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Megathrust EQ prediction Information

Nation of EQs        Mega EQ warnings        Nankai-trough M9.1?        EQ prediction info        Shikoku median tectonic line


Physical Wavelets        Keiiti Aki        Work with us        Membership


Japan is a nation of EQs located in subduction zones. Japans 20 km-mesh seismograph network has seen megathrust and significant EQ genesis processes with Physical Wavelets, suggesting the predictability of the focuses, fault movements, sizes, and rupture times around two weeks to three months before the events occur. Similarly, the Japanese GPS network has seen the 2011 Tohoku megathrust EQ genesis process with Physical Wavelets, suggesting the predictability of the EQ and tsunami two months before the events. Their time-prediction accuracies are within a day by real-time monitoring of the expected rupture processes. To describe the equations of the EQ genesis processes in real-time for the predictions, Physical Wavelets quantify the stochastic EQ source parameters of the online seismic catalogs and the non-differentiable daily displacements of the GPS network.


We can now use real-time EQ prediction information as disaster prevention warnings like typhoons and hurricanes. A summary is here to look for worldwide collaborations.


Megathrust earthquake prediction information

Megathrust and many significant earthquakes (EQs) occur in subduction zones. The subducting oceanic plates are the Northwestern Pacific plate and the Philippine Sea plate. A nations earthquake (EQ) prediction information is the megathrust and significant EQ genesis processes. Physical wavelets quantify the real-time genesis processes with GPS stations' daily displacements and online seismic catalogs. The EQ genesis processes evolve into disaster prevention warnings like typhoons. The 2011 Tohoku megathrust EQ genesis of 15 months had a disaster prevention warning for the last three months. We begin the megathrust EQ genesis process like violent typhoon information for the Nation of EQs.

A Nation of EQs

The EQs having M 6 from 1983 to 2019 has a distribution overlayed on a google map.


According to seismic catalogs, a Nation of EQs (Nation 3) had EQs having M 6 from 1983 to 7 Sep 2022, 1024 shallow EQs with DEP < 200 km, and 116 deep EQs with DEP 200 km.


Megathrust EQ (Tsunami) disaster-prevention warning

The technical details, background physics, and observations in Japanese patent 5798545  (130 pages with 85 figures) have extensive updates in arXiv.  

【1】Takeda, F. (2021). A megathrust earthquake genesis process observed by a Global Positioning System. arXiv.


【2】Takeda, F. (2022). Large earthquake genesis processes observed with Physical Wavelets. arXiv.


【3】Takeda, F. (2022). Significant and megathrust earthquake predictions by real-time monitoring of the genesis processes with Physical Wavelets. arXiv.


The observed GSIs daily displacement at every GPS station in Tohoku and the Northwestern Pacific Ocean is a noisy and non-differentiable time series. A mathematical tool named Physical Wavelets observed the megathrust earthquake genesis process by quantifying the noisy displacements. Ryoutsu2 (West coast), Murakami (Top), and Onagawa (East coast) stations are at the dotted-red line cross-section to show the genesis of the Tohoku crustal bulge deformation, which was a megathrust earthquake genesis process.





The 2011 Tohoku M9 and tsunami genesis process

The Tohoku east coast is at the tectonic plates eastern edge, overriding the subducting oceanic plate.

The fault plane (500 km in length, 200 km in width) had coupled two plates together for hundreds of years.

The megathrust earthquake genesis process is shown as cross-sectional schematics at the red dotted line. Physical Wavelets quantified Japans GPS observations on the 2011 Tohoku M9 megathrust EQ.





In the schematics, the east and west coast face the Northwestern Pacific Ocean and the Japan Sea. The E, W, and Top are for the East coast (Onagawa station), West coast (Ryoutsu2 station), and Top (Murakami station). The Top is a ridge line in Tohoku. Tohoku had three distinctive phases of crustal bulge deformation, the initial, transitional, and final phases.


