Global View of Great Earthquakes and Large Volcanic Eruptions Matched to Polar Drift and its Time Derivatives

Transcription

1 Global View of Great Earthquakes and Large Volcanic Eruptions Matched to Polar Drift and its Time Derivatives by Douglas W. Zbikowski, Institute for Celestial Geodynamics Draft posted 7 March 2012 Introduction [1] The rotational axis of Earth moves with respect to two reference frames the celestial and terrestrial. Axial motion with respect to the celestial frame has been traditionally divided into two parts, precession and nutation. Precession is a smooth motion of the axis that traces out a cone in space with its apex at Earth's center and an angular radius of This secular motion, with a 25,800- year cycle, is produced by gravitational torquing on Earth's aspherical, equatorial bulge by the Moon, Sun, and in much smaller amounts by solar system planets. Nutation is a small amplitude, periodic 'nodding' of the axis along that conical path and is comprised of short-period components. The dominant component, with the largest amplitude (9 arcseconds) and longest period, is associated with the year lunar-nodal cycle. The total combined movement of the rotational axis with respect to the celestial frame is entirely astronomically forced. [2] Axial motion with respect to the terrestrial frame is motion referenced to the net surface of Earth. Net surface represents an averaging of all crustal motions due to global tectonics. In 1991, the International Union for Geodesy and Geophysics (IUGG) approved a reference system model, the International Terrestrial Reference System (ITRS), that defined requirements for suitable reference frames. Requirements included, in part, an origin that is the geocenter of Earth's masses including oceans and the atmosphere and a coordinate frame that has no residual global rotation with respect to horizontal motions at Earth's surface. [3] Axial motion with respect to the terrestrial frame is usually divided into three categories, polar wobble, polar drift, and polar wander. Polar wobble is the annual motion of the rotational pole on the net surface in a roughly circular figure that varies in size, the diameter being about 12 m during Polar wobble has two main components the Chandler and annual wobbles. The Chandler wobble is a free oscillation with a period of about 435 days, which is excited by a combination of atmospheric and oceanic processes, with the dominant excitation mechanism being ocean bottom pressure fluctuations. 1 The annual wobble is a forced oscillation due to seasonal displacements of air and water masses. Polar drift is residual movement along the path of annual mean poles, which averages about 15 cm/yr. The speed and direction of polar drift can vary considerably in just a few years. Polar wander is the large amplitude geographic motion of polar drift on the geologic timescale. Polar drift and polar wander are reasoned to be caused mainly by slow redistributions of mass within or on Earth (especially suspect, currently, are post-glacial rebound and polar ice loss). This premise is challenged, herein, by differentiating the drift path into its time-derivative curves, drift speed and acceleration, which both show cyclical patterns thereby producing a basis in rotational dynamics for suspecting cyclical forcing, hypothetically, with astronomical causes. The cyclical time derivatives of polar drift are also shown to correlate strongly with global earthquakes and volcanic eruptions, thereby raising the possibility of forecasting such events. [4] Note: 1. Gross, R. S. (2000), The excitation of the Chandler wobble, Geophys. Res. Lett., 27(15), , doi: /2000gl Figure 1. A tsunami wave crashes over a sea wall and street in Miyako City, Iwate Prefecture, in northeastern Japan shortly after a record M9.0 earthquake struck off the coast on March 11,

2 Figure 2 Drift Path of North Rotational Pole [5] Figure 2 shows the secular drift path of the north rotational pole for Dr. Daniel Gambis, Director of EOP PC at the Observatoire de Paris and Board Member of the International Earth Rotation and Reference Systems Service (IERS), supplied sequential mean poles for every 0.30 year ( days) in , every 0.15 year (54.79 days) in , and every 0.05 year (18.26 days) in In computing the mean poles, Dr. Gambis filtered pole components to remove both wobble terms, the Chandler and annual. Resolution of the roughly circular path of polar wobble is provided using modern astrometrical methods Very Long Baseline Interferometry (VLBI) and Global Positioning System (GPS). Using GPS, the motion of polar wobble is determined daily with a precision of +/- 0.2 milliarcsecond 3 (0.6 cm on surface). [6] On this graph, one-tenth second (0".10) of geocentric arc equals meters on the Earth's surface near the North Pole. 4 Decades are marked and labeled to show the nonuniform nature of drift speed. It is apparent that when drift direction is changing more rapidly, the pole drifts more slowly. Although the century trend of the path is toward 80 W., path detail shows extended excursions from that direction. The accuracy of the path prior to 1890 seems suspect in that those mean poles are found to be positioned more irregularly than the rest and did not produce, with incremental calculation, consistent drift directions. The calculation of direction should not have yielded such inconsistency solely from the relatively longer 0.30-year intervals. [7] The filtered path of secular polar drift, with mean poles calculated for periodically varying but regular intervals, will be utilized to calculate both aspects of drift velocity (1) velocity magnitude (speed) and its sequential time derivative, acceleration, and (2) velocity direction. Drift-velocity aspects and their time derivatives will be shown to affect the timing, location, and intensity of earthquakes and volcanic eruptions on the globe. [8] 2. On 21 March 2011, Dr. Daniel Gambis supplied a homogeneous solution of mean poles for , with pole components filtered to remove the Chandler and annual terms IERS retrieved 23 December Using the derived polar radius, b = 6,356, m, from Department of Defense World Geodetic System 1984, NSN , 23 Jun 2004 rev.

