Mitigation of Ecuadorian Earthquake Impact

The mechanism of “Bing-Bang-Channeling-Cut” was proposed to reduce the volcanic energy (“Bing”) from the Galapagos Hot Spot (GHS) for the mitigation of Ecuadorian earthquake impact (“Bang”). The lag time between the volcanic eruptions in the GHS and Ecuadorian earthquake was probably caused by the undersea seamounts of the Carnegie Ridge (CAR) (“Channeling”). Experimental results from the water reservoir showed that the lag time decreased when increasing the number of drilled holes (“Cut”) in the bottom of reservoir. The present study showed that there was an additional vector initiating the Ecuadorian earthquake from the volcanic eruption in the GHS through the CAR. It was concluded that the harmful effects of Ecuadorian earthquakes could be mitigated by releasing the volcanic energy through the enlarged exit diameters in Holes of Site 1239 (A, B, C) with the presently productive upwelling chlorophyll system at the northeastern CAR.


Introduction
Throughout the year of 2016 there were strong earthquakes around the world. They include earthquakes in India (4 January, M 6.7), Taiwan (China) (6 February, M 6.4), Japan (15 April, M 7.3), Ecuador (16 April, M 7.8), Myanmar (24 August, M 6.8), Italy (24 August, M 6.2), New Zealand (13 November, M 7.8), and Indonesia (6 December, M 6.5), among which the strongest and the deadliest one was the Ecuadorian earthquake with a death toll of 673. Ecuador's recorded seismic history dates back to 1541, and records show a cumulative death toll of more than 80,000 [1]. The Galapagos Islands are reported to be a "hot spot", which is the region of high thermic flux due to the presence of a magmatic plume ascending from the earth's mantle (700 -3000 km) [2]. Galapagos Islands are basaltic rocks produced by volcanic activities caused by magma upwelling (700˚C ~ 1300˚C) in the Galapagos Hot Spot (GHS). The hot energy side of the

Initiative Experiment
An initiative experiment was designed to examine the distribution of potential energy of a water reservoir with the increase of the number of drilled holes. The water reservoir (diameter = 44 cm, height = 43 cm) was prepared to release its water stepwise through 12 drilled holes (ID = 0.4 cm) at the bottom side, as shown in Figure 1.
Lag time, as a function of hole number for the release of reservoir water from the top (40 cm high) to the bottom, is analogous to the lag time of occurrences between the volcanic eruptions in the GHS and the Ecuadorian earthquake, as shown in Figure 2

Carnegie Ridge with Similarity between Ecuadorian and
Mexican Earthquakes conditions that allowed partial melting to occur for a long period of time. The slab is not flat beneath Ecuador, but, instead it regularly dips to the east with an angle of 25˚ -35˚. Estimates derived from [6] showed that geological expression For the sudden release of the reservoir water (ln1 = 0) in the present system, the number of holes should be about 40 (n = 40). of subduction of the CAR only requires a 300 km penetration of the CAR beneath Ecuador.
The direction of energy transfer from the CAR to Ecuador should be perpendicular to the surface between the CAR and Ecuador Continental Shelf (ECS) according to the principle of Pascal. The coastal margin of Ecuador comprises Pliocene sediments of marine terraces (Tablazos) [7] such as Esmeraldas, Manta, and Santa Elena [8]. Major Ecuadorian earthquakes mainly occurred in the northwestern Ecuador over Tablazos of marine terraces and Coastal cordillera Local constructional volcanism was at a distances of 2 km for 12 high-and 9 low-temperature hydrothermal vents along the East Pacific Rise (EPR) axis between 9˚49'-51'N (the Clipperton and Siqueiros transforms). There were actively venting black smokers with chimney structures of Tube Worm Pillar ( Figure  3) in 1991, 1992, 1994, 1996, 1997, 1998, and 2002, during which no earthquakes occurred in Mexico. On the other hand, earthquakes were observed in 1985, 1995, 1999, 2003, and 2009 in Mexico [10]. It was thus postulated that high-temperature (≥350˚C) hydrothermal black smoker vents released the thermal energy of the EPR continuously, so that no earthquakes have occurred during such venting periods in Mexico, whose western coast is in junction with the EPR.
The numbers of volcanoes and earthquakes in Table 1 were added together to get the overall numbers in large order in Chile (270), Mexico (106), Peru (85), Ecuador (68), Guatemala (54), Colombia (41), El Salvador (38), Nicaragua (8). The order is in good agreement with Figure 4 of the solar radiation map except Ecuador, which has a low solar radiation energy. On the other hand, Ecuador has many volcanoes (43) and earthquakes (24) in Table 1. It can be thus postulated that the required energy for the plate movement to cause Ecuadorian volcanic eruptions and earthquakes is provided by the volcanic energy in the GHS via submarine CAR of Nazca Plate which is subducted beneath Ecuador of South American Plate in convergent plate boundary associated with Ecuadorian volcanoes and earthquakes.
Thermal energy (Q) produced by volcanic eruption in the GHS is transferred to the CAR due to CAR formation of volcanic plateau over the GHS [3]. This thermal energy (Q) is converted to work (W) by exerting force (F) with displacement change (∆x). Since pressure (P) is the force (F) per unit area (A), energy (Q) can be expressed as, where in Q  is the input rate of energy from volcanic eruptions in the GHS,   Figure 3) in CAR. It is therefore possible that Ecuadorian earthquakes can be mitigated during venting periods, as observed in Mexican earthquakes [10]. Local constructional volcanism was at a distance of < 2 km in EPR [10] while CAR-Ecuador margin collision length is 160 km [8].
Considering the CAR margin, it is suggested that 80 (= 160/2) drilled holes be

