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[1] The directivity method of Warren and Silver (2006) has been used to distinguish the fault planes of deep earthquakes in the Tonga and Middle America subduction zones. These studies identified exclusively subhorizontal fault planes between 100 and 300 km depth, raising the question of whether the observations represent new constraints on the physical mechanism of the earthquakes or a bias in the methodology. Here, the strengths, weaknesses, and biases of the method are investigated through the comprehensive analysis of 120 synthetic earthquakes with varying depth, rupture vector orientation, rupture complexity, signal-to-noise ratio, and station distribution. These synthetic tests, which allow the evaluation of the effect of each of the varied parameters on the rupture vector determination, show that fault planes can be identified for a wide variety of conditions. The method underestimates rupture velocities by 76%–94%, but this does not affect the determination of the orientation of the rupture vector. The most important parameter for determining the orientation of the rupture vector, and thereby allowing identification of the fault plane, is the distribution of stations recording the earthquake; better coverage around the earthquakes results in tighter constraints on the rupture vector. The broader distribution of recording stations for deeper earthquakes results in tighter constraints on the rupture vectors for deeper earthquakes and, therefore, more ease in identifying the fault plane. However, the difference in resolution does not systematically prohibit the identification of certain orientations of fault planes at shallower depths and suggests that previous observations of exclusively subhorizontal fault planes between 100 and 300 km depth are not the result of systematic bias in the methodology. Instead, the observed dominance of subhorizontal fault planes provides important constraints on the physical mechanism of intermediate-depth earthquakes. The observed subhorizontal fault orientation is inconsistent with the reactivation of the dominant trenchward-dipping outer rise normal faults.

[1] We make use of rupture directivity to analyze 82 deep earthquakes (≥100 km depth) in the Tonga-Kermadec subduction zone. Identifying the fault planes for 25 of them, we are able to place new constraints on both the physical mechanism of intermediate- and deep-focus earthquakes and deformation within the subducting slab. We find that half of deep earthquakes with MW ≥ 6 have detectable directivity. We compare the obtained fault orientations with those expected for the reactivation of outer-rise normal faults and with those expected for the creation of new faults in response to the ambient stress field. Earthquakes >300 km depth match the patterns expected for the creation of a new system of faults: we observe both subhorizontal and subvertical fault planes consistent with a downdip-compressional stress field. Slip along these faults causes the slab to thicken. Rupture propagation shows no systematic directional pattern. In contrast, at intermediate depths (100–300 km), all ruptures propagate subhorizontally and all identified fault planes, whether in the upper or lower region of the double seismic zone, are subhorizontal. Rupture propagation tends to be directed away from the top surface of the slab. After accounting for the angle of subduction, the subhorizontal fault plane orientation is inconsistent with the orientation of outer-rise normal faults, allowing us to rule out mechanisms that require the reactivation of these large surface faults. Subhorizontal faults are consistent with only one of the two failure planes expected from the slab stress field, suggesting that isobaric rupture processes or preexisting slab structures may also influence the fault plane orientation. If all deformation takes place on these subhorizontal faults, it would cause the slab to thin. Assuming the slab is incompressible, this implies that the slab is also lengthening and suggests that slab pull rather than unbending is the primary force controlling slab seismicity at intermediate depths.

[1] Transformation-induced faulting has been studied extensively in natural olivine, ice, and a variety of other olivine analog systems over the last 15 years and remains a likely candidate mechanism for initiating deep focus earthquakes. The mechanism involves the formation of microscopic packets of fine-grained denser materials from a metastable host, which then behave as mode I features that coalesce to allow bulk mode II shear failure. We present evidence for a new class of transformation microstructures that also allows shear failure at high pressures but which does not require the formation of widely distributed mode I features prior to shear failure. We have observed thin planar zones of transformation in coarse-grained (∼150 μm) Mg2GeO4 olivine that form along crystallographic planes in deformed grains at temperatures cooler than those that allow significant development of anticracks. The development of these zones is rapid and only occurs after ∼25% bulk strain. Increasing strain leads to progressive development of these zones, in turn leading to bulk shear failure once a continuous pathway of fine-grained spinel is formed that traverses the specimen. Transmission electron microscopy analysis shows that slip bands in olivine along (011) and (010) formed from dislocation pileups on these slip planes transform preferentially to a nanocrystalline aggregate of the denser spinel phase, aided by the high strain energy of these bands. This new, partially strain-driven mechanism compliments shear failure by anticracks as described in previous studies and adds new possibilities for the triggering of bulk shear failure by rapid mineralogical transformations.

