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[S17-01] Tsunami and Megathrust Earthquake Predictions: Real-time Monitoring of the Genesis Processes with Physical Wavelets
Japan’s seismograph and GPS network, located on the subduction zones, provide comprehensive records on earthquakes (EQs) in the form of displacement time series data {c}, which is stochastic or noisy. For example, the GPS time series is represented as {c}={d (c, 0), ., d (c, j), .}, where d (c, j) denotes the daily displacement at a GPS station’s position with the geographic axis c representing E (eastward), N (northward), and h (upward) in right-handed coordinates (E, N, h) and at time j expressed in days. Environmental factors make d (c, j) noisy and non-differentiable.
Physical Wavelets (PWs) are mathematical operators denoted by DDW (t − τ), VDW (t − τ), and ADW (t − τ) in equations (1) – (3). The PWs define displacement D (c, τ), velocity V (c, τ), and acceleration A (c, τ) at time τ on such non-differentiable {c}. D (c, τ) provides the average of d (c, j) over a time interval of j = τ ± w, and s represents a differential time. The time-reversal operation changes τ to − τ and confirms that D (c, − τ) = D (c, τ), V (c, − τ) = − V (c, τ), and A (c, − τ) = A (c, τ), affirming the differentiable property of the D (c, τ) and V (c, τ) derived from the non-differentiable d (c, j).
The plate driving forces describe the megathrust EQ’s genesis process through PWs, enabling the EQ rupture time prediction with remarkable accuracy within a day, up to three months preceding the EQ event1. The 2011 Tohoku M9 EQ and the tsunami resulted from complex interactions between the subducting and overriding plates, which caused bulge-bending deformation (BBD) over the Tohoku subduction zone. The BBD refers to the gradual bending of the overriding plate of Tohoku by the eastward continental plate-driving force, causing the overriding crust of Tohoku to bulge downwards and upwards by a few millimeters. The BBD suddenly appeared from the consistent deformation expected over the preceding three hundred years. Figures 1 and 2 illustrate a schematic cross-section of the deformation, which grew in three phases over 15 months:
· An initial phase of Fig. 2a
· A transitional phase of Fig. 2b
· A final phase of Fig. 2c
The initial had regular slow deformation changing the west coast deformation from non-elastic to elastic, which generated a restoring force of the compressed west coast with gradual subsidence of 1 to 2.8 mm across Tohoku starting in January 2010. The east coast subsided by 2.8 mm during segment S0 in Fig. 3a, effectively gripping significant barriers on fault (increasing the static friction).
The transition was from the regular to a BBD of segment S1 in Fig. 3a with further gradual subsidence of 3 mm. During S1, the east coast pulled down the subducting Pacific Plate, as indicated by a dot-arrow on the fault in Fig. 2b, while firmly grasping the fault. The overriding eastward plate-driving force compression on the west coast elastically pulled the east coast westward. The westward pulling (A (E, τ) < 0) started to drag the subducting oceanic plate in July 2010, accelerating the oceanic plate motion to reach the highest westward V (E, τ) = − 0.69 mm/day on December 22, 2010, as shown in Fig. 3b.
The final phase began in November 2010 with a gradual upheaval growth of 1.2 mm on the east coast during segment S2, generating the lifting force as shown A (h, τ) > 0 above a dot-line in Fig. 3a. The lifting force buildup on the east coast along the Tohoku subduction zone eventually caused the shear stress to exceed the static frictional strength of the subduction interface, causing the overriding and subducting plates to decouple. The lifting force on the entire Tohoku region helped the decoupling process, releasing a massive recoil force of the compressed west coast against the eastward-plate-driving force. The recoil rapidly restored the BBD of the east and west coasts, elastically compressed by the overriding plate-driving eastward force. This rapid restoration led to the Tohoku M9 earthquake and tsunami on March 11, 2011.
The pulling action of the east coast during segments S1 and S2 in Fig. 3a, coupled with the subducting oceanic plate motion (westward), as shown in Fig. 3b, was recorded at Chichijima in the Northwest Pacific Ocean. The movement paths on the D (E, t) – V (E, t) and D (E, t) – A (E, t) planes can automatically detect the abnormal oceanic plate motion, serving as a real-time tsunami warning up to the event.
