Cutoff Depth Research Articles

Nucleation of large earthquakes determined by the seismic–aseismic boundary: agreement between models and observations

Using a slip-dependent constitutive law, we investigate how the seismic–aseismic boundary determines the nucleation process of large earthquakes. We model the depth variation of the breakdown strength drop and the critical weakening displacement on the basis of several studies by Ohnaka and co-workers. In this model, the breakdown strength drop increases linearly with depth in an unstable seismogenic zone and decreases sharply in a seismic–aseismic transition at the bottom of the seismogenic zone. On the other hand, the critical weakening displacement is almost constant in the seismogenic zone, and increases sharply with depth in the seismic–aseismic transition at the bottom of the seismogenic region as the fracture energy remains constant. It has been reported that large intra-plate earthquakes appear to initiate at the place where the cut-off depth of seismicity changes sharply. We examine a case in which there is a steep depth change in the seismic–aseismic transition at the bottom of the seismogenic region. The results of the simulation show two stages of the accelerating slip: slip velocity enhancement widely along the seismic–aseismic transition at the bottom of the seismogenic region, and subsequent localized accelerated slip in the region of a steep depth change in the seismic–aseismic transition at the bottom of the seismogenic region. The first stage of the accelerating slip will be important for the intermediate-term earthquake prediction. We also consider a broad aseismic weak zone in the seismogenic zone. In this case, first, slip velocity is enhanced in a broad weak zone, then nucleation starts at lower corner of the surrounding strong region. Our numerical results can explain the location of rupture initiation of some recent large earthquakes.

Is the plastic flow uniformly distributed below the seismogenic region?

The cut-off depth of seismicity in and around the Nojima fault broken by the 1995 Kobe earthquake occurring in the intraplate Japan was compared with a brittle-ductile transition depth of the widely-accepted strength profile model of the crust. It was found that the cut-off depth is much deeper than the transition depth under the assumption that wet granite is deformed at a strain rate of 10−15/s. Such a small strain rate implies that the plastic flow is uniformly distributed below the seismogenic region. When the strain rate is assumed to be greater than 10−13, the cut-off depth can be attributed to the transition depth. This suggests that deformation is localized in a narrow fault zone below the seismogenic region even in the intraplate region.

3-D crustal structure of the extensional Granada Basin in the convergent boundary between the Eurasian and African plates

Three-dimensional P and S wave velocity models of the crust under the Granada Basin in Southern Spain are obtained with a spatial resolution of 5 km in the horizontal direction and 2 to 4 km in depth. We used a total of 15407 P and 13704 S wave high-quality arrival times from 2889 local earthquakes recorded by both permanent seismic networks and portable stations deployed in the area. The computed P and S wave velocities were used to obtain three-dimensional distributions of Poisson's ratio ( σ) and the porosity parameter ( V p× V s). The 3-D velocity images show strong lateral heterogeneities in the region. Significant velocity variations up to ±7% in P and S velocities are revealed in the crust below the Granada Basin. At shallow depth, high-velocity anomalies are generally associated with Mesozoic basement, while the low-velocity anomalies are related to the neogene sedimentary rocks. The south–southeastern part of the Granada Basin exhibits high σ values in the shallowest layers, which may be associated with saturated and unconsolidated sediments. In the same area, V p× V s is high outside the basin, indicating low porosity of the mesozoic basement. A low-velocity zone at 18-km depth is found and interpreted as a weak–ductile crust transition that is related to the cut-off depth of the seismic activity. In the lower crust, at 34-km depth, a clear slow V p and V s anomalous zone may indicate variations in lithology and/or with the rigidity of the lower crust rocks.

Seismogenic layer, reflective lower crust, surface heat flow and large inland earthquakes

Regional variations in the cutoff depth of seismicity in southwest Japan are derived from more than 60,000 well-determined earthquakes. The thickness of the seismogenic layer is closely related to the strength of the crust and accordingly to the occurrence of large inland earthquakes, since the seismic–aseismic boundary is thought to be related to the brittle–ductile boundary in the crust. Large inland earthquakes are likely to occur in the area where the cutoff depth of seismicity changes abruptly. It is therefore important to survey the regional variations in this depth to evaluate the potential of large inland earthquakes. The cutoff depth of seismicity roughly coincides with a temperature range of 300–400°C in the crust. In addition, distinct S-wave reflectors as well as a reflective lower crust have generally been observed in some areas in Japan. The depths of the reflector and the top of the reflective lower crust lie several kilometers below the cutoff depth of seismicity and they seem to coincide with a temperature range of about 300–450°C. Therefore, in those areas where no earthquakes occur but a reflective layer exists, the cutoff depth can be mapped from a survey of reflectivity in the crust. The heterogeneity of the crust is very important for understanding the nature of the crust where large earthquakes are frequent. This paper proposes a model of crust inhomogeneity based on observation results.

