ISSN 1028-334X, Doklady Earth Sciences, 2017, Vol. 476, Part 1, pp. 1109–1112. © Pleiades Publishing, Ltd., 2017. Original Russian Text © B.W. Levin, M.V. Rodkin, E.V. Sasorova, 2017, published in Doklady Akademii Nauk, 2017, Vol. 476, No. 3, pp. 343–346.

GEOPHYSICS

Effect of the Earth’s Rotation on Subduction Processes Corresponding Member of the RAS B. W. Levina,b, M. V. Rodkina,c *, and E. V. Sasorovab Received May 22, 2017

Abstract—The role played by the Earth’s rotation is very important in problems of physics of the atmosphere and ocean. The importance of inertia forces is traditionally estimated by the value of the Rossby number: if this parameter is small, the Coriolis force considerably affects the character of movements. In the case of convection in the Earth’s mantle and movements of lithospheric plates, the Rossby number is quite small; therefore, the effect of the Coriolis force is reflected in the character of movements of the lithospheric plates. Analysis of statistical data on subduction zones verifies this suggestion. DOI: 10.1134/S1028334X17090252

It is known that the rotation of the Earth produces whirling of atmospheric vortices and considerably affects the character of oceanic currents. This is caused by Coriolis force F which acts on a body moving at speed v relative to the inertial reference system rotating at angular speed w; the value of force F is set by multiplication of vectors v and w to double the mass of the body: F = 2m[v × w].

(1)

The fact whether the Coriolis force considerably affects the character of a flow or not is determined by the Rossby number, which is the ratio between the force of inertia and the Coriolis force. The formula for the Rossby number (Ro) is Ro = U/Lf,

(2)

where U is the characteristic rate of the process; L, the spatial scale of motion; f, the Coriolis parameter, f = 2wsinϕ (w is the angular speed of the Earth’s rotation and ϕ is the latitude). The Coriolis parameter is zero at the equator and f ≈ 1.45 × 10–4 s–1 at the pole. If the value of the Rossby number is small, then the Coriolis force has considerable influence on the character of motion [1]. For convective flows in the mantle and movements of lithospheric plates, we can assume U ≈ 10 cm/yr a Institute

of Marine Geology and Geophysics, Far East Branch, Russian Academy of Sciences, Yuzhno-Sakhalinsk, 693022 Russia b Shirshov Institute of Oceanology, Russian Academy of Sciences, Moscow, 117218 Russia c Institute of the Theory of Earthquake Prediction and Mathematical Geophysics, Russian Academy of Sciences, Moscow, 117997 Russia * e-mail: [email protected]

and L ≈ 1000 km; then the Rossby number is Ro ≈ 2 × 10–11; i.e., this parameter is quite small and the Coriolis force can considerably affect the character of motions. The degree of such an effect will depend on concurrency with the other processes, in this case, with convective turbulent flows in the mantle, which are of larger energy as is seen from the close relationship between mantle convection and volcanism. Let us investigate whether the tendencies expected in the case of a noticeable effect of the Coriolis force on the character of mantle motions are observed. In particular, we should expect that the Taylor–Proudman rule, which is well known in hydrodynamics, will be satisfied in this case; this rule reads that if the Rossby number is small and friction is negligible, then incompressible fluid flows in the planes perpendicular to the rotation vector. Naturally, friction cannot be negligible in the case of mantle convection and motions of lithospheric plates, but if the influence of the Coriolis force is significant, we should expect these motions to be concentrated in the planes perpendicular to the rotation axis of the Earth. In this respect, it is remarkable that mid-ocean ridges are oriented predominantly in the submeridional directions, indirectly indicating that currents in the upper mantle are mostly sublatitudinal. Despite the great advances in seismic tomography, more accurate verification of data on mantle convection in the Earth’s interior is quite difficult because of the high uncertainty about the character of convection. However, the character of convection in the mantle is manifested in movements of the lithospheric plates, and these movements are quite well known today (see [2, 3] and others). Below, we will attempt to reveal and interpret the peculiarities of subduction that are related to rotation of the Earth on the basis of the data on subduction zones summarized by R.D. Jarrard [4].

