Slab buckling and its effect on the distributions and focal mechanisms of deep-focus earthquakes

Geophysical Journal InternationalGeophys. J. Int. (2013) 192, 837–853 doi: 10.1093/gji/ggs054

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Slab buckling and its effect on the distributions and focalmechanisms of deep-focus earthquakes

R. MyhillDepartment of Earth Sciences, Bullard Laboratories, University of Cambridge, Cambridge CB3 0EZ, United Kingdom∗. E-mail: [email protected]

Accepted 2012 November 1. Received 2012 October 29; in original form 2012 June 10

S U M M A R YThis integrated study of deep earthquake locations and focal mechanisms investigates therelationship between the shape of subducting slabs and seismic behaviour in Wadati-Benioffzones. High quality earthquake locations are used to map the shapes of subducting slabs whichhave reached the upper-lower mantle boundary. The resulting slab models reveal the presenceof large slab folds in the mantle transition zone. The distributions and focal mechanisms ofdeep earthquakes are analysed to determine whether these folds have a role in governingWadati-Benioff zone seismicity.

Bands or lineations of dense seismicity are associated with the hinge zones of identifiedfolds. The focal mechanisms of earthquakes within these bands reveal that the mapped foldhinges are commonly perpendicular to the directions of maximum coseismic extension andcompression. The hinges plunge at a variety of angles, resulting in systematic deviations fromthe downdip stress field expected within planar slabs. Slab synforms are typified by earthquakefocal mechanisms indicating in-plane compression (e.g. Izu-Bonin, Tonga), while antiformshave earthquake focal mechanisms indicating in-plane extension (e.g. Solomons) or a mixtureof in-plane compression and extension (e.g. Tonga).

Slab buckling explains both the clustering of earthquakes and the observed focal mechanismorientations within fold hinges. The localization of strain within buckle zones results inseveral of the peaks observed in regional earthquake depth distributions. During buckling, thedirections of maximum shortening and extension are expected to be perpendicular to the foldhinges, in agreement with deep earthquake moment tensors. Displacement of the minimum-strain surface away from the centre of each seismogenic zone can explain the predominanceof in-plane compression within synforms and in-plane extension within antiforms. Morecomplex local variation in focal mechanism orientations in the Tonga slab can be explainedby a superposition of in-plane compression and bending strain.

Buckling appears to be a common mechanism facilitating convergence between subductingslabs and the lower mantle. The consequent rotation and translation of fold limbs may explainthe discrepancy between estimates of convergence based on subduction velocities and long-term coseismic strain.

Key words: Seismicity and tectonics; Subduction zone processes; Dynamics of lithosphereand mantle; Folds and folding; High strain deformation zones.

1 I N T RO D U C T I O N

Earthquakes with hypocentral depths >60 km are generally ob-served only in areas of current or recent subduction. This deepseismicity forms narrow, inclined Wadati-Benioff zones which indi-cates the presence of cold lithosphere within hot convecting mantle(Isacks & Molnar 1971). The global frequency of earthquakes de-creases exponentially between the surface and ∼300–350 km depth,after which a broad secondary peak is observed at ∼550 km depth

∗Now at Bayerisches Geoinstitut, University of Bayreuth, 95440 Bayreuth,Germany

(Sykes 1966; Isacks et al. 1968). Several Wadati-Benioff zonesreach 670–680 km depth, but do not appear to extend into the lowermantle (Stark & Frohlich 1985).

The distributions of earthquakes vary between Wadati-Benioffzones. Seismicity in younger or more slowly subducting slabs isusually restricted to the upper 300 km of the mantle (e.g. Wortel1982). In contrast, slabs formed of older or more rapidly subductinglithosphere are often associated with Wadati-Benioff zones whichare continuous throughout the upper mantle. Clusters and elon-gate zones of increased seismicity are common in several of theseWadati-Benioff zones, most notably in the slab beneath the TongaIslands (Giardini & Woodhouse 1984).

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Subduction zones also exhibit variability in earthquake focalmechanism orientations (Isacks & Molnar 1971). In regions whereseismicity is restricted to <300 km depth, earthquakes typicallyhave focal mechanisms indicating that the slab is thinning andextending downdip. Wadati-Benioff zones which extend beyond300 km depth (such as South America) often have intermediate-focus (60–300 km) earthquakes indicating downdip extension anddeep-focus (300–700 km) events indicating downdip compression.Slabs which have reached the base of the upper mantle typicallyexperience dominant downdip compression at all depths. This is in-ferred to be the result of increased resistance to subduction caused bya viscosity jump across the upper-lower mantle boundary (Isacks &Molnar 1971; Vassiliou 1984).

These broad statements disregard significant additional complex-ity in earthquake distributions and focal mechanism orientationsnoted in more recent studies (Apperson & Frohlich 1987; Chenet al. 2004). At intermediate depths, double seismic zones are com-monly observed, many (but not all) of which indicate compressionin the upper plane and extension in the lower plane (e.g. Engdahl &Scholz 1977; Brudzinski et al. 2007). To further complicate matters,earthquakes in several slabs have focal mechanisms with principalaxes not aligned with the local slab reference frame, or aligned ina way not expected from a slab experiencing downdip compressionor extension (e.g. Marianas, Aleutians; see Apperson & Frohlich1987; Chen et al. 2004). Apperson & Frohlich (1987) report that 50per cent of all deep-focus earthquake P-axes lie more than 28◦ awayfrom the downdip direction. The P (T)-axis of an earthquake fo-cal mechanism corresponds to the direction of maximum coseismiccompression (extension). The axis orthogonal to P and T is denotedthe B or ‘null’ axis.

2 P O T E N T I A L FA C T O R S C O N T RO L L I N GWA DAT I - B E N I O F F Z O N E S E I S M I C I T Y

Earthquake activity requires a source of stress and a material thatcan experience unstable strain localization. The negative buoyancydriving subduction and viscous resistance to flow are importantsources of tensional and compressional stress in subducting slabs(e.g. Isacks & Molnar 1971; Vassiliou et al. 1984; Vassiliou & Hager1988). In particularly cold slabs, low density olivine may be pre-served metastably in the transition zone, introducing an additionalcomponent of in-plane compression (Bina 1997; Bina et al. 2001).The patterns of flow in the mantle relative to the slab are likely tomodify the detailed pattern of extension and compression withinsubducting slabs (Gurnis et al. 2000; Carminati & Petricca 2010),which may consequently influence levels of seismic activity.

Slab morphology modifies the state of stress within subduct-ing slabs. For example, bending and unbending have been suc-cessful in explaining the apparent state of stress in double seis-mic zones at intermediate depths (e.g. Engdahl & Scholz 1977).Along-strike tension and compression at intermediate depths inthe Marianas and Aleutians slabs can be explained by changes inalong-strike slab curvature (Creager & Boyd 1991; Chen et al.2004). At >300 km depth the role of slab morphology is less clear.Apperson & Frohlich (1987) conduct a global study of Wadati-Benioff zone seismicity and conclude that the majority of deep-focus earthquake focal mechanism orientations are not controlledby slab shape in any simple way. Nothard et al. (1996) show that thedistribution of earthquakes in the Tonga slab cannot be explained bythe end-member scenario where slab deformation is prescribed bya rigid mantle wedge ‘template’. Nevertheless, numerical modelsincorporating the 3-D shape of subducting slabs are able to match

many of the broad features of deep seismicity (Alpert et al. 2010;Alisic et al. 2010; Bailey et al. 2012).