NW Pacific slab rheology, the seismicity cutoff, and the olivine to spinel phase change

Along the Kamchatka-Kuril-Japan-Izu-Bonin-Mariana subduction zones, the old age of the subducting Pacific Plate and the rapid subduction rate together suggest that earthquakes should occur to the bottom of the transition zone. However, the seismicity cutoff varies in depth between 350 km and 650 km. Along these subduction zones, the largest deep-focus earthquakes invariably occur near the depth of the local seismicity cutoff regardless of its depth. The events near the seismicity cutoffs also have systematically different focal mechanisms than shallower events. Furthermore, data from S660P arrivals, residual sphere analysis, and tomographic studies all show that the slab dip consistently steepens to a near-vertical orientation at the seismicity cutoff. This change in slab dip indicates a strength loss in the slab. We hypothesize the following causal connection among all these observations: The cold temperatures in the slab kinetically hinder the olivine to spinel phase change and allow the olivine to persist metastably to depths well below its equilibrium pressure. When the phase transition occurs, it nucleates very fine-grained spinel which acts as a lubricant, allowing the initiation of earthquake faulting at high confining pressures which further nucleates additional fine-grained spinel. The cold anomaly of the slab severely inhibits the growth of the nucleated spinel crystals. The presence of the fine-grained spinel crystals reduces the strength of the coldest part of the slab by several orders of magnitude, allowing high slab deformation rates. Additionally, the phase change, by increasing the density, provides a negative buoyancy force. Combined, these processes reduce the slab membrane strength and allow the slab to descend at a steeper dip.

P‐wave tomographic images in the Central Betics‐Alborán Sea (South Spain) using local earthquakes: Contribution for a continental collision

To investigate the relationship between shallow and intermediate‐depth earthquakes and the crust and upper mantle structure beneath the Betic‐Cordillera and Alborán sea region, we have applied seismic tomography to 2569 P‐wave arrival times from 367 microearthquakes recorded by both permanent and temporary seismic stations deployed in the region. These earthquakes occurred in the depth range of 0 to 110 km beneath the Central Betic Cordilleras and Alborán sea. Our results have revealed significant structural heterogeneities in the crust and upper mantle beneath the study area. In the upper crust there is a high‐velocity anomaly at Sierra Gorda (western boundary of the Granada basin) penetrating to 15 km depth, which is in good agreement with the aeromagnetic anomaly. In the Granada basin, a low‐velocity anomaly is located in the middle crust, which coincides with a previously detected greater cutoff depth of seismicity, and are considered to be associated with a highly fractured zone generated by an intracrustal detachment. The northern boundary of the Alborán sea (Málaga coast) is well imaged as low velocities from 50 to 90 km depths. This low‐velocity zone in the upper mantle is associated with the intermediate‐depth seismicity, which outline a section of continental crust related to the collision/subduction beneath the northern part of the Alborán sea‐southern part of the Central Betics.

The Compound Matrix Method for Multi-Point Boundary-Value Problems Depending on a Parameter

Boundary-value problems for ordinary differential-equation (ODE) systems often depend on a parameter. It is shown how derivatives of the solution with respect to the parameter can be computed using compound matrices in the linear multi-point case. In the applications, such derivatives are useful e.g. in inversion theory when the parameter is to be estimated. When the dependence on the parameter is analytic, an integral of boundary-problem solutions with respect to the parameter can typically be expanded as a sum of residues. Such integrals and expansions have theoretical as well as practical interest, and an explicit formula is derived for the residue contributions. It is given in terms of eigensolutions to the original problem and an appropriately defined adjoint problem. It is shown how the quantities involved can be computed in a stable way using compound matrices. For the application case with wave-propagation in a range-independent multi-region fluid-solid medium, a solution to the adjoint problem is obtained directly from a solution to the original problem, and the well-known formula for modal excitation coefficients is extended to leaky modes. Modal depth functions can be computed reliably without experimentation with a cut-off depth for an artificial homogeneous half-space.