The final phase of S2 (after M7.9 EQ in Fig. 3b) can provide real-time information on the impending megathrust EQ and tsunami, allowing for the most effective disaster prevention warnings and hazard mitigations.
The findings suggest they can deterministically predict the anticipated megathrust EQ and tsunami, like Cascadia and Nankai-Trough events.
1. Takeda, F. (2022). https://doi.org/10.48550/arXiv.2208.09486
Physical Wavelets (PWs) are mathematical operators denoted by DDW (t − τ), VDW (t − τ), and ADW (t − τ) in equations (1) – (3). The PWs define displacement D (c, τ), velocity V (c, τ), and acceleration A (c, τ) at time τ on such non-differentiable {c}. D (c, τ) provides the average of d (c, j) over a time interval of j = τ ± w, and s represents a differential time. The time-reversal operation changes τ to − τ and confirms that D (c, − τ) = D (c, τ), V (c, − τ) = − V (c, τ), and A (c, − τ) = A (c, τ), affirming the differentiable property of the D (c, τ) and V (c, τ) derived from the non-differentiable d (c, j).
The plate driving forces describe the megathrust EQ’s genesis process through PWs, enabling the EQ rupture time prediction with remarkable accuracy within a day, up to three months preceding the EQ event1. The 2011 Tohoku M9 EQ and the tsunami resulted from complex interactions between the subducting and overriding plates, which caused bulge-bending deformation (BBD) over the Tohoku subduction zone. The BBD refers to the gradual bending of the overriding plate of Tohoku by the eastward continental plate-driving force, causing the overriding crust of Tohoku to bulge downwards and upwards by a few millimeters. The BBD suddenly appeared from the consistent deformation expected over the preceding three hundred years. Figures 1 and 2 illustrate a schematic cross-section of the deformation, which grew in three phases over 15 months:
· An initial phase of Fig. 2a
· A transitional phase of Fig. 2b
· A final phase of Fig. 2c
The initial had regular slow deformation changing the west coast deformation from non-elastic to elastic, which generated a restoring force of the compressed west coast with gradual subsidence of 1 to 2.8 mm across Tohoku starting in January 2010. The east coast subsided by 2.8 mm during segment S0 in Fig. 3a, effectively gripping significant barriers on fault (increasing the static friction).
The transition was from the regular to a BBD of segment S1 in Fig. 3a with further gradual subsidence of 3 mm. During S1, the east coast pulled down the subducting Pacific Plate, as indicated by a dot-arrow on the fault in Fig. 2b, while firmly grasping the fault. The overriding eastward plate-driving force compression on the west coast elastically pulled the east coast westward. The westward pulling (A (E, τ) < 0) started to drag the subducting oceanic plate in July 2010, accelerating the oceanic plate motion to reach the highest westward V (E, τ) = − 0.69 mm/day on December 22, 2010, as shown in Fig. 3b.
The final phase began in November 2010 with a gradual upheaval growth of 1.2 mm on the east coast during segment S2, generating the lifting force as shown A (h, τ) > 0 above a dot-line in Fig. 3a. The lifting force buildup on the east coast along the Tohoku subduction zone eventually caused the shear stress to exceed the static frictional strength of the subduction interface, causing the overriding and subducting plates to decouple. The lifting force on the entire Tohoku region helped the decoupling process, releasing a massive recoil force of the compressed west coast against the eastward-plate-driving force. The recoil rapidly restored the BBD of the east and west coasts, elastically compressed by the overriding plate-driving eastward force. This rapid restoration led to the Tohoku M9 earthquake and tsunami on March 11, 2011.
The pulling action of the east coast during segments S1 and S2 in Fig. 3a, coupled with the subducting oceanic plate motion (westward), as shown in Fig. 3b, was recorded at Chichijima in the Northwest Pacific Ocean. The movement paths on the D (E, t) – V (E, t) and D (E, t) – A (E, t) planes can automatically detect the abnormal oceanic plate motion, serving as a real-time tsunami warning up to the event.
The final phase of S2 (after M7.9 EQ in Fig. 3b) can provide real-time information on the impending megathrust EQ and tsunami, allowing for the most effective disaster prevention warnings and hazard mitigations.
The findings suggest they can deterministically predict the anticipated megathrust EQ and tsunami, like Cascadia and Nankai-Trough events.
1. Takeda, F. (2022). https://doi.org/10.48550/arXiv.2208.09486