The 2011 Tohoku Earthquake
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Analysis of seismic magnitude differentials (mb−Mw) across megathrust faults in the vicinity of recent great earthquakes
Earth, Planets and Space volume 64, Article number: 14 (2012)
Spatial variations in underthrusting earthquake seismic magnitude differentials (mb − Mw) are examined for plate boundary megathrusts in the vicinity of the 26 December 2004 Sumatra-Andaman (Mw 9.2), 2010 Maule, Chile (Mw 8.8), and 11 March 2011 Tohoku, Japan (Mw 9.1) great earthquakes. The magnitude differentials, corrected for ω-squared source spectrum dependence on seismic moment, provide a first-order probe of spatial variations of frequency-dependent seismic radiation. This is motivated by observations that the three great earthquakes all have coherent short-period radiation from the down-dip portions of their ruptures as imaged through back-projections, but little coherent short-period energy from shallower regions where large coseismic slip occurred. While there is substantial scatter in the magnitude measures, all three regions display some increase in relative strength of short-period seismic waves with depth, with the pattern being strongest for Sumatra and Japan where the deeper portion of the seismogenic zone is below the overriding crust. Other regions such as the Kuril Islands, Aleutians, Peru, and Southern Sumatra/Sumba show little, if any, depth pattern in the magnitude differentials. Variation in material and frictional properties over particularly wide seismogenic megathrusts likely produce the depth-dependence observed in both mb−Mw residuals and great earthquake seismic radiation.
Seismic radiation from earthquakes on interplate megathrust faults has long been known to vary spatially (e.g., Lay et al., 1982; Kanamori, 1986). The most dramatic example of this is provided by “tsunami earthquakes”, which are large tsunamigenic thrust faulting earthquakes that rupture shallow (<15 km) depths of megathrusts and have anomalously low surface wave and body wave magnitudes relative to their long-period moment magnitudes (Mw) (Kanamori, 1972). The deficiency in short-period seismic energy release is generally attributed to unusually low rupture expansion rate or slow particle dislocation velocities that may result from the presence of low rigidity sediments and pore fluids in the fault zone at shallow depths (e.g., Kanamori and Kikuchi, 1993; Newman and Okal, 1998; Polet and Kanamori, 2000; Lay and Bilek, 2007). Large tsunami earthquakes are relatively rare, but widespread smaller un-derthrusting ruptures at depths less than 15 km can exhibit similarly anomalous long source durations relative to typical sources (Bilek and Lay, 1999, 2002; Lay and Bilek, 2007; Bilek, 2007; Bilek et al., 2012).
Large earthquake ruptures deeper on the megathrust also vary in complexity of seismic radiation, which is generally attributed to heterogeneity in fault strength and/or frictional properties (e.g., Lay et al., 1982; Kanamori, 1986; Kikuchi and Fukao, 1987; Yamanaka and Kikuchi, 2004; Lay et al., 2012). Spatial variations of megathrust rupture process are observed both along trench strike and along slab dip (e.g., Yomogida et al., 2011). The underlying causes of the variability are uncertain, but likely contributing factors include variations of temperature, normal stress, fault zone fluids, megathrust geometry and roughness, sediments, and fault zone rock properties.
Several recent great megathrust earthquakes have ruptured across entire seismogenic widths, and availability of extensive seismic data has enabled the first detection of frequency-dependent radiation as a function of depth on the fault during the ruptures (e.g., Lay et al., 2012). This has been demonstrated for the 26 December 2004 Sumatra-Andaman (Mw 9.2), 27 February 2010 Maule, Chile (Mw 8.8), and 11 March 2011 Tohoku, Japan (Mw 9.1) earthquakes (Fig. 1), as discussed below.
The cause of this depth-variation in seismic radiation is not yet fully understood, and it is important to establish whether it is produced by distinctive rupture processes that only occur during great earthquakes or is a manifestation of material properties and stress heterogeneity that also affects smaller events. We address this question by considering whether seismic magnitude measures that characterize relative short-period and long-period seismic radiation for smaller events on megathrusts also indicate depth-dependent patterns. Seismic magnitudes provide limited characterization of the source spectra, but evidence is found for depth variation in magnitude differentials consistent with the seismic radiation observations for great earthquake ruptures near the 2004 Sumatra-Andaman, 2010 Maule, Chile and 2011 Tohoku, Japan events.