Drilled Holes
Locations of Sites 1238-1242 near CAR are shown in Figure 6.
There can be prospective locations for drilling vents as below. There can be momentum ( m  ) and heat flow ( Q  ) rates as follows, Equations (5) and (6) reduce to, where Q  = heat flow rate through drilling vent, ρ = density of undersea water, P C = heat capacity of undersea water, u = linear flow velocity passing through drilling vent, D = diameter of drilling vent, ∆T = temperature difference between vent exit (T 2 ) and vent surrounding (T 1 ).
In order to release high hydrothermal flux ( Q  ) through drilling vents, it is necessary to enlarge the diameter (D) in Equation (7).

Solar Radiation Energy
The work (dW) required to move an object a finite distance (dx) with a thrust force of magnitude (F) is defined as, where ∆x = length of earth movement by earthquake.
The energy balance for a steady-state process reduces to [21] 2 0 2 If molar heat 0 Q = due to adiabatic process, then, Combining Equations (9) and (12), Equation (13)  and thrust force (F) are assumed constant.
Sunlight is composed of 3 processes of reflection, absorption and transmission.
As for subaerial volcanoes and submarine seamounts, they absorb the sunlight and convert it into thermal energy with heat transfer medium like magma, lava, air and seawater. Solar radiation energy activates the plate movement to cause earthquakes and volcanic eruptions. Incoming solar radiation is 174 PW and 89 PW absorbed by land and oceans, as shown in Figure 7. Since 71% of the Earth is surface is the Ocean, 62 PW of solar radiation is available to be 36% {= (62/174)(100)} of incoming solar radiation for the Ocean where more than 30,000 submarine volcanic seamounts are present. The Galapagos Hot Spot (GHS) provides its own thermic energy from magma. Therefore, overall energy at the hot GHS from solar radiation and magma are transferred to the cold CAR according to the second law of thermodynamics.
If the solar energy is 89 PW, 71% is ocean and 30,000 seamounts, there are a maximal 2,100 MW per seamount. If 100,000 seamounts; maximal 620 MW per seamount. CAR is a relatively large seamount (600 km) among seamounts of Chile Rise (2250), Juan Fernandez Ridge (900), Iquique Ridge (600), Nazca Ridge (1000), Malpelo Ridge (300), Coiba Ridge (150), and Cocos Ridge (1000). Even if the solar energy absorbed to the ocean is mostly absorbed to the seawater above CAR, a significant amount of the solar energy is absorbed to the CAR, which moves along with the Nazca Plate relative to the GHS. The CAR stands 1.2 ~ 1.4 to 2.7 ~ 3.1 km higher than the surrounding seafloor, and presently is being subducted beneath the Southern American Plate (5.8 cm/yr) [4].  Arc [5]. The CAR-Ecuador margin collision length is 160 km [4]. In order to reduce the Ecuadorian earthquake effects, the thermal energy of the CAR can be Therefore, as the solar radiation makes higher T, the more emissive power of the CAR is produced. If a volcano or earthquake is activated by one of 3 types of convergent, divergent and transform plate boundaries, the resultant heat output (Q) from seamounts volcano is,  Table 1 shows volcanoes and earthquake events in Ecuador, Colombia, and Peru from 1977 to 2016, where volcanoes in the GHS and those in the inland are shown in white parts and black shaded parts, respectively. The solar radiation energy in the Galapagos Islands had the highest during one peak value (~30˚C) in the Equator (2 volcanic eruptions in January, 2 in March, 2 in April , 3 in May) and another peak in the Equator (2 in August, 4 in September, 1 in October, 2 in November), as shown in Figure 8. The volcanic energies, together with solar energy in the GHS propagated to the CAR, resulted in Ecuadorian earthquakes with an elapse time of 287 days (Table 2) in the extremely frequent earthquake events (9 times in May), as shown in the monthly solar energy variation at the Equator with dual peaks in Figure 8. It is postulated that frequent volcanic eruptions in September (5 recorded events) were due to the solar radiation energy in the GHS. Ecuadorian earthquake event (y) was dependent upon the volcanic eruptions in the GHS (x) with relationship as, y = 0.47x + 2.79 (R = 0.32) ( Figure 9), whose data were obtained from Table 3.