Local variations in focal mechanism orientations have led to sug-gestions that volume changes may contribute to stress fields withinsubducting slabs. Double seismic zones with their upper planesin compression can by explained by thermal stresses (Fujita &Kanamori 1981), providing an alternative to stresses induced byunbending. The negative volume change as olivine reacts to formwadsleyite or ringwoodite has also been suggested as a source ofstress facilitating deep-focus seismicity (Wiens et al. 1993; Guestet al. 2003, 2004). The importance of these volume changes as lo-cal sources of stress remains uncertain; it is possible that they arelargely relaxed during phase nucleation and growth (Karato 1997).

Whatever the sources of stress in Wadati-Benioff zones, the local-ized deformation associated with earthquakes requires an appropri-ate slab rheology. If the mechanism responsible for deep earthquakegeneration is not a strong function of pressure or mineralogy, thendistributions and moment release within individual slabs will cor-relate well with concentrations of stress. Indeed, some features ofWadati-Benioff zone seismicity can be recreated with both weak(e.g. Tao & O’Connell 1993) and strong (e.g. Billen & Hirth 2007)slabs (see Alisic et al. 2012, for a recent review). Bilek et al. (2005)suggest that the relative levels of seismic activity between subduc-tion zones reflect the degree of lithospheric weakening at the trench.Nevertheless, the propensity for earthquake generation may also bea function of slab mineralogy. In this case, distributions of earth-quakes may not correlate with regions of high stress. For example,the broad peak in deep-focus seismicity at ∼500 km depth has beenvariously attributed to (1) transformational faulting in metastableolivine (Green & Burnley 1989; Kirby et al. 1996) and garnet (Es-tabrook 2004), (2) adiabatic shear instabilities (Hobbs & Ord 1988)promoted by weak, fine grained wadsleyite (Karato et al. 2001), or(3) to embrittlement related to fluid released from hydrous phasessuch as antigorite, phase A and brucite (Isacks et al. 1968; Omoriet al. 2004).

Despite the potential of several physical mechanisms to producea peak in seismic depth distributions at 400–600 km depth, thebreadth of the observed peak represents a composite of different re-gional maxima (e.g. Sykes 1966) with characteristics that cannot beattributed easily to known mineral reactions. This study seeks to as-sess whether the distinct regional characteristics of seismicity canbe explained without appealing to specific earthquake-generatingmechanisms. At intermediate depths, much of the range and distri-bution of different earthquake focal mechanisms can be explainedby variations in slab shape (e.g. Chen et al. 2004). The followinganalysis investigates the potential role played by complexities inslab shape at >300 km depth.

Contour maps of Wadati-Benioff zone seismicity (Gudmunds-son & Sambridge 1998; Hayes et al. 2012) have revealed the pres-ence of kinks and folds in several deeply subducted slabs. Theseare prime locations for concentrations of stress and strain, andmay indicate locations where slabs are buckling in the upper man-tle. Buckling has been discussed in the context of the Tonga slab(Giardini & Woodhouse 1984) and modelled numerically (House-man & Gubbins 1997). If earthquake distributions reflect distribu-tions of stress due to buckling, then deep-focus seismicity shouldexhibit the following characteristics:

(i) High levels of seismic activity close to the hinge zones of slabfolds.

(ii) Alignment of earthquake focal mechanisms such that nullaxes are commonly parallel to the hinge and P- and T-axes areparallel and perpendicular to the local slab normal.


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(iii) Spatial separation of different focal mechanism types, withincreasing in-plane compression towards the core of each fold.

Here, I constrain the locations and characteristics of folds withinseveral slabs in the western Pacific. These details are used to com-pare the distributions and focal mechanisms of deep-focus earth-quakes with the behaviour expected during slab buckling.

3 M E T H O D O L O G Y A N D DATA S E T S

3.1 Constraining slab shape

Deep earthquakes are primarily confined to the interiors of down-going plates, where temperatures are sufficiently low to enable seis-micity at geological strain rates. The locations of earthquakes withinWadati-Benioff zones can therefore be used to estimate the shapes ofsubducting slabs (e.g. Apperson & Frohlich 1987; Gudmundsson &Sambridge 1998; Chen et al. 2004; Hayes et al. 2012).

Wadati-Benioff zones in the mantle transition zone exhibit mor-phologies which cannot be approximated as 2-D planar or axisym-metric (e.g. Gudmundsson & Sambridge 1998). Rotation of deepearthquake focal mechanisms into the local slab reference frametherefore requires an effort to model slab shape in three dimen-sions. Two existing data sets contain contour sets or grids definingapproximate surfaces of subducting slabs based on deep seismicity.The Regionalized Upper Mantle (RUM) seismic model (Gudmunds-son & Sambridge 1998) includes contours defining the surface ofthe major subducting slabs worldwide. The Slab 1.0 project (Hayeset al. 2012) consists of computed grids of slab shape derived fromboth passive and active-source seismological data. The modellingstrategies in both projects favour smooth surfaces, removing someof the subtle features constrained by the distribution of seismicity.Furthermore, the Slab 1.0 modelling procedure cannot accuratelymap overturned slabs (Hayes et al. 2012). For these reasons, thecurrent study includes the construction of a new set of slab models.

I use well-constrained earthquake locations from the EHB cata-logue between 1960 January and 2007 October (Engdahl et al. 1998,Engdahl, personal communication) to approximate the best-fittingsurface to seismicity in three dimensions. Earthquake locations arenot used if they are of low quality (standard error >35 km; Engdahlcode XEQ), have a standard error in depth >15 km (LEQ) or wherethe maximum azimuthal gap of teleseismic observations is greaterthan 180◦ (codes prefixed with a Z).

The strategy used to find the best-fitting surface to seismicityis illustrated in Fig. 1. First, the best-fitting plane to seismicity isfound. An adjustable tension continuous-curvature surface-griddingalgorithm (Smith & Wessel 1990) is used to find the optimal surfaceby calculating a set of deviations from the best-fitting plane. Toavoid surfaces with areas that are highly oblique to the averageslab plane, the Izu-Bonin-Marianas, Solomons and Tonga Wadati-Benioff zones are subdivided before analysis.

Individual earthquake hypocentres are scattered around the coldcore of the slab and are subject to location errors. For this reason,the surface to seismicity is fitted to average earthquake locations,calculated for a series of boxes with square cross-sections parallelto the average slab plane. Block spacings were chosen to maximizedetail in the slab models while avoiding artefacts due to the sparsityof earthquake hypocentres. In this study, block spacings of 50–150 km were used (Table 1). Comparisons with the slab modelsproduced by Gudmundsson & Sambridge (1998) and Hayes et al.(2012) are provided as supporting information.

Figure 1. A graphical representation of the Wadati-Benioff zone surface-fitting and focal mechanism-orienting procedure. (a) High quality earth-quake locations are selected from the EHB catalogue (Engdahl et al. 1998)and converted into cartesian coordinates. (b) The best-fitting plane to theselocations is found. (c) The surface fitting algorithm of Smith & Wessel (1990)is used to find the best fit surface (where the z-vector is perpendicular to thebest-fitting plane). The EHB earthquake locations are projected onto thissurface. (d) The best-fitting great circle to the slab poles at each projectedearthquake location is used to constrain fold orientations. The axial planeis found by bisecting the interlimb angle. (e) The slab poles at projectedEHB earthquake locations are used to rotate gCMT focal mechanisms intothe local slab reference frame. Orientation clustering is used to colour eachearthquake according to similarities between focal mechanisms.