2. Depth Variations of Seismic Radiation for Great Earthquakes
Characterizing frequency-dependent variations of seismic radiation on megathrusts is challenging due to the intrinsic variability and size scaling of earthquakes, the limitations on coverage and bandwidth of seismic observations, and the spatial averaging effects of seismic waves. The recent evidence for distinctive seismic radiation from the deeper portion of the seismogenic zone for the three great earthquakes in Fig. 1 has come from back-projection of large aperture network recordings of teleseismic P waves, following methods introduced by Ishii et al. (2005). Coherent localized sources of short-period (~1 s) radiation (Fig. 1) have been imaged for the 2004 Sumatra-Andaman earthquake (e.g., Ishii et al., 2005; Krüger and Ohrnberger, 2005; Lay et al., 2012), 2010 Chile earthquake (Lay et al., 2010; Kiser and Ishii, 2011; Wang and Mori, 2011b; Koper et al., 2012), and 2011 Tohoku earthquake (Ishii, 2011; Koper et al., 2011a, b; Meng et al., 2011; Wang and Mori, 2011a; Yao et al., 2011; Zhang et al., 2011). For the 2011 Tohoku earthquake the sources of teleseismic short-period radiation are located close to sources of strong ground motion accelerations determined by Kurahashi and Irikura (2011), suggesting a common origin.
The source locations for coherent ~1 s short-period radiation to teleseismic distances are found to be in the down-dip portions (30–55 km deep) of the megathrusts. This is deeper than the regions of large coseismic slip determined by many inversions and modeling of seismic, geodetic, and tsunami observations for the 2004 Sumatra-Andaman earthquake (e.g., Ammon et al., 2005; Vigny et al., 2005; Chlieh et al., 2007; Rhie et al., 2007), 2010 Chile earthquake (e.g., Lay et al., 2010; Lorito et al., 2011; Pollitz et al., 2011b; Vigny et al., 2011), and 2011 Tohoku earthquake (e.g., Ammon et al., 2011; Fujii et al., 2011; Hayes, 2011; Ide et al., 2011; Iinuma et al., 2011; Ito et al., 2011; Koketsu et al., 2011; Lay et al., 2011; Lee et al., 2011; Maeda et al., 2011; Ozawa et al., 2011, 2012; Pollitz et al., 2011a; Shao et al., 2011; Simons et al., 2011; Yokota et al., 2011; Yoshida et al., 2011; Yue and Lay, 2011; Wei et al., 2012). The various finite-fault rupture models differ in precise placement of slip on the fault, notably with geodetic inversions locating the slip closer to the coast than do seismic inversions for the 2010 Chile and 2011 Tohoku events. However, the overall offset of regions with large slip from locations of sources of short-period coherent radiation is quite systematic, as summarized in Fig. 1. The shallowest portion of the 2011 Tohoku rupture appears to have behaved as in a tsunami earthquake, and very large slip of 40–80 m has been estimated offshore near the trench, but no coherent 1-s sources of short-period radiation are imaged there. It is not yet resolved whether the 2010 Chile event ruptured to the trench, but recent geodetic inversions (e.g., Vigny et al., 2011) favor large slip being relatively far offshore as in some seismic models (Lay et al., 2010), although not peaking near the trench as for the 2011 Tohoku rupture. Recent tsunami modeling indicates that the same is true for the 2004 Sumatra-Andaman event (Poisson et al., 2011).
