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[MIS04-P06] Megathrust earthquake and Tsunami genesis processes observed with Physical Wavelets
Keywords:Megathrust earthquake genesis, Tsunami genesis, Real-time earthquake predictions, Physical Wavelets
Physical Wavelets (PWs) can describe the megathrust and significant earthquake (EQ) genesis processes to predict their focuses, fault movements, sizes, and rupture times up to three months in advance [1-4]. The time accuracies are within a day by real-time monitoring of the expected rupture processes.
Mathematical tool
The PWs in Fig. 1 can define the equations using cross-correlation with stochastic motion [1-4]. For example, the tool describes the 2011 Tohoku M9 EQ genesis process with the non-differentiable daily displacement time series collected at GPS stations in the subduction zone [2]. Denoting the geographic axis c by E (eastward), N (northward), and h (upward) in (E, N, h), the time series is {c}={d (c, 0 ), ., d (c, j ), .}. The j is the time in days. PWs define noise-free displacement D (c, τ), velocity V (c, τ), and acceleration A (c, τ) at time τ, as in Fig. 2a showing d (c, j) in green, D (c, τ) in red, V (c, τ) in black, and A (c, τ) in blue with parameter w = 200 and s = 300 in Fig. 1b. The V (c, τ) and A (c, τ) are in a relative scale from the graphical origin 0. The path in D (c, τ)-V (c, τ) has the upper half c-ward with positive V (c, τ). The lower half is the opposite c-ward and negative. The right half is c-ward of an offset origin. The path shows the M9 EQ genesis of 15 months, having the last 3 months of disaster prevention warning [1,2,4]. The genesis is a crustal bulge deformation process. The bulge evolved from the regular deformation of 1.5 mm/y up and 6 mm/y down on the west and east coast in Jan 2010. The initial phase S0 began with a uniformly increasing lifting force of A (h, τ)>0 on the east coast, as in Fig. 2a. The west coast of A (h, τ) > 0 followed in 6 months. By Jun 2010, the east coast lineally subsided by 2.8 mm, preparing a transition from regular deformation to a bulge-bending. A further linear subsidence of 3.1 mm started in June 2010 as S1 in Fig. 2a. The bulge-bending began pulling down the subducting oceanic plate, generating the D (E, τ) trend change in the plate motion at the 2010/07/11, as in Fig. 2b with w = 7 and s = 20. The lunar synodic tidal force loading appears as a periodic A (E, τ) of 30 days. The east coast pulling was a new external force to the tidal loading, gradually changing the amplitudes and phases of the periodic loading to the plate motion. Suppose an anomaly is a change comparable to the amplitudes of the observed fluctuations in {c} like d (E, τ) appearing in the changes in their phases and magnitudes at the trend change in Fig. 2b-2e. In that case, it will be indistinguishable from the background fluctuations. In such a case, a well-established power monitoring automatically detects the anomalous paths of D (E, τ)-V (E, τ) and D (E, τ)-A (E, τ) [1,2,4]. The power monitoring uses the kinetic energy rate change defined by PW (E, τ) = V (E, τ)×A (E, τ) > Th (threshold) with the current time j = τ + w + s as in Fig. 1b. The regular power 1 sets Th at level 2 in Fig. 2d for the unexpected [2,4].
The plate's speed reached the highest of V (E, τ) = – 0.69 mm/day on 22 Dec 2010, 3 times that on 11 Jul, as in Figs. 2b and 2e. The abnormal westward motion triggered the M7.9 EQ in the Pacific nearby the GPS station [2].
The linear upheaval of 1.2 mm on the east coast began in Nov 2010, as S2 in Fig. 2a. The upheaval decelerated V (E, τ) to zero on 25 Feb and reversed to the eastward of +0.06 mm/day on 8 Mar 2011, as in Figs. 2b and 2c. Thus, the tool could have provided the D (c, τ)-V (c, τ) path as the megathrust EQ and Tsunami real-time warning before the impending M9 EQ on 11 Mar 2011. However, there will be significant challenges to effectively informing societal decisions [2,5].