It is assumed that the surface of seismicity determined here faith-fully reflects the shape of the subducting slab. This is a reasonable as-sumption; proposed deep-focus earthquake generating mechanismsare all temperature dependent (e.g. Hobbs & Ord 1988; Green &Burnley 1989; Omori et al. 2004), such that earthquakes shouldcluster around the surface defined by the parts of the slab withthe lowest temperature, ∼20–30 km below the upper slab interface(Emmerson & McKenzie 2007). The averaging of hypocentral lo-cations from double seismic zones (Wiens et al. 1993; Iidaka &Furukawa 1994; Peacock 2001) will produce similar results to aver-aging of single zones. Systematic location errors (e.g. Syracuse &Abers 2009) should have little effect on the determination of slabshapes in the mantle transition zone.

3.2 Finding fold hinges and axial planes

The technique used to obtain the orientation of fold hinges from eachslab model is adapted from the β-diagram procedure commonlyused in structural geology. First, a point on the Earth’s surfaceis chosen to provide a reference frame for the reporting of poleand hinge orientations. The locations for each slab are providedin Table 1. Next, the poles to the slab are found at the locationscorresponding to the high quality EHB catalogue hypocentres. Thebest-fitting great circle to these poles provides an estimate of theorientation of fold hinges within each slab (Fig. 1).

Irregularities in the modelled slab surface along the region ofgreatest curvature result in small variations in the plunge and trendof each hinge. To estimate the locations of fold hinges, the axialplanes of each fold are found by bisecting the limbs either sideof the region of greatest curvature. The hinges drawn in each ofthe diagrams in Section 5 (Figs 3–10) represent the locus of pointswhere the modeled slab surface is orthogonal to the axial plane. This


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Table 1. Estimated geometrical parameters for major folds in the western Pacific slabs. Each foldis determined from the distribution of deep seismicity and described in the main text. Block lengthdescribes the side length of the boxes used to average earthquake locations. The centres of the cross-sections were used as reference points at which to define the orientations of each fold hinge and axialplane. The orientations of the fold hinges are given in plunge/trend form and the axial planes using dipdirection/dip.

Region Block length (km) Centre of cross-section Hinge (p/t) Axial plane (d-dir/d)

Kurils 150 [51.27◦N, 142.13◦E] 28/008 088/71Izu-Bonin 100 [29.03◦N, 137.15◦E] 10/156 077/45Marianas 100 [17.50◦N,143.01◦E] – –West Solomons 50 [03.05◦S, 150.25◦E] 40/257 224/45East Solomons 60 [04.50◦S, 156.10◦E] 01/159 242/15South Tonga 75 [25.25◦S, 175.99◦W] 08/010 094/50North Tonga — [18.15◦S, 178.88◦W] 45/135 113/47

technique provides a reasonable estimate of hinge location even forslab folds that are not perfectly cylindroidal.

3.3 Rotating focal mechanisms into the slab referenceframe

Focal mechanisms are taken from the gCMT catalogue between1976 January and 2011 July (Dziewonski et al. 1981; Ekstrom et al.2012). Each mechanism is projected into the local slab referenceframe by translating the EHB catalogue location for that earthquake(or the gCMT catalogue location for events after 2007 October) ontothe best-fitting surface to seismicity along the normal to the averageslab plane (Fig. 1). Most events are positioned less than 20 kmfrom the surface, so the difference in location between this plane-normal mapping and the surface-normal (least-distance) mappingis small. The local pole to the surface is then used to rotate eachfocal mechanism into the coordinate system of the slab.

Fault plane solutions are derived from the double-couple com-ponent of the moment tensor. These are usually the dominant com-ponent, but compensated linear vector dipole (CLVD) componentsare sometimes significant (e.g. Kuge & Kawakatsu 1993; Frohlich1995). In this study, the CLVD components are removed, both forease of analysis and because determination of the absolute size ofmoment tensor eigenvalues is complicated by uneven station cover-age and unmodelled near-source velocity structure such as high andlow velocity channels within subducting slabs (Kuge & Kawakatsu1993; Tada & Shimazaki 1994).

3.4 Visualizing variations in focal mechanism orientation

In regions of dense seismicity, plotting every focal mechanism ontomaps and cross sections produces cluttered images that are difficultto analyse. Several methods have previously been used to simplifythis information and aid interpretation. Regional summation of mo-ment tensors (e.g. Bailey et al. 2012) reduces the number of focalmechanisms at the risk of combining dissimilar events. Plotting ori-entation information such as P- and T-axes on lower hemisphereplots preserves information from individual events but removesspatial information (e.g. Vassiliou 1984; Chen et al. 2004). Theconventional description of earthquakes as downdip P, T or B (orany intermediate) enables focal mechanism information to be plot-ted on a ternary diagram (Frohlich 1992), but using only a singleternary diagram can make dissimilar mechanisms look identical.For example, events with downdip P axes events are mapped to thesame point regardless of the angle between the T (or B) axis andalong-strike vector.

If some non-uniqueness in mapping can be tolerated, encodingof moment-tensor orientation can be based on some measure offocal mechanism similarity, rather than an explicit relationship be-tween the principal axes and the orientation of the slab. There aremultiple ways to assess similarity between focal mechanisms (seeTape & Tape 2012). In this study, similarity in B-axis orientation isimportant. The minimum 3-D rotation angle ξ 0 (Kagan 1991) be-tween mechanisms provides a suitable measure of focal mechanismsimilarity in this case. I use the group-mean hierarchical clusteringscheme of Rowe et al. (2002) to sort the earthquakes into groupsaccording to their dissimilarity (1 − ξ 0/120). The number of clus-ters is varied to provide a balance between single-cluster variabilityin focal mechanism and the required level of interpretation for eachregion. Each cluster is assigned a unique colour for plotting pur-poses.

4 S T U DY R E G I O N S

To study the relationship between slab shape and deep-focus seis-micity, the morphology of the slab must be sufficiently constrainedby the seismicity. This requirement is satisfied by the Kurils-Kamchatka, Izu-Bonin, Marianas, Tonga-Kermadec and Solomonsslabs, which all have seismicity extending to the base of the uppermantle (Fig. 2). With the exception of the Solomons slab, all ofthese subduction zones have almost continuous seismicity from thesurface to 600–700 km depth. Despite the scarcity of deep earth-quakes in the Solomons Wadati-Benioff zone, the distribution ofseismicity is sufficient to estimate the shape of the slab.

The slabs studied here contain the majority of all deep-focusearthquakes. Not included in the current analysis are the Philip-pines and Java-Sunda-Banda Wadati-Benioff zones, which are wellapproximated by simple slab morphologies (Hayes et al. 2012).Brief descriptions of the deep-focus seismicity in both of theseslabs are included as supplementary materials. A few deep-focusearthquakes also occur beneath South America, New Zealand andSpain, but slab shape and continuity in these regions are poorlyconstrained as a result of large gaps in the distribution of seismicity.

5 R E S U LT S

5.1 Izu-Bonin

The Izu-Bonin slab is the result of the Pacific Plate subductingbeneath the Philippines plate between Japan and the Volcano Is-lands. At 100–300 km depth, the slab is slightly overturned at thesouthern end of the study area. The dip decreases further along the


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Figure 2. Seismicity of the western Pacific and eastern Asia. Coloured dotscorrespond to high quality EHB locations, coloured according to hypocentraldepth. Major subduction zone systems which are active throughout the uppermantle are named. The regions analysed in this study are outlined.

subduction zone; at the northern end of the study area the slab hasa 40–50◦ dip. At 300–500 km depth, the dip of the slab decreasesto 0–30◦ along a bend whose hinge plunges 10–15◦ towards thesoutheast (marked by synform symbols in Fig. 3). A broad, denseband of seismic activity accompanies this hinge.

