Validity of assumptions
We first discuss the validity of the assumptions made in this study in order to categorize the calculated slip-deficient areas. We rate the reliability of these areas as follows: category A—strong candidate for strain-accumulated area; category B—a candidate with some uncertainty; and category C—a minor candidate that does not show a large area of slip deficit and has a large uncertainty.
This study was based on the following assumptions:
-
1.
Each interplate earthquake has a stick–slip patch around its centroid. Once a stick–slip patch is defined by an interplate earthquake, it will only slip by earthquake motion, not by creep
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2.
Stick–slip patches within the rupture area of potential huge earthquakes should accumulate a slip deficit during the interseismic period. Grid points that have slip deficits larger than half of the relative plate displacement during this period are regarded as slip-deficient grid points. In contrast, grid points with cumulative slips larger than half of the slip expected from the relative plate motion are regarded as sufficiently slipping grid points. Areas that include slip-deficient grid points and that do not include any sufficiently slipping points are regarded as accumulating strain
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3.
The magnitude of each hidden potential earthquake is calculated from the size of the area that contains slip-deficient grid points and that contains no sufficiently slipping grid points, rather than from the slip-deficit value
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4.
The stick–slip patches are defined only for interplate earthquakes listed in the GCMT catalog. All earthquakes that slipped on the stick–slip patches prior to the GCMT catalog are regarded as interplate earthquakes
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5.
The accumulated relative plate displacement during the period of investigation is sufficient to evaluate slip deficit
The first and second assumptions are the basic principles of this study and are supported by previous studies, as described in the “Introduction” section. Since the results of the tests conducted for the source areas of the six huge earthquakes that have occurred during the past 110 years support these basic principles, we consider that these assumptions are valid. It could be argued that stick–slip patches for M7-class earthquakes should be detected by the geodetic observations if the patches are locked during the interseismic period, but this is not always the case. For example, geodetic studies of the interseismic period around the Tohoku-Oki rupture area (e.g., Loveless and Meade 2011) show only one large coupling area around the centroid of the Tohoku-Oki earthquake. Loveless and Meade (2011) carried out a checkerboard test and showed that it is difficult to resolve off-shore locked patches with diameters of <100 km using geodetic inversions, as all stations are located on-shore. Conversely, results from small repeating earthquakes do show coupling around some past M7-class earthquakes (Uchida and Matsuzawa 2013).
The third assumption could lead to large errors because one slip-deficient grid point combined with a vast surrounding aseismic region can generate large areas of apparent accumulated strain. In terms of the fourth assumption, the misclassification of intraplate earthquakes as interplate earthquakes would result in an overestimate of the total seismic slip. The fifth assumption is also critical, as the short duration of the investigated periods results in large uncertainties in determining whether the plate motion is sufficient for the analysis. The impact of these three assumptions on the uncertainty of the results is evaluated below.
First, we discuss the case where a few slip-deficient grid points are surrounded by a vast aseismic region, which generates a large calculated apparent magnitude. We classified the areas showing a large calculated magnitude (as delineated by the ellipses in Fig. 6) into categories A and B based on the localization of slip-deficient grid points. Category A areas contain a good coverage of slip-deficient grid points and do not contain any vacant spaces larger than the rupture ellipse of a magnitude 9.0 earthquake on the plate boundary. The following 20 areas were classified as category A: the southern part of the Kuril trench; the northern part of the Ryukyu trench; the southern part of the Izu–Bonin trench; western and central Aleutian trench; the South Sandwich trench; northern, central, and southern Central America trench; western and eastern South Java trench; the Manila trench; the Ecuador-Peru trench; northern Chile trench; the New Britain trench; the New Hebrides trench; the Tonga trench; and northern Kermadec trench. It is probably that the interplate seismic slip in these areas is suppressed due to the locked regions that will likely be responsible for future huge earthquakes. The remaining five areas contain large vacant spaces equivalent to the rupture ellipses of M9.0 earthquakes and are recognized as category B: the central part of the Ryukyu trench; the northern and southern parts of the Mariana trench; central South Java trench; and southern Kermadec trench. For these areas, we cannot deny the possibility that the few “slip-deficient” grid points and the surrounding vast aseismic regions have generated the large calculated magnitudes. Although category A areas are relatively reliable, there is still some uncertainty in the calculated expected earthquake magnitudes, as older interplate earthquakes that occurred outside the defined stick–slip patches are ignored. In the Nankai Trough, though which is “unreliable” area, two M8-class interplate earthquakes that occurred in 1944 and 1946 are ignored in our analysis because no stick–slip patches were defined through the GCMT catalog calculations. We cannot discount the possible existence of such missed stick–slip (and sufficiently slipping) patches in the category A areas. In such a case, the magnitude of the hidden potential earthquake would be overestimated. However, significant overestimation is unlikely in subduction zones with high convergence rates because if M8 (not M9) is the largest capable event, such an event with a slip of ~3 m should have occurred within the past 110 years.