A lithospheric cross-section through the Swiss Alps-II. Constraints on the mechanical structure of a continent-continent collision zone

SUMMARY The calculation of strength profiles along the European Geotraverse (EGT) through the Swiss Alps yields constraints on the large-scale vertical and lateral mechanical structure through the Alpine continent-continent collision zone. Strength profiles are evaluated for different assumptions on petrological stratification and strain rate and are based on temperature-depth profiles derived from transient thermo-kinematic modelling of the Neoalpine orogeny. The main contribution to the total strength results from the mantle lithosphere, which is strongly controlled by temperature. In contrast, the crustal contribution is mainly determined by variations in petrological stratification. A direct correlation between surface heat flow and the total strength of the crust, the mantle lithosphere and the entire lithosphere (crust and mantle lithosphere) is not observed. Our results demonstrate that in tectonically active areas a transient thermal model, along with detailed knowledge of the deep structure and petrology, is necessary to evaluate lithospheric strength envelopes. Inside the collision zone, strain rate has a strong control on the bottom of the mechanically strong crust, whereas outside the collision zone the effect is less significant. The cut-off depth of seismicity along the profile, which correlates largely with the bottom of the mechanically strong crust, deviates from the 300-400°C isotherm. The inferred effective elastic thickness for the Molasse Basin north of the Alps is in agreement with flexural modelling results, whereas for the Southern Alps the predictions deviate.

Distinct S wave reflector in the midcrust beneath Nikko‐Shirane volcano in the northeastern Japan arc

Distinct S waves reflected from a midcrustal seismic velocity discontinuity are detected beneath Nikko‐Shirane volcano in the southernmost part of the northeastern Japan arc. A detailed travel time analysis of the reflected S waves by using data acquired through a dense seismic network temporarily set up in this region shows that this unusual S wave reflector is distributed over an area of 15 × 15 km2 at depths ranging from 8 to 15 km. The reflector has a conical shape becoming shallow toward the summit of Nikko‐Shirane volcano. Observed amplitude spectral ratios of reflected S waves to direct S waves show that the reflector body has a strong velocity contrast to the surrounding medium and its thickness is of the order of 100 m at most. The reflector body is approximated by two thin layers probably filled with partially molten materials. Cutoff depth for shallow seismicity in this area is 3–5 km above the reflector and becomes shallow toward Nikko‐Shirane volcano, nearly parallel to the reflector. The depth to brittle‐ductile transition zone seems to be prescribed by the existence of the reflector body, which is perhaps a thin magma body.

Compound-matrix methods for computation of wave fields in horizontally layered fluid–solid media

The wave field is decomposed into its frequency-wave-number components, and a compound-matrix ODE theory is formulated for multiregion fluid–solid media using multipoint boundary conditions. Forward propagation of compound entities is done to a matchingdepth, from which stabilized backward propagation to the receivers is performed. Wave-number integration as well as modal synthesis is covered. Source arrays and receivers may be arbitrarily located. An appropriate adjointproblem is defined and solved. The formula for modal excitation coefficients is generalized to cover leakymodes, which have an exponential increase with depth. Three methods for stable and automatic computation of modal depth functions, in solid as well as fluid regions, are proposed. In work by M. B. Porter and E. L. Reiss [J. Acoust. Soc. Am. 77, 1760–1767 (1985)] the mode shapes in the solid bottom were left aside, and the method by F. Schwab etal. [Bull. Seismol. Soc. Am. 74, 1555–1578 (1984)] involves experimentation with a cutoff depth for an artificial homogeneous half-space. For a medium composed of homogeneous layers, it is shown how efficient computations are obtained by writing the propagator matrices involved as products of sparse matrices, which are applied in sequence. Numerical stability can be achieved without artificially splitting thick homogeneous layers.

特集 火山活動と地殻応力場 地溝幅が火山付近で狭くなる現象について：雲仙‐島原地溝の場合

The central Kyushu is a north-south spreading region characterized by east-west trending grabens and abundant active volcanoes. Available data indicate that the width of graben is 11-12 km apart from eruption centers of Unzen volcano, whereas it narrows down to about 7 km dose to the eruption centers. Focal mechanisms of earthquakes suggest that north-south tensional axis is not altered by the presence of volcanic conduit. Width of graben in general is pos tively correlated with thickness of lithosphere, and the width of graben is narrowed locally in accordance with the thinning of lithosphere beneath active volcanoes by the presence of magma chamber in middle crust. Evidences supporting this idea include shallow cutoff depth of seismicity and mid-crust low velocity area beneath the active volcano, shallow Curie temperature distribution, and high oxygen isotopic composition of the volcanic rocks.

