the olivine spinel transformation and the rheology of subducting lithosphere during subduction relatively hot lithospheric slabs are expected to deform in a superplastic flow regime below a depth of 300 km if olivine reacts to fine grained spinel this process reduces the flow strength of such slabs below the phase boundary so that they become aseismic at about this depth in colder slabs temperatures are too low for superplastic deformation and a high flow strength and seismic activity are maintained to a depth of 600 700 km

garnets recording deep crustal earthquakes syn eclogite facies pseudotachylytes of the bergen arcs western norway were formed during co seismic faulting at a depth of 60 km during caledonian continent collision concurrent with fluid induced partial eclogitization of precambrian anorthositic granulites the pseudotachylytes contain the high pressure assemblage omphacite garnet and kyanite and formed in the metastable granulites at the border of eclogitized areas rock volumes corresponding to outcrops of 100 m2 in area were shattered by pseudotachylytes associated with ultramylonites cataclasites and shear zones the granulite facies garnets unzoned and inclusion free away from the pseudotachylyte veins display planar and curved fractures brecciation and melting with decreasing distance from the veins sieve textured garnet developed by the disintegration of granulite facies garnet crystallization of eclogite facies mineral inclusions and welding together of garnet fragments fractured granulite facies garnets trend to more almandine rich compositions with variable grossular contents in the pseudotachylyte veins a second generation of minute 10 200 m euhedral or dendritic garnets has a higher femg ratio than the granulite facies garnet and a wide range in grossular content grs11 grs89 suggesting rapid growth and cooling fracturing of garnet and its preferential disappearance in the pseudotachylyte show that garnet has a relatively low fracture toughness seismic faulting caused enhanced reaction rates during ongoing fluid induced eclogitization of the deep crust by increasing the surface to volume ratio of garnet and its dislocation density the sudden volume reduction associated with eclogitization of metastable crust may have nucleated further faulting and pseudotachylyte formation

systematic analysis of deep seismicity 200 centroid moment tensor solutions for earthquakes between 1977 and 1980 summary a systematic study of deep seismicity is performed using waveform data from the gdsn between 1977 and 1980 and the centroid moment tensor method of dziewonski et al two hundred new cmt solutions are found for events deeper than 100km their moments obtained using the same algorithm range between 7 x and 1 4 x lo2 dyne cm a factor of 20 000 a statistical analysis of the cmt parameters provides important conclusions among these the shift in origin time for deep events is found to be almost independent of the seismic moment providing an indication of the complexity of deep earthquakes the deviation from the double couple model appears to be correlated to the state of stress of the subducting slabs mechanisms showing down dip compression are generally dominated by the eigenvalue corresponding to the compression axis and down dip tension correlates with the predominance of the tensional eigenvalue comparison with moment tensors obtained by other authors using different waveform data shows good agreement between different methods comparison with published focal plane mechanisms confirms the precision and reliability of the cmt method examples of cmt solutions used to identify patterns of seismicity associated with deep fault planes are shown

tectonic implications of serpentinite weakening summary the observation that serpentinite becomes weak and brittle at its dehydration temperature provides an experimental basis for the hypothesis that mantle earthquakes are caused by shear fracturing where interstitial fluid pressure effectively reduces the frictional resistance to a low or negligible value if convection currents in the mantle turn down at the foredeeps of the pacific island arcs dehydration of an oceanic crust of serpentinite and downward convection of the dehydration products beneath the island arc would give rise to the anomalously low shallow mantle velocities and heat flows in the region between the trenches and island arcs seismic activity would be confined to the zone along which the weak and brittle dehydration products move downward against the immobile continental mantle and would be concentrated at the leading edge of the focal zone due to release of stored elastic strain upon the initiation of weakening pore fluid pressures giving rise to faulting in the deepest earthquakes are considered to be due to interstitial magma

reaction enhanced ductility the role of solid solid univariant reactions in deformation of the crust and mantle abstract in collision belts and subduction zones penetrative deformation of thrust sheets may be catalyzed by metamorphic reactions if the reactions have a significant effect on the mechanical properties of rocks reaction enhanced ductility may result if a reaction produces a significant decrease in grain size thus allowing the rock to deform superplastically the product grain size of a reaction is a function of the ratio of nucleation and growth rates this ratio varies along any pressure temperature time ptt path and only attains a significant value at a certain distance from an equilibrium boundary a comparison of rates of change of p and t along typical segments of ptt paths for crustal rocks leads to the conclusion that a high nucleation rate a small grain size and resulting superplastic deformation are more likely to be achieved when reaction boundaries are crossed during underthrusting rather than during the thermal readjustments of a perturbed geotherm following crustal thickening or during uplift an example of reaction enhanced ductility occurs in eclogite facies metagranitoids in the sesia lanzo zone western alps where medium grained plagioclase reacted to fine grained jadeite quartz during early alpine underthrusting microstructural evidence from shear zones shows that the jadeite quartz aggregates were highly ductile and it is inferred that the small grain size allowed superplastic deformation further evidence suggests that this process operated during regional deformation of metagranitoids rubie 1982 the reaction of olivine to spinel or the beta phase by metastable overstepping of the two phase stability fields in a subducting plate ringwood 1975 may result in fine grained products and thus may be analogous to the albite jadeite quartz reaction the consequent decrease in effective viscosity is likely to have important consequences for plate dynamics at and below the depths of major phase transitions

shear localization in transformation induced faulting first order similarities to brittle shear failure abstract transformation induced faulting a leading candidate for the mechanism of deep focus earthquakes leads to catastrophic shear failure in laboratory specimens by the growth and coalescence of microscopic mode i anticracks or packets of denser microcrystalline transformed material we have studied this phenomenon in mg 2 geo 4 olivine undergoing a polymorphic phase transformation to its denser spinel phase at 2 7 gpa and 1200 k under applied stress in order to better understand the details of anticrack growth and coalescence which leads to localized shear zones and macroscopic failure here we report observations that address the early stages of shear localization preserved in one experiment of this series are microstructures typical of anticrack nucleation and growth as well as those involved in the self organization of these features during the shear localization process we have analyzed sem and optical images of individual anticrack reaction interfaces and coalesced structures from this experiment and another experiment conducted under similar conditions but with a different strain history we have isolated the reaction boundaries in these images and have performed fractal analysis of these boundary lines we find that the fractal dimension of isolated uncoalesced anticrack structures is consistently higher than that of structures formed from coalescence and coarsening of fine grained reaction products this result is consistent with the varying effects of stress and thermal feedback at these interfaces and also represents an interesting parallel with the fractal nature of brittle cracks and fault surfaces we also measured the length of the long axis of uncoalesced anticrack structures found in the experiment arrested at failure and find a roughly log normal distribution of sizes very similar to the distribution of microcrack lengths reported in experiments involving brittle shear failure microcracks and microanticracks both also commonly nucleate on grain boundaries intracrystalline flaws and phase boundaries shear zones faults formed by either of these mechanisms also regularly form at 30 to maximum compression from this set of observations we conclude that the general phenomenon of shear failure creates similar features in both systems perhaps in any system which generates a shear instability despite the major differences in the detailed microphysics because of the detailed and unambiguous measurements that are possible with images of transformation induced faulting experiments further studies of this faulting mechanism may provide new insights into brittle failure and shear localization processes