[1] Olivine within the lowest temperature regions of subducting oceanic lithosphere may persist metastably to depths well below the equilibrium phase boundary for transformation to β phase. This may produce a tapering low seismic velocity wedge within the slab in the transition zone; transformational faulting of such metastable olivine has been proposed as a possible explanation of deep earthquakes. Detecting seismic velocity structure associated with metastable olivine within a slab using seismic wave arrival time information alone has proven problematic. Motivated by previous two-dimensional numerical calculations for upgoing and downgoing seismic waves, a three-dimensional Gaussian beam method is used to assess whether the azimuthally varying teleseismic amplitude signature produced by a slab with an internal wedge of metastable olivine is distinguishable from that for a slab with equilibrium transitions. Five slab velocity structures are considered: a thermal model with horizontal phase transitions at the same depths as in ambient mantle, two models incorporating equilibrium transitions within the slab, and two models with tongues of metastable olivine. A depth- and temperature-dependent thermal conductivity term and the effect of the latent heat of transformation of olivine to β phase are included in the thermal modeling. Three-dimensional dynamic ray tracing and Gaussian beam summation are performed for events located at different depths and lateral positions for each of the slab models. For sources near 400 km depth the presence of low-velocity metastable olivine produces relatively complex azimuthal shear wave amplitude patterns compared to thermal and equilibrium models. Comparison with observed amplitudes for four events in the Kurile slab indicates that allowing for internal slab velocity complexity in the transition zone provides better agreement with observations than simple thermal and equilibrium slab models. This indicates that careful modeling of teleseismic shear wave amplitude patterns may have the resolution to detect and characterize the presence of metastable olivine in deep slabs.

[1] The shear velocity structure of the subducted Kurile slab is modeled using shear wave amplitude residual spheres. We measure long-period SH and ScSH phase amplitudes for 10 intermediate and deep focus earthquakes recorded at World-Wide Standardized Seismograph Network and Canadian Seismic Network stations from 1967 to 1986. After correction for source radiation pattern, geometric spreading, and empirical receiver/upper mantle effects, the data for intermediate depth Kurile slab events show smoothly varying amplitude residual sphere patterns with low amplitudes concentrated in the direction down the slab dip. The data are modeled using three-dimensional dynamic ray tracing and a three-dimensional Gaussian beam method. Starting models are taken from previous P and S wave arrival time residual sphere studies. Three-dimensional ray tracing indicates that ray patterns and resulting amplitudes are very sensitive to the depth extent of the slab and to the position of the event relative to the across-slab velocity gradient. This sensitivity allows us to place some constraints on the Kurile slab geometry, position of each event within the slab, and penetration depth of coherent slab structure. Our final slab model is defined by an asymmetric error function that peaks at 4% higher velocity than Preliminary Reference Earthquake Model 25 km from the top of the slab. The total width of the thermal anomaly averages 140 km. The slab is tabular and extends to 670 km in the northern half of the Kurile subduction zone. In the southern half of the subduction zone the slab flattens along the 670 km discontinuity and deflects laterally, persisting to 750 km depth.

The locations of earthquakes with depth in the mantle provide direct evidence of the trajectory and state of stress of subducting lithosphere. The occurrence over the last decade of isolated large deep earthquakes outside the main Wadati-Benioff zones in the Kurile, Izu-Bonin, and Chile deep seismic areas (in addition to the observed flat distributions of deep seismicity beneath the Banda Sea and Fiji Plateau areas and the large number of deep earthquakes located away from the main slab in the Tonga arc) supports recent tomographic and other seismological studies, leading to a reconsideration of slabs as simple planar structures sinking undeformed into the lower mantle. The focal geometries of these isolated earthquakes, which often exhibit near vertical compressional stresses, are distinct from adjacent events in the main Wadati-Benioff zone. They are also different in orientation from events in the deflecting toe of the slab and from the stress orientation expected if the deflected slab acts as a stress guide. These isolated mantle earthquakes are interpreted to take place in subducted lithosphere that has deflected to a horizontal posture at the base of the upper mantle. Conversely, the deep seismicity in the adjacent Wadati-Benioff zone is associated with the deflection of the subducting lithosphere.

Samples of metastable Mg2GeO4 olivine fail by faulting when loaded at temperatures where the incoherent nucleation and growth of spinel (the stable phase) just becomes possible. At lower temperatures, where the transformation is inhibited, metastable olivine is ductile and strong, while at higher temperatures, where the transformation happens very quickly, samples are ductile and weak. Microfaults that have just been created and have slipped very little contain only very fine-grained spinel. Those that have slipped more contain a mixture of fine-grained spinel and larger, broken, olivine fragments. A new type of transformation microstructure that develops only under nonhydrostatic stress occurs in all specimens that failed; the spinel nucleates on grain boundaries and on subgrain boundaries within olivine and grows as fine-grained, lens-shaped bodies with a strong preferred orientation normal to maximum compression. The correlation between the onset of transformation, the new microstructure, and the mechanical instability suggests a cause and effect relationship. The grain size of the spinel within the microfaults suggests that these zones have superplastic properties; in this case the instability should not be suppressed by increasing pressure as normal frictional processes are suppressed. Analogous conditions exist in down going slabs of lithosphere in the mantle, and we postulate that the same mechanism that causes faulting in our samples operates in the mantle causing deep-focus earthquakes.