(a)  Initial phase

The fault surface had coupled two plates at the subduction zone, generating the tectonic eastward-up and the oceanic westward-down movement for hundreds of years. The coupling had created a regular deformation, as shown. The regular slow deformation had the initial bulge phase characterized by a uniformly increasing upward (lifting) force in January 2010.

(b)  Transitional phase

The transition is from the regular to a bulge deformation, pulling down (dotted arrow) the subducting Northwestern Pacific Plate by the fault coupling. A massive action in the transition from the regular to bulge deformation made the overriding tectonic plates eastern edge take hold of a significant barrier (on fault) 2.8 mm deep. The pull began in July 2010.

(c)  Final phase

The final phase is the upheaval deformation rupturing the fault surface and activating an enormous reaction (dotted arrow) to generate the megathrust EQ and a tsunami on March 11, 2011. The upheaval began in November 2010.


The Pacific plates abnormal motion and a megathrust EQ disaster-prevention warning

1.      A bulge deformation of a few millimeters over Tohoku started an initial phase of three processes in Jan 2010.

2.      In June 2010, the east coast changed the deformation to the next phase and, in one month, began pulling the subducting Pacific Plate westward, nine months before the M9 EQ on Mar 11, 2011.

3.      The motion gradually gained westward speed, reaching an abnormal 0.69 mm/day on Dec 22, 2010, three times higher than usual.

4.      About one month before the highest speed observation, the east coast began the final deformation phase with an upheaval growing.

5.      Its linear growth decelerated, stopped, and reversed the westward motion by two weeks before the event.

6.      The upheaval grew to 1.2 mm over 115 days, rupturing the fault plane and releasing an enormous reaction force to generate the megathrust earthquake.


The fifteen-month megathrust earthquake genesis process suggests that such events are predictable in real-time. From Dec 22, 2010, the megathrust EQ genesis was in the final process.

Thus, we identify the last three-month process of the oceanic plate motion as a megathrust EQ disaster-prevention warning, like a typhoon warning.


Pulling action

The subducting oceanic plates westward movement is under the lunar synodic tidal force loading for 30 (29.5) days. The east coast bulge deformation started to pull down the subducting plate as a new external force. Any external force coupling with the westward oceanic plate motion gradually changes the 30-day periodic lunar responses in amplitudes and phases.

The unusual change began in July 2010, 9 months before the 2011 Tohoku M9 EQ. The regular westward movement rate per day was about twice that of a humans fingernail growth rate of 0.1o/day.

The unusual movement reached the highest speed of about three times the usual on 22 Dec 2010. Then, the motion got to slow down and stooped on 25 Feb 2011. The movement reversed the direction and reached eastward 0.06 mm/day on 8 Mar 2011.

The unusually decelerated movement of the subducting plate is a real-time reflection of the last three months of the megathrust genesis process. The unusual move is the abnormal paths on D (displacement)V (velocity) and D A (acceleration) planes. Thus, observing the unique oceanic plate motion becomes a real-time disaster prevention warning for the megathrust EQ and tsunami.

Megathrust EQs real-time disaster prevention warning is the abnormal DV and DA path in subducting plate movements

As detailed in reference [1], Physical Wavelets observe the Tohoku megathrust EQ genesis process in a noisy d (E, j ) at Chichijima station

 with D V and D A pathand PW (Eτ) in real-time.


Drawing descriptions

1)   The green d (E, j ) is the daily displacement (from West to Eastward) of Chichijima station at day j. The displacement is the stations movement from an arbitrarily chosen initial position.

2)   The vertical offset scales (left) are in m (meters) with a magnification of 2500 (/2500). The horizontal scales are time in days. The expanded time window is from j = 3500 (December 23, 2009), to j = 3940 (March 8, 2011)

3)   The offset origin (m) is arbitrarily chosen for graphics. The origin has a value of 0.35 m from the stations initial reference position. The minus is downward (westward) from the position.