fast rise times and the physical mechanism of deep earthquakes earthquakes at depths of 300 km are similar to shallower events in that they are dominantly of double couple character1 implying that shearing motion has taken place at depth but because increased friction at these high pressures inhibits brittle fracture2 3 various other mechanisms related to phase transformations have been invoked to explain the occurrence of deep earthquakes4 10 as yet however no consistent differences have been found between the source characteristics of deep 300 km and intermediate depth 300km earthquakes2 11 13 here we report a systematic global survey of the rise times and stress drops of deep and intermediate earthquakes the rise time is defined as the time from rupture initiation to peak moment release rate when the rise times are scaled to the seismic moment release of the events their average is nearly twice as fast for events deeper than 450 km as for shallower events this difference may ultimately provide an experimental means of testing proposed mechanisms for the generation of deep seismicity

the depths of the deepest deep earthquakes the maximum depth of seismic activity is a fundamental observation providing a constraint on models of mantle dynamics although most recent investigations of mantle seismicity and dynamics state that seismicity extends to about 700 km focal depths of 720 km have been reported for large earthquakes as well as depths greater than 800 km for small events we have examined focal depths of events in several catalogs and conclude that 1 the deepest reliable focal depths are at about 670 680 km and events with focal depths beneath 600 km occur in several widely separated geographic regions 2 observations supporting focal depths exceeding 680 km are usually few poor or inconsistent 3 the reduction of seismic activity beneath about 650 km is quite abrupt however we cannot determine whether activity stops completely at 670 680 km or the maximum size of events decreases gradually beneath 650 km with magnitudes of 6 5 7 0 occasionally occurring at 650 km magnitudes of 5 5 6 0 at 680 km 4 0 4 5 at 695 km etc several models can explain the absence of seismic activity in the lower mantle two models are consistent with the abrupt termination of activity at about 650 680 km in widely separated areas a barrier which resists penetration by the subducting lithosphere or a phase transition which modifies the properties of the subducted material as it goes into the lower mantle

aftershocks and temporal clustering of deep earthquakes this paper evaluates how the focal depth the geographic location and magnitude affect the incidence of aftershocks and the occurrence of temporal clustering of nearby events for selected deep earthquakes h 70 km in the catalog of the international seismological centre for comparison we also evaluate shallow h 70 km and deep earthquakes for which locations and moment tensors are reported by the harvard group the primary conclusions are as follows 1 the incidence of aftershocks depends strongly on focal depth with aftershocks being less common for events between 100 and 450 km depth than for shallower or deeper events events with focal depth shallower than 40 km have a higher incidence of aftershocks and more pronounced temporal clustering than do deeper events 2 for the data available at present the incidence of aftershocks and amount of temporal clustering for deep events are independent of geographic region except for dependence caused by regional differences in the focal depths of events 3 deep earthquakes with large magnitudes are more likely to have aftershocks than are smaller magnitude events in accordance with models where the number of aftershocks is a poisson random variable that is a function of magnitude however several large events are anomalous in that they have many more aftershocks or many fewer aftershocks in the catalog than predicted by the model

the depth dependence of earthquake duration and implications for rupture mechanisms the duration of rupture is a fundamental characteristic of earthquakes and is important for understanding the mechanics of faulting1 2 the complexity of the seismic source and the incoherence of the high frequency seismic wavefield often inhibit the identification location and timing of features in the later part of earthquake rupture here we sum many teleseismic records from regional seismic arrays producing an unusually clear depiction of the earthquake source at short periods by suppressing background noise and coda generated near the receivers the ending as well as the beginning of rupture is clearly identifiable for most earthquakes examined measurements of 130 large earthquakes show that near 100 km depth rupture duration averages 11 s when scaled to a moment of 1026 dyn cm this decreases to 5 5 s at 650 km depth models of faulting suggest that duration should be inversely proportional to the shear wave velocity and the cube root of stress drop thus to explain the observed twofold decrease in duration with depth stress drops would have to increase by a factor of four as shear velocity increases with depth by only about 20 however observed stress drops show no strong trend with depth3 4 suggesting that the faulting process changes with depth

ruptures of deep focus earthquakes in the north western pacific and their implications on seismogenesis summary the high resolution of broad band seismic data is highly effective in studying ruptures associated with deep focus earthquakes in this study we report results from an analysis of p and sh waveforms from eight of the largest deep focus earthquakes that occurred between 1987 and 1992 along the north western pacific in this region broad band data recorded at close in distances directly above the source zone offer an unusual source receiver geometry that complements observations at teleseismic distances among the eight earthquakes studied six showed clear indications of directivity the best constraint on the extent of rupture came from the steeply dipping izu bonin wadati benioff zone where subhorizontal ruptures typically originate in the interior of subducted slab and propagate toward the top at high angles in particular rupture of the 1988 september 7 event consists of two en echelon line sources at a depth of approximately 480 km the overall rupture length of this earthquake constrains the minimum thickness of the seismogenic zone to be 27 12 km at this depth our estimated thickness of the seismogenic zone seems remarkably close to the maximum thickness 35 km predicted by the metastable olivine wedge model of seismogenesis this model interprets deep focus earthquakes as a result of transformational faulting within a region bounded approximately by the 700 c isotherm the extent of rupture during the largest events in this region seems to be only slightly larger than the 20 25 km spacing between the two layers of a double seismic zone found at depths between 300 and 400 km in the same general area beneath the island of sakhalin a rupture speed greater than that of the shear wave is not required for the large deep focus earthquake 615 km of 1990 may 12 almost all complexity in observed waveforms for this event can be explained by a northward propagating subhorizontal rupture composed of only two subevents