3. mb−Mw Differential Magnitude Patterns
Spatially isolating regions of distinct source spectrum within a great rupture is very difficult, and back-projection methods do not provide robust absolute amplitude constraints on the source spectrum at any depth. Systematic analysis of rupture processes or spectra of moderate and small events on the megathrust is a worthwhile, but massive undertaking (e.g., Bilek and Lay, 1999; Bilek et al., 2012), so we take an alternate approach in this study of comparing short-period and long-period seismic magnitudes to give a first-order measure of any systematic spectral differences. Teleseismic P wave magnitudes, mb, compiled by the United States Geological Survey (USGS) National Earthquake Information Center (NEIC) are used as azimuthally averaged measures of relative source strength near 1 s period, and seismic moment magnitudes, Mw, determined from global long-period seismic wave inversions tabulated in the global Centroid-Moment Tensor (gCMT) catalog are used as measures of relative long-period (>30 s) source strength. We compute magnitude differentials, mb−Mw for events with Mw ≥ 5.0 for earthquakes with focal mechanisms and locations indicative of megathrust underthrust-ing events. The gCMT catalog for Mw ≥ 5.0 is probably quite complete in each of our source areas. Shallow dipping thrust mechanisms with dip values from 10° to 30° were retained. This is performed for the subduction zones where the three great events in Fig. 1 ruptured, as well as for four other subduction zones (Kuril Islands, Aleutian Islands, Southern Sumatra/Sumba, and Peru) where tsunami earthquakes have occurred, indicating some depth-dependent variations. The entire gCMT catalog is considered, using all solutions and USGS magnitudes from January 1976 to August, 2011.
For events with Mw < 5.0, relatively few gCMT solutions are available, and the source durations of such events are typically less than 1 s, so mb and Mw should be equal on average. As seismic moment increases, the source spectrum corner frequency lowers, progressively causing mb to be lower than Mw yielding mb − Mw differentials that are increasingly negative. This shift of corner frequency is also accompanied by an intrinsic bias in the routine estimation of mb for teleseismic short-period P-waves caused by using only the first few seconds of rupture to measure the peak 1-s period amplitude. The source duration exceeds that time window for events larger than about Mw = 6.5. For great earthquakes with very long source durations, the mb and Mw values clearly differ due to these saturation effects (for 2004 Sumatra, mb = 6.8, mb − Mw = −2.4; for 2010 Chile, mb = 7.2, mb−Mw = −1.6; for 2011 Tohoku, mb = 7.2, mb −Mw = −1.9). Thus, using any significant range of earthquake sizes to evaluate spatial patterns in mb −Mw differences requires a correction of the differential magnitudes for size dependence.
We correct for the saturation effect on mb − Mw measures using the ω-squared source spectrum scaling of Brune (1970). For this model, the far-field source time function spectrum is given by D(ω) = Mo/[1 + (ω/ωc)2], where ωc is the corner frequency for a given seismic moment, Mo. We can either specify the corner frequency and its seismic moment scaling in terms of a stress parameter, ωc = 2πcβ(Δσ/Mo)0.33, where β is shear wave velocity and the constant c = 0.49 for SI units, and assume a constant stress parameter Δσ, or we can relate the corner frequency to a characteristic source duration and scale that with Mo. Observationally, we know that a typical Mw = 6.0 interplate thrusting event on the central megathrust(Mo = 1.25× 1018Nm;Mw = [log10(Mo) − 9.1]/1.5) has a duration of about 3 ± 1 s (e.g., Tanioka and Ruff, 1997; Bilek and Lay, 1999), and for self-similar ruptures the duration should approximately scale proportional to (e.g., Aki, 1967; Kanamori and Anderson, 1975). For a reference Mw = 5.0; Moref = 3.94 × 1016 N m with duration tref = 0.95 s. Using that reference, the relative 1 s spectral amplitude is computed as a function of Mw using the equations above, and the differential shift relative to Mw is tabulated as a correction to mb −Mw differentials. Other choices of reference Mw give very similar data trends, and do not affect our conclusions, and use of Mw = 5.0 sets a convenient baseline of mb−Mw = 0.0 since the typical corner frequency is expected to be near the period for which mb is measured. For Mw = 9.2 the correction is −.8, which is generally compatible with the great earthquake observations. This correction is only approximate; for example it assumes that measured Mw is based on true static displacement Mo value when it is typically made in the 30–200 s period band, and that mb is measured exactly at 1 s period without bias due to using too short of a time window. For Mw = 6.5, the mb− Mw correction is −0.44, and the estimated source duration is just over 5 s, so the procedure used is reasonable for the magnitude range Mw 5.0 to 6.5, and we will constrain our assessment of depth dependence to that range. We find that for that range, the effect of applying the source scaling corrections is very small for any depth-dependent trends because there is substantial scatter and little correlation exists between event size and source depth. We explored using a data base of short-period P wave amplitude measures made using longer time windows for large events (K. Creager, personal communication, 2011), but the number of stations available and the coverage of events in our regions of interest was too limited to extend the magnitude range with unbiased (although still saturated) mb values.