Seismograms of Peru-Brazil deep focus earthquakes recorded on the nearby Carnegie broadband station at Cuzco, Peru (CUS) are characterized by an anomalous large-amplitude P wave arrival that follows about 1.5 s after direct P. The anomalous arrival is interpreted to be an underside wide-angle reflection from the upper surface of the descending Nazca plate somewhere in the depth range 150–400 km and in a region where the slab is wholly aseismic. Particle motion analysis of the CUS seismograms shows that the direct P wave has arrival angles as predicted from simple ray tracing. The large, impulsive anomalous phase (termed Pr) also arrives as a P wave but is of opposite polarity and about 1.5 times the amplitude of the direct P arrival. The back azimuth of Pr is about 20° clockwise from the path of direct P, and its angle of emergence is significantly larger. Forward modeling calculations indicate that the seismic observations are consistent with a model in which Pr originates as a P wave that travels up (inside) the slab from the source and is then reflected at wide angle from the steeply dipping upper plate boundary. Results from modeling lead to the following conclusions: (1) the descending Nazca plate exists in and is probably continuous through the aseismic region between 150 and 500 km depth; (2) the plate is very steeply dipping (∼70°) below depths of about 150 or 200 km; and (3) the velocity discontinuity at the reflection point must be relatively sharp, probably less than about 10 km in thickness.

The earthquake focus is represented by a bilateral bidirectional fault model in which the final fault area is rectangular. The transfer functions for body waves for this fault model have been derived. The directivity functions for body waves are defined by taking the ratio of the transfer functions corresponding to two observation stations. The sensitivity of the directivity function for P waves to the kinematic parameters and to the orientation of the fault plane is demonstrated. The S wave directivity function appears to be relatively insensitive to the change in the kinematic parameters. A deep focus earthquake (H = 600 km, mb = 7.0) has been investigated and the kinematic parameters have been successfully recovered using the modulus of the P wave directivity function. The kinematic parameters are as follows: The fault plane is the y-z nodal plane of the focal mechanism solution, the faulting is of the bilateral bidirectional type with total rupture along the y axis of 75 km and total rupture along the z axis of 29.5 km; the rupture speed along the y axis is 3.97 km/sec and along the z axis is 2.98 km/sec. The fault area is 2212 km2 and the dislocation is estimated to be 26 cm.

Seismic and echo sounder profiles in the aftershock region of the 1964 Alaskan earthquake define a pre-existing zone of discontinuous faults in the area of maximum aftershock strain release. Steep reverse faults and possibly other types of steep faults occur in the zone; surface rupture has probably not been continuous along its full length during any Recent earthquake. The fault zone may represent a narrow area of maximum flexure and uplift in the broader area deformed during the 1964 earthquake. An anticline at the continental margin with local large structural relief was also uplifted during the earthquake.

Eight exceptionally deep earthquakes have occurred in the New Hebrides region near 13°S, 170°E. The hypocenters of these events were all restricted to depths between 600 and 650 km. These earthquakes may be indicative of a region of unusual physical properties at depth in the region between the New Hebrides Islands and the Andesite line. The recent detection of exceptionally deep earthquakes in the New Hebrides, in New Zealand, and in the western Mediterranean indicates that the occurrence of similar events in other regions should be considered.

An extension of the technique of multipolar analysis of earthquake radiation patterns yields a new method of calculating seismic moment from the amplitudes of long-period pulses without recourse to spectral analysis. To allow for sources more general than a double couple, the shear invariant L is introduced; for a double couple it reduces to Mo/μ.