4)   The graphical origin shares the origin 0 for velocity V (E, τ) and acceleration A (E, τ)in relative scales. The plus scale is upward and eastward, and the minus is downward and westward.

5)   The green d (E, j ) is from up to down, indicating the westward movement of the GPS station; namely, the northwestern Pacific plate is moving westward.

6)   The red D (E, τ) is the moving average of green d (E, j ) over 15 days (2w +1, w = 7), and time τ is in days. The time τ is τ= j w.

7)   Velocity V (, τ) in black and acceleration A (, τ) in blue are the first- and second-order difference rates of s = 20 days.

The green d (E, j ) fluctuates due to various environmental noises, which is non-time differentiable. The correlation integrals of d (E, j ) with Physical Wavelets define D (,τ), V (,τ), and A(E,τ). The time-reversal operation is to change τ to τ, for which D (E, τ), V (E, τ), and A (E, τ) have the properties of D (E, τ) = D (E, τ), V (E, – τ) = V (E, τ), and A (E, τ) = A(E, τ). They satisfy the time differential properties on the differentiable D (E, τ) and V (E, τ).

8)   The vertical relative scale for power PW (Eτ) = V (E, τ) × A (E, τ) is on the right column.

9)   The monitoring with PW (Eτ) 350 detected an anomalous lunar synodic loading on d (E, j ). The predetermined threshold of 350 at the red level was about twice the expected standard power level. The anomalous V (Eτ) and A (Eτ) were bold under PW (Eτ) 350. The red column height difference is the corresponding power change at the first detection.

10)The timeτlags asτ= jsw = j27. Thus, a real-time automated PW (Ej) monitoring is PW (Ej ) = V (E, j ) × A (E, j ) with j = τ + s + w = τ+ 27 and standard thresholds.

11)The (Eτ)(Eτ) and (Eτ)(Eτ) path monitoring on the  and D  A plane

 The (D, V) = (4 cm, 1 mm/day) plane has an offset origin at the blue-line-scale 50, (Eτ) = 0.22 m ( 0.2 50/2500). The (Eτ) origin is 0 mm/day.

The right half of the D (E, τ) V (E, τplane is east of the offset origin. The upper half is eastward and positive V (Eτ). The lower half is westward and negative.

The (D, A) = (32 mc, 0.04mm/day2) has the same property of (D, V). The (Eτ) origin is 0mm/day. The upper half is positive with the eastward acceleration.


A real-time megathrust EQ genesis process revealed by the subducting oceanic plate movement in Figures b & c



The lunar synodic tidal force loading of the 29.5-day-period has 30 days on the blue A (Eτ).

The date label 2010/07/11 is the(E, τ) trend change (bulge deformation in transition) at τ3700 (July 11, 2010), starting to pull down the oceanic plate.

The M7.9 is the off-Chichijima EQ triggered by the abnormal oceanic plate movement.

The EQ is M7.9 (2010/12/22) in the strain energy accumulation and release cycles in Nation 3.


The real-time disaster prevention warning with the megathrust EQ genesis process of the last three months in Figures b & c



The motion gradually gained westward speed, reaching an abnormal 0.69 mm/day on December 22, 2010, three times higher than usual, rupturing the M7.9 EQ.

The movement stopped on February 25, 2011. It reversed the move. The eastward speed reached 0.06 mm/day on March 8, 2011 (the last operational day at Chichijima station).


No disaster prevention warnings as of 2022/09/07


As of September 7, 2022, the subducting northwestern Pacific Plate and the Philippine Sea Plate do not have abnormal movements; no disaster prevention warnings exist.

However,  the Mw 9.1 EQ and a 34 m-height tsunami anticipated by Japans cabinet office do not have any scientific evidence like the megathrust EQ genesis process observed in the 2011 Tohoku M9 EQ and tsunami.



Nankai trough M9.1

Three major EQs anticipated at any time in the Nankai trough are

Tokai EQ (1), Tonankai EQ (2), and Nankai EQ (3).