rapid changes and near stationarity of the geomagnetic field during a polarity reversal one of the most important suggestions from many of the new reports of sedimentary geomagnetic records is that the time dependence of the changes of the geomagnetic field during a reversal might be more complex than early records indicated indeed alternating periods of rapid and slow field changes are apparent in some sedimentary records1 4 in volcanic records very fast directional changes recorded by individual lava flows during their progressive cooling have been reported5 6 but a major problem when inferring the temporal behaviour of the transitional field is that the extrusion rate of the successive lava flows is much more variable and more difficult to evaluate than the rate of accumulation of the sedimentary sequences here we report the results of a detailed study of a geomagnetic reversal recorded in middle miocene marine clays with temporal resolution almost comparable with that of the volcanic records and in our opinion a more reliable chronological control the record displays large fluctuations in the rate of directional change and different episodes of collapse and recovery of the field intensity a very fast n s directional change may be entirely controlled by a frozen flux dominated reversal mechanism

olivine wadsleyite pyroxene topotaxy evidence for coherent nucleation and diffusion controlled growth at the 410 km discontinuity we have synthesized a hydrous peridotite composition sample at 13 gpa and 1400 c with co existing coarse grains 100 lm of olivine wadsleyite clinoenstatite plus melt in a multi anvil press some of the olivine grains contain fine scale 0 5 2 lm wide lamellae of wadsleyite and clinoenstatite that likely resulted from transformation caused by small temperature fluctuations during the four hour experiment phase compositions were determined by electron probe microanalysis epma and secondary ion mass spectroscopy sims the olivine ranges from fo94 to fo90 in composition and contains about 4000 ppm wt h2o the wadsleyite is fo87 1 in composition and contains about 10 000 ppm wt h2o the clinoenstatite is en93 1 in composition and about 1400 ppm wt h2o transmission electron microscopy of the wadsleyite lamellae and host olivine shows that the two phases share their close packed oxygen planes so that the wadsleyite lamellae are nearly planar and perpendicular to the 1 0 0 of olivine the wadsleyite lamellae thus have their 1 0 1 and 0 2 1 planes parallel to the 1 0 0 plane of olivine additionally larger incoherent grains of wadsleyite in olivine are found dislocation microtexures in the olivine and iron concentration profiles across the lamella interface suggest heterogeneous nucleation and diffusion controlled growth of coherent wadsleyite lamellae on defects in the olivine followed by the nucleation of faster growing incoherent grains on the lamellae the results show that under hydrous conditions the olivine wadsleyite transformation occurs close to equilibrium at conditions of the 410km discontinuity furthermore inheritance of crystallographic preferred orientations and therefore seismic anisotropy across the 410 km discontinuity is unlikely to be significant in addition hydrogen distributions among the various phases indicate that dehydration by melt extraction at 410 km will be inefficient and that h contents greater than about 4000 ppm wt h2o are needed to initiate melting at 410 km 2012 published by elsevier b v

effect of pressure on stress strain properties of materials the transition from brittleness to ductility in the mechanical behavior of materials with increase in the hydrostatic component of the stress reflects differences in the pressure dependence of the stress needed to initiate particular processes of fracture or flow the simple hypothesis that processes involving ordinary friction in the relative movement of grains or fracture fragments are highly pressure dependent whereas crystallographic slip and twinning are not is examined in the light of recent experimental results on phyllite galena and magnesium oxide there is indication that some slip systems perhaps intrinsically hard ones can be fairly pressure dependent so that the above generalization may not always be valid but more experimental evidence is needed 23 refs

intraslab earthquakes dehydration of the cascadia slab we simultaneously invert travel times of refracted and wide angle reflected waves for three dimensional compressional wave velocity structure earthquake locations and reflector geometry in northwest washington state the reflector interpreted to be the crust mantle boundary moho of the subducting juan de fuca plate separates intraslab earthquakes into two groups permitting a new understanding of the origins of intraslab earthquakes in cascadia earthquakes up dip of the moho9s 45 kilometer depth contour occur below the reflector in the subducted oceanic mantle consistent with serpentinite dehydration earthquakes located down dip occur primarily within the subducted crust consistent with the basalt to eclogite transformation

phase transformations earthquakes and the descending lithosphere abstract the energy dissipated from metastable phase transformations is investigated in this paper in addition to the kinetic energy envisaged by randall at least two other major forms of energy latent heat and metastability energy are involved in a metastable phase transformation the seismic energy density for metastable phase transformation is of the order of 10 24 10 25 erg km 3 for most mantle silicates as an example an earthquake of magnitude m 7 5 would require only 0 01 0 03 or 0 04 km 3 of basalt olivine or pyroxene respectively undergoing metastable phase transformation earthquakes caused by both faulting and phase transformation mechanisms have been observed in high pressure laboratory experiments the energy density associated with a faulting mechanism appears to be four to five orders of magnitude less than that associated with metastable phase transformations of mantle silicates confirming theoretical expectations according to all of the thermal models for the descending lithosphere available in the literature metastable phase transformations almost certainly occur in the descending lithosphere enormous energies would be released suddenly in association with these metastable phase transformations thus earthquakes within the descending lithosphere at depths greater than 100 km may be induced by metastable phase transformations however metastable phase transformations in the descending lithosphere have little or an opposing effect on the tectonic engine driving the motion of plates into the mantle

three dimensional location and waveform analysis of microseismicity in multi anvil experiments we present an acoustic emission ae monitoring technique to study high pressure p 1 gpa microseismicity in multi anvil rock deformation experiments the application of this technique is aimed at studying fault mechanisms of deep focus earthquakes that occur during subduction at depths up to 650 km ae monitoring in multi anvil experiments is challenging because source locations need to be resolved to a submillimetre scale due to the small size of the experimental assembly aes were collected using an 8 receiver array located on the back truncations of the tungsten carbide anvils each receiver consists of a 150 1000 khz bandwidth pzt transducer assembly data were recorded and processed using a high speed amsy 5 acquisition system from vallen systems allowing waveform collection at a 10 mhz sampling rate for each event signal 3 d hypocentre locations in the assembly are calculated using standard seismological algorithms the technique was used to monitor fault development in 3 mm long x 1 5 mm diameter olivine cores during axisymmetric compression and extension the faults were generated during cold compression to similar to 2 gpa confining pressure subsequent aes at 2 6 gpa and 900 degrees c were found to locate near these pre existing faults and exhibit high pressure stick slip behaviour