Optimum depth of partial cut off with blanket in stratified foundations of Kapur Dam : Goel, M C; Mandavia, A B Proc Ninth Asian Regional Conference on Soil Mechanics and Foundation Engineering, Bangkok, 9–13 December 1991V1, P319–322. Publ Thailand: Southeast Asian Geotechnical Society, 1991

Optimum depth of partial cut off with blanket in stratified foundations of Kapur Dam : Goel, M C; Mandavia, A B Proc Ninth Asian Regional Conference on Soil Mechanics and Foundation Engineering, Bangkok, 9–13 December 1991V1, P319–322. Publ Thailand: Southeast Asian Geotechnical Society, 1991

Earthquake cutoff depth as a possible geothermometer—applications to central Japan

Geothermal models of the Earth's crust are constructed for eight individual structural units of Honshu island, Japan. For each unit, thermal models responding to possible property variations are calculated. In addition to conductive heat transfer, the considered geothermal models account also for the thermal effects of fluid circulation within the crust and tectonic motions across the faults. On the basis of these geothermal models Theological models of the crust are derived. Those thermal models are considered as most reliable where there is reasonable correspondence between rheological stratification of the crust and the variations of crustal seismicity. It is demonstrated that earthquake cutoff depth, serving as a kind of “geothermometer”, can be used as additional information to decrease the uncertainties involved in the geothermal models.

SOUND PROPAGATION IN SHALLOW WATER: IMPLICATIONS FOR ACOUSTIC COMMUNICATION BY AQUATIC ANIMALS

ABSTRACT Measurements of sound propagation were made in a shallow, sloping bottomed freshwater pond. The frequency responses of the pond had a highpass characteristic with a sharp cutoff frequency. Cut-off frequency of the response was inversely related to the depth of water at the shallowest transducer (either projector or receiver) and was the same whether propagating downslope or upslope (reciprocity). The relationship between cut-off frequency and depth was significantly different from that expected for propagation in a channel with either a rigid or pressure release (gas) bottom. The highpass characteristic is due to modal propagation in the ‘waveguide’, and the effect of this environmental filtering is 30–60 dB between frequencies that propagate and those that do not. Thus, the physical constraints of this shallow-water environment on acoustic communication by aquatic animals are much greater than those measured in terrestrial environments. These constraints are discussed relative to selection for behavioural adaptations of acoustically signalling aquatic animals and are compared to similar adaptations found in terrestrial systems.

Cutoff depth of seismicity and large earthquakes near active volcanoes in Japan

Abstract Cutoff depths of seismicity in the earth's crust change from place to place over a range of 5–25 km. These variations are closely related to the values of the surface heat flow. In order to examine regional variations in greater detail, available cross sections of well-determined focal depths have been collected for five areas located near active volcanoes, where the thermal structure is considered to change abruptly. The seismic-aseismic boundary is located at depths of about 5–8 km immediately below the craters, with increasing depth towards the flanks of the volcanoes. The boundary is found at depths of 10–15 km at distances of about 10 km from the center of the volcanoes. Further, an examination was performed of the magnitudes of earthquakes versus the distances from the craters for seven volcanoes, near which large earthquakes ( M ≥ 6) occurred during the past 30 years. All of the large earthquakes were found to have occurred at distances of approximately 10 km or greater from the center of the volcanoes. Moreover, the distances between active volcanoes and earthquakes were calculated for all large intra-plate earthquakes in Japan that have occurred during the period 1885–1990. It was found that all the large earthquakes occurred at distances of more than 10 km from active volcanoes. These facts suggest that the seismogenic layer near the center of an active volcano is thin and not strong enough to accumulate sufficient stress for the occurrence of large earthquakes.