Japans cabinet office anticipates a chain coupling of the three fault ruptures that will generate an M.1 megathrust EQ.

However, the anticipated three-fault coupling rupture has no scientific evidence like the 2011 Tohoku megathrust EQ genesis process outlined above. The GPS observation of Tohoku and the subducting northwestern Pacific plate over 15 years before the Tohoku M9 EQ had anticipated a megathrust EQ and tsunami at any time. As the GPS observations in reference [1] show, there is no scientific evidence for the anticipated megathrust EQ and tsunami in the Nankai trough like the 2011 Tohoku M9 events.


The GPS observation on the Nankai trough as of 2022/09/07

The GPS observations on Omaezaki (Tokai EQ), Shiono Misaki (Tonankai EQ), and Muroto Misaki (Nankai EQ) area show that each fault locally couples the subducting Philippine Sea plate with overriding western Japans east coast. Thus, we anticipate each significant EQ at any time. However, there is no three-fault coupling evidence observed.


A monthly analysis like the figure summary in references [1-3] above and the megathrust EQs disaster prevention warning is available only for a membership.



Major EQ prediction info

An EQ event has the property of the hypocenter (in latitude LAT, longitude LON, and depth DEP), its origin time (event time), and magnitude MAG. They are the so-called EQ source parameters. The interval between consecutive event times is the inter-event interval (INT).

We express an EQ parameter as d (c, m) at the chronological event-index time m, where c = LAT, LON, DEP, INT, and MAG. The consecutive EQ events change parameter d (c, m), drawing a zigzagged trajectory in the c-coordinate space. Each component path is non-time differentiable. Physical Wavelets are the only mathematical tool to observe significant and megathrust EQ genesis processes by quantifying such stochastic pathways.

A strain-energy accumulation and release cycle

Nation 3

The observations until 2022/09/17 and 2022/09/18

As in references [2] and [3], Physical Wavelets observe a strain-energy accumulation and release cycle during the significant and megathrust EQ genesis processes with an online JMA seismic catalog having one- or two-day latency.  An automated Hi-Net record may fill the latency.

One group of figures is until 2022/09/17, and another is until 2022/18. They show the Taiwan M 6.6 EQ on 2022/09/17 and the Taiwan M 7.3 on 2022/09/18. The catalog has assigned the M6.6s DEP as 0 km, separating figures to the EQs with DEP 0km and another with the EQs of DEP > 0km. The strain-energy cycle generally peaks a few days before a significant event occurs in wide regions like Nation 3.

Thus, a rapid decrease from the peak accumulation in the 2022/09/17 figure shows the M6.6. The M7.3 main shock is yet to appear on the cycle.




中程度の精度で自動的に生成された説明 グラフ, 散布図


Observation until 2022/09/18

The Taiwan M 7.3 on 2022/09/18 appears.



自動的に生成された説明 グラフ, 散布図



Figure descriptions

A moving j sum of 2s consecutive d (INT, j )s and 2s d (DEP, j )s at the index time m express the strain energy density in a selected region. Significant and megathrust EQ genesis processes in the region accompany the strain energy accumulation and release cycles. Their normalized cycles with the past maximums are NCI (m, 2s) for d (INT, j ) and NCD (m, 2s) for d (DEP, j ). The summing total number is 2s = 100 and 30 for NCI (m, 2s) and 2s = 30 for NCD (m, 2s). The NCD (m, 2s) excludes EQs cataloged with d (DEP, j ) = 0 km.

For a region of Nation 3, EQs are d (MAG, j ) 4; namely, M 4.

1)    The left vertical axis is the normalized scales for NCI (m, 2s) and NCD (m, 2s).

2)    The horizontal axis is the chronological event index m, one-to-one correspondence to event (origin) time. The 2010/01/01 is m = 1.

3)    The right vertical scales are magnitude M for d (MAG, m ) 6.