deep earthquake rupture histories determined by global stacking of broadband p waveforms 1 we conduct a systematic investigation of time histories of moment release in deep earthquakes whose physical mechanism remains unknown we have constructed source time functions stfs of 111 large deep earthquakes depth 100 km and mw 6 4 by stacking p waveforms from broadband seismograms recorded by the global seismographic network aligning and stacking waveforms cancels noise and allows us to identify the rupture initiation and termination times accurately each stf is scaled to a reference moment of 1019 n m using the duration moment relation m01 3 in order to investigate depth dependence of the stfs we bin them into three depth ranges 100 350 km 350 550 km and deeper than 550 km based on physical properties of the mantle and the distribution of the data we infer a change in character near 550 km earthquakes deeper than about 550 km are shorter have simpler time functions and are more uniform in their characteristics further we find longer than expected scaled durations and greater complexity in the 350 550 km depth range the scaled durations of the 350 550 km earthquakes do not decrease with depth as 1 vs instead possessing a slightly longer average scaled duration than those 100 350 km deep we further categorize the earthquakes by subduction zone and find a similar depth dependence within individual zones finally the events that have achieved highest moment rate in the first 1 2 s after initiation tend to be deeper and or larger events the latter suggesting that dynamic rupture propagation affects the final size of the earthquake the depth dependence of duration and complexity suggests more complicated rupture histories between 350 and 550 km and a possible change in the physical mechanism of rupture at about 550 km

localized polymorphic phase transformations in high pressure faults and applications to the physical mechanism of deep earthquakes earthquake mechanisms based on frictional instabilities are widely accepted for relatively shallow earthquakes such mechanisms in unmodified form are highly unlikely for deep earthquakes because of the expected high frictional shear stresses at depths of 300 700 km several alternative mechanisms have been proposed here i discuss a new type of shear instability observed in experiments on ordinary polycrystalline ice and polycrystalline tremolite by my colleagues and me these shear instabilities lead to rapid stress drops and sound emissions and have the following characteristics 1 a single sharp shear zone forms in the maximum shear stress orientation 2 confining pressure does not suppress the instability and under some conditions raising confining pressure pc lowers the differential stress at which it occurs 3 stress drops can occur repeatedly after reloading at about the same differential stress 4 the mean stress vs temperature conditions at which the instabilities occur in ice and tremolite place them in the fields of thermodynamic stability of ice ii and diopside talc respectively although i have not as yet confirmed the existence of these high pressure phases in the shear zones transformation in the shear zone is implicated because such shear instabilities do not occur in similar materials in which polymorphic phase changes do not occur reconstructive polymorphic phase changes localized along shear zones may be a general phenomenon in crystalline materials stressed non hydrostatically near transition boundaries moreover by analogy the reconstructive phase transformations that are thought to occur in deeply subducted lithosphere may lead to localized shear instabilities manifested by deep earthquakes and produce the observed double couple first motion distribution finally if this is the earthquake source mechanism in deeply subducted lithosphere then earthquakes should shut off when all of the polymorphic phase changes have occurred this may explain the maximum depth of earthquakes at about 680 km

deep seismicity and modes of deformation in tonga subduction zone the geometry of deep 400 km earthquakes in the subducting western edge of the pacific plate when related to the local distribution of seismic activity reveals a complex pattern of planes of shear failure enabling the modes of deformation by which the descending plate shortens and thickens to be identified the deepest part of the slab is displaced laterally suggesting that it fails to penetrate the discontinuity at 670 km

experimental constraints on the depth of olivine metastability in subducting lithosphere the hypothesis that metastable olivine persists in some subducting slabs into the transition zone has wide implications for mantle dynamics and rheology in order to evaluate this possibility we derive new thermo kinetic subduction zone models to predict the extent of olivine metastability within the stability fields of its high pressure polymorphs wadsleyite and ringwoodite our updated models improve on previous work by incorporating experimental kinetic data on realistic mantle compositions mg fe 2sio4 rather than analogue systems furthermore latent heat due to the transformation is fed back into both the kinetics and the thermal model we also consider the effects of transformation stress on growth kinetics and the possibility of an intracrystalline transformation mechanism previously thought to be important only at high shear stresses our models predict significantly smaller wedges of metastable olivine than previous work in the case of tonga for example where high values of lithospheric age 100 140 million years and convergence rate 14 cm per year are most favorable for metastability models considering only grain boundary nucleation and interface controlled growth predict olivine metastability to 600 km depth in contrast to 660 km predicted previously by kirby et al rev geophys 34 1996 261 when intracrystalline transformation is considered the depth of metastability is further reduced by as much as 100 km due to the large increase in the density of nucleation sites inhibition of growth by transformation stress can increase the depth interval over which the transformation takes place but is unlikely to be a dominant factor especially if the intracrystalline mechanism operates these results indicate that the existence of metastable olivine at depths corresponding to those of the deepest earthquakes 680 km requires subduction of old lithosphere 100 million years and a high vertical subduction velocity 15 cm per year such conditions currently may only be achieved in the very northern part of the tonga subduction zone yet earthquakes occur at depths down to 680 km in other subduction zones in which lithospheric age and or subduction velocity are relatively low e g indonesia and the marianas therefore mechanisms other than transformational faulting in metastable olivine must operate to cause the deepest earthquakes

deep and intermediate depth non double couple earthquakes interpretation of moment tensor inversions using various passbands of very broadband seismic data summary analysis of moment tensor inversions using various passbands of very broadband seismic data provides clear evidence that some non double couple moment tensors of intermediate depth and deep earthquakes result from the superposition of different double couple sources whose predominant principal axes are aligned with the predominant strain state within the subducting slabs the analyses are performed for three intermediate depth and deep earthquakes 1984 january 1 south of honshu 386 km 1985 april 23 luzon 181 km and 1987 may 7 northern sea of japan 417 km consistent non double couple moment tensors obtained using different sets of seismic waves in various low frequency bands suggest that these three significant non double couple components are not caused by unmodelled propagation errors of seismic waves in the inversion procedure because the various sets of seismic waves traverse very different ray paths for the south of honshu and the luzon events two major arrivals in the broadband p wave diplacement seismograms are observed with varying relative amplitudes or polarities from station to station the different double couple mechanisms which model the two phases combine to produce the significant non double couple moment tensors obtained at long periods the principal axes of the subevents closest in orientation to the predominant strain states within the slabs tend to be quite stable whereas the other two principal axes rotate between subevents this observation may explain the global nature of non double couple components in relation to the strain regime within the slab for the northern sea of japan event two major phases are observed in the p wave displacement waveforms but the variation in mechanism of two subevents that we model is not enough to explain the large non double couple component observed at long periods however since the non double couple component is exceptionally large compared with those for other deep earthquakes changes of focal mechanism with shorter delays than we can resolve appear to explain the overall radiation most simply