Volcanoes in the GHS and Ecuadorian Earthquake Events
It is evident that there is a dual peak system in the insolation profile with monthly distribution of the Equator (0˚ latitude), which is similar to the patterns in Figure 8. It is therefore postulated that the volcanic eruption and earthquakes in Ecuador are greatly effected by solar energy due to Ecuadorian location near Equator. Table 4 Table 1 and Table 2). The profiles of volcanic eruptions and earthquakes are similar to dual peaks of monthly solar energy variation at the Equator (Figure 9).

Drilled Holes for Mitigation of Ecuadorian Earthquake Impacts
There are three vectors initiating Ecuadorian earthquakes as follows; 1) one from the CAR moving on the subduction interface along the plate boundary, 2) one from Ecuadorian Andes volcanoes, and 3) one from deformation within the South American Plate and the Nazca Plate. The present study suggests that there    Table 3. Monthly distributions of the number of volcanic eruptions in the Galapagos Hot Spot and the number of earthquake events in-land from 1977 and 2016 (data from Table  2).  ("Bing") to Ecuador ("Bang") should be mitigated by releasing the volcanic energy reserved in the CAR ("Channeling") through drilled Holes ("Cut") in the CAR-Ecuador margin collision length of 160 km [8]. The lag time τ , is simply the time needed for a particle of fluid to flow from the entrance to the exit of the pipe defined as [23], volume of pipe volumetric flow rate τ = (16) or AL q τ = (17) where L is the distance between the GHS and Ecuador (926 km), A, the cross-sectional area of the CAR (160 km × 2.5 km), 160 km collision