4)    The upper vertical scales are relative to d (LON, m ). Localized consecutive dots are EQ swarms or aftershocks of significant EQs.


The NCI(m, 2s) and NCD(m, 2s) generally peak a few days before a significant event occurs in large regions. NCI(m, 2s) and NCD(m, 2s) increase to their peaks together, and then they rapidly decrease from their peaks, during which a large shallow event occurs, as the Taiwan M6.6 and M7.3.

If the expected event is significant and deep, like EQs in the Wadati-Benioff zone, NCD(m, 2s) keeps increasing.


Normalized strain-energy cycle on the 2011 Tohoku M9 in Nation 3



Normalized strain-energy cycle on the off-Chichijima M7.9 (2010/12/22), a foreshock M7.5(2011/03/09), and the Tohoku M9 (2011/03/11)


 (a) The normalized strain-energy-density time series (cycle) of NCI(m, 30) and NCD(m, 30) from 12 Aug 2010 to 11 Mar 2011. Their time series are the EQs of MAG 4 from the JMA unified focus catalogs for the region of LAT = 16°52° N and LON = 116°156° E. The 22 Dec 2010 M7.9 at m = 16695 is a precursory event to the 2011 Tohoku M9, which occurred near Chichijima (an island in the Pacific Ocean). A large foreshock to the M9 event at m = 17287 is the 9 Mar 2011 M7.5. Time m has the following corresponding date: m = 16500 to 3 Oct 2010; m =16700 to 22 Dec 2010; m =16900 to 28 Dec 2010; m =17000 to 10 Jan 2011; m =17100 to 25 Jan 2011; m =17200 to 16 Feb 2011; m =17300 to 9 Mar 2011. (b) The normalized and magnified strain-energy cycle of NCI(m, 30) and NCD(m, 30) from m = 17200 (16 Feb 2011 at 02:23) to 17500 (11 Mar 2011 at 22:35). The NCI(m, 30) and NCD(m, 30) are respectively magnified by 20 and 5 times after m = 17317 (9 Mar 2011 at 16:56) pointed with the up-arrow on the m axis. The peaks for NCI(m, 30) and NCD(m, 30) are at m = 17359 (11 Mar 2011 at 13:12) and m = 17358 (11 Mar 2011 at 10:41), respectively. The 11 Mar 2011 M9 (the 2011 Tohoku M9) occurred at m = 17361 (11 Mar 2011 at 14:46). Time m has the following corresponding date and time: m = 17300 to 9 Mar 2011 at 13:04; m = 17400 to 11 Mar 2011 at 16:36.


The strain energy cycle in every small region

Available for Membership


Regional EQ prediction Information and disaster prevention warnings

We express an EQ parameter as d (c, m) at the chronological event-index time m, where c = LAT, LON, DEP, INT, and MAG. The consecutive EQ events change parameter d (c, m), drawing a zigzagged trajectory in the c-coordinate space. Each component path is non-time differentiable.

Online seismic catalogs have d (c, m) at event index time m where c = LAT, LON, DEP, INT, and MAG. The GPS observes noisy daily displacement data; d (c, m), where c is the geological axis c, denoted by E (west to east), N (south to north), and h (down to up) in right-handed coordinates (ENh).


The Physical Wavelets observations of significant and megathrust EQ genesis processes hidden in such stochastic time-series d (c, m) are available for




Shikoku median tectonic line

Shikoku has a median tectonic line whose sudden movement anticipates an M8 EQ once in 10002000 years.

The white arrowed movement along the dotted fault length of 280Km  anticipates M8.7 EQ.


A GPS monthly analysis with Physical Wavelets is available for



Physical Wavelets can quantify various systems characterized by noisy and non-time differentiable time series.