On a bound for the frequency of surface waves trapped near a cylinder spanning a channel

There has been substantial effort recently put into proving, for a variety of different geometries, the existence of trapped waves, that is unforced time-harmonic motions which do not radiate energy to large distances. Thus it is known that such motions can exist in a deep channel which includes a cylinder spanning the channel, for various shapes of cylinder. The converse problem of proving the absence of such trapped waves has received much less consideration, and the only relevant uniqueness proof for a channel spanned by a cylinder is that of McIver (1991). In an appendix to that paper, McIver demonstrates that no trapped-wave motions can exist for the case in which the cylinder is surface piercing and is entirely contained between vertical planes through the free-surface intersections. This is exactly the same geometrical condition which John (1950) found would ensure uniqueness in water-wave radiation and scattering problems, in finite or infinite depth. Both John and McIver achieved their uniqueness results by consideration of integrals of the potential along vertical lines down from the free surface. John's work was extended by Simon and Ursell (1984) who established uniqueness for a wider class of two-dimensional radiation and scattering problems by consideration of integrals along nonvertical lines. The work presented in this paper is the corresponding extension of McIver's work; although this extension does not rule out trapped waves at all frequencies for any geometry except that already considered by McIver, it does yield an easy lower bound for the ratio of the trapped-mode frequency to the cut-off frequency, in finite or infinite depth.

Implications of the distribution of seismicity near Lake Bogoria in the Kenya Rift

SUMMARY Previous seismicity studies in the Kenya Rift have not been able to determine accurately depths of earthquakes, nor have most of them determined epicentres precisely enough to allow correlation of the seismicity with particular surface features. We operated a small dense seismic array for 3 months near Lake Bogoria in the Kenya Rift with the aim of locating microearthquakes in 3-D. 572 earthquakes, 81 per cent with ML < 1.0, have been located. The majority of the events are associated with the larger older faults on the Rift shoulder rather than the young ‘grid’ faults in the centre of the Rift. Seismic activity in the central trough cannot be related directly to the surface faulting; we infer that it indicates the presence of deep buried faults. This possibility has important implications for extension estimates and models of the Rift. Most of the activity occurs at depths less than 12 km, and no normal activity is deeper than 16 km. There is a peak in seismic activity at a depth of 9–10 km and the cut-off depth for brittle failure is taken at 12 km. The depth distribution of these earthquakes is similar to that found in other intracontinental areas with similar heat flow which suggests that the crust beneath the Kenya Rift is of normal rheology.

The geometry of Aleutian subduction: Three‐dimensional kinematic flow model

We construct a steady state kinematic model of slab flow along the Aleutian Arc assuming the slab's geometry is known. The slab geometry is constrained by local network data where the slab is seismically active and by P wave residual‐sphere analysis of 11 earthquakes and one nuclear explosion where it is aseismic. The slab is approximated by a thin Newtonian sheet subducting in a less viscous and incompressible mantle. Particles enter the trench at known rates of relative plate motion and are required to subduct along the predefined slab geometry. For discrete, but small (0.1 m.y.) time steps, we determine the speed and direction of each slab particle that minimizes dissipation power as the spherical shell (oceanic lithosphere) deforms to obtain the observed slab shape. Because the dip of the slab in the central Aleutians is steep relative to the radius of curvature of the trench, the slab must stretch along arc to obtain its present configuration. Our kinematic model represents one internally consistent flow that results in the observed geometry. Furthermore, it provides a lower bound on the total amount of internal in‐plane deformation required by the shape and an estimate of stream lines and of the orientation and spatial distribution of the deformation rate. The predicted in‐plane strain rate field is dominated by along arc extension, reaching values as large as 10−15s−1 in the central Aleutians and decaying by an order of magnitude to the east and west. The slab accumulates an in‐plane strain of 10% by the time it reaches the depth of the seismicity cutoff. Along‐arc variations in both the magnitude and orientation of calculated strain rates are consistent with the spatial distribution of seismic moment release and source mechanism orientations of intermediate‐depth earthquakes, suggesting that in order to understand intermediate‐focus earthquakes one must consider along‐arc deformation. Three‐dimensional analyses of subduction in a spherical geometry, such as the present study, are required to model along‐arc effects. Relative plate motions along the trench vary from nearly normal in the eastern Aleutians to transform farther west. Coincident with this change, the maximum depth of seismicity within the descending slab decreases from 250 to 50 km and active andesitic volcanism ceases. The kinematic flow model predicts that the slab subducted obliquely along the central portion of the Aleutian Arc is transported laterally westward producing cold slab material to a depth of at least 300 km along the entire arc after only 15 m.y. of subduction. The lack of volcanic activity in the western Aleutians is apparently related to the lateral transport of the slab, perhaps indicating that the slab is dehydrated and incapable of producing the volatiles necessary for arc magmatism. The along‐arc variation in the maximum depth of seismicity can be explained thermally. We construct temperature estimates within the slab using a quasi three‐dimensional finite difference scheme, including entrained mantle flow, stream lines from the kinematic model and the time history of the age of the subducting lithosphere as a function of position along the trench. The theoretical temperature at the seismicity cutoff depth is remarkably close to a constant fraction of the depth‐dependent mantle solidus along the entire arc. This observation is consistent with the hypothesis that seismicity terminates because of the initiation of high‐temperature, steady state creep and provides an explanation for the lack of intermediate‐focus earthquakes in the western Aleutians even though slab material exists there.