Month
Since the volcanic energy flow rate from the GHS ( G Q  ) is given by, where P C is the specific heat at constant pressure (1 cal•g −1 •c −1 ), Ti is the temperature of the volcanic material (350˚C) [10].
Therefore, G Q  is given by, As shown in Table 2, the highest energy flow rate of Ecuadorian earthquakes ( E Q  ) from 1977 to 2016 was 2.1 × 10 19 J•d −1 for event #10 with Mw 7.9, which was far less (1%) than The total number of holes (n) required to mitigate the impact of Ecuadorian earthquakes determined, for example, for the equivalent case of earthquake event number 8 in Table 2, ( E Q  ), as 5 × 10 15 J•d −1 , converted to,  Since Kilauea Volcano in Hawaii showed channel velocities of 1 ~ 3 m•s −1 [24] to be approximated as 2.3 m•s −1 , then 12 1 10 n ≅ × (27) Therefore, an almost infinite number of drilling holes ( ) 12 1 10 n = × is required to entirely negate the impact of Ecuadorian earthquakes by event #8. In order to minimize the harmful effects of Ecuadorian earthquakes ("Bang"), the volcanic thermal energy from the GHS ("Bing") was released through drilled Holes at the CAR ("Channeling-Cut"). When drilled Holes are present in the CAR, the volcanic energy from the volcanic eruption in the GHS is no longer reserved in the CAR, but released to the seawater of the Ecuadorian Trench through drilled Holes around the contour of 2500 m in depth (Figure 6(a)). Since the CAR shares its geological origin with the Galapagos Islands [12], the resonance is expected between the GHS and the CAR, so that volcanic energy from the GHS is amplified in the CAR due to the constructive interference during volcanic eruptions to cause the increased earthquake magnitude. Further-T.-J. Kim more, the marine terraces on the Ecuadorian coast with Pliocene sediments [7] cause oscillatory behavior of enhanced earthquake frequency with activated energy followed by the Planck-Einstein relation [25]. Therefore, a reduced number of drilled Holes (n) than 1 × 10 12 may be required if the impulse input of volcanic energy from the GHS is continuously released to the Ecuadorian Trench through 20 to 80 drilled Holes in the northeastern CAR. Since there are less accumulated net energies from 1) volcanic energy in the GHS, 2) resonant energy with similar materials of the CAR, and 3) solar radiation energy over the CAR, the inland Ecuadorian earthquakes are mitigated by less oscillatory behaviors in the northeastern Tablazos.
The monthly profile of volcanic eruptions was similar to that of earthquake events ( Figure 8). The number of volcanic eruptions (x) were plotted with respect to number of earthquake events (y) to see the linear relationship of y = 0.47x + 2.79, R = 0.32 (Figure 9). It was possible to provide an early-warning to prepare for Ecuadorian earthquakes which were induced by volcanic eruptions in the GHS with the lag time ranging from 8 to 751 days, mean ± standard deviation of 287 ± 219 days ( Table 2).
The national geological map of Ecuador shows the marine terraces composed of mainly Tertiary, partially Cretaceous, and Quaternary sedimentary rocks [26].
Since the CAR shares the geological characteristics of the GHS [27], the volcanic energy in the GHS is amplified in the CAR due to the principle of resonance between similar materials under constructive interference [25] to be propagated to Ecuador as enhanced earthquakes. Furthermore, oscillatory behavior by Ecuadorian Pliocene sediments of marine terraces (Tablazos) for a unit-impulse forcing function of volcanic eruption in the GHS is expressed by Newton's law of motion [23] as, where Y(t) is the travel distance variable with time (t), K, the Hooke's constant of the CAR, C, the viscous damping coefficient of Pliocene sediments at Ecuadorian marine terraces (Tablazos), F(t), the driving force of the Ecuadorian earthquake, W, the mass of Ecuador, g c , the gravitational constant.
3 cases of 1) oscillatory ( 1 ζ < ), 2) critically damped ( 1 ζ = ), and 3) nonoscillatory ( 1 ζ > ) solutions are available, where the damping ratio ( ζ ) is given by, 2 4 c g C WK ζ = (29) Since g c , W, and K are constant, ζ is proportional to C of Tablazos and less than 1 [23] to be oscillatory. The freguency propagated from the CAR is in-T.-J. Kim Open Journal of Earthquake Research creased due to oscillatory behavior of Tablazos in Ecuador. Damping ratios of Tertiary and Quaternary were less than 20% in seismic response [28]. Therefore, the Ecuadorian earthquakes occurring at marine terraces have been large earthquakes in Tablazos [29], and 2016 (Mw 7.8). Volcanic energies from the GHS propagate through the CAR to Ecuadorian Tablazos in the form of enhanced oscillatory earthquakes for strong damage. Besides, the subduction of the Nazca plate beneath the South American plate proceeds with a N90˚E convergence and a rate of 8 cm•year −1 [8]. Furthermore, major earthquakes shook northwestern Ecuador and southwestern Colombia so that the Esmeraldas and Manta terraces in northwestern Ecuador were considered as an area of high seismic risk [30]. It was thus recommended to drill hydrothermal vents at the CAR in front of areas between the Esmeraldas and Manta terraces.
Specifically, more drilled holes can be allocated in the northeastern CAR to block the propagation of volcanic energy from the GHS toward the Esmeraldas area to reduce the impact of Ecuadorian earthquakes.
For the sake of simplicity, Ecuadorian earthquakes could be mitigated by releasing the volcanic energy through the enlarged Holes of Site 1239 (A, B, C) with the highly productive upwelling chlorophyll system at the northeastern CAR. Table 5 shows the relative similar cases for the mechanism of Bing-Bang-Channeling-Cut in Japan, California (USA), Chile, Peru, Mexico, and Italy. Each case consists of Bing, Bang, Chaneling, and Cut. Similar technology of Cut described in the present study can be hypothetically applicable to each case to reduce the impact of Bing to Bang through Channeling.

Conclusions
The mechanism of "Bing-Bang-Channeling-Cut" was proposed to reduce the volcanic energy ("Bing") from the Galapagos Hot Spot (GHS) to limit the damage from Ecuadorian earthquakes ("Bang"). The lag time between the volcanic eruption and Ecuadorian earthquake was presumably caused by the volcanic seamounts of the Carnegie Ridge ("Channeling"). Similar cases could be appli-   The present study showed that there was an additional vector initiating the Ecuadorian earthquakes caused by the volcanic eruption in the GHS through the Carnegie Ridge (CAR). It was found that the impact of Ecuadorian earthquakes could be mitigated by releasing the volcanic energy through the enlarged exit diameters in Holes of Site 1239 (A, B, C) with the presently productive upwelling chlorophyll system at the northeastern CAR.