spatial patterns of aftershocks of deep focus earthquakes this paper presents precise relative relocations for aftershocks of 59 intermediate and deep earthquakes using p pp and pkp arrival times read by us or reported in the literature these aftershocks included 36 rupture subevents occurring within 1 min of the initial event and 71 true aftershocks occurring later and identified statistically as being related to the initial event we compare the relative locations with the orientations of the wadati benioff zones and with the available focal mechanisms using statistical methods not previously applied to earthquake data surprisingly neither true aftershocks nor rupture subevents cluster along the nodal planes of intermediate or deep earthquake focal mechanisms aftershocks more than 20 km from the initial events occur preferentially in the plane of the wadati benioff zone while those lying closer have isotropically distributed directions rupture subevents occur after the travel time of the s wave from the initial event larger magnitude earthquakes generally possess rupture subevents lying farther from the initial event whereas true aftershocks can occur 50 km or more from initial events having magnitudes as small as 5 3 except following a few unusually large earthquakes with focal depths of about 100 km we find no rupture subevents or true aftershocks more than about 80 km from the initial hypocenter the existence of many aftershocks far from nodal planes does not favor models in which deep earthquake failure is simply slip along a planar fault rather the aftershocks may occur in response to a general redistribution of stress caused either by the occurrence of the initial event or possibly by nearby continuing phase transitions alternatively the failure zones of deep earthquakes may be surfaces which are frequently curved by 40 or more from the orientation of the initial nodal plane perhaps due to inhomogeneous stress distributions

a hypothesis for the seismogenesis of a double seismic zone summary the seismogenesis of a double seismic zone in particular the lower layer of a double seismic zone has not been adequately explained in the literature on the basis of seismic data and geothermal structures along three well studied cross sections in the kuril kamchatka and japan subduction zones we investigate the temperature pressure conditions associated with seismogenic structures of the double seismic zones the corresponding tip loci seem to suggest that earthquakes observed in the lower layer and in the lower part below approximately 130 20 km of the top layer of a double seismic zone were caused by metastable phase transition a mechanism similar to that responsible for deep focus earthquakes only at lower temperature pressure conditions under this hypothesis the wedge shaped configuration of a double seismic zone is interpreted to represent the loci of the kinetic boundary of the phase transition according to theoretical experimental studies and the constraints imposed by our observations a likely candidate for such a phase transition is the metastable al rich enstatite decomposing into the assemblage of al poor enstatite plus garnet earthquakes in the upper part of the top layer were most probably due to conventional mechanisms such as dehydration of subducted materials and or facies change from basalt to eclogite that the top layer involves more than one seismogenic mechanism is also implied by the distinct behaviour of seismicity in the vicinity of 130 f 20 km because the presence of deviatoric stress is critical to the reaction rate of a metastable phase transition it is inferred that single seismic zones are also caused by the same mechanisms except that the implicit layer of a supposed double seismic zone is missing due to the insufficient amount of appropriate metastable minerals or to the lack of appropriate deviatoric stresses in the source region

thermodynamic constraints on phase changes as earthquake source mechanisms in subduction zones abstract application of thermodynamic equations for phase transitions with a shock wave output from metastable to stable phases that are believed to occur in subduction zones indicates that while many show a volume reduction and thus may contribute to slab pull mechanisms of plate tectonics they do not satisfy criteria for the generation of shock waves of the reactions considered only one antigorite clinoenstatite forsterite talc satisfies the criteria and for this case the shock wave pressure is in fact less than the pressure calculated for the leading edge of the subduction zone this would imply that if the transition does occur under shock conditions in the subduction zone dilatational rather than compressional first motions for the associated earthquake are expected

seismological constraints on the mechanism of deep earthquakes temperature dependence of deep earthquake source properties abstract seismological observations are of vital importance for understanding the mechanism of deep earthquakes most of the seismological observables for earthquakes deeper than 300 km are similar to shallow earthquakes deep earthquakes clearly represent shear failure on a planar surface as shown by their double couple mechanisms deep earthquake aftershock sequences show temporal decay rates and magnitude frequency relations b values that are similar to shallow earthquakes with the aftershocks occurring preferentially along the mainshock fault planes in addition deep earthquake rupture velocities are similar to those of shallow earthquakes however there are also some observations that are clearly distinctive relative to shallow earthquakes stress drops of deep earthquakes show a large variation but are larger on average than shallow earthquakes different deep seismic zones show very different b values in contrast to shallow earthquakes which show similar b values worldwide in addition deep earthquakes show fewer aftershocks than shallow earthquakes a variety of observations suggest that deep earthquakes are highly sensitive to the temperature of the slab both deep earthquake b values and the rate of deep earthquake aftershock occurrence are inversely correlated with the temperature of the deep slabs suggesting that these factors are temperature controlled to an extent much greater than with shallow earthquakes large deep earthquakes in warm slabs show slower rupture velocities larger stress drops and lower seismic efficiencies than similar earthquakes in cold slabs the width of deep seismic zones is also probably temperature controlled but deep earthquake rupture can propagate outside the normal limits of benioff zone seismicity simple thermal models for the tonga slab near the 1994 deep earthquake suggest that the temperature at the rupture termination point was at least 200 c warmer than the temperature that limits smaller earthquakes in the slab these observations can be used to evaluate physical models for deep earthquakes including brittle slip along fluid weakened faults transformational faulting and thermal and perhaps melt lubricated shear instabilities it is difficult to explain the large fault widths of some deep earthquakes using a fluid weakening model since hydrated materials are expected in only a narrow depth zone at the top of the slab and the fault planes do not have the expected orientations for reactivated faults the lateral extent of the largest deep earthquakes cast doubt on the transformational faulting model in which events should be confined within a narrow metastable wedge seismological studies have also failed to find evidence for the existence of metastable olivine in slabs the temperature dependence of deep earthquakes argues in favor of a temperature activated phenomenon such as thermal shear instabilities and perhaps fault zone melting