1109

1110

LEVIN et al.

Vsubd, cm/yr

Dip angle of slab 90° 80° 70° 60° 50° 40° 30° 20° 10°

12 10 8 6 4 2 0

0 50

100

150

200

250 300 350 Azimuth, deg

50

100 150 200 250 300 350 Azimuth, deg

Fig. 2. Dip angle of a slab in the middle part (150–400 km), depending on the dip azimuth. Westward and eastward dipping zones are marked, respectively. Eastward dipping Benioff zones can have small dip angles, whereas zones dipping westward (except for one zone) all have steep angles.

Fig. 1. The values of dip azimuths and subduction rates for different subduction zones.

This comprehensive work provides probably the most complete and consistent set of values for the main parameters of these zones, discusses these parameters, and interprets the empirical regression relations linking these values. Jarrard distinguished and characterized as many as 39 subduction zones [4], which facilitates certain statistical processing of the respective data. It is natural that any subdivision of subduction zones into groups will have a certain degree of subjectivity. For example, it is unclear how many minor subduction zones should be distinguished in the major subduction zone dipping beneath South America and how exactly. It seems logical to consider separated fixed-length (e.g., 200 km long) segments of subduction zones instead of entire subduction zones, as was done in [7]. However, such a subdivision was not accompanied by a complete and homogeneous database of comparable parameters [4]. Additionally, because of the small variability in the parameters along the course of the subduction zone, segmentation leads in fact only to the increase in the size of the analyzed sample by a factor of 5–7, without the essential changes in the data proper. Given the above, in our analysis below we will apply segmentation with the reservation that segmentation would lead to multiple increase in the sample size without essential changes in the correlation values. In terms of analyzing the possible role of the Earth’s rotation, it is natural to verify first how the number of zones and their subduction rates depend on the dip azimuth (whether a plate dips in the same direction as the Earth rotates or in the opposite one). Let us illustrate the notion of the dip azimuth of a subduction zone through the following examples: the Mariana zone dips almost exactly westward at azimuth 270о, whereas the Aleutian zone dips northward at azimuth 0о [4]. The distribution of a number of subduction zones depending on their dip azimuth appeared to be very

nonuniform (Fig. 1). Subduction zones definitely tend to dip at azimuths of the sublatitudinal directions, whereas there are scarce zones dipping in submeridional directions. Indeed, there is the only the subduction zone dipping in the range of azimuths of 110° to 240° (180° ± 60° in the submeridional range), and absolutely no zones dipping at 340°–360°. This tendency is consistent with the Taylor–Proudman rule mentioned above stating that motions concentrate in the planes perpendicular to the rotation vector; i.e., they are oriented predominantly in the sublatitudinal directions. The high statistical significance of this tendency is undoubted. Taking the revealed peculiarity of movements of the lithospheric plates into account, let us further consider the two subsets of subduction zones: one is zones dipping eastward (conformably with the direction of the Earth’s rotation) and westward (opposite to that direction). The Coriolis force affects the movements of these plates differently. For example, let us consider the simplest case of a slab dipping in the direction of the Earth’s rotation and against this direction in the near-equatorial latitudinal plane. When a slab dips in the direction of the Earth’s rotation, the additional inertia force will act on this slab and tend to move the slab further eastward. This causes the effect of increased weight of the dipping slab. The oppositely directed effects take place if a slab dips westward. Figure 2 presents the dependence of dip angles of subduction zones (as defined for the depth range of 150– 400 km) on dip azimuths of these zones. We can see that small dip angles are typical almost exclusively in subduction zones dipping eastward. If we apply the bootstrap method of numerical simulation [5], then the mean values of dip angles for Benioff zones in the directions along and against that of the Earth’s rotation will be 45° ± 6° and 56° ± 3°, respectively, and the probability of overlapping of