This paper combines the recent measurements of P and S wave travel times from intra-plate earthquakes with travel times from deep-focus earthquakes reported earlier to infer the velocity structure of the mantle. It is reasonable that the source bias for intra-plate earthquakes is less pronounced than that for other shallow-focus earthquakes such as those occurring in island arcs. The inclusion of intra-plate earthquakes compensates for the lack of uniform areal distribution exhibited by the deep-focus earthquake data and augments the number of high quality travel time observations. The features observed in the variation of teleseismic travel times from intra-plate earthquakes are consistent with the travel time variation determined from deep-focus earthquakes (especially the P wave travel time variation). The combined intra-plate and deep-focus earthquake travel time data were converted to determine an average (spherically symmetric) compressional and shear velocity model and, subsequently, a three-dimensional compressional velocity model for the earth's mantle. Lateral variation in the mantle accounted for most of the scatter in the observed P wave travel times. The average compressional velocity model suggests two rapid velocity increases at 500 and 670 km depths and a small velocity gradient in the depth interval of 100–450 km. The 3-D model determined from the augmented travel time data set corroborated the earlier findings (1) that the lateral heterogeneities are more pronounced near the upper-mantle and near the core-mantle boundary and (2) that the surface tectonic features are correlated with compressional velocity anomalies near the upper mantle, but not with velocity anomalies below the upper mantle.

Seismic and volcanic activity in the Philippine Islands was examined in an attempt to decipher the tectonics of this region. Several new fault plane solutions for shallow, intermediate, and deep focus earthquakes were determined. This study has revealed the presence of a zone of eastward underthrusting in the western Philippines which is well developed near Negros Island. Fault plane solutions of several shallow earthquakes in the western Philippines show thrust faulting with slip vectors toward east or northeast. As active eastward subduction of the Eurasian plate is also taking place along the Manila trench near west central Luzon, it suggests that the underthrusting of the Eurasian plate may have occurred at one time along the western Philippines from Taiwan to Sulawesi in the Molucca Sea. Subduction has ceased along sections where continental crust is present. This interpretation is consistent with the geology and gravity anomalies in the area. Near the eastern Philippines the westward subduction of the Philippine Sea plate occurs (1) along the Philippine trench and (2) in a localized zone near the western edge of the Benham rise. The Philippine Islands are therefore flanked in the east and west by active but disjointed subduction systems. Left lateral strike slip faulting has been deduced near one end of several of these active trench systems and suggests movement on transverse features. Seismic activity on the Philippine fault is concentrated in the zone between 10°N and 15°N and appears to be due to stresses generated by opposing movements of the Philippine and Eurasian plates which are not released in underthrusting. Fault plane solutions of shallow earthquakes associated with the Philppine fault show left lateral strike slip motion consistent with field observations. Our study suggests that the extent and magnitude of earthquake activity on the Philippine fault forms one component of movement between the Eurasian plate and the Philippine Sea plate.

Previous workers have pioneered statistical techniques to study the spatial distribution of aftershocks with respect to the focal mechanism of the main shock. Application of these techniques to deep focus earthquakes failed to show clustering of aftershocks near the nodal planes of the main shocks. To better understand the behavior of these statistics, this study applies them to the aftershocks of six large shallow focus earthquakes in California (August 6, 1979, Coyote Lake; May 2, 1983, Coalinga; April 24, 1984, Morgan Hill; August 4, 1985, Kettleman Hills; July 8, 1986, North Palm Springs; and October 1, 1987, Whittier Narrows). The large number of aftershocks accurately located by dense local networks allows us to treat these aftershock sequences individually instead of combining them, as was done for the deep earthquakes. The results for individual sequences show significant clustering about the closest nodal plane and the strike direction for five of the sequences and about the presumed fault plane for all six sequences. This implies that the previously developed method does work properly. Nonrandom behavior was also found about the slip directions, the P axis, the T axis, and the B axis, but this is probably caused by the lack of independence between these axes and the previously mentioned features of the focal mechanisms. Given that the method does work and that deep aftershocks were not shown to cluster about the main shock nodal planes, the shallow focus data were used to simulate the deep focus study. The goal is to determine if there are artificial factors that make clustering in the deep focus data unobservable. To more closely mimic the work on deep earthquakes, the largest aftershocks from each of the six sequences were combined and studied with respect to their respective main shock focal mechanisms. This reduced the significance of the clustering about the focal mechanism parameters, but not below 95% confidence. Gaussian noise was then added to the aftershock hypocenters in order to determine if the larger hypocentral and focal mechanism errors in the deep focus data could account for the previous negative result. The conclusion is that the following reasons are sufficient to explain the lack of clustering about the main shock nodal planes for the deep focus aftershocks: the need to combine aftershocks from several sequences, the size of the hypocentral location and focal mechanism errors, and the alignment of distant aftershocks with the Wadati-Benioff zone.

Deep-focus earthquakes—Earthquakes with extremely deep loci occur in well-defined areas. The deepest foci, 600 km and more, are to be found in Japan, the Philippines, the Moluccas, and the Java Sea, in the Polynesian Archipelago, and in South America. Everywhere they are situated along an inclined surface, from the borders of the ocean sloping down below the continents. The slope of this surface is 30° to 40°.