At intermediate depths, earthquake focal mechanisms exhibit amixture of in-plane compression (i.e. compression in the local planeof the slab, but not necessarily downdip; orange in Fig. 3), downdipextension (blue) and along-strike shortening (cyan). The dense bandof seismicity associated with the fold hinge at 300–500 km depthis dominated by earthquakes indicating in-plane compression (or-ange). These earthquakes have B-axes which are parallel to thefold hinge, rotated 10–20◦ clockwise from the along-strike direc-tion. The deepest earthquakes mostly have gCMT solutions with Baxes oriented approximately slab-normal and P-axes downdip (lilac,dark orange events). The intersections of the northeast-strikingnodal planes and the best-fitting surface to seismicity are colinearwith narrow streaks of deep-focus earthquakes, which may repre-sent shear zones within the subducting slab (Lundgren & Giardini1992).

Most of the deep Izu-Bonin slab experiences relatively little seis-micity. The clustering of earthquakes close to the major synform isin marked contrast to this sparse seismicity and indicates a muchhigher rate of deformation. The dense seismicity and orientationof focal mechanisms are in excellent agreement with the hypoth-esis that buckling is currently taking place in the Izu-Bonin slab.The shallow plunge of the hinge means that the inferred buck-ling can efficiently accommodate convergence between the slab andupper-lower mantle boundary. The lack of in-plane extension withinthe deep fold in the slab suggests that the surface of minimumstrain lies below the seismogenic zone (see Section 6 for furtherexplanation).

5.2 Kurils-Kamchatka

The Kurils-Kamchatka slab represents the part of the Pacific Platewhich is currently subducting beneath the Sea of Okhotsk, northof Japan. The Wadati-Benioff zone is almost planar north of 50◦N

(Fig. 4). Further south it is gently warped about a synformal hingeplunging northwards at ∼28◦ (Table 1, dashed line in Fig. 4). A moresubtle synform hinge plunges northwestwards in the slab model(dotted line in Fig. 4).

Seismicity in the Kurils-Kamchatka slab is patchy at >200 kmdepth. A diffuse band of earthquakes plunges northeastwards atthe southern end of the study area, typified by strike-slip events(coloured green and teal). Weak clustering of earthquakes is ob-served at 400–500 km depth at the northern half of the slab (−7◦

to −1◦ in Fig. 4d).The identified hinge zone in the Kurils-Kamchatka slab is not

associated with any significant increase in the level of seismicity.However, it does separate regions with distinct focal mechanismtypes. At intermediate depths, downdip extensional events (blue)dominate in the south, and downdip compressional events (pink)dominate in the north. The overlap region between the two inferredhinges exhibits a double seismic zone (Kao & Chen 1994). Thehinge zone is also the site of a transition in deep-focus earthquakefocal mechanisms. In-plane shear gCMT solutions (green) dominatesouth of 47◦N, while downdip compressional events dominate northof 49◦N (pink).

Deep-focus earthquakes in the hinge zone typically have in-planecompressional focal mechanisms (red, brown). The direction ofmaximum compression for these events is not downdip, makingthem distinct from those at the northern end of the study area. In-stead, the B-axes are rotated towards the orientation of the modelledslab hinges.

At the northern end of the Kurils-Kamchatka slab, the downdipcompressional stress field is the expected consequence of resistanceto subduction of a subplanar slab into the lower mantle, as proposedby Isacks & Molnar (1971). Further south, the influence of theupper-lower mantle boundary appears to wane, as indicated by thetransition to downdip extensional intermediate-depth earthquakes(Kao & Chen 1994) and strike-slip deep-focus events. The focalmechanism orientations in the hinge zone suggests that the slab foldis currently influencing the local strain field. However, the lack ofintense seismicity in this region suggests that folding is significantlyslower than in the Izu-Bonin slab. This interpretation is consistentwith the orientation of the fold, which pitches steeply in the plane ofthe Wadati-Benioff zone and is therefore poorly orientated to takeup convergence between the slab and the lower mantle.

5.3 Marianas

The Marianas slab represents a subducted fragment of the PacificPlate, being overridden by the Philippines Plate between the Vol-cano Islands and Guam. Deep-focus earthquakes are restricted toan arc extending from 16◦N to 20◦N. The best-fitting model fromthe distribution of deep seismicity reveals a saddle-shaped Wadati-Benioff zone which dips steeply towards the west between 100 and400 km depth, becoming overturned towards the base of the uppermantle (see contours in Fig. 5).

Available deep-focus earthquake focal mechanisms indicate thatthe overturned part of the Wadati-Benioff zone is undergoingdowndip compression. Although most of the focal plane solutionshave T-axes perpendicular to the modelled surface (red), there are afew earthquakes which have along-strike T-axes (blue, cyan, green).The two types of earthquakes are spatially separate; the events indi-cating along-strike extension/downdip compression occurred withina 40–50 km wide strip at 500–600 km depth. The upper boundary


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Figure 3. Analysis of earthquakes in the Izu-Bonin slab. (a) Map view of the slab and earthquakes. Bathymetry is shown east of the trench. Grey contourscorrespond to the best-fitting surface to seismicity. EHB locations are plotted as grey dots, while earthquakes with gCMT solutions are plotted as largercoloured dots. Each colour represents a different focal mechanism type, as shown in (c). For ‘downdip’ compressional events (orange), B-axes are also drawn.The dashed black line with synform symbols marks the computed hinge of a concave-up fold in the slab. (b) EHB earthquake locations looking along the hingeof the fold, coloured according to their distance from the closest event. The orientation and position of the fold axial plane is shown as a black dashed line. (c)Focal mechanism types (lower hemisphere azimuthal equal-area projection), rotated into the local orientation of the slab. Downdip is down, and inward-facingslab-normal into the page. Individual P- and T-axes are superimposed on each focal mechanism type. (d) Cross-section projected along the line A–A′. Elementsare as described in (a). Grey contours correspond to the distance from the line of section to the best-fitting surface to seismicity.

of this zone plunges shallowly towards the south at a similar angleto the B-axes of the shallower in-plane compressional earthquakes.

The hypothesis proposed in Section 2 is inconsistent with thechanges in focal mechanism observed in the Marianas slab. The

mechanisms are also different to those expected within a planarhomogeneous slab deforming by pure shear. The exchange of T-and B-axes and single in-plane extensional earthquake within thestrip could indicate a component of bending in addition to the


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Figure 4. Analysis of earthquakes in the Kurils slab. (a) Map view of the slab and earthquakes. Bathymetry is shown southeast of the trench. Grey contourscorrespond to the best-fitting surface to seismicity. EHB locations are plotted as grey dots, while earthquakes with gCMT solutions are plotted as larger coloureddots. Each colour represents a different focal mechanism type, as shown in (c). For in-plane compressional events (brown, reds, peach), B-axes are also drawn.The dashed black line with synform symbols marks the computed hinge of a concave-up fold in the slab. A dotted line marks a less prominent hinge. (b) EHBearthquake locations looking along the computed hinge of the fold, coloured according to their distance from the closest event. The orientation and positionof the fold axial plane is shown as a black dashed line. (c) Focal mechanism types (lower hemisphere azimuthal equal-area projection), rotated into the localorientation of the slab. Downdip is down, and inward-facing slab-normal into the page. Individual P- and T-axes are superimposed on each focal mechanismtype. (d) Cross-section projected along the line A–A′. Elements are as described in (a). Grey contours correspond to the distance from the line of section to thebest-fitting surface to seismicity.

dominant downdip compressional field, but earthquake locationsdo not indicate the presence of a fold at these depths, and there is noidentified double seismic zone to corroborate this possibility. Moredetailed investigations are required to determine the causes of focalmechanism variation in the Marianas slab.