DOKLADY EARTH SCIENCES

Vol. 476

Part 1

2017

EFFECT OF THE EARTH’S ROTATION

these mean values will be 15%. A close level of significance (0.16) is obtained by estimation of the difference between empirical distribution functions for dips of Benioff zones along and against the direction of the Earth’s rotation based on the Kolmogorov–Smirnov criterion. The statistical significance of this difference is not high, but a few aspects should be taken into account: (1) the statistical reliability of regression relations between the parameters of Benioff zones cannot be high, and the values of the correlation coefficient can be about 50% only in extreme cases [7]; (2) if we proceed to consideration of 200-km-long segments instead of entire Benioff zones, then the statistical significance of the difference will become clear; (3) in our case, the problem is not to reveal and validate the earlier unknown regression relationship, but to clarify whether the theoretically expected tendency is virtually observed. Remarkably, there is evidence supporting (although not very strikingly in terms of statistics) not only one but several theoretically expected tendencies. Below we provide examples of these tendencies; their statistical significance is analogous to that considered above and will not be specially discussed because of limits on space. It is seen in Fig. 3 that all subduction zones dipping westward are characteristic of large mean values of the ages of plates; therefore westward dipping slabs have a higher mean density. It is natural to suppose that this difference is related to the compensation mentioned above for the decrease in th weight of slabs under the effect of the Coriolis force by the higher density of slabs dipping eastward, and there is an argument for this. As one can see in Fig. 1, the plates dipping eastward, along the direction of the Earth’s rotation, are generally characteristic of slightly higher mean rates of subduction compared to the plates dipping westward. Such a tendency could be caused by the effect of the Coriolis force that increases the weights of slabs dipping eastward and tends to shift the slabs moving in this direction further. It is natural to raise the question whether the predominant sublatitudinal orientation of dip azimuths originated initially or whether the Coriolis force causes gradual rotation of dip azimuths towards this direction. To discuss this problem, let us introduce the values of deviation of the real dip azimuth of the subduction zone from the nearest E–W direction (90° or 270°) and denote this parameter DAz. First of all, it should be recalled that the spinning horizontal effect of the Coriolis force is absent in the equatorial plane. Indeed, all Benioff zones dipping at azimuths very different from the sublatitudinal one (|DAz| > 60°) are located near the equator (according to [4], their mean latitude is 12° ± 8°). Figure 4 shows the values of DAz depending on the ages of subduction zones (in turn, these ages are estimated from the ages of the respective island arcs). The statistical significance of the relationship is not seen in DOKLADY EARTH SCIENCES

Vol. 476

Part 1

2017

1111

Age of plate, Ma 160 140 120 100 80 60 40 20 0

50

100 150 200 250 300 350 Azimuth, deg

Fig. 3. Ages of dipping slabs depending on dip azimuths of subduction zones. On average, younger (lighter) slabs dip eastward, whereas older (heavier) ones dip westward. Westward and eastward dipping zones are marked, respectively.

this figure; however, it is easy to show that the typical deviations from the E–W direction for younger subduction zones (younger than 200 Ma, 32 zones) are noticeably higher (37°, on average) compared to subduction zones older than 200 Ma (6 zones), for which the mean value of DAz is twofold smaller (18°). Hence, we can suggest that the tendency of a subduction zone to approach its orientation to the sublatitudinal direction (E–W) increases with the age of the island arc. This approach to the sublatitudinal direction of motions with time is consistent with the Taylor–Proudman rule mentioned above. The differences between the parameters of subduction zones dipping westward and eastward are not manifested in this case; hence, all zones in Fig. 4 are indicated in the same way. It is seen from the above that the influence of inertial forces produced by the Earth’s rotation on the character of subduction processes is noticeable. Owing to the effect of the Coriolis force, sublatitudinally directed movements gain a certain advantage in the rotating Earth, whereas submeridional movements have a tendency to cease. Such an assumption is supported by the earlier observation that the mid-ocean ridges have predominantly submeridional orientations. Movements in convection swells corresponding to this orientation of mid-ocean ridges will be predominantly sublatitudinal. Earlier, the authors obtained a number of regularities regarding how the contemporary seismic regime of the Earth is related to its rotation [6]: we have shown that the relationship between subduction process and rotation remains significant for large time intervals corresponding to the geological evolution of the subduction zones. The revealed regularities (except for those shown in Fig. 1), taken separately (if we consider the set of subduction zones rather than the set of their segments), are not statistically significant and reliable. However, these different tendencies correspond to those expected theoretically under the effect of the Coriolis

1112

LEVIN et al.

based on the use of a concrete empirical sample as a general statistical set and usually yields slightly overestimated values of reliability. This slight overestimation was taken into account in the estimates given above.

