Heki, K., Snow Load and Seasonal Variation of Earthquake Occurrence in Japan

Earth Planet. Sci. Lett., 207, 159-164, 2003.

2. Secular and Seasonal Stress Changes

In discussions of earthquake triggering we often use change of CFF (DCFF), which consists of shear stress change resolved on the fault plane (positive in the fault slip direction) added to the change in the fault-normal stress multiplied by friction coefficient (positive for unclamping). Here I assume that a shear stress increases secularly by tectonic loading, being perturbed by various DCFF, and the fault rupture starts when the total stress exceeds a critical value. Thus addition of a positive (negative) DCFF would allow the next earthquake to occur earlier (later). An instantaneous change in CFF occurs in response to a nearby earthquake, and snow load, solid earth tide, ocean tidal loading, etc, cause roughly cyclic DCFF. Significance of the periodic DCFF depends on its amplitude relative to the secular stress increase during the period [7]. The probability of earthquake occurrence in a unit time would vary periodically in proportion to the instantaneous increase rate of the total stress. Let the secular annual stress rate be a, and the amplitude of the annual DCFF change b, then the stress rate would vary between a-2pib and a+2pib (Fig. 1a), where 2pi comes from the angular velocity (1/yr) of the annual perturbation. A high rate brings a large earthquake occurrence probability; the quantity 2pib/a equals P_m/P₀ (Fig. 1a), the amplitude of the periodic component relative to the stationary seismicity (see equation (4) of [7]).
A stress drop and recurrence interval of a typical interplate earthquake would be a few MPa and one hundred years, respectively, which suggests a to be a few tens of kPa/yr. Intraplate (inland) earthquakes generally have larger stress drops, but their longer recurrence intervals would keep a similar. As seen in Fig. 1a, b only 0.1 times as large as a could modulate the seismicity significantly (P_m/P₀~0.6). The seismicity peak is predicted to coincide with the dDCFF/dt peak, a quarter year earlier than the peak of DCFF itself (since snow causes compression and negative DCFF, the highest seismicity would come with spring thaw rather than in snow-free summer), although time delay is likely because seismic nucleation phase needs finite duration. Fig. 1b shows another case, where periodic term is relatively large, i.e. a < 2pib (tidal triggering of earthquakes usually corresponds to this case). There the total stress experiences negative stress changes, and the probability of earthquake would temporarily remain zero until the stress exceeds the previous maximum (�gstress shadow�h by [7]). This would also let the seismicity peak shift from the maximum dDCFF/dt toward the maximum DCFF.
Ohtake and Nakahara [4] estimated the DCFF at the plate interface (mainly due to shear stress increase) brought by high atmospheric pressure in winter of 1 kPa to be only a few tens of Pa, too small to significantly perturb the secular stress buildup. According to Heki [6], although the snow load is equivalent to as much as 10 kPa atmospheric pressure increase, the increases of the shear stress at the offshore fault surface remains ~0.1 kPa (this is due to the distance between the snow cover and the trench), again unlikely to modulate seismicity. On the other hand, such surface loads cause significant stress disturbance directly below them, and thus may influence the occurrence of inland crustal earthquakes. Past studies focused on relatively large earthquakes (e.g., Mogi [2] considered M>8 historic and M>7.5 modern earthquakes, and Ohtake and Nakahara [4] examined only M>7.9 earthquakes), and excluded most inland earthquakes because their magnitudes seldom exceed 7.5. Here I focus on the seasonality of inland seismicity, and discuss its correlation with the snow load.