a simple explanation for the depth distribution of deep earthquakes in a model for the depth distribution of deep earthquakes i assume that deep earthquakes occur only above a critical deviatoric stress and that where the stress is achieved the seismicity rate is proportional to the strain rate the model seismicity rate increases sharply before terminating in agreement with the observed depth distribution since the assumptions are valid for most plausible seismic processes no large stresses or unusual earthquake mechanisms near the termination of seismicity are required

the rheology of faults triggered by the olivine spinel transformation in mg2geo4 and its implications for the mechanism of deep focus earthquakes the relevance of the anticrack faulting mechanism to the origin of deep focus earthquakes depends critically on the physical processes operating during fault generation and movement we show here that the resistance to sliding on fault zones produced by this mechanism in mg2geo4 depends only weakly on confining pressure but strongly on sliding rate both of these characteristics are inconsistent with friction the microstructures of the fault zones and the crystal plastic rheology of the constituent phases indicate that sliding must occur primarily by grain boundary sliding previously we reported that anticrack faulting is accompanied by elastic radiation of energy acoustic emissions and that it can operate during the transformation in mg fe 2sio4 at the pressures and temperatures at which deep earthquakes occur the present results and the recent demonstration that metastable olivine is present in the subducting slab beneath japan provide additional support for the anticrack theory of deep focus earthquakes

unbending combined with dehydration embrittlement as a cause for double and triple seismic zones 1 using a model of elastic perfectly plastic plate i demonstrate that plate unbending combined with dehydration embrittlement can account for the morphology and stresses of double or triple seismic zones dsz s or tsz s observed in many subducting slabs densifying metamorphic reactions may induce tensile stresses as well as high pore fluid pressures in the slab crust and thus generate the upper seismicity band of the tsz limited dehydration may moderately elevate the fluid pressure in the slab mantle but unbending usually dominates mantle stresses and results in another two seismicity bands dsz s are underdeveloped tsz s

deformation of a weak subducted slab and variation of seismicity with depth oceanic lithosphere is assumed to possess platelike properties whether it is lying at the earth s surface or descending deep into the mantle yet the geometries of subducting slabs indicate significant deformation as they descend through the mantle1 4 suggesting that lithospheric plates might be so weakened during subduction as to act not as a rigid solid but as a viscous fluid numerical and laboratory experiments have shown that fluid slabs can indeed take on realistic profiles5 7 however it has not been clear whether a fluid or weak model of slab dynamics can account for deep earthquakes which are usually ascribed to the deformation of a rigid or strong slab here we show using numerical simulations of slab evolution that a weak slab model is in fact consistent with seismic observations assuming that earthquakes occur at a rate proportional to deformation rate we reproduce the observed variation with depth of seismicity rate and focal mechanisms and the cessation of seismicity at 670 km depth provided that sinking material encounters resistance at depth here modelled as a viscosity jump at 670 km the pattern of seismicity can be explained by any mechanism for deep earthquakes in which the rate of seismicity is proportional to strain rate in the slab

two types of deep seismicity in subducting slabs the relation between variation of seismic activity with depth and temperature structure in the subducting slabs in five subduction zones kuril ne japan izu bonin mariana and tonga is investigated when the temperature of the core of the slab at depths of 300 350 km is higher than the kinetic cut off temperature of the olivine spinel phase transformation there is no seismicity maximum in the slab below that depth range when the temperature of the core of the slab at 300 350 km depths is lower than the kinetic cut off temperature there is a depth range of relatively high seismic activity in the slabs moreover estimated temperature in the depth range of relatively high seismicity is near the kinetic cut off temperature it is inferred that the phase transformation of meta stable olivine triggers deep earthquakes and causes high seismic activity below the depths of 300 350 km in relatively low temperature slabs when the phase transformation is the cause of deep earthquakes in relatively high temperature slabs however it is considered that the phase transformation occurs in nearly equilibrium conditions and meta stable olivine does not exist other mechanisms in addition to the phase transformation are required to explain observed deep seismicity especially in relatively high temperature slabs

simultaneous long term and short term slow slip events at the hikurangi subduction margin new zealand implications for processes that control slow slip event occurrence duration and migration 1 we document a sequence of simultaneous short term and long term slow slip events sses at the hikurangi subduction zone during the 2010 2011 period the sequence of short term events each 2 3 weeks in duration ruptured much of the shallow plate interface 15 km at central and northern hikurangi over a 6 month period was accompanied by microseismicity and involved patchy irregular migration of sse slip we suggest that the patchy migration of the short term sse is due to large scale 100 3500 km heterogeneities on the plate interface related to seamount subduction and sediment subduction and or underplating this is in contrast to a 2010 2011 long term sse at the central hikurangi margin which evolved steadily over 1 5 years and ruptured much of the plate interface between 20 and 70 km depth we suggest that the occurrence of long term versus short term sses at hikurangi is related to differences in effective normal stresses and relative heterogeneity of the subduction interface the long term sse sequence began 1 year before the short term sequence coulomb stress change models suggest that the long term sse may have triggered initiation of the subsequent short term sse sequence initiation of the short term sequence occurred in a region just updip of or within an interseismically locked portion of the plate interface and may be located within the updip transition from seismic to aseismic behavior alternatively it could be characteristic of a region undergoing partial interseismic coupling this is in contrast to sses observed elsewhere in the world that typically occur within the downdip transition from seismic to aseismic behavior

the nature of deep focus earthquakes wadati 1928 first proved convincingly that some earthquakes occur at depths well beneath the earth s crust he essentially proposed the nomenclature used today by the international seismological centre isc i e earthquakes with focal depths exceeding 300 km are deep earthquakes and those with depths between 70 and 300 km are intermediate earth quakes however when there is little reason to distinguish between the two groups both types are called simply deep earthquakes to avoid confusion in this paper we refer to those with focal depths exceeding 300 km as very deep earthquakes and those with focal depths between 70 and 300 km as intermediate earthquakes deep earthquakes are of interest for at least four reasons first they are exceedingly common between 1964 and 1986 they constituted no less than 22 of all earthquakes having mb greater than 5 0 in the isc catalog second they most often occur in association with deep ocean trenches and volcanic island arcs in subduction zones one of the great achievements of twentieth century geophysics was the recognition that their occurrence in inclined planar groups or wadati benioff zones apparently delineates the cold down going cores of convection cells in the uppermost mantle third seismologists use body waves of deep earthquakes dispro portionately more often than those of shallow earthquakes to inves tigate core mantle and crustal structure this is because a deep earth quakes often possess relatively more impulsive sources b their body phases traverse the heterogeneous uppermost mantle only once on the ray path from hypocenter to station and c surface waves do not contaminate these body phase arrivals on seismograms finally deep earthquakes are