5.4 New Britain-Solomons

The Solomon Sea Plate is currently being subducted under thePacific Plate, beneath New Britain in the west and the SolomonIslands in the east. The sea plate is probably early to mid-Tertiary in


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Figure 5. Analysis of earthquakes in the Marianas slab. (a) Map view ofthe slab and earthquakes. Bathymetry is shown east of the trench. Greycontours correspond to the best-fitting surface to seismicity. EHB locationsare plotted as grey dots, while earthquakes with gCMT solutions are plottedas larger coloured dots with lines corresponding to mechanism B-axes.Each colour represents a different focal mechanism type, as shown in (b). (b)Focal mechanism types (lower hemisphere azimuthal equal-area projection),rotated into the local orientation of the slab. Downdip is down, and inward-facing slab-normal into the page. Individual P- and T-axes are superimposedon each focal mechanism type. (c) Cross-section projected along the lineA–A′. Elements are as described in (a). Grey contours correspond to thedistance from the line of section to the best-fitting surface to seismicity.

age (see review in Honza et al. 1987). Along the New Britain Trenchsubduction velocity is estimated to be 55–130 mm yr−1 (Wallaceet al. 2004). The young age of the plate compared to the Pacificimplies that slab temperatures are higher than in the other regionsinvestigated in this study.

Deep seismic activity beneath New Britain and the Solomonsis sparse but sufficient to estimate the shape of the subductingslab from the surface down to 500–600 km depth. The Wadati-Benioff zone is best visualized as two separate segments (Fig. 6).The western segment dips steeply to the northwest beneath NewBritain. At 350–500 km depth, hypocentral locations are consistentwith an antiform with a hinge plunging westward at 40◦ and alower overturned limb (Table 1, Figs 6b and e). The eastern segmentstrikes northwest, dipping almost vertically between 200 and 400 kmdepth. Hypocentral locations indicate that a synform with a nearlyhorizontal hinge exists at ∼400 km depth (Table 1, Figs 6c andf). A poorly constrained antiform is present in the slab model at450–550 km depth (dotted line in Figs 6a and f).

At >300 km depth, most of the earthquakes within the SolomonsWadati-Benioff zone cluster along lineations. In the western studyarea, a short lineation plunges at ∼40◦ towards the west, colinearwith the antiform hinge identified from earthquake hypocentres.

Earthquakes in this lineation have focal mechanisms have in-planeT-axes and B-axes parallel to the hinge (blue, Fig. 6e).

The most prominent lineation within the eastern segment is co-linear with the synform hinge obtained from the distribution ofseismicity. Available focal mechanisms indicate in-plane compres-sion with B-axes colinear with the lineation (red, Fig. 6f). Theantiform tentatively identified at 450–550 km depth is associatedwith a few in-plane extensional earthquakes with B-axes parallel tothe lineation (blue).

The data presented in Fig. 6 is in excellent agreement with thehypothesis that buckling controls the behaviour of deep-focus earth-quakes in the Solomons slab. Antiforms in the eastern and westernsegments have earthquakes with focal mechanisms that indicate in-plane extension. This is the expected mode of deformation withinthe nose of folds, suggesting that the surface of minimum strainlies deeper within the slab than the seismogenic zone. The in-planecompressional focal mechanisms associated with earthquakes in thesynform hinge are in the orientation expected for deformation inthe core of an active fold.

Buckling is preferred over localized slab thickening or thinningas an explanation for the regions of increased seismicity becauseof the close proximity of earthquakes with in-plane compressionaland extensional mechanisms (Fig. 6e). The antiforms and synformsidentified here can both be attributed to resistance to slab penetrationinto the lower mantle. In this model, the zone of in-plane extensionis a local feature within a slab undergoing net shortening parallel toits average dip-direction.

The relatively low levels of seismic activity and the presenceof narrow lineations of earthquakes distinguish the Solomons slabfrom the other studied slabs. The differences may be related tohigher temperatures within the Solomons slab at 300–600 km depth(see Section 6). Nevertheless, the lack of earthquakes between theeastern and western segments of the Solomons slab requires a dif-ferent hypothesis. It is possible that the slab is torn between the twosegments at 200–700 km depth. Alternatively, as the apparent cur-vature between the two Wadati-Benioff zones remains similar withdepth and the hinge is approximately parallel to the subduction di-rection (Wallace et al. 2004), it is possible that slab material is beingadvected parallel to the hinge without significant deformation.

5.5 Tonga

The Tonga-Kermadec subduction zone accounts for more than halfof all deep-focus seismicity worldwide. Cold slab temperatures (e.g.Emmerson & McKenzie 2007) and high strain rates imposed by thehigh relative plate velocities at the Tonga Trench probably contributeto the conditions required to sustain such dense seismicity. PacificPlate subduction velocities increase from south to north, and exceed100 mm a−1 when back-arc spreading in the overriding plate is takeninto account (Muller et al. 2008).

The Tonga Wadati-Benioff zone is saddle shaped north of 22◦S(Fig. 7). The strike rotates anticlockwise moving north along thezone, while dip increases with depth in the lower half of the up-per mantle. South of 22◦S, a marked decrease in dip is observedat 500 km depth, followed by an increase at 550–600 km depth.At ∼500 km depth the slab may be tearing, with the tear currentlyat ∼23◦S and propagating southwards (e.g. Giardini & Woodhouse1984).

Seismic activity in the Tonga Wadati-Benioff zone generally de-creases between 150 and 250 km depth. A weak increase in seismicactivity at 400 km depth is observed in the northern half of the


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Figure 6. Analysis of earthquakes in the New Britain-Solomons slab. (a) Map view of the slab and earthquakes. Bathymetry is shown south of the trench.Grey contours correspond to the two (east and west) best-fitting surfaces to seismicity. EHB locations are plotted as grey dots, while earthquakes with gCMTsolutions are plotted as larger coloured dots with lines corresponding to mechanism B-axes. Each colour represents a different focal mechanism type, as shownin (d). The dashed black lines with synform and antiform symbols marks the computed hinges of concave-up and convex-up folds in the slab. A dotted linemarks a further possible hinge (discussed in the text). (b, c) EHB earthquake locations looking along the computed hinges of the folds, coloured according totheir distance from the closest event. The orientation and position of the fold axial planes are shown as black dashed lines. (d) Focal mechanism types (lowerhemisphere azimuthal equal-area projection), rotated into the local orientation of the slab. Downdip is down, and inward-facing slab-normal into the page.Individual P- and T-axes are superimposed on each focal mechanism type. (e, f) Cross sections projected along the lines A–A′ and B–B′. Elements are asdescribed in (a). Grey contours correspond to the distance from the line of section to the best-fitting surface to seismicity.

region. At 500–650 km depth an extremely dense band of seismic-ity in the south Tonga region plunges northwards at ∼10◦.

Fig. 8 illustrates the range of gCMT focal mechanisms relativeto the local slab reference frame along most of the Tonga slab,except for the region marked (b) in Fig. 7 (treated separately inSection 5.5.2). Although there must be multiple factors influencing

the distributions of different focal mechanism orientations, severalimportant features can be identified:

(i) The most common mechanism type has a ‘downdip’ P-axisand ‘slab-normal’ T-axis, indicating downdip compression as de-scribed by Isacks & Molnar (1971).