The event selection process and mb − Mw differentials, corrected for source spectrum scaling over the full range of Mw (5.0 to 9.0) for the subduction zone near the 2011 Tohoku earthquake are illustrated in Fig. 2. The gCMT best double couple focal mechanisms are plotted at the gCMT centroid locations with colors indicating the centroid depth and symbol sizes scaled proportional to Mw. These events were judged to be interplate megathrust events based on their locations, depths and shallow-dipping thrust mechanisms. The corresponding mb−Mw measures with corrections are shown on the right map, also plotted at the centroid epicenters and with symbol sizes scaled proportionally to Mw. Redder colors indicate positive mb − Mw differences, which have relatively more short-period energy than the average source model predicts. These display a tendency to plot closer to the Honshu coastline (down-dip on the megathrust). The bluer colors indicate relatively less short-period energy than the average source model, with the largest, slightly negative value, circle corresponding to the Mw 9.1 2011 Tohoku event. Of course, all of the events differ in finite-source area, and the latter event would tend to reflect some spatial average over the early portion of the expanding rupture for the signal interval in which mb was measured; it is not a point estimate of the spectral behavior at the centroid location.
Similar plots of gCMT focal mechanisms of selected events and the corresponding corrected mb−Mw differences are plotted for the subduction zone regions around the 2004 Sumatra-Andaman earthquake source region (Fig. 3) and the 2010 Chile earthquake source region (Fig. 4). All events are again shown, including the great events for which the centroid locations are not representative of the total depth-range ruptured. There is a clear tendency for the red symbols, indicating positive mb−Mw (relatively enriched short-period magnitude) to plot down-dip along northern Sumatra, and a corresponding, but weaker, trend along central Chile. There is, however, significant scatter and non-uniformity of coverage. This might allow an interpretation of contribution from along-strike variations as well, but we will focus on the depth trends here given the sparse distributions.
The corrected mb−Mw differentials for events with Mw in the range 5.0 to 6.5 are plotted as functions of the gCMT centroid depth estimates for the three great earthquake source regions in Fig. 5. The gCMT centroid depths are used because they share any common bias, but the gCMT depth estimates can be 10–20 km deeper than USGS NEIC or JMA hypocentral depths in some regions. The trends of mb−Mw differentials versus source depth are very similar if we use either of those catalog depth locations instead. The depth-dependent trends apparent in the map views of Figs. 2, 3 and 4 are evident, in that we see positive mb−Mw differentials at greater depth and overall positive regression slopes, but are obscured by large scatter at each depth. This is not at all unexpected; there is always substantial scatter in seismic magnitude determinations, due to variability in the network average, directivity effects, focal mechanism effects, etc. Nonetheless, the Japan and Sumatra-Andaman data indicate systematic depth variation, and while the Chile data are sparse at larger depths, they are still compatible with a depth dependent increase in relative short-period signal energy. These trends appear to correlate with the depth-dependence in moment-scaled source durations for events larger than 6.0 found by Bilek and Lay (1998, 1999) and Bilek (2007).