an implosive component to the source of the deep sea of okhotsk earthquake of 24 may 2013 evidence from radial modes and cmt inversion abstract we study the spectral amplitudes of the first two earth radial modes 0 s 0 and 1 s 0 excited by the sea of okhotsk earthquake of 24 may 2013 the largest deep event ever recorded in the search for an isotropic component to its source in contrast to the case of the 1994 bolivian earthquake we detect an implosive component m i 1 1 10 27 dyn cm equivalent to 3 of the full scalar moment but 14 of the lone deviatoric component exciting the earth s radial modes an independent moment tensor inversion using the standard globalcmt algorithm but after relaxing its zero trace constraint similarly yields an implosive isotropic component albeit with a larger amplitude while it fails to document one in the case of the 1994 bolivian deep earthquake an implosive component to the source is expected in the model of transformational faulting in which deep earthquake rupture nucleates and grows upon transformation of metastable olivine to ringwoodite in the cold subducting slab this interpretation is supported by quantitative estimates 0 9 4 m of the thickness of the transformed shear zone which scale favorably relative to earthquake fault length with the upper end of the range of laboratory results reported for ices germanates and silicates the resulting extent of the transformation in the metastable wedge is consistent with the local geometry of the deep slab as recently determined by rupture modeling and aftershock distribution our results are in contrast to those for the two runner up largest deep earthquakes the 1994 bolivian and 1970 colombian shocks for which a similar isotropic component could not be detected we attribute this difference to variability in the ratio of isotropic to deviatoric components which combined with the smaller size of the 1970 and 1994 events would make any putative implosive component fall below detection levels especially in the case of the 1970 colombian earthquake for which only analog narrow band records were available

tectonic overpressure in competent mafic layers and the development of isolated eclogites variation in the state of stress during heterogeneous deformation should be reflected in variation in the effective pressure of metamorphic reactions whether this is mean stress or the normal stress acting across the reacting interface the magnitude of this pressure variation will determine whether it is discernible in the preserved metamorphic mineral assemblages of heterogeneously deformed rocks the magnitude of the mean stress difference across a non slipping interface between two materials with viscosity ratio c 20 1 is effectively equal to the maximum shear stress for flow in the more viscous material progressive shortening of the interface results in a higher mean stress in the more competent material whereas extension results in a lower mean stress for high p low t eclogite facies conditions current experimental data indicate that clinopyroxene and garnet rich layers of eclogite should be very strong and that pressure differences of up to 800 mpa 8 kbar between competent layer and weaker matrix may be possible such high values can be obtained in widely separated competent layers for values of bulk stress in the overall multilayer that are much lower by a factor approaching the viscosity ratio extrusion of material between more rigid plates which has been proposed as a regional mechanism of lateral continental escape for both the alps and the himalayas should also be accompanied by a lateral gradient in effective pressure otherwise extrusion could not occur maximum mean stresses with magnitudes that are many times the maximum shear stress required for plastic flow should develop for deformation zones that are long relative to their width e g around 20 times for a width to thickness ratio of 10 tectonic overpressure in progressively shortened competent layers particularly in regions of extrusion between more rigid plates might help explain the occurrence of isolated layers and pods of low t eclogite c 550 c the dramatic weakening of clinopyroxene in the power law creep field precludes the development of significant overpressures in eclogite layers

creep mechanism in mg2geo4 effects of a phase transition we deformed polycrystalline mg2geo4 olivine and spinel in a griggs type solid medium apparatus flow of mg2geo4 olivine can be represented by 6 5 l07 3 5 exp 105 kcal mol rt where kbar is the differential stress and s 1 is the natural strain rate for mg2geo4 spinel the flow law is 2 6 104 2exp 73 kcal mol rt the low stress exponent and activation enthalpy coupled with fine grain size 3 m suggest that mg2geo4 spinel deformed by a superplastic mechanism flow parameters for the olivine phase suggest a dislocation creep mechanism comparison of theoretical superplastic flow laws for mg2geo4 olivine with the spinel phase data suggests that strain rates in mg2geo4 spinel are only about a factor of 3 lower than for mg2geo4 olivine of the same grain size a similar estimate holds for dislocation creep of the two phases if it is controlled by diffusion transformation from mg2geo4 olivine to spinel reduced grain size to approximately 3 m thus we might expect a similar reduction in grain size in the earth s transition zone which could result in superplastic deformation of the transformed phase and cause a weak decoupling zone at the transition boundary in the mantle superplasticity brought about by transformation induced reduction in grain size may also provide a mechanism for deep focus earthquakes and an explanation for the correlation observed between their distribution with depth and the depths of phase transitions within the mantle

modeling the tonga slab can travel time data resolve a metastable olivine wedge we present the results of detailed modeling of the tonga slab with the goals of determining whether high resolution travel time data 1 can be fit by simple thermal and petrological slab models and 2 can resolve a metastable olivine wedge at depths greater than the equilibrium olivine spinel phase boundary we model arrival times recorded by a 1000 km line of 23 ocean bottom seismometers obs and island broadband seismic stations extending from the lau backarc basin across the tonga trench and onto the pacific plate the data consist of 388 local p wave travel times from 17 deep and 3 intermediate earthquakes recorded during the 3 month obs deployment in late 1994 we locate the events using both local and teleseismic arrival times and apply a relocation operator to the theoretical travel times to simulate the biases introduced in the data by locating the events with a reference earth model the modeling consists of grid searches using a three dimensional finite difference algorithm to compute local first arriving travel times for equilibrium and metastable p wave velocity models constructed from thermal mineralogical and morphological constraints the travel time anomalies are well fit by standard slab thermal models and p velocity temperature derivatives of 0 4 to 0 3 ms 1 c 1 forward calculations indicate that the presence of a metastable olivine wedge has a subtle effect on the travel times due to the tendency of first arriving waves to avoid the low velocity region wedge velocity models provide a slightly better fit to the data than equilibrium models but f tests indicate the improvement is not significant at the 95 level our results suggest that providing direct seismological evidence of a wedge of metastable olivine in subduction zones will require either waveform modeling or the observation of later arriving phases created by the depressed phase boundary