DAz 90° 80° 70° 60° 50° 40° 30° 20° 10° 0

ACKNOWLEDGMENTS This work was supported by the Russian Foundation for Basic Research, project no. 16-05-00089.

50

100

150

200 250 Age of arc, Ма

Fig. 4. Dependence of the difference between the azimuth of orientation of subduction zones from 90° and 270° (DAz, deg) on the duration of subduction (age of arc, Ma). The gray line denotes the zone where submeridionally oriented subduction zones became progressively absent with the age of the plate.

force. All this on aggregate allows us to consider the concluded effect of the Earth’s rotation on subduction as true. To conclude, let us note that the statistical significance of the given differences was estimated by the numerical bootstrap method [5]; this approach is

REFERENCES 1. B. M. Bubnov and G. S. Golitsyn, Dokl. Akad. Nauk SSSR 281 (3), 552–555 (1985). 2. O. G. Sorokhtin and S. A. Ushakov, Evolution of the Earth (Moscow State Univ., Moscow, 2002) [in Russian]. 3. V. E. Khain, The Main Problems on Modern Geology (Nauchn. Mir, Moscow, 2003) [in Russian]. 4. R. D. Jarrard, Rev. Geophys. 24 (2), 217–284 (1986). 5. B. Efron, Ann. Stat. 7 (1), 1–26 (1979). 6. E. V. Sasorova, B. W. Levin, and M. V. Rodkin, Adv. Geosci. 11, 1–7 (2013). 7. W. P. Schellart and N. Rawlinson, Phys. Earth Planet. Inter. 225, 41–67 (2013).

DOKLADY EARTH SCIENCES

Translated by N. Astafiev

Vol. 476

Part 1

2017

GEOPHYSICS

Effect of the Earth’s Rotation on Subduction Processes Corresponding Member of the RAS B. W. Levina,b, M. V. Rodkina,c *, and E. V. Sasorovab Received May 22, 2017

Abstract—The role played by the Earth’s rotation is very important in problems of physics of the atmosphere and ocean. The importance of inertia forces is traditionally estimated by the value of the Rossby number: if this parameter is small, the Coriolis force considerably affects the character of movements. In the case of convection in the Earth’s mantle and movements of lithospheric plates, the Rossby number is quite small; therefore, the effect of the Coriolis force is reflected in the character of movements of the lithospheric plates. Analysis of statistical data on subduction zones verifies this suggestion. DOI: 10.1134/S1028334X17090252

It is known that the rotation of the Earth produces whirling of atmospheric vortices and considerably affects the character of oceanic currents. This is caused by Coriolis force F which acts on a body moving at speed v relative to the inertial reference system rotating at angular speed w; the value of force F is set by multiplication of vectors v and w to double the mass of the body: F = 2m[v × w].

(1)

The fact whether the Coriolis force considerably affects the character of a flow or not is determined by the Rossby number, which is the ratio between the force of inertia and the Coriolis force. The formula for the Rossby number (Ro) is Ro = U/Lf,