One could infer either gradual increases of mb−Mw with depth or perhaps a step change in constant levels as visible around 37 km deep for the Japan and Sumatra regions. In those two regions, the upper plate has relatively thin crust, so the increase in high frequency content may correspond to transition to mantle/slab contact at around 35 km, which is not the case for Chile, where the upper crust is about 45 km thick. We do not think detailed statistical treatments will provide meaningful assessment given the large scatter and the likely contribution of along-strike heterogeneities, but the basic pattern is compatible with the observations for great ruptures that extend over these full depth ranges; the deeper portion of the megathrust appears to radiate more, or more coherent short-period teleseismic signal for smaller events. It is important to recognize that the back-projection applications intrinsically apply a coherency filter to the short-period data, so they are tuned to detect localized coherent sources and the overall spectral amplitude levels are not determined. Thus, the systematic patterns in the magnitude differences provide new and independent support for depth variations. It is also clear that the sampling of the shallowest megathrust region is very limited for events in the selected range of Mw = 5 to 6.5; this may be due to the presence of quasi-static slip at shallow depths with rupture of conditionally stable regions only occurring in large tsunami earthquakes that initiate at greater depth and rupture into the shallow portion of the fault. As such, the magnitude differential plots may intrinsically underestimate the total range of variability with depth. We found that the basic patterns were not modified if we included the corrected mb−Mw values for larger events (Mw 6.5 to 9.2) in these depth comparisons, mainly because they are few in number and are spread over all depths. We omit them here because we are concerned that the large corrections and measurement bias for those events make those data too uncertain.
Similar comparisons of mb−Mw differentials as functions of gCMT source depth estimates were made for 4 additional regions, all of which have experienced tsunami earthquakes and deeper megathrust events. These are the Kuril Islands-Kamchatka arc from 41° to 55°N, the Aleutian Islands arc from 165° to 210°E, the Peru subduction zone from 0 to 17°S, and the Southern Sumatra/Sunda arc from 100° to 130°E. Interplate thrust events were identified based on the location, depth and gCMT focal mechanisms, and mb−Mw differences were corrected in the same fashion. The corrected mb−Mw values for the range of Mw from 5.0 to 6.5 for each region are shown as functions of the gCMT source depth estimates in Fig. 6. Weak trends may be present for the Sumba and the sparsely sampled Peru source regions, but no clear trend is apparent for the well-sampled Kuril and Aleutian arcs and linear regressions did not give significant slope estimates. Maps of data distributions indicate that localized areas along subregions such as Java (also see Bilek and Engdahl, 2007; Convers and Newman, 2011) or Kamchatka may have depth-dependent trends, but the along-arc averaging obscures this as there is large scatter in the data. Since the localized regions tend to have fewer data, we will defer further analysis of other regions to future detailed studies that improve the depth estimates and more fully characterize the source spectra of events on the megathrust. We have not detected any systematic patterns in the depth trends of magnitude residuals with respect to subducting plate age or bathymetric structures, but more detailed analyses should be performed to address that issue rigorously.
4. Discussion and Conclusions
The seismogenic zone is expected to have varying properties as confining pressure and temperature increase, as sediments indurate and undergo phase transitions, as subducted fluids migrate, and as fault roughness from subducted bathymetric topography evolves with increasing depth. The nature of the fault contact also varies from sediment-crust, to crust-crust, to mantle-crust contrasts in lithology. The role that each of these complex factors plays in determining the fault frictional properties that govern seismic wave generation during earthquakes remains obscure. It is perhaps not surprising that earthquake rupture behavior varies with depth, but quantifying what controls the variations is a major challenge.
Use of seismic magnitude measures appears to provide a first-order probe of the depth- and lateral-variations on the megathrust, but the large scatter in magnitude parameters indicates that many other contributions to the observed values need to be accounted for. To the extent that mb represents the 1 s relative spectral amplitudes, it provides a readily available measure, but short-period radiation is influenced by details of individual ruptures that are not readily quantified, such as directivity, depth phase interference, and source velocity structure. For example, if fault zone rigidity varies systematically with depth along the megathrust, as proposed by Bilek and Lay (1999) and Lay and Bilek (2007), there should be systematic increase in shear velocity with depth, and a concomitant increase in rupture velocity. This could influence the source dimensions for a given moment earthquake, affecting the corner frequency and mb measures. So, one possible interpretation of the trend of increasing mb−Mw differential depth in Fig. 5 is that there are smooth or step-wise increases in shear velocity with depth along the megathrust due to progressive sediment induration or lithological contrast changes with depth.