Second, we evaluate the impact of misclassification of the earthquake mechanism. All earthquakes that occurred before the beginning of the GCMT catalog with slip areas on the plate interface that include stick–slip grid points are considered to be interplate earthquakes, which should overestimate interplate cumulative slip to some extent. We evaluate the degree of this overestimation using the GCMT catalog for earthquakes that occurred after 1976. Figure 7 shows the spatial distribution of the ratio of the total slip of interplate earthquakes to the total slip of all earthquakes. The ratio λ
j
for the jth grid point is calculated using all earthquakes within 220 km of the grid point:
$$ {\lambda}_j=\frac{{\displaystyle {\sum}_I{D}_I}}{{\displaystyle {\sum}_I{D}_I}+{\displaystyle {\sum}_K{D}_K}}, $$
(7)
where D
I
and D
K
represent D
max (Eq. 5) for each interplate and intraplate earthquake, respectively. The distance of 220 km corresponds to the long axis of the M9.0 stick–slip patch. In this calculation, we omit the earthquakes with slips (from Eqs. 2, 3, 4, and 5) larger than their respective relative plate displacements over the 34 years of GCMT data used in this study. The inclusion of such large and rare earthquakes would cause the results to be unstable and unreliable. The resulting ratios are generally low in the Southwest Pacific (Fig. 7). Figure 7 shows that interplate earthquakes are not prevalent in the Ryukyu trench, most trenches around the Philippine Islands, and the southern Kermadec trench. Consequently, slip deficits based on these results would be underestimated. This is especially true around the Philippine Islands, where calculated magnitudes based on the spatial extent of slip-deficient grid points do not exceed 9.0 except for the Manila trench (Fig. 6e). Therefore, the calculated magnitude may be underestimated around the Philippines. In the Kermadec trench, the calculated magnitude exceeds 9.0 in the south but is smaller in the central part of the trench at ~30° S and is therefore underestimated in this region. We categorize the areas in which the calculated magnitudes do not exceed 9.0 and interplate slip is less than half of the total slip as category C. Such areas include the northern Kermadec trench (~30° S) and the northern Philippine trench (Fig. 6e, g). This evaluation contains additional uncertainties due to the short duration of the test period using GCMT solutions.
Finally, we evaluate the uncertainty of the results due to the short duration of measurements of relative plate displacements. Regions with relatively low plate velocities have larger uncertainties in slip deficit. Figure 8 shows a schematic illustration of the slip history of a huge stick–slip patch (M9) and surrounding smaller patches. The section of the hanging wall around the patch is dragged by the subducting slab (via the stick–slip patch) and its motion relative to the subducting slab is consequently reduced. Therefore, the cumulative seismic slip of the surrounding small stick–slip patches becomes smaller due to this reduced relative motion. Our analysis is designed to detect this slip-deficient area by summing the seismic slip (white areas in Fig. 8); however, we cannot extract the hidden source area using earthquakes with slips larger than the relative plate displacement (Fig. 8b). If we focus on a stick–slip patch with a unit slip smaller than the cumulative plate motion within a given period, the absence of seismic slip might indicate that some larger stick–slip patches also exist behind. However, if we focus on a stick–slip patch with a slip larger than cumulative plate motion, neither the absence nor the presence of seismic slip would provide information on hidden potential earthquakes because the occurrence of an earthquake within the given period is simply a matter of probability. It would be ideal to make observations until the cumulative relative plate motion exceeds the slip of the stick–slip patch used as the slip-deficit indicator. However, it is not easy to know how much displacement of the relative plate motion is sufficient for the estimation because we do not know the size of the potential earthquakes hidden behind the apparent seismicity. As a practical measure of the sufficiency of the period, we compare the total relative plate motion over 110 years with the seismic slip of a single M7.5 earthquake for various subduction zones. Peak slip for an M7.5 earthquake is 4.28 m. Relative plate motions smaller than this are shown in dark blue in Fig. 6 and include those at the Puerto Rico, Solomon, and Northern Java trenches, as well as the trenches around the Philippine Islands, except for the Manila trench. In these regions, the estimated slip-deficit distribution should be affected by relatively small earthquakes and the uncertainties in the results are large compared with other regions. In Table 1, these areas, which display large uncertainties in slip deficit due to small relative plate motions, are listed as uncertain areas, in addition to the Nankai Trough in Japan and Cascadia in North America where no stick–slip patches have been defined.
