"A proof or scientific evidence to show that earthquakes are almost random and memoryless phenomena"

      Several Italian seismologists were accused and indicted for having been responsible for 2009 terremoto dell'Aquila disaster (2009 Central Italy Earthquake Disaster).
      In the popular American TV drama series "BONES", FBI agent Booth said eWe needed a trifecta, Bones. Physical evidence, murder weapon, crime scene.f
      We don't seem to need an emotional argument but scientific evidence. We would like to present a proof or scientific evidence to show that they were not necessarily responsible for the disaster as follows:

 

1.1 Relation between an outbreak pattern of damage earthquakes in Japan and the geometric distribution

       East Japan great earthquake of magnitude 9.0 and maximum seismic intensity 7 occurred on March 11, 2011 and North Nagano earthquake of magnitude 6.7 and maximum seismic intensity over 6 occurred on the next day; March 12, and aftershocks of these earthquakes followed for a long time. The former earthquake caused serious human and property damages in the Pacific coast of the Tohoku and Kanto districts, and triggered the first Fukushima nuclear power plant accident. The latter also caused considerable human and property damages in Nagano and Niigata prefectures.

      We are afraid that if we treat each earthquake as one mathematical event, it might touch a raw nerve for the victims of these and other earthquakes. Furthermore, if a person without technical expertise on earthquakes speaks about an outbreak pattern of earthquakes, seismologists might think it will lead the public to misunderstanding.

      However, we would like to propose the following comparison from just a point of view that earthquakes can be treated as game-like phenomena dominated by the ordinary geometric distribution, wherein the rate that a trial succeeds for the first time after (k-1) times of trials is expressed as p(1-p)k-1 (p is an event probability: k is a positive integer). It should be noted that any geometric distribution has the important property, i.e. the memoryless property.

      In addition, from the fact that East Japan great earthquake was followed by North Nagano earthquake, we incline to think by intuition that earthquakes occur more successively than the rate calculated by the geometric distribution. Here we will check if the rate of earthquakesf successive occurrences is higher than the theory by using the outbreak pattern of past damage earthquakes in Japan.

 
1.2 Chronological Scientific Tables have the past earthquake data of Japan

      The Chronological Scientific Tables edited by National Astronomical Observatory of Japan (Vol. 65, pp. 822-852, Maruzen Co., Ltd. (1991)) include a chronicle of damage earthquakes that caused human and/or property damages at least to some degree in Japan from 416 A. D. to the present. But, on the chronicle, the average occurrence rate of damage earthquakes from 416 through 1700 is much less than that from 1701 to the present. This doesnft mean that the average occurrence rate has been increased from the past but that the accuracy of recording natural disasters has been improved. It seems to us that the system for recording damage earthquakes throughout Japan was established in about 1700 A.D.

      Thus, we analyzed the outbreak pattern of damage earthquakes from 1701 to 1950 A. D. listed in the Chronological Scientific Tables by excluding the record thought as the aftershocks of previous earthquakes.

 

1.3 Outbreak pattern of earthquakes from 1701 through 1950 in Japan

      The damage earthquakes occurred at the rate of 0.936 times per year (about once in one year and one month) in the period. Since if the occurrence rate is almost one the difference between the real outbreak pattern of earthquakes and the geometric distribution is very small, we treated the rate for every four months. The damage earthquakes in the period occurred at the rate of 0.312 times per four months. The corresponding geometric distribution has the event probability of 0.312/four months, which means that if an earthquake occurs within four months from the previous one the trial (to make an earthquake) succeeded successively, and if an earthquake occurs after seven months from the previous one the trial succeeded after one trial, and so on.

Comparison between real earthquake pattern and geometric distribution

      Figure 1 shows the curve A of the geometric distribution with the event probability of 0.312/four months. The curve A shows a series of theoretical rates of the number of earthquakes which occurred successively (k=1), after 4 months (one trial)(k=2), after 8 months (two trails)(k=3), and so on from the previous one, wherein the rate of successive occurrences (k=1) is 31% and the rate of occurring after 4 months (k=2) is 21%.

      Figure 1 also shows the curve B of the real outbreak pattern of damage earthquakes from 1701 through 1950 in Japan. The curve B shows a series of real rates of the number of earthquakes which occurred successively (k=1), after 4 months (k=2), after 8 months (k=3), and so on from the previous one, wherein the rate of successive occurrences is 32% and the rate of occurring after 4 months is 22%. As the curve B matches the curve A well, the damage earthquakes which occurred from 1701 through 1950 in Japan seems to have followed the geometric distribution.  This means that those earthquakes were almost random phenomena and the real rate of successive occurring of earthquakes were not necessarily higher than the theoretical value. Consequently, we suppose that the geometric distribution can apply to earthquake occurrences generally.

 

1.4 Outbreak pattern of earthquakes has the memoryless property: it is hard to predict the occurrence of them

      Since earthquake occurrences follow the geometric distribution, the outbreak pattern of earthquakes has the memoryless property: it seems to be hard to predict the occurrence place and/or time of earthquakes from the past occurrence pattern. It should be noted that this doesnft deny the usefulness of other prediction methods, e.g. methods for predicting the occurrence of earthquakes from disturbance of the geomagnetism, the change of a concentration of some element in a water source, or so called earthquake clouds.

 

1.5 We might already have a solution

      As mentioned above, it seems to be hard to predict the occurrence of earthquakes from the past pattern. But, we already have a rather useful prediction method, i.e. the urgent earthquake alarm system? The alarm system predicts the occurrence place and the maximum seismic intensity of the now-occurring earthquake from catching the initial subtle vibration wave (p-wave).

      The alarm system will be more useful if it predict the occurrence place more precisely and more faster, e.g. about 10 seconds faster than the present system. Then we can afford to reduce the speed of streetcars, stop elevators, and put out the fire of the cookers before the main vibration wave of the earthquake strikes us.

      On the contrary, it doesn't seem to be possible for us to predict precisely the occurrence place and time and the intensity of the earthquake which will occur in the future under the circumstances that we cannot predict the occurrence place and the intensity of the now-occurring earthquake quickly and precisely. In other words, it might lead to the useful system for predicting the future earthquakes to improve or refine the present urgent earthquake alarm system.

1.6 As for tsunamis we do not need to "predict" it

      As for tsunamis (seismic sea waves), it seems to us that we do not need to "predict" the height and arrival time of the tsunami after an earthquake has occurred in an ocean floor. We only have to measure the difference between the height of the sea level over the epicenter and that of other sea areas by using a meteorological satellite.

      In conclusion, since the present science cannot predict the occurrence place and time of the future earthquakes from the past earthquake pattern, the accused Italian seismologists seem to be not responsible for 2009 terremoto dell'Aquila disaster (2009 Central Italy Earthquake Disaster).

 Copyright: 2012 Consulting Division of Omori Patent Office. All rights reserved. No reproduction or republication without written permission except for the use for the accused Italian seismologists.
(Mail to: o-pat-consulting@hotmail.co.jp)
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