3 Figure 3 Global Great Quakes and Large Eruptions Matched to Drift Speed, Acceleration, and Jerk [9] Figure 3 shows speed and acceleration of drift of Earth's north rotational pole with respect to the net surface. The relative motion of the rotational axis in this tip-over mode (TOM) 5 of the spinning Earth physically requires proportionate angular migration of the ellipsoid via equipotential adjustment of the figure. Figure adjustment generates commensurate crustal strain, the most being created where the ellipsoid migrates fastest on the meridian great circle that is aligned with drift direction. In the time domain, abrupt changes in crustal strain/stress may plausibly trigger quakes and volcanic eruptions. To investigate this possibility, such events are plotted on the acceleration trace to check for event correlation with abrupt changes in the rate of acceleration a likely generator of abrupt changes in strain/stress. [10] Markers on the LOESS-smoothed acceleration trace indicate the timing and categorical size of great earthquakes and large volcanic eruptions. 6,7 Note that most quakes and eruptions occur when the acceleration rate-of-change is changing rapidly the trace curves markedly at full turning arcs and the events of greatest energy usually occur at or near maximum or minimum turning points. Also, event groupings of extreme energy appear to match acceleration turning points that occur immediately after or during periods of unusually high drift speed. Correlations shown between seismic or volcanic triggering and time derivatives of drift may result because the timescales of seismic or volcanic nucleation are fulfilled by the timescale of drift-driven strain/stress fluctuations. Changing rate-of-change of acceleration is called jerk and the cyclical TOM acceleration and slow jerk may be astronomically forced. [11] The TOM acceleration appears regularly forced, hypothetically, by varying gravitational torque that arises from the combination of orbital variations within local celestial-mechanical cycles: the year lunar-nodal cycle, the 8.85-year revolution of lunar perigee, and Earth's annual solar orbit (supporting graphs not shown here). Notice that the total cyclic forcing regularly produces 59-year super peaks in acceleration (e.g , , ) and about 8 years later in speed (e.g. 1901, 1960, 2021?). Commensurabilities of resonance may be: (18.61 yr x 3 = 55.83) and (8.85 yr x 7 = 61.95) with (( )/2 = 58.89). A spectral analysis should be performed to test this hypothesis and a celestial-mechanical model completed to corroborate the result. [12] While the last two drift-speed super peaks in 1901 (23 cm/yr) and 1960 (24.5 cm/yr) had significantly greater speed than interim levels, the next super peak may actually be a mega peak in comparison. Projections indicate that a drift speed of 52 cm/yr may be reached by The rarity of the 32 cm/yr drift speed of 2011 is evidenced in its effect by the March 2011 Japanese quake of M9.0 following a long history of many centuries of regional quakes never exceeding M8.5. Also, judging from the timing of some great events in history, super peak regularity in drift speed may extend at least back to 1783 (1901 (2 x 59) = 1783) with the infamous Laki fissure eruption in Iceland that killed, possibly, millions globally. [13] Showing correlations between global great quakes or large eruptions and time derivatives of drift is intriguing, but is not, in itself, a tool for usefully forecasting such events. The problem is that although strong associations hint at polar drift driving equipotential adjustments (this mechanism is hereinafter called ellipsoidal demand), which generates crustal strain fluctuations that may trigger quakes and eruptions, event locations are not indicated. For ellipsoidal demand to be proven useful for forecasting events, a significant history of its time derivatives at a potential site must be determinable and correlate well with the record of local seismic and/or volcanic events. [14] 5. The 'TOM' used here is not the tilt-over mode of axial motion with respect to the celestial frame that results in precession and nutation, but the tip-over mode of the planet's net surface with respect to the rotational axis.