Focal areas of M9-class earthquakes in the past 110 years
As described above, we developed a method of evaluating strain accumulation on subduction plate boundaries and we applied this method to the six known M9-class earthquakes that have occurred in the past 110 years. We also applied the method to circum-Pacific subduction zones and calculated earthquake magnitudes from the spatial extents of slip-deficient areas. In this section we discuss the correlation between the slip-deficient area and the rupture area of the known M9-class earthquakes. The areas that were calculated from the catalog to have magnitudes of ≥9 prior to the 2011 Tohoku, 2004 Sumatra, and 2010 Chile M9-class interplate earthquakes correlate closely with the rupture areas of the actual M9-class events (Fig. 5). The rupture area of the 2004 Sumatra earthquake is unreliable because the absence of interplate thrust earthquakes in this region during the time when GCMT solutions are available means that we cannot judge whether the area contains a stick–slip patch. In contrast, the results around the source areas of the 2011 Tohoku and the 2010 Chile earthquakes are regarded as being highly reliable because these areas contain widespread stick–slip grid points with slip deficits compared with the relative plate motions. Large magnitudes are estimated in the southern extension of the rupture area of the 2004 Sumatra earthquake from 5° S to 5° N (Fig. 5b). In this area, huge earthquakes occurred in 1833 (~M9.0; Briggs et al. 2006) and 1797 (~M8.4), which correspond to the area with the large calculated magnitude. Six M8-class events have also occurred since 2004 with source areas that correspond to those of the expected large-magnitude earthquakes.
The slip deficits after the 1960 Chile, 1952 Kamchatka, and 1964 Alaska M9-class events evaluated from the catalog also show good correlations between the calculated large-magnitude areas and the rupture areas (Fig. 5c, e). This result reflects a lull in seismicity after an almost full release of seismic moment around the rupture area and may also suggest that the strong and/or large stick–slip patches capable of producing M9-class earthquakes are persistent and recover their locking behavior immediately after huge interplate earthquakes.
Correspondence between historical huge events and the areas where huge earthquakes are expected from the slip-deficit analysis
Our result over the circum-Pacific region using the catalog prior to 2011 shows 25 category A and B segments (Fig. 6). Historical studies point to several more M9-class interplate earthquakes than the six huge events shown in Fig. 5. For example, the 1700 Cascadia (M9.0), 1868 Peru (M9.0), 1877 North Chile (M8.8), and 1906 Ecuador (M8.8) earthquakes are listed as ≥M8.8 by the USGS (http://earthquake.usgs.gov/earthquakes/world/historical_mag.php last updated November 25, 2015). For Cascadia, our method cannot evaluate the slip deficit because no interplate earthquakes occurred during the time covered by the GCMT catalog. Instead, our results indicate that the region along the Ecuador–Peru–Chile trench is classified as category A. Figure 6f shows our result along the trench, as estimated from the catalog for the period from 1907 to 2010 together with the rupture areas of the historical M9-class earthquakes. Around the rupture areas of the 1906 M8.8, 1868 M9.0, and 1877 M8.8 earthquakes, our analysis anticipates M9 or larger earthquakes, although the spatial extents and the locations of these events do not agree exactly with those of the actual earthquakes. The reliability of the expected magnitude around the 1906 source area is low because only a few stick–slip grid points exist in this region. The area with expected magnitudes of >M9 for the 1868 and 1877 events is localized along only one border of the actual rupture areas, which were widely spread along the trench.