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Figure 7. Study areas along the Tonga subduction zone. Coloured dots rep-resent EHB earthquake locations, coloured according to hypocentral depth.Contours of seismicity are calculated as described in the text. A depth profilethrough A–A′ is shown in Fig. 8.

(ii) The majority of in-plane shear focal mechanisms appearat >400 km depth and indicate downdip compression. The northend of the Tonga subduction zone between 300 and 400 km depth(near A) has a number of in-plane shear mechanisms which have anearly vertical nodal plane.

(iii) Far from being restricted to shallow depths, earthquakes within-plane extensional focal mechanisms are observed along mostparts of the subduction zone system at >400 km depth, especiallyat the southern end of the Tonga slab. Several of the deepest in-planeextensional events at the southern end of the area have downdip B-axes.

Here I present a detailed analysis of two large subregions of theTonga subduction zone [marked (a) and (b) in Fig. 7]. A range offocal mechanism orientations are observed in each region.

5.5.1 South Tonga, 350–700 km depth

Seismicity in the south Tonga slab is sparse between 200 and 300 kmdepth, and increases only slightly down to ∼480 km depth (Fig. 9).A large number of deep-focus earthquakes cluster along two nearlylinear features which strike northnortheast at ∼500 and ∼550 kmdepth (Fig. 9a). The deeper band of earthquakes is further west thanwould be consistent with a planar slab. Its presence has variouslybeen interpreted as evidence for a detached slab fragment (Fischer &Jordan 1991; Fischer et al. 1991), or folding of a single coherent slab(Giardini & Woodhouse 1984). Several well-located hypocentresin the EHB database lie in a ‘bridge’ between the two features,suggesting that the slab is continuous at least as far north as 23◦S, inagreement with Giardini & Woodhouse (1984). The distribution ofseismicity in the south Tonga slab at 500–600 km depth is thereforemost consistent with the existence of a paired fold. The fold ismore developed in the north; the Wadati-Benioff zone is planar slabat 26◦S, but forms a near-horizontal bench between the two fold

Figure 8. Locations and focal mechanisms of deep earthquakes along theprofile A–A′ from Fig. 7, parallel to the Tonga-Kermadec trench. EHB lo-cations are plotted as grey dots, while earthquakes with gCMT solutionsare plotted as larger coloured dots. The three plots show the distribution ofearthquakes with (a) compressional, (b) in-plane shear and (c) extensionalfocal mechanisms. Each colour represents a different focal mechanism type,represented above each section. Mechanism types with few associated earth-quakes or not easily fitting into the categories in (a), (b) or (c) are displayedin (d). Individual P- and T-axes are superimposed on each focal mechanismtype. Downdip is down, and inward-facing slab-normal into the page.

hinges at 23◦S. The best-fitting hinge plunges northwards at ∼10◦

(Table 1). As a result of this plunge, the axial planes superimposedon the cross section in Fig. 9(b) are schematic.

With the exception of the earthquakes around the antiformin the slab, the south Tonga Wadati-Benioff zone is domi-nated by events with focal mechanisms which indicate in-plane,


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Figure 9. Analysis of earthquakes in the south Tonga slab. (a) Map view of the slab and earthquakes. Bathymetry is shown east of the trench. Grey contourscorrespond to the best-fitting surface to seismicity (poorly constrained at intermediate depths). EHB locations are plotted as grey symbols (either dots or starsdepending on their location in the main WBZ or further to the west). Earthquakes with gCMT solutions are plotted as larger coloured symbols. Each colourrepresents a different focal mechanism type, as shown in (e). For ‘downdip’ compressional events (red, orange), B-axes are also drawn. The dashed black lineswith synform and antiform symbols marks the computed hinges of concave-up and convex-up folds in the slab. (b, c, d) Cross-sections projected along the linesA–A′ and B–B′. Elements are as described in (a). Grey contours correspond to the distance from the line of section to the best-fitting surface to seismicity. (e)Focal mechanism types (lower hemisphere azimuthal equal-area projection), rotated into the local orientation of the slab. Downdip is down, and inward-facingslab-normal into the page. Individual P- and T-axes are superimposed on each focal mechanism type.

approximately downdip compression (red, orange). This is mostmarked near to the location of the modelled synform at 480–550 kmdepth. The earthquakes closest to the hinge have distinct focal mech-anism orientations with B-axes rotated towards the hinge (red). Rel-ative to these focal mechanisms, slightly deeper events have B-axesrotated clockwise (orange). The spatial separation and difference inB-axis orientation is most visible in plan view (Fig. 9a). North of24◦S where the slab may be torn (Giardini & Woodhouse 1984),earthquake focal mechanisms indicate a mix of in-plane extension(purple) and shear (green). A few other events at 300–500 km depth

also indicate in-plane extension (blue, purple). These earthquakesconstitute the upper plane of a double seismic zone reported at350–420 km depth (Wiens et al. 1993).

Close to the antiform in the slab, the majority of earthquakes havefocal mechanisms, which indicate in-plane tension (blue, purple) orshear (green). Most of the in-plane tensional focal mechanismshave B-axes which are oriented downdip and perpendicular to theantiform hinge.

A sketch interpretation of the data analysed from earthquakes inthe south Tonga slab is provided in Fig. 9(b). Buckling of the slab


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results in a zone of compression in the core of the mapped synform,as observed in the Izu-Bonin and Solomons slabs. Compressionextends along the entire length of the slab, with zones of in-planeextension restricted to the noses of antiforms. The few in-planeextensional earthquakes above 480 km depth are interpreted as ev-idence for the formation of a broad antiform, although it shouldbe noted that this is not clearly visible from EHB hypocentres.Wiens et al. (1993) interpret the double seismic zone at 350–460 kmas evidence for stresses induced by transformational faulting, butthey acknowledge that bending is also consistent with the observedvariety of focal mechanisms.

The hypothesis that buckling is a major contributor to coseismicstrain in subducting slabs does predict a zone of extension withinthe antiform in the slab, but the observed hinge-parallel extensionis incompatible with folding alone. Along-strike extension can beexplained by the superposition of a downdip compressional strainfield on the strain field due to bending. The observed exchangeof focal mechanism B- and T-axes is the expected result if bothcomponents of the total strain are of similar magnitude.

5.5.2 North Tonga, 500–650 km depth

The northernmost end of the Tonga slab between 500 and 650 kmdepth represents one of the most seismically active volumes in theEarth. Deep-focus earthquakes in this region can be exceptionallylarge and have prolific aftershock sequences. For example, the MW

7.6 event earthquake on 1994 March 9 had 40 aftershocks withMW > 4.5 (Wiens et al. 1994). The Wadati-Benioff zone in planview and cross section appears to be planar (Giardini & Woodhouse1984; Wiens & Snider 2001; Fig. 10), but the densest seismicityis better described as a band plunging southeastwards at an angleof ∼45◦ (Fig. 10b). The sparsely populated Wadati-Benioff zoneabove this band is nearly vertical. Deeper ‘outboard’ earthquakesare displaced southwestwards from the main seismicity.