3. Annual Variation of Inland Seismicity in Japan

Fig. 2 shows the epicenters of past inland earthquakes (M>6.0) compiled by Usami [8] (the oldest earthquake dates back to the 5th century, and only destructive earthquakes are listed). Their mechanisms vary between the northeastern and the central to southwestern Japan (for general description of Japanese earthquakes, see Earthquake Research Committee [9]). In northeastern Japan, they occur on high-angle thrust faults that often bound the backbone range and adjacent basins, and a typical event is the 1896 Riku-u earthquake (M7.2). These faults strike normal to the plate convergence direction and parallel with the arc (and the snow cover). Most inland earthquakes in the central to southwestern Japan occur on strike-slip faults. Because the plate converges WNW-ESE there (Fig. 2) [10], faults strike either WSW-ENE (e.g. the 1995 Kobe earthquake, M7.2) or NNW-SSE (e.g. the 1891 Nobi earthquake, M8.0), which are roughly parallel with and normal to the arc (and the snow cover), respectively.
Fig. 3a and 3b show the changes in the stress normal to the reverse and strike-slip fault planes, respectively, under a simple (but realistic) arc and snow cover geometry. The arc is 200 km wide and extends 1,000 km N-S. The snow cover, also running N-S, extends from the west coast to 40 km east of the backbone range axis (140 km wide), and is the deepest (2.5 m) at 30 km west of the range axis. With the snow density 0.4 g/cm³, the maximum load is comparable to 1 m water column, or 10 kPa surface pressure. The reverse fault was assumed to dip 45 degrees westward, and both reverse and strike-slip faults strike parallel with the arc (and with the snow cover). The elastic response of the Earth is calculated after Farrell [11] assuming crustal rigidity of 30 GPa and the Poisson�fs ratio of 0.25. A simple elastic half space approximation is used rather than the spherical Earth since the problem is local and most inland earthquakes are shallower than 15~20 km [9]. In both Fig. 3a and 3b, snow load causes compression (negative stress change) larger than 5 kPa beneath the snow cover (in the strike-slip case, changing the fault strike to arc-normal reduces the compression by 1/3). In the reverse fault case, shear stress also changes (~1/3 of the compression, in the discouraging sense), and contributes to the negative DCFF (if the friction coefficient is 0.5, the total DCFF is ~-5 kPa). For both the arc-normal and arc-parallel strike-slip faults, the snow load does not change shear stresses, and the normal stress change multiplied by the friction coefficient becomes the DCFF (-2~-3 kPa with the friction coefficient of 0.5). In both cases, seasonal DCFF amplitudes amount to a few kPa, sufficient to significantly perturb the secular stress build-up of a few tens of kPa/yr as shown in Fig. 1a.
Okada [3] first separated inland earthquakes into those under the snow cover and the snow-free region, and investigated the monthly distribution of their occurrence, and found higher seismicity under the snow cover in spring and summer. Fig. 4 confirms this trend, based on the new earthquake catalog [8], and more precise definition of the snowy region, i.e., area where the average values of the maximum snow depths of the last five winters exceeded 20 cm (Automated Meteorological Data Acquisition System, or AMeDAS, run by Japan Meteorological Agency). Fig. 4a and 4b compare bimonthly distributions of earthquakes in the snowy and snow-free regions. Following past studies [2,3], I excluded aftershocks, and counted only the first one if multiple earthquakes of comparable sizes occurred nearby (< 30 km for 7.0>M>6.0 earthquakes, and < 100 km for M>7.0 earthquakes) within a year. In Fig. 4c are plotted snow depths, and M>7.0 inland earthquake epicenters within (circles) and outside (triangles) the snowy region.
Fig. 4a (red histogram) shows distribution of occurrence times for the twenty-six M>7.0 earthquakes in the snowy region; they occur more in spring-summer than in fall-winter, a result consistent with Okada [3] (those in the snow-free region, shown in Fig. 4b, seem to occur randomly). According to the classical statistical test by Schuster [12], we cannot discard the null hypothesis that this is a result of a random process at the 95 % confidence level. This is, however, due to insufficient number of earthquakes, and does not necessarily mean lack of seasonality. In fact, the observed ratio of the periodic to the stationary term of the earthquake probability density function (P_m/P₀) [7] is ~0.5 (red curve in Fig. 4a), a value larger than the case reported by Wilcock [13], one of the most significant cases of the tidal triggering of earthquakes. If earthquakes keep occurring with the monthly distribution similar to Fig. 4a, it will pass the Schuster�fs test with the 95 % confidence when number of earthquakes exceeds 54. Although this will take another millennium, this number is certainly small considering hundreds and thousands of earthquakes often necessary to verify significance of tidal triggering [14]. The motivation of the present work is not the discovery of seasonal variation of earthquakes, but the identification of a mechanism (snow load) responsible for seasonal crustal deformation and its evaluation as an earthquake trigger mechanism. Hence I do not claim statistical significance of seasonal variation seen in Fig. 4a here, but just emphasize that the phase (peak in middle June) and amplitude (P_m/P₀~0.5 means b, the annual term amplitude, is about an order of magnitude smaller than a, the secular change in a year) there support the geophysical speculation that the removal of the snow load may increase the DCFF in shallow faults underneath and activate seismicity.

4. Discussion

As pointed out by Mogi [2] and Okada [3], the seasonality is not so apparent for smaller earthquakes. In Fig. 4a, bimonthly distribution of 7.0>M>6.0 earthquakes in the snowy region (gray histogram) do not show clear seasonal variation. The enhancement of seasonal variation for larger earthquakes might be due to longer durations required for the premonitory nucleation phase of larger earthquakes. Shibazaki and Matsu�fura [15], based on the rate- and state-dependent friction law [16], hypothesized that an earthquake starts as a (1) slow quasi-static nucleation process, (2) followed by dynamic acceleration phase, (3) eventually running into the main rupture. Ellsworth and Beroza [17] analyzed the initial phases of seismic records, which correspond to the second (dynamic acceleration) phase in the above sequence, and inferred that a longer duration of nucleation precedes an earthquake with larger eventual size. Although there have been no clear geodetic observations for the duration of the first process (quasi-static nucleation), it is possible that larger earthquakes need longer duration for this process (1) as well as for the process (2). In fact, Kato and Hirasawa [18], from a numerical simulation using the friction law, suggested that a precursory fault slip (i.e. quasi-static nucleation) of a large interplate earthquake occurs over a few days. If the total nucleation process for a M>7.0 earthquake always takes more than a few days, they would not react to shorter-term disturbances such as semidiurnal tides, but would be sensitive to longer-term disturbances such as seasonal loads. Smaller earthquakes with shorter nucleation phases, on the other hand, would be more easily triggered by shorter-term disturbances including tides and atmospheric pressure variations, and their seasonality might be blurred. Smaller earthquakes often fail to show clear correlation with tides [19], and this issue would need further investigations.
Groundwater may play a certain role in the seismicity in snowy regions. In spring, snowmelts would penetrate into cracks of crustal rocks, and might reach the fault surface. It could increase the CFF by reducing the effective normal stress with excess pore pressure as suggested by Okada [3] and Matsumura [20], although it is difficult to evaluate this effect as DCFF. The present study does not rule out its possibility, but we prefer the snow load mechanism since it has a quantitative model that can be tested in snow-covered areas with high seismicity in other parts of the world.

Acknowledments. I thank Tadahiro Sato for discussion, Naoji Koizumi for sending a reprint, John Vidale, Nick Beeler and Joan Gomberg for valuable comments.

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