Along the Ecuador–Peru trench, a huge area extending from 2° S to 10° S has a large calculated magnitude. Historical records give no indication that a great earthquake has occurred in this region during the last 400 years (Kelleher 1972). Although McCann et al. (1979) classified this region as the site of no great earthquakes based on its earthquake history, our results show that it contains many stick–slip patches with cumulative seismic slips smaller than the relative plate motion, indicating that this region is a likely location of future M9-class events.
Subduction with back-arc spreading
Our results show large expected magnitudes of >9.0 in several subduction zones that have back-arc spreading, including the Mariana, Ryukyu, South Sandwich, and Izu–Bonin trenches, which are classified as Mariana-type trenches. Uyeda (1982) described the differences between Mariana-type and Chilean-type trenches and pointed out that earthquakes with magnitudes significantly larger than 8.0 do not occur in Mariana-type trenches. Scholz and Campos (1995) evaluated this relationship quantitatively and proposed that seismic coupling in Mariana-type trenches is suppressed due to a reduction in the normal force at the plate interface, which is related to the absolute velocity of the upper plate and the length of the subducting slab. The seismic coupling correlates with the calculated normal force, which was explained in the context of the rate- and state-dependent friction law (e.g., Ruina 1983), which states that a reduction in normal force increases the sliding stability of the interface. We should note that their theory only evaluates the likelihood that a plate interface is a region of stable slip, and it does not exclude the possibility that great earthquakes may occur if unstable sliding patches exist. Our results show that stick–slip patches with cumulative seismic slips smaller than the relative plate motions occur in the Mariana trench and other Mariana-type trenches. These patches should compensate for the slip deficit by slipping seismically in the future, unless the frictional properties of these patches change from stick–slip to stable slip; we cannot exclude the possibility of M9-class earthquakes in these regions.
Frequency of M9-class earthquakes
Seismologists have attempted to correlate the history of earthquakes over the past century with subduction zone properties such as convergence rate, slab age, type of overriding plate, and fault temperature, in order to understand the limits on earthquake size. For example, Ruff and Kanamori (1980) showed significant correlations between characteristic earthquake size in subduction zones and the convergence rates and ages of the subducting slab. They suggested that a young and fast-moving slab would be subducted into the mantle at a lower angle and would stick more strongly to the overriding plate, resulting in larger earthquakes. However, later studies (e.g., Pacheco et al. 1993; Stein and Okal 2007) that incorporated more recent earthquake data and improved data show weaker correlations than those proposed by Ruff and Kanamori (1980). Furthermore, the underlying idea that some subduction zones may never produce an M9-class earthquake has been called into question with the occurrence of the 2004 Sumatra Mw9.2 and the 2011 Tohoku Mw9.0 earthquakes. Our study does not consider the physical properties of subduction zones and is based purely on the idea of slip deficit. As a result, the calculated magnitudes in 31 areas exceed M9.0. This number may be considered too high in terms of the number of areas that are likely to be candidates for M9-class earthquakes. However, it should not be surprising from a statistical viewpoint. Figure 9 shows the magnitude–frequency relationship for earthquakes occurring between 1900 and 2010 with magnitudes of >7.5. For magnitudes between 7.5 and 9.5, the relationship seems to follow the Gutenberg–Richter law (GR law), suggesting that M9-class earthquakes are not unusual ones in global subduction zones.
If we accept that the observed frequency of M9-class events, at six in the past 110 years, is reasonable in terms of the GR law, we can assume that the same number of events will occur each 110 years. Upcoming M9-class events should occur in regions other than the six known areas because the recurrence interval of each M9-class event should be longer than several hundred years. Consequently, it would not be surprising if the number of areas capable of producing an M9-class earthquake is several times greater than this value of six. Indeed, 31 such areas are defined by our study, which is within the range of this estimate.