Regional variations of the cutoff depth of seismicity in the crust and their relation to heat flow and large inland-earthquakes.

More than 8, 000 earthquakes have been relocated to derive regional variations of the seismic-aseismic boundary in the mid-crust of the northern Kinki district of Japan. The boundary depths are estimated as 13-15 and 18-20 km in the southwestern and northeastern parts of the study area, respectively. The relationship between the seismic cutoff depth and the cause of large intraplate earthquakes is studied, making use of the present observations and other available data of seismicity and surface heat-flow, on the basis of the brittle-ductile transition of rock deformation. The regional variations in the cutoff depth of seismicity appear to be well correlated with the thermal structure of the crust. The cutoff depths in various heat-flow provinces in Japan and other countries are found to be inversely proportional to the surface heat-flow values, with the depths roughly corresponding to isotherms of 200-400°C. The shape of the depth-frequency distribution of earthquakes calculated from high-quality data is quite similar to that of the shear resistance calculated using a simple brittle-ductile transition model. Large intraplate earthquakes appear to originate at the peak or just below the peak in the depth-frequency distribution, which also corresponds to the deepest portion of the seismogenic layer. Furthermore, in the source area of large earthquakes, rupture seems to start where sharp changes occur in the cutoff depth of seismicity. Thus, the seismic-aseismic boundary is closely related to large intraplate earthquakes and, in turn, to the tectonics of island arcs.

Plastic instabilities: Implications for the origin of intermediate and deep focus earthquakes

Adiabatic or catastrophic plastic shear has been reported in metals, polymers, and metallic glasses. The phenomenon is associated with rapid stress drops and audible pings or clicks as the material deforms in a plastic manner. The driving force for the plastic instability is the stored elastic strain energy of the loading system, and in many respects the behavior is reminiscent of the shear stress response arising from stick slip events during unstable frictional sliding, although the precise mechanism is different. It is shown here that adiabatic plastic shear is capable of explaining the detailed distribution of intermediate and deep focus earthquakes within subduction zones, the earthquake events being the result of instabilities in material undergoing plastic flow. It is argued that for a particular strain rate there exists a critical temperature, TC, which is depth dependent; for temperatures below TC the material is strain rate softening and, for a soft enough loading system, may undergo catastrophic plastic shear. For temperatures above TC the material is strain rate hardening and is always stable during plastic shear. The cutoff depth for deep focus earthquakes then corresponds to the transition from strain rate softening to strain rate hardening material, and for commonly accepted geothermal gradients within the slab corresponds to approximately 800 km. The precise distribution of earthquakes within the slab is a function of the subtle interplay between the geothermal gradient and the TC gradient. In particular, a decrease in seismic activity is to be expected below about 300 km in the slab with total stress drops decreasing from a maximum of 700 MPa above 300 km to a maximum of ≈ 50 MPa below 300 km. The differences in foci distribution between subduction zones such as Tonga, New Hebrides, and Peru result from minor differences in the geothermal gradients within the slabs. The model predicts the development of triple seismic zones high in the slab, double seismic zones down to approximately 300 km, and single seismic zones down to ≈ 800 km. Such a distribution is to be expected of relatively young, cool slabs; as the slab heats up, the seismic activity retreats up the slab. The paper only proposes a deformation mechanism for earthquake generation, it does not address the stress field within the slab but only the distribution of strength. Thus the distribution of focal plane mechanisms is not considered, only the locations where earthquakes due to plastic instabilities are possible. The absence of earthquakes does not necessarily mean that the slab does not exist, it only means that the slab is too hot to undergo plastic instability. This means that aseismic subduction is a distinct possibility in many regions of high geothermal gradient within the slab (i.e. &gt; circa 3°C km−1).