experimental evidence for wall rock pulverization during dynamic rupture at ultra high pressure conditions abstract the mechanisms triggering intermediate and deep earthquakes have puzzled geologists for several decades there is still no consensus concerning whether such earthquakes are triggered by brittle or ductile mechanisms we performed a deformation experiment on a synthetic lawsonite bearing blueschist at a confining pressure of 3 gpa and temperatures from 583 to 1 073 k after deformation the recovered sample reveals conjugated shear fractures garnet crystals are dissected and displaced along these narrow faults and reveal micro and nanostructures that resemble natural pulverization structures as well as partial amorphization formation of such structures at low confining pressures is known to require high tensile stresses and strain rates and is explained by the propagation of a dynamic shear rupture the absence of shearing in the pulverized wall rock is taken as evidence that these structures pre date the subsequent heat producing frictional slip in analogy to observations at low pressure we infer that the garnet structures in our experiment result from rapid propagation of a shear fracture even at the high pressure exerted on the sample and thus suggest that brittle deformation is possible at lower crustal to upper mantle depths

measurement of differential rupture durations as constraints on the source finiteness of deep focus earthquakes 1 the physical mechanism of deep earthquakes can be constrained by identifying their fault planes resolving the fault plane ambiguity is a classical problem in seismology and we present a method to distinguish the fault plane using observations of source finiteness source finiteness is observable on seismograms at different azimuths and distances for single event ruptures as variations in the apparent rupture duration and for complex ruptures as differences in the traveltime delay between subevents for each earthquake the rupture duration or traveltime delay will be shortest in the direction of rupture propagation and longest in the opposite direction rather than measuring the actual rupture duration at each station we use a cross correlation technique that includes a stretching factor to measure the differential rupture duration between each pair of stations these differential measurements then allow us to identify the rupture direction rupture velocity and fault plane for each earthquake first we test the method on two synthetic earthquakes which represent earthquakes composed of one and two events the method works well for both examples although attenuation can bias the determined rupture direction for the single event case next we apply this method to p waves from broadband seismograms from four intermediate and deep focus earthquakes composed of two subevents the 23 january 1997 bolivian earthquake mw 7 1 276 km depth the 27 october 1994 earthquake south of the fiji islands mw 6 7 549 km depth the 21 july 1994 japan sea earthquake mw 7 3 471 km depth and the 11 november 1998 fiji islands earthquake mw 6 3 149 km depth each focal mechanism contains a subvertical and a subhorizontal nodal plane for three of the events our analysis shows that rupture propagated subhorizontally and we identify the subhorizontal nodal plane as the fault plane for the smallest event the rupture azimuth but not the rupture dip is well constrained and we cannot conclusively identify the fault plane rupture velocities vary from 0 18 to 0 63 of the local p wave velocity

deep earthquakes and the thermal assimilation of subducting lithosphere two problematic aspects of deep seismic zones are investigated the maximum depth about 700 km of seismic activity and the relative maximum in seismic energy release in the 500 700 km depth range it is shown that both features can be accounted for by a model based on thermal assimilation this implies that no barrier is required at a depth of 650 700 km to explain the observations

metastable mantle phase transformations and deep earthquakes in subducting oceanic lithosphere earth s deepest earthquakes occur as a population in subducting or previously subducted lithosphere at depths ranging from about 325 to 690 km this depth interval closely brackets the mantle transition zone characterized by rapid seismic velocity increases resulting from the transformation of upper mantle minerals to higher pressure phases deep earthquakes thus provide the primary direct evidence for subduction of the lithosphere to these depths and allow us to investigate the deep thermal thermodynamic and mechanical ferment inside slabs numerical simulations of reaction rates show that the olivine spinel transformation should be kinetically hindered in old cold slabs descending into the transition zone thus wedge shaped zones of metastable peridotite probably persist to depths of more than 600 km laboratory deformation experiments on some metastable minerals display a shear instability called transformational faulting this instability involves sudden failure by localized superplasticity in thin shear zones where the metastable host mineral transforms to a denser finer grained phase hence in cold slabs such faulting is expected for the polymorphic reactions in which olivine transforms to the spinel structure and clinoenstatite transforms to ilmenite it is thus natural to hypothesize that deep earthquakes result from transformational faulting in metastable peridotite wedges within cold slabs this consideration of the mineralogical states of slabs augments the traditional largely thermal view of slab processes and explains some previously enigmatic slab features it explains why deep seismicity occurs only in the approximate depth range of the mantle transition zone where minerals in downgoing slabs should transform to spinel and ilmenite structures the onset of deep shocks at about 325 km is consistent with the onset of metastability near the equilibrium phase boundary in the slab even if a slab penetrates into the lower mantle earthquakes should cease at depths near 700 km because the seismogenic phase transformations in the slab are completed or can no longer occur substantial metastability is expected only in old cold slabs consistent with the observed restriction of deep earthquakes to those settings earthquakes should be restricted to the cold cores of slabs as in any model in which the seismicity is temperature controlled via the distribution of metastability however the geometries of recent large deep earthquakes pose a challenge for any such models transformational faulting may give insight into why deep shocks lack appreciable aftershocks and why their source characteristics including focal mechanisms indicating localized shear failure rather than implosive deformation are so similar to those of shallow earthquakes finally metastable phase changes in slabs would produce an internal source of stress in addition to those due to the weight of the sinking slab such internal stresses may explain the occurrence of earthquakes in portions of lithosphere which have foundered to the bottom of the transition zone and or are detached from subducting slabs metastability in downgoing slabs could have considerable geodynamic significance metastable wedges would reduce the negative buoyancy of slabs decrease the driving force for subduction and influence the state of stress in slabs heat released by metastable phase changes would raise temperatures within slabs and facilitate the transformation of spinel to the lower mantle mineral assemblage causing slabs to equilibrate more rapidly with the ambient mantle and thus contribute to the cessation of deep seismicity because wedge formation should occur only for fast subducting slabs it may act as a parachute and contribute to regulating plate speeds wedge formation would also have consequences for mantle evolution because the density of a slab stagnated near the bottom of the transition zone would increase as it heats up and the wedge transforms to denser spinel favoring the subsequent sinking of the slab into the lower mantle