[1] Takeda, F. (2015) https://patents.google.com/patent/JP5798545B2/ja
[2] Takeda, F. (2021) https://doi.org/10.48550/arXiv.2107.02799
[3] Takeda, F. (2022) https://doi.org/10.48550/arXiv.2201.02815
[4] Takeda, F. (2022) https://doi.org/10.48550/arXiv.2208.09486
[5] https://www.epi21.org
Mathematical tool
The PWs in Fig. 1 can define the equations using cross-correlation with stochastic motion [1-4]. For example, the tool describes the 2011 Tohoku M9 EQ genesis process with the non-differentiable daily displacement time series collected at GPS stations in the subduction zone [2]. Denoting the geographic axis c by E (eastward), N (northward), and h (upward) in (E, N, h), the time series is {c}={d (c, 0 ), ., d (c, j ), .}. The j is the time in days. PWs define noise-free displacement D (c, τ), velocity V (c, τ), and acceleration A (c, τ) at time τ, as in Fig. 2a showing d (c, j) in green, D (c, τ) in red, V (c, τ) in black, and A (c, τ) in blue with parameter w = 200 and s = 300 in Fig. 1b. The V (c, τ) and A (c, τ) are in a relative scale from the graphical origin 0. The path in D (c, τ)-V (c, τ) has the upper half c-ward with positive V (c, τ). The lower half is the opposite c-ward and negative. The right half is c-ward of an offset origin. The path shows the M9 EQ genesis of 15 months, having the last 3 months of disaster prevention warning [1,2,4]. The genesis is a crustal bulge deformation process. The bulge evolved from the regular deformation of 1.5 mm/y up and 6 mm/y down on the west and east coast in Jan 2010. The initial phase S0 began with a uniformly increasing lifting force of A (h, τ)>0 on the east coast, as in Fig. 2a. The west coast of A (h, τ) > 0 followed in 6 months. By Jun 2010, the east coast lineally subsided by 2.8 mm, preparing a transition from regular deformation to a bulge-bending. A further linear subsidence of 3.1 mm started in June 2010 as S1 in Fig. 2a. The bulge-bending began pulling down the subducting oceanic plate, generating the D (E, τ) trend change in the plate motion at the 2010/07/11, as in Fig. 2b with w = 7 and s = 20. The lunar synodic tidal force loading appears as a periodic A (E, τ) of 30 days. The east coast pulling was a new external force to the tidal loading, gradually changing the amplitudes and phases of the periodic loading to the plate motion. Suppose an anomaly is a change comparable to the amplitudes of the observed fluctuations in {c} like d (E, τ) appearing in the changes in their phases and magnitudes at the trend change in Fig. 2b-2e. In that case, it will be indistinguishable from the background fluctuations. In such a case, a well-established power monitoring automatically detects the anomalous paths of D (E, τ)-V (E, τ) and D (E, τ)-A (E, τ) [1,2,4]. The power monitoring uses the kinetic energy rate change defined by PW (E, τ) = V (E, τ)×A (E, τ) > Th (threshold) with the current time j = τ + w + s as in Fig. 1b. The regular power 1 sets Th at level 2 in Fig. 2d for the unexpected [2,4].
The plate's speed reached the highest of V (E, τ) = – 0.69 mm/day on 22 Dec 2010, 3 times that on 11 Jul, as in Figs. 2b and 2e. The abnormal westward motion triggered the M7.9 EQ in the Pacific nearby the GPS station [2].
The linear upheaval of 1.2 mm on the east coast began in Nov 2010, as S2 in Fig. 2a. The upheaval decelerated V (E, τ) to zero on 25 Feb and reversed to the eastward of +0.06 mm/day on 8 Mar 2011, as in Figs. 2b and 2c. Thus, the tool could have provided the D (c, τ)-V (c, τ) path as the megathrust EQ and Tsunami real-time warning before the impending M9 EQ on 11 Mar 2011. However, there will be significant challenges to effectively informing societal decisions [2,5].
[1] Takeda, F. (2015) https://patents.google.com/patent/JP5798545B2/ja
[2] Takeda, F. (2021) https://doi.org/10.48550/arXiv.2107.02799
[3] Takeda, F. (2022) https://doi.org/10.48550/arXiv.2201.02815
[4] Takeda, F. (2022) https://doi.org/10.48550/arXiv.2208.09486
[5] https://www.epi21.org