(2)

where U is the characteristic rate of the process; L, the spatial scale of motion; f, the Coriolis parameter, f = 2wsinϕ (w is the angular speed of the Earth’s rotation and ϕ is the latitude). The Coriolis parameter is zero at the equator and f ≈ 1.45 × 10–4 s–1 at the pole. If the value of the Rossby number is small, then the Coriolis force has considerable influence on the character of motion [1]. For convective flows in the mantle and movements of lithospheric plates, we can assume U ≈ 10 cm/yr a Institute

of Marine Geology and Geophysics, Far East Branch, Russian Academy of Sciences, Yuzhno-Sakhalinsk, 693022 Russia b Shirshov Institute of Oceanology, Russian Academy of Sciences, Moscow, 117218 Russia c Institute of the Theory of Earthquake Prediction and Mathematical Geophysics, Russian Academy of Sciences, Moscow, 117997 Russia * e-mail: [email protected]

and L ≈ 1000 km; then the Rossby number is Ro ≈ 2 × 10–11; i.e., this parameter is quite small and the Coriolis force can considerably affect the character of motions. The degree of such an effect will depend on concurrency with the other processes, in this case, with convective turbulent flows in the mantle, which are of larger energy as is seen from the close relationship between mantle convection and volcanism. Let us investigate whether the tendencies expected in the case of a noticeable effect of the Coriolis force on the character of mantle motions are observed. In particular, we should expect that the Taylor–Proudman rule, which is well known in hydrodynamics, will be satisfied in this case; this rule reads that if the Rossby number is small and friction is negligible, then incompressible fluid flows in the planes perpendicular to the rotation vector. Naturally, friction cannot be negligible in the case of mantle convection and motions of lithospheric plates, but if the influence of the Coriolis force is significant, we should expect these motions to be concentrated in the planes perpendicular to the rotation axis of the Earth. In this respect, it is remarkable that mid-ocean ridges are oriented predominantly in the submeridional directions, indirectly indicating that currents in the upper mantle are mostly sublatitudinal. Despite the great advances in seismic tomography, more accurate verification of data on mantle convection in the Earth’s interior is quite difficult because of the high uncertainty about the character of convection. However, the character of convection in the mantle is manifested in movements of the lithospheric plates, and these movements are quite well known today (see [2, 3] and others). Below, we will attempt to reveal and interpret the peculiarities of subduction that are related to rotation of the Earth on the basis of the data on subduction zones summarized by R.D. Jarrard [4].

1109

1110

LEVIN et al.

Vsubd, cm/yr

Dip angle of slab 90° 80° 70° 60° 50° 40° 30° 20° 10°

12 10 8 6 4 2 0

0 50

100

150

200

250 300 350 Azimuth, deg

50

100 150 200 250 300 350 Azimuth, deg

Fig. 2. Dip angle of a slab in the middle part (150–400 km), depending on the dip azimuth. Westward and eastward dipping zones are marked, respectively. Eastward dipping Benioff zones can have small dip angles, whereas zones dipping westward (except for one zone) all have steep angles.

Fig. 1. The values of dip azimuths and subduction rates for different subduction zones.

This comprehensive work provides probably the most complete and consistent set of values for the main parameters of these zones, discusses these parameters, and interprets the empirical regression relations linking these values. Jarrard distinguished and characterized as many as 39 subduction zones [4], which facilitates certain statistical processing of the respective data. It is natural that any subdivision of subduction zones into groups will have a certain degree of subjectivity. For example, it is unclear how many minor subduction zones should be distinguished in the major subduction zone dipping beneath South America and how exactly. It seems logical to consider separated fixed-length (e.g., 200 km long) segments of subduction zones instead of entire subduction zones, as was done in [7]. However, such a subdivision was not accompanied by a complete and homogeneous database of comparable parameters [4]. Additionally, because of the small variability in the parameters along the course of the subduction zone, segmentation leads in fact only to the increase in the size of the analyzed sample by a factor of 5–7, without the essential changes in the data proper. Given the above, in our analysis below we will apply segmentation with the reservation that segmentation would lead to multiple increase in the sample size without essential changes in the correlation values. In terms of analyzing the possible role of the Earth’s rotation, it is natural to verify first how the number of zones and their subduction rates depend on the dip azimuth (whether a plate dips in the same direction as the Earth rotates or in the opposite one). Let us illustrate the notion of the dip azimuth of a subduction zone through the following examples: the Mariana zone dips almost exactly westward at azimuth 270о, whereas the Aleutian zone dips northward at azimuth 0о [4]. The distribution of a number of subduction zones depending on their dip azimuth appeared to be very