If the deep north Tonga slab is taken to be subplanar and al-most vertical (ignoring the ‘outboard’ events), then many of thefocal mechanisms have nodal planes subparallel to the slab surface(Figs 10a–d, brown, red, orange mechanisms). Giardini & Wood-house (1984) suggest that this nodal plane corresponds to a narrow

Figure 10. Analysis of earthquakes in the north Tonga slab. (a–d) Results without including ‘outboard’ events (a) Map view of the slab and earthquakes.Grey contours correspond to the best-fitting surface to seismicity. EHB locations are plotted as grey dots. Earthquakes with gCMT solutions are plotted aslarger coloured dots. Each colour represents a different focal mechanism type, as shown in (d). (b, c) Cross sections projected along the lines A–A′ and B–B′.Elements are as described in (a). (d) Focal mechanism types (lower hemisphere azimuthal equal-area projection), rotated into the local orientation of the slab.Downdip is down, and inward-facing slab-normal into the page. Individual P- and T-axes are superimposed on each focal mechanism type. (e–h) Same as(a–d), but the shape approximating the surface to seismicity has been manually adjusted to account for the presence of a fold in the slab along the band ofdensest seismicity. The hinge of this fold is marked as a dashed black line. In-plane compressional events (brown, red, orange) have B-axes plotted (e) in planview and (f) along section A–A′. (g) Section line B–B′ is plotted looking down and to the southeast along the hinge line of the inferred fold in the slab. EHBlocations are shaded according to their distance from the profile plane (with darker symbols closer to the viewer). The modelled slab surface is shown as a lightgrey line. The orientation and position of the fold axial plane is shown as a black dashed line.


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shear zone, facilitating slab movement down and to the west rela-tive to the mantle wedge. Further from the slab surface, the majorityof earthquakes have gCMT focal mechanisms with in-plane P-andT-axes (blue, cyan), indicating extension parallel to the band ofdensest seismicity.

The insights gleaned from other subduction zones can be used toadvance an alternative to the slab-parallel shear-zone interpretation.The band of seismicity plunging towards the southeast is reminis-cent of the clustering of earthquakes observed along the fold hingesin the Izu-Bonin, Solomons and south Tonga study areas. A cross-section perpendicular to this band (Fig. 10g) reveals a fold in theWadati-Benioff zone, with a slightly overturned upper limb and alower limb containing the previously neglected ‘outboard’ earth-quakes.

The study area is too small to accurately constrain the shape ofthe slab with the automated technique used to analyze the otherstudy areas. Instead, the shape is prescribed by assuming that thefold is cylindroidal, with a cross sectional shape defined by the greyline in Fig. 10(g). Re-analysing the gCMT data with this modi-fied slab shape (Figs 10e–h), the focal mechanisms with subverticalnodal planes (brown, red, orange) now indicate in-plane compres-sion. The B-axes of these earthquakes are parallel to the band ofseismicity and fold hinge, as observed in other subduction zones.Moving northeast, away from the surface of the slab, the focal mech-anisms indicate a transition from hinge-perpendicular compressionto hinge-parallel extension via in-plane shear.

The focal mechanisms in the synform in the north Tonga slabmatch the variety observed in the antiform in south Tonga. Likein south Tonga, this range can be attributed to a superposition ofin-plane compressional and bending strain fields in a region ofbuckling. The only difference is that in the south Tonga slab, thenose of the fold is close to the surface of the slab.

6 D I S C U S S I O N

6.1 The origins and development of slab folding

Earthquake location and focal mechanism data support the hypoth-esis that the Izu-Bonin, Marianas, Solomons and Tonga slabs arecurrently folding in the lower half of the upper mantle. This fold-ing is probably the result of hindrance to subduction into the lowermantle imposed by the endothermic ringwoodite → ferropericlase+ perovskite phase transition (e.g. Christensen & Yuen 1984) andaccompanying ∼30-fold increase in viscosity at the upper-lowermantle boundary (e.g. Hager 1984). The history of slab-lower man-tle interaction, patterns of slab rollback and changes in subductionrates along each system are all likely to have contributed to the rangeof hinge orientations determined in this study (Table 1). Interlimbangles are likely to be a function of the amount of convergence sincethe inception of each fold.

Folds can develop in multiple ways. To take two examples whichmay be relevant to subduction zone systems, buckling usually am-plifies folds without hinge zone migration, whereas draping involvestransport of material through fold hinges. Numerical models haveshown that a combination of viscoplastic rheology and rapid roll-back of narrow slabs (widths <2000 km) can result in draping atthe 410 km discontinuity (Schellart et al. 2007). However, the slabsinvestigated in this study exhibit little evidence for unbending in thelower limbs of each fold, suggesting that buckling is the dominantmode of folding.

A cartoon of fold development during buckling of the Izu-Boninslab and its relationship with strain and deep-focus seismicity isshown in Fig. 11. Most of the deep slab is in compression apartfrom the nose of the synform, which is undergoing extension. Thelack of focal mechanisms with in-plane T-axes suggests that the

Figure 11. An interpretation of the earthquake behaviour in the Izu-Bonin Wadati-Benioff zone. (a) Cartoon cross-section of the slab, and its deformationthrough time. The central sketch shows the slab at the present-day. Lines represent the principal direction and magnitude of shortening. Note the high strainrates associated with the bend in the slab. The dashed line represents the boundary between in-plane compression and extension. The latter lies outside theseismogenic zone. (b) The depth distribution of earthquakes. Red bars represent the earthquakes within a cylinder of 50 km radius marking the band ofseismicity associated with the hinge zone.


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region of extension is deforming aseismically, possibly because ofhigher temperatures compared with the seismically active zone ofin-plane compression.

Although most of the seismicity associated with hinges identi-fied in this study is consistent with buckling as proposed in Sec-tion 2, modifications are required to explain the variety of focalmechanism orientations for earthquakes associated with the an-tiform and inferred synform at the southern and northern endsof the Tonga slab. A spatial progression in focal mechanism ori-entation is most clearly visible in North Tonga, where from foldcore to nose focal mechanisms indicate hinge-normal compres-sion, in-plane shear (with hinge-normal compression and hinge-parallel extension) and then hinge-parallel extension. The sameset of mechanisms is observed in the antiform in southern Tonga.The observed progression can be explained by invoking a com-ponent of in-plane uniaxial compression perpendicular to the foldhinge. This interpretation is consistent with the CLVD componentsof deep-focus earthquakes in several slabs, which also indicatethat the eigenvector corresponding to the maximum compressionalstrain commonly has the greatest absolute eigenvalue (Kuge &Kawakatsu 1993; Bailey et al. 2012).

6.2 The distributions of deep-focus earthquakes

Buckling provides a coherent explanation for the presence andshapes of many of the peaks in regional depth distributions ofseismicity recognized by Sykes (1966). For example, the band ofseismicity associated with the shallowly plunging synform hinge inthe Izu-Bonin slab is responsible for the broad peak in the seismicdistribution between 320 and 520 km depth (Fig. 11b). The otherhinges in Table 1 (with the exception of the hinge in the Kurils-Kamchatka slab) are also responsible for peaks in regional earth-quake depth distributions. Each of these contributes to the broadpeak in global depth distributions, and a significant proportion ofthe seismic moment released in the middle of the mantle transitionzone (see Fig. S1).

The relative levels of seismicity in cold slabs may be controlledby the rates of buckling. For example, the highly active folds in theIzu-Bonin and Tonga slabs are ideally orientated to accommodateconvergence between the slab and upper-lower mantle boundary.Sparse seismicity beneath the Kurils is probably the result of amuch slower rate of deformation.

If temperature is the dominant rheological control within slabsin the mantle transition zone, then warm slabs are able to deformviscously at higher strain rates than cold slabs. This may explain thelower levels of seismicity and narrower bands of earthquakes asso-ciated with folds in the Solomons slab. Similar bands of earthquakesare also observed near the base of the upper mantle beneath Chile(e.g. Barazangi & Isacks 1976) and New Zealand (Boddington et al.2004), suggesting that they too may represent slab buckling near thebase of the upper mantle. Beneath South America, the recumbentlimb required to confirm this hypothesis may be represented by iso-lated ‘outboard’ earthquakes east of the deep lineation (Lundgren &Giardini 1994).