Seismic tomography of the detailed seismogenic fault zone under the overlying wedge (e.g., Kennett et al., 2011; Zhao et al., 2011) could address this issue independently, but requires fine resolution of the source region that is difficult to obtain. Reflection profiling can also contribute to constraining the velocity structure and layering. For the Japan and Sumatra subduction zones, the depth to the upper plate Moho is about 30 km, so the change from crustcrust to mantle-crust contact might influence the magnitude differences. The Chile zone has a thicker overriding continental crust with Moho depth about 45 km deep, perhaps suppressing the depth-varying behavior relative to the island arcs. The behavior of the other zones that were investigated does not give a clear distinction between island arcs and continental arcs in terms of the depth-dependence of the mb−Mw differences.
We chose teleseismic measures of the source spectra in order to relate the results to the teleseismic observations for the great earthquake ruptures for which backprojections have been performed. For the Japan source region there are local measures of high frequency magnitude, such as the Japanese Meteorological Agency (JMA) MJ, or Hi-net magnitude, MHinet, as well as local CMT solutions from regional wave inversion that provide Mw (regional) estimates. We examined MHinet−Mw (regional) variations over the Japan subduction zone, motivated by preliminary results by Y. Asano (personal communication, 2011), but the patterns are different from those for mb−Mw and future work will need to address how mb and MHinet or MJ differ in frequency content and event size-scaling behavior. The use of teleseismic magnitude data also allows comparison of regions that do not have dense local seismic networks.
Ultimately, we view the use of magnitude measures as a preliminary step, and feel the best characterization of source variations with position on the megathrust will require full spectral analysis with network isolation of the source spectrum and path/receiver effects, referencing the full spectral behavior to a reference ω-squared model (e.g., Allmann and Shearer, 2009; Bilek et al., 2012; Ye et al., 2012). However, this study supports the basic inference of some degree of enhanced short-period radiation from down-dip on the megathrust as proposed in the megathrust domain model shown in Fig. 7, from Lay et al. (2012). This behavior is detected in both moderate size and great ruptures, so it is an intrinsic feature of the megathrust, not a dynamic rupture attribute. This conceptual framework identifies a shallow Domain A, in which quasi-static slip or tsunami earthquakes occur with very low short-period radiation (and very few moderate size events, so this study does not sample it well), a mid-megathrust Domain B in which large slip can happen in large earthquakes with minor coherent short-period radiation, and a deep-megathrust Domain C which has enriched short-period radiation during failure in isolated events or as part of a great event which ruptures multiple domains. Further along the megathrust there is a transitional Domain D, present in regions with young subducting lithosphere, in which slow slip events, seismic tremor and low frequency earthquakes may occur. There is no direct evidence for Domain D existing in the great earthquake regions examined here, but a transition to stable sliding or anelastic deformation must occur down-dip of Domain C. While simple, this type of conceptual framework does provide a context for further examination of earthquake spectral variations with depth along the megathrust.
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This work made use of GMT software. The on-line USGS NEIC and Global Centroid-Moment Tensor Catalogs were utilized extensively. We thank guest editor Steve Kirby, Annemarie Baltay and 2 anonymous reviewers for their helpful comments on the manuscript. We thank Ken Creager for directing us to the IRIS measurements of short-period amplitudes for large events. We also thank Y. Asano for providing access to his regional CMT catalog and for examples of his analysis of MHinet−Mw magnitude differences along Honshu. This work was supported by NSF grant EAR0635570.
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Rushing, T.M., Lay, T. Analysis of seismic magnitude differentials (mb−Mw) across megathrust faults in the vicinity of recent great earthquakes. Earth Planet Sp 64, 14 (2012). https://doi.org/10.5047/eps.2012.08.006
- 2011 Tohoku earthquake
- megathrust faults
- subduction zones
- great earthquake rupture process
- tsunami earthquakes