nonuniform (Fig. 1). Subduction zones definitely tend to dip at azimuths of the sublatitudinal directions, whereas there are scarce zones dipping in submeridional directions. Indeed, there is the only the subduction zone dipping in the range of azimuths of 110° to 240° (180° ± 60° in the submeridional range), and absolutely no zones dipping at 340°–360°. This tendency is consistent with the Taylor–Proudman rule mentioned above stating that motions concentrate in the planes perpendicular to the rotation vector; i.e., they are oriented predominantly in the sublatitudinal directions. The high statistical significance of this tendency is undoubted. Taking the revealed peculiarity of movements of the lithospheric plates into account, let us further consider the two subsets of subduction zones: one is zones dipping eastward (conformably with the direction of the Earth’s rotation) and westward (opposite to that direction). The Coriolis force affects the movements of these plates differently. For example, let us consider the simplest case of a slab dipping in the direction of the Earth’s rotation and against this direction in the near-equatorial latitudinal plane. When a slab dips in the direction of the Earth’s rotation, the additional inertia force will act on this slab and tend to move the slab further eastward. This causes the effect of increased weight of the dipping slab. The oppositely directed effects take place if a slab dips westward. Figure 2 presents the dependence of dip angles of subduction zones (as defined for the depth range of 150– 400 km) on dip azimuths of these zones. We can see that small dip angles are typical almost exclusively in subduction zones dipping eastward. If we apply the bootstrap method of numerical simulation [5], then the mean values of dip angles for Benioff zones in the directions along and against that of the Earth’s rotation will be 45° ± 6° and 56° ± 3°, respectively, and the probability of overlapping of

DOKLADY EARTH SCIENCES

Vol. 476

Part 1

2017

EFFECT OF THE EARTH’S ROTATION

these mean values will be 15%. A close level of significance (0.16) is obtained by estimation of the difference between empirical distribution functions for dips of Benioff zones along and against the direction of the Earth’s rotation based on the Kolmogorov–Smirnov criterion. The statistical significance of this difference is not high, but a few aspects should be taken into account: (1) the statistical reliability of regression relations between the parameters of Benioff zones cannot be high, and the values of the correlation coefficient can be about 50% only in extreme cases [7]; (2) if we proceed to consideration of 200-km-long segments instead of entire Benioff zones, then the statistical significance of the difference will become clear; (3) in our case, the problem is not to reveal and validate the earlier unknown regression relationship, but to clarify whether the theoretically expected tendency is virtually observed. Remarkably, there is evidence supporting (although not very strikingly in terms of statistics) not only one but several theoretically expected tendencies. Below we provide examples of these tendencies; their statistical significance is analogous to that considered above and will not be specially discussed because of limits on space. It is seen in Fig. 3 that all subduction zones dipping westward are characteristic of large mean values of the ages of plates; therefore westward dipping slabs have a higher mean density. It is natural to suppose that this difference is related to the compensation mentioned above for the decrease in th weight of slabs under the effect of the Coriolis force by the higher density of slabs dipping eastward, and there is an argument for this. As one can see in Fig. 1, the plates dipping eastward, along the direction of the Earth’s rotation, are generally characteristic of slightly higher mean rates of subduction compared to the plates dipping westward. Such a tendency could be caused by the effect of the Coriolis force that increases the weights of slabs dipping eastward and tends to shift the slabs moving in this direction further. It is natural to raise the question whether the predominant sublatitudinal orientation of dip azimuths originated initially or whether the Coriolis force causes gradual rotation of dip azimuths towards this direction. To discuss this problem, let us introduce the values of deviation of the real dip azimuth of the subduction zone from the nearest E–W direction (90° or 270°) and denote this parameter DAz. First of all, it should be recalled that the spinning horizontal effect of the Coriolis force is absent in the equatorial plane. Indeed, all Benioff zones dipping at azimuths very different from the sublatitudinal one (|DAz| > 60°) are located near the equator (according to [4], their mean latitude is 12° ± 8°). Figure 4 shows the values of DAz depending on the ages of subduction zones (in turn, these ages are estimated from the ages of the respective island arcs). The statistical significance of the relationship is not seen in DOKLADY EARTH SCIENCES