Physical wavelets are a mathematical tool for real-time analysis of chaotic or stochastic time-series data, as in the schematic above. The tool can detect any faint anomaly from noisy signals and assign physical laws to it. The detected anomaly is a deterministic and physics-based precursor to an imminent disaster under critical observation. For example, V and As product defined with Physical Wavelets is proportional to the kinetic energy (KE) rate change, which is the power. Monitoring the power by comparing it with predetermined threshold levels automates detecting any abnormal power leading to the disaster. The automatic or manual threshold setting is adaptive to the maximum rate change in a routine operation. Such precursor detections have prevented the sudden material fractures of rotating heavy manufacturing machinery a few hundred milliseconds before possible disasters. The detected precursor has physical laws that help the manufacturing system improve.


Physical Wavelets are the indispensable tool to quantify real-time megathrust and significant earthquake genesis processes

with GPS displacements and online regional seismic catalogs.


Keiiti Aki (1930/03/032005/05/17

By Fumihide Takeda

I have been an engineering consultant with a physics background, not a seismologist.

Professor Aki had built the foundation of quantitative seismology. He was the only seismologist who could share my prediction method like his. Before our first accidental meeting in 2002, Professor Aki and I devised the same earthquake (EQ) prediction idea in 2002 and 2001, respectively. He encouraged me to keep challenging myself to accomplish the EQ prediction of his dream. He was one of my great mentors in making me achieve the real-time EQ prediction outlined on this website.

Professor Aki pioneered almost every field in seismology. I point out just two here.

In 1966, he introduced seismic moments to our scientific world with his extraordinary physical insight to grasp fault motion with his solid mathematical background.

In 1980, he proved first time in the world that the EQ genesis processes among many earthquakes are statistically fractal; namely, EQ genesis processes in various sizes are statistically self-similar. Thus, predicting only a significant EQ is impossible. On the other hand, accomplishing EQ prediction had been his dream throughout his life. Thus, his life-long work was to search for seismogenic processes deviating from fractal nature to achieve his EQ prediction dream.

As in Appendix C3 of reference [2], in January 2005, Professor Aki went through my EQ paper, preprint, and Japanese Patent 4608643 (Application date, 2003.01.17Issued, 2011.01.12) and wrote me inspirational emails from Reunion in the Indian Ocean almost every day in early 2005 like two of them dated Jan 27, 2005.  

Dear Takeda-san:

I finished reading through all the documents you sent me, and I now feel that our accidental meetings might have been planned by someone in heaven.


Thank you for the exciting time I have had since reading your emails.

With best regards,

Kei Aki 

Dear Takeda-san:

My excitement continues from reading your paper.


I have a feeling that my dream about the future of earthquake prediction described in that paper may be realized by you. Perhaps that was the intention of someone in heaven who arranged several accidental meetings between you and me!

With best regards,



I believe I have achieved his dream about the EQ prediction, as in arXiv (the megathrust and significant earthquake genesis processes).


Could you work with us?

Please read the EQ genesis processes references above, and work with us to mitigate EQ and other natural disasters. Your working environment will be very flexible. Graduate students are also welcome with financial support to stay in Japan.
Please email your resume, preferable working environment, expected achievements, and how to work with us in pdf. We use your pdf application only for our consideration. Our email address is epi21 at mark cap.ocn.ne.jp.


Membership Application

Financial support from various corporations and organizations will make Epi21 a permanent public interest organization. The public Epi21 will open EQ disaster prevention warnings to the public for free, like typhoon warnings.
The current generation has enjoyed a peaceful life after WW 2 through the unimaginable sacrifices of previous generations, except for the 1995 Kobe EQ and the 2011 Tohoku megathrust EQ with tsunamis. Anticipated large EQs and megathrust EQs with tsunamis will ruin the next generation's happy life. Public support for Epi21 is essential to mitigate significant and megathrust EQ (tsunami) disasters in one to hundreds of years. Epi21's Physical Wavelets to formulate EQ genesis processes can also make global warming prevention disaster warnings.


Weekly earthquake prediction information is available for a paid membership. Membership is for local authorities and corporations. Please make membership inquiries by email to epi21 at mark cap.ocn.ne.jp.


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