4 6. Earthquake data, retrieved 24 July 2011: Pre-1900 NOAA The Significant Earthquake Database, parameter search: magnitude M8.0, focal depth 230 km (preference given to this database for geographic coordinates) USGS Historic World Earthquakes, compiled list Post-1900 NOAA The Significant Earthquake Database, parameter search: magnitude M8.0, focal depth 230 km (preference given to this database for geographic coordinates) USGS Magnitude 8 and Greater Earthquakes Since 1900, compiled list 7. Volcanic data from the Smithsonian Institution's Global Volcanism Program, retrieved 22 July 2011: Volcano list (name, subregion, eruption date, eruption size) Link to coordinates (latitude, longitude, description) Figure 4 Global Great Earthquakes and Large Eruptions Related to Drift Direction [15] Figure 4 relates the epicenters of great earthquakes and locations of large volcanic eruptions to the direction of polar drift for The line of drift direction is constructed incrementally from numerous polar drift directions that are calculated as tangents sequentially from the data set of mean poles, which has been filtered to remove both wobble terms, the Chandler and annual. 2 [16] For graphic simplicity, the energetic events and drift direction are plotted on only the Eastern Hemisphere, by designating the eastern meridian of the meridian great circle (MGC) upon which they are located. To permit graphical continuity of the line of drift direction, the 'Eastern Hemisphere' displayed extends from E. longitude. This method of projection takes advantage of the hemispherical symmetry involved in the kinematics of polar drift. When the pole drifts, territory along the MGC that is aligned with drift direction experiences the fastest migration of ellipsoidal profile. Therefore, along this MGC, equipotential forces driving figure adjustment will generate the greatest crustal strain/stress fluctuations and may have the greatest potential to trigger events. So, to accurately display the energy relationship between events and drift direction the total event response from along the entire driftaligned MGC is recorded over time. And for clarity, all events may be projected onto one hemisphere that is selected to best display drift direction. [17] Global earthquakes of category 8.8 M 9.5 appear to be strongly correlated to the MGC of drift direction. Five of these seven quakes occurred years after epicenter coincidence with the drift MGC, averaging 9.3 years afterward. The other two occurred either 5.1 years after the 1901 peak or 4.2 years after the 1960 peak in drift speed, as shown in figure 3. The first, a quake in Ecuador, occurred when the approaching drift MGC was 15 in longitudinal distance and the second, a quake in Prince William Sound, Alaska, lagged a 14 longitudinal proximity with the drift MGC by 22 years. The category 8.4 M 8.7 with 25 quakes, appears less correlated to drift direction, with eleven quakes occurring within 5 years of epicenter coincidence to the drift

5 MGC. However, this category also appears correlated to peaks in drift speed with ten quakes within 5 years of the 1901 peak and three quakes within 5 years of the 1960 peak. Category 8.0 M 8.3 with 115 quakes, has no clear correlations to drift direction or speed and would require spatial-statistical analysis to evaluate. From the above, it appears that the greater a quake's magnitude, the more sequentially probable it is that: (1) a coincidence of its epicenter with a drift direction MGC preceded quake release by 5 13 years, 8 or (2) the quake occurred within 5 years of the 1901 or 1960 peaks in drift speed, or (3) its epicenter is close in longitude to the concurrent drift MGC. [18] Global volcanic eruptions of Volcanic Explosivity Index (VEI) category 5>VEI 6 also appear to be correlated to the MGC of drift direction. Three of these five eruptions occurred years after site coincidence with the drift MGC, averaging 9.1 years afterward. The fourth, a eruption in Guatemala, occurred 1.8 years after the 1901 peak in drift speed and when the approaching drift MGC was 18.5 in longitudinal distance. The fifth, a eruption on the Alaska Peninsula, occurred 11.4 years after the 1901 peak in drift speed and when the drift MGC was 71 in longitudinal distance. The category 4<VEI 5 with ten eruptions, appears