6.3 Plate rheology

The shapes of subducting slabs depend strongly on negative buoy-ancy and rheology. Numerical models show that slabs with asmall negative buoyancy deform by viscous flexure, while in-creasing the density contrast results in buckling and thinning

(Houseman & Gubbins 1997). Slabs with stress-dependent vis-cosity exhibit localized deformation in narrow hinge zones. Innature, the stress-dependence of seismic activity will contributefurther to strain localization in subducting slabs. Slab volumes farfrom fold hinges may therefore escape significant deformation inthe upper mantle.

Estimates of slab rheology are complicated by local weak zonesand by the presence of earthquakes. This study suggests that bothof these phenomena influence deformation in subduction zones. Ifthey are important, then failure to account for them by using linearviscous rheologies will result in estimates of slab viscosity whichare much lower than actual material strength (King 2001; Alisicet al. 2012). For example, geoid anomalies (Moresi & Gurnis 1996;Zhong & Davies 1999), numerical modelling (e.g. Houseman &Gubbins 1997) and CLVD components (Bailey et al. 2012) have allbeen used to imply that the effective viscosity of the slab is <200times the upper mantle viscosity. Such estimates are much lowerthan laboratory estimates (e.g. Mei et al. 2010).

6.4 Slab kinematics

Coseismic strain in slabs can be estimated from moment-slip scalingrelations (Kostrov 1974). Such estimates typically underestimatelong-term strain rate because of large rare events not yet repre-sented in earthquakes catalogues. After adjusting for this uncer-tainty, estimated seismic strains are still only a small fraction ofthe total required to keep homogeneously deforming slabs fromentering the lower mantle. For example, the long term seismicstrain rate in the Tonga slab is estimated to be ≤60 per centof the value required to accommodate convergence between theslab and the lower mantle (Holt 1995). The actual percentage islikely to be ≤30 per cent, as Holt (1995) neglects rapid backarcspreading in the South Fiji Basin (e.g. Sdrolias & Muller 2006)in his estimate of subduction rate.

The discrepancy between convergence rate and estimates of longterm seismic strain rate can be explained in several ways. Pa-rameter values for the scaling relationships between moment re-lease and slip may be inaccurate, but it is unlikely that the val-ues can explain such large discrepancies. Direct penetration intothe lower mantle is a plausible explanation for the lack of seis-micity in some slabs, but tomographic studies suggest that theTonga slab is confined to the upper mantle at the present-day(Gurnis et al. 2000). A large amount of aseismic strain could alsoaccount for the relative lack of seismicity, but only if slabs arequite weak. Finally, the assumption that earthquakes reflect homo-geneous strain throughout the slab (e.g. Fischer & Jordan 1991)may be faulty. If coseismic deformation is linked to buckling, alarge amount of convergence can be accommodated by transla-tion and rotation of fold limbs rather than slab deformation. Giventhe results of this study, this is hypothesis is plausible and sug-gests that aseismic deformation may be of minor relevance withincold slabs such as Tonga and Izu-Bonin.

Buckling may influence other aspects of slab and mantlekinematics. Changes in slab shape through time will affectflow in the surrounding mantle (Anderson 2001). Specifically,the space created by the increasing depth of fold hinges islikely to increase trench-perpendicular flow. Slab morphologyhas also been proposed to influence aspects of surface tectonicssuch as trench retreat and backarc spreading (Bott et al. 1989;Schellart et al. 2007).


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7 C O N C LU S I O N S

Buckling is observed in several slabs that have reached the upper-lower mantle boundary, arising from the interaction between thenegative buoyancy of the slab and resistance to flow in the lowermantle. This buckling creates large folds with localized hinge zonesthat can be mapped using the distributions of earthquakes. Promi-nent fold hinges in the Tonga, Izu-Bonin and Solomons slabs arezones of high strain rate, which are marked by bands of earthquakes.The distribution and orientation of these bands is responsible forseveral of the peaks observed in regional earthquake depth distri-butions. Taken together, bands associated with fold hinge zones arethe dominant contributor to the broad peak in earthquake frequencyat 500–600 km seen in compilations of global earthquake depths.

Folding in subducting slabs provides an important control on thefocal mechanisms of deep-focus earthquakes. Earthquakes withinsynforms typically have focal mechanisms with B-axes parallel tothe hinge and T-axes normal to the slab, indicating in-plane com-pression. Within antiforms, P-axes are typically slab normal, indi-cating in-plane extension. The presence of single mechanism typessuggests that the surface of minimum strain often lies well belowthe centre of the Wadati-Benioff zone in regions of bending. Twofolds in the Tonga slab exhibit hinge-normal compression in theircores and hinge-parallel extension towards the noses. The compo-nent of hinge-parallel extension can be explained by a combinationof bending strains and in-plane compression.

This study provides further evidence that interaction between theslab and lower mantle dominates the generation of stress in sub-ducting slabs that have reached the upper-lower mantle boundary.Many of the deep-focus earthquakes with focal mechanisms thatdiffer from the dominant downdip compressional type recognizedby Isacks & Molnar (1971) can be explained without invoking ad-ditional sources of stress.

This paper only considers the subset of Wadati-Benioff zonesthat are continuous throughout the upper mantle; the seismicity inother regions is likely to be controlled by other factors. Even in theslabs studied, some earthquakes remain unexplained. For example,the spatial segregation of earthquakes with different focal mech-anism in the Marianas slab is not clearly associated with folding.Similarly, the range of mechanisms along the Kurils-KamchatkaWadati-Benioff zone are not trivially related to observed changes inslab orientation. Finally, buckling in subducting slabs may be usedto yield information on slab rheology and may influence mantledynamics. It is hoped that further work will constrain the relativeimportance of faulting with respect to viscous flow within sub-ducting slabs, the conditions required to initiate buckling, and theeffects of this deformation on plate motions and the broader scalesof mantle flow.

A C K N OW L E D G M E N T S

The author would like to thank the editor (Saskia Goes), Iain Bai-ley and an anonymous reviewer for a number of excellent com-ments which substantially improved this paper. He would also liketo acknowledge Dan McKenzie, Keith Priestley, Jessica Irving, TimCraig and those at the inaugural ‘Lithoscussion’ of the tectonicsgroup at the Bullard Labs for commenting on early versions of thismanuscript. This research was funded by a Natural EnvironmentResearch Council studentship, with further support from Magda-lene College, Cambridge. Figures were created using the GenericMapping Tools (Wessel & Smith 1998). Plate boundaries in the mapfigures are adapted from Bird (2003).

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S U P P O RT I N G I N F O R M AT I O N

Additional Supporting Information may be found in the online ver-sion of this article:

Figure S1. The depth distribution and moment release of earth-quakes in the EHB catalogue (Engdahl et al. 1998). Each bar startsat the x-axis origin. The visible part of the blue bars represent theearthquakes in a cylinder with a radius of 50 km centred on thehinge zones identified in this study (http://gji.oxfordjournals.org/lookup/suppl/doi:10.1093/gji/ggs054/-/DC1).

Please note: OUP is not responsible for the content or functionalityof any supporting materials supplied by the authors. Any queries(other than missing material) should be directed to the correspond-ing author for the article.


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http://gji.oxfordjournals.org/lookup/suppl/doi:10.1093/gji/ggs054/-/DC1


Slab buckling and its effect on the distributions and focal mechanisms of deep-focus earthquakes

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