Vol. 476

Part 1

2017

1111

Age of plate, Ma 160 140 120 100 80 60 40 20 0

50

100 150 200 250 300 350 Azimuth, deg

Fig. 3. Ages of dipping slabs depending on dip azimuths of subduction zones. On average, younger (lighter) slabs dip eastward, whereas older (heavier) ones dip westward. Westward and eastward dipping zones are marked, respectively.

this figure; however, it is easy to show that the typical deviations from the E–W direction for younger subduction zones (younger than 200 Ma, 32 zones) are noticeably higher (37°, on average) compared to subduction zones older than 200 Ma (6 zones), for which the mean value of DAz is twofold smaller (18°). Hence, we can suggest that the tendency of a subduction zone to approach its orientation to the sublatitudinal direction (E–W) increases with the age of the island arc. This approach to the sublatitudinal direction of motions with time is consistent with the Taylor–Proudman rule mentioned above. The differences between the parameters of subduction zones dipping westward and eastward are not manifested in this case; hence, all zones in Fig. 4 are indicated in the same way. It is seen from the above that the influence of inertial forces produced by the Earth’s rotation on the character of subduction processes is noticeable. Owing to the effect of the Coriolis force, sublatitudinally directed movements gain a certain advantage in the rotating Earth, whereas submeridional movements have a tendency to cease. Such an assumption is supported by the earlier observation that the mid-ocean ridges have predominantly submeridional orientations. Movements in convection swells corresponding to this orientation of mid-ocean ridges will be predominantly sublatitudinal. Earlier, the authors obtained a number of regularities regarding how the contemporary seismic regime of the Earth is related to its rotation [6]: we have shown that the relationship between subduction process and rotation remains significant for large time intervals corresponding to the geological evolution of the subduction zones. The revealed regularities (except for those shown in Fig. 1), taken separately (if we consider the set of subduction zones rather than the set of their segments), are not statistically significant and reliable. However, these different tendencies correspond to those expected theoretically under the effect of the Coriolis

1112

LEVIN et al.

based on the use of a concrete empirical sample as a general statistical set and usually yields slightly overestimated values of reliability. This slight overestimation was taken into account in the estimates given above.

DAz 90° 80° 70° 60° 50° 40° 30° 20° 10° 0

ACKNOWLEDGMENTS This work was supported by the Russian Foundation for Basic Research, project no. 16-05-00089.

50

100

150

200 250 Age of arc, Ма

Fig. 4. Dependence of the difference between the azimuth of orientation of subduction zones from 90° and 270° (DAz, deg) on the duration of subduction (age of arc, Ma). The gray line denotes the zone where submeridionally oriented subduction zones became progressively absent with the age of the plate.

force. All this on aggregate allows us to consider the concluded effect of the Earth’s rotation on subduction as true. To conclude, let us note that the statistical significance of the given differences was estimated by the numerical bootstrap method [5]; this approach is

REFERENCES 1. B. M. Bubnov and G. S. Golitsyn, Dokl. Akad. Nauk SSSR 281 (3), 552–555 (1985). 2. O. G. Sorokhtin and S. A. Ushakov, Evolution of the Earth (Moscow State Univ., Moscow, 2002) [in Russian]. 3. V. E. Khain, The Main Problems on Modern Geology (Nauchn. Mir, Moscow, 2003) [in Russian]. 4. R. D. Jarrard, Rev. Geophys. 24 (2), 217–284 (1986). 5. B. Efron, Ann. Stat. 7 (1), 1–26 (1979). 6. E. V. Sasorova, B. W. Levin, and M. V. Rodkin, Adv. Geosci. 11, 1–7 (2013). 7. W. P. Schellart and N. Rawlinson, Phys. Earth Planet. Inter. 225, 41–67 (2013).

DOKLADY EARTH SCIENCES

Translated by N. Astafiev

Vol. 476

Part 1

2017