mildly associated with drift direction and drift speed, with three eruptions occurring within 5 years of site coincidence to the drift MGC and three eruptions within 5 years of the 1960 peak in drift speed. Category 3.9 VEI 4 with 82 eruptions, has no clear associations to drift direction or speed and would require spatial-statistical analysis to evaluate. Volcanic eruptions involve mechanisms of fluid transport (e.g. rock melt and water), extreme thermal effects on materials (e.g. chemical, phase, viscosity, and density changes), bulk material properties (e.g. strength and weight), and other parameters. Thus, eruption nucleation is likely a more complicated phenomenon than earthquake nucleation. However, triggering of the largest eruptions does appear to be affected by ellipsoidal demand, as evidenced by the spatial association of eruptions to drift MGC and possibly drift speed. [19] A majority of the greatest quakes and largest eruptions appear to follow a coincidence between the event location and the drift MGC, averaging ( )/2 = 9.2 years afterward. In the interpretation of figure 3, a hypothesis was advanced which, in part, proposed that varying gravitational torque caused by the year lunar-nodal cycle may be responsible for some of the cyclical forcing of drift acceleration. It was also noted that "events of greatest energy usually occur at or near maximum or minimum turning points [in drift acceleration]." Because turning points occur twice per cycle, the time between points influenced, hypothetically, by the dominant torque of the lunar-nodal cycle might tend toward 18.61/2 9.3 years. Proximity to this mean should depend on precisely how the two lunar cycles the nodal and revolution of perigee factor together throughout time to produce the gravitational torque applied to Earth by the Moon. Thus, it seems supportive of the proposed hypothesis that triggering of the majority of greatest quakes and largest eruptions averages 9.2 years after event locations coincided with the drift MGC. [20] 2. On 21 March 2011, Dr. Daniel Gambis supplied a homogeneous solution of mean poles for , with pole components filtered to remove the Chandler and annual terms Californians may note that the corresponding location MGC for San Francisco is E. The famous 1906 M7.8 earthquake (almost a great quake) occurred 8.6 years after the drift MGC matched that longitude. Summary [21] Ellipsoidal demand, hypothetically driven indirectly by celestial-mechanical forcing, may be an important control for triggering great earthquakes and large volcanic eruptions. However, plate dynamics, as driven by the mechanisms generally accepted in the theory of plate tectonics slab pull, ridge push, and basal traction from lateral components of convection currents, must surely be a major contributor to lithospheric loading. Such loading has been accumulating over geologic time, and the usual levels of strain/stress in many regions may be sub-critical of energetic release by amounts small enough to allow an additional effect that is fluctuating to control triggering. Scholz assesses this sub-critical possibility, stating that... a large part of Earth s lithosphere must be stressed [near] to failure, even in regions not undergoing active tectonic deformation. 9 Regardless of exactly how the two strain-generating regimes work together, the relevant fields of Geophysics and Public Safety would be advanced by investigating the contributions of ellipsoidal demand at many potentially hazardous locations around the world. [22] Note: 9. Scholz, C. H. (2002). The Mechanics of Earthquakes and Faulting, p.350. Cambridge: Cambridge University Press. Acknowledgements [23] I wish to thank Dr. Daniel Gambis, Director of EOP PC at the Observatoire de Paris and Board Member of the International Earth Rotation and Reference Systems Service (IERS) for the pole data; Amelia A. McNamara, Ph.D. candidate at UCLA, for statistical programming and graphing; Dr. Debra J. Blake for non-technical editing; Delores M. Zbikowski for funding; and the Minnesota Library Information Network (MnLINK) for providing interlibrary book loans. Dedication I dedicate this work to the memory of William A. Zbikowski, my father, who never tired of my little reports of progress. Institute for Celestial Geodynamics BY-ND-02March2012