FOR FIGURES 2.5 & 2.6

6/19/13 1:54 PM

68

FOR FIGURE 2.4

Suresh Dande

permission to copy Jeanette Hammann To: Suresh Dande

Wed, Jun 19, 2013 at 12:43 PM

Dear Suresh, Thank you for your message. Yes, permission is granted for use of the figure in your thesis as described below. Citation of the source in the style of your publisher is all that is needed. Best regards, Jeanette Jeanette Hammann Associate Director, Publications Geological Society of America 3300 Penrose Place - P.O. Box 9140 Boulder, CO 80301-9140 1-303-357-1048 fax 1-303-357-1073 [email protected]

On Wed, Jun 19, 2013 at 11:33 AM, Suresh Dande wrote:

Hello GSA, This is Suresh Dande, a Geophysics graduate student at Southern Illinois University, Carbondale, IL, USA. My thesis work is on "Determination of the Down-dip limit of the Tonga seismogenic zone using OBS data". As part of my thesis I used a figure from a paper on "The role of subduction erosion on seismicity", which is published in Geology journal. The author and publication details are: Susan L. Bilek, May 2010, v. 38; no. 5; p. 479-480; doi: 10.1130/focus052010.1. I used Figure 1 to show the erosional and accretionary margins. Since I have used that I need your permission in order to submit my thesis to graduate school. Therefore, I request you an email that shows your permission and I will include that email in the appendices of my thesis. Thank you for your time and consideration --------------------------------------Suresh Dande Graduate Teaching Assistant Geology Department Southern Illinois University,

6/19/13 1:54 PM

69 Carbondale, IL, USA. Mobile: 6183036124 Off. 6184537384 E-mail: [email protected] http://www.linkedin.com/in/ sureshdandegeo ----------------------------------------

6/19/13 3:25 PM

FOR FIGURE 1.2

70 Suresh Dande

Permission arnauld heuret Reply-To: arnauld heuret To: Suresh Dande

Tue, Jun 18, 2013 at 5:53 PM

Hello Suresh, Thanks for your interest on my work You have my permission to use the figure 2 of my paper "Physical characteristics of subduction interface type seismogenic zones revisited" for your thesis work on "Determination of the Down-dip limit of the Tonga seismogenic zone". Best regards, Arnauld Heuret

De : Suresh Dande À : [email protected] Envoyé le : Mardi 18 juin 2013 18h27 Objet : Permission

Hello Dr. Arnauld Heuret, This is Suresh Dande, a Geophysics graduate student at Southern Illinois University, Carbondale, IL, USA. My thesis work is on "Determination of the Down-dip limit of the Tonga seismogenic zone". As part of my thesis I used a figure from your paper on "Physical characteristics of subduction interface type seismogenic zones revisited". I used figure 2 to show the parameters defining the subduction parameters. It is a great figure to easily understand the geometry of the seismogenic zone. Since I have used that I need your permission in order to submit to my graduate school. Therefore, I request you an email that shows your permission and I will include that email in the appendices of my thesis. Thank you for your time and consideration ------------------------------ --------Suresh Dande Graduate Teaching Assistant Geology Department Southern Illinois University, Carbondale, IL, USA. Mobile: 6183036124 Off. 6184537384

6/19/13 3:25 PM

71 E-mail: [email protected] http://www.linkedin.com/in/ sureshdandegeo ------------------------------ ----------

72 VITA Graduate School Southern Illinois University Suresh Dande [email protected] Acharya Nagarjuna University Bachelor of Science, April 2005 Andhra University Master of Science in Geophysics, April 2009 Thesis Title: Estimation of Down-dip limit of the Tonga Seismogenic from Ocean Bottom Seismograph data. Major Professor: James A. Conder