The recovery rates that can be predicted in materials near the surface after the earthquake damaged

Seismic overlapping

We have calculated the six self-relationships (EE, NN; ZZ, EN, EZ, NZ) for the PatcX station after liquidating the antiquities in the 3-6 Hz and seismic segments in which the capabilities do not follow the distribution of the ritual possibilities 27. We calculated cross -hour correlation functions for an hour for an hour that we have stated for daily overlapping relationships. To measure the speed changes, the 45 expansion technology has been applied in a 7-16 second window of daily correlation functions. In the last step, the average results of the six self -relationships are calculated.

Correction of temperature

We first estimated the periodic temperature stage (captured at Iquique Airport, 30 km from the station) and the DV/V seasonal changes. The temperature data was first softened using the 30-day savitzy-Gailen candidate and a 3-day request. Savitzky-Galay candidate softens the data using a damage with a multi-border instead of the COXCAR function (a simple average average is Savitzy-Galay from the ranking 1). This has the advantage of maintaining more high -frequency information in the time chain to keep more potential data peaks in the smoothing window 46. To bring the periodic contrast, we calculated the average temperature and speed by accumulating the annual temperature and the DV/V series and the installation of the intermediate stack With sinus function (Figure S1). The installation of speed data gives a first correction of the thermal speed changes (the red line in the S3). The phase between the temperature and the speed is about 19 days.

We assumed that the speed changes arise from the thermal dynasty that was observed in the depth of one Z due to the thermal spread in a surface layer of thermal spread κ. To fluctuate periodic temperature on the surface (from the period ω), the delay of the phase of the temperature T at the depth of Z with the following equation 47:

$$ T = {t} _ {0}+\ Delta T \ Exp \ Exp \ Left (-Z \ SQRT {\ frac {\ OMEGA} {2 \ kappa}} \ Right) \ Cos \ left (\ OMEGA TZ \ sqrt {\ frac {\ Omega} {2 \ kappa}} \ right). $$

(1)

In this relationship, one can see that the delay of the phase equals \ (-z \ sqrt {\ frac {\ OMEGA} {2 \ kappa}} \). From the difference in the calculated stage before and after specifying the period ω to one year, we get the value of the ratio Z2/2κ, which determines the behavior of the system. Assuming now a general thermal proliferation of κ = 1.10−2 CM2/S, we can design speed changes from the temperature that is observed in the distinctive depth of the ratio (Z = 1.25 m). Delivery of these values ​​in a digital simulation of 1D thermal spread (calculated using an EULER chart for front) and using a surface temperature series (Figure S2A), we got the temperature depth profiles shown in the S2B Figure. We extracted the temperature at the depth z = 1.25 meters and expanded its range to speed through α factor, which represents the expansion of rocks in the surface (α ~ 0.053). This scaling is made on the 2007 speed data before the Tokopilla earthquake. The S3a chain of the speed of this simulation shows.

The detained temperature model is taken as an average between the DV/V series, similar to (Figure S3A). In fact, we combine the best of corrections as 1. The numerical correction depends on the temperature of the temperature and may have the best correction of the stage of the changes caused by the temperature and 2.

Measure

We used to express Snieder et al. , To find the maximum relaxation period \ ({\ tau} _ {\ max} \), which controls the period of recovery after the earthquakes:

Trem

(2)

From the equation (2), one can see that the function R (T) is thus an overlapping of the Si -recovery that is characterized by the time system τ. From a previous post on the Patcx Field Site27, we know that the minimum relaxation time \ ({\ tau} _ {\ min} \) is lower than one minute. In the accuracy of the daily time of the time chain of the recovery speed of this study, we also do not analyze ({\ tau} _ {\ min} \). Therefore, we fixed \ ({\ tau} _ {\ min} \) for one day and we wrote R

(3)

In this equation, V is the temporal series that we want to predict, VM is the expected time series of a model and (\ bar {v) \) is the average of the designated time chain. We got NSE = 0.68 of the model that features slicing and NSE = – 2.61 for the model that features a continuous relaxation scale. The negative laboratory indicates that the model with the continuous time of relaxation is less efficient in data prediction than the average seismic speed changes.

State variable theory

We are looking for a homogeneous equation for speed changes and we choose a vibrant sporty model with the logarithm development of recovery. We assume a complete recovery of seismic speed before Earthquake (there is no generation of new contact/defects). A general equation for DV/DT speed differences can be expressed

$ thread[-Bv

(4)

Where A, B and C are constants with A and C have the same dimension from DV/DT, and b it has 1/v.

Note that the expression (4) has the same form of Arrhenius 29 equation, used for the modeling of the thermal processes and crawling rates. Fixed A is generally interpreted as a distinctive molecular collision of the physical system of play while B is associated with reacting card. We added C to impose an end to the recovery in which the speed change rate (DV/DT = 0) does not change so that the recovery is complete. Based on the dimension of the constants, we do more transactions (4) to highlight time τ: Allow B = 1/V*, C = V*/τ and \ (a = {v}^{*} {e} ^^ {{v} _ {\ infty}/{v}^{*}}/\ tau \), we get

cover[-\frac{{v}_{\tau }

(5)

Where V∞ is the value of the fixed state speed in the absence of earthquakes, V* is the speed of adjusting the pre -factor and the term and Vτ is the speed associated with a specific relaxation time τ. We consider many communications or defects with different distinctive time domains τ, which affect speed changes. The overall change of the widowed speed V (T) is a function of these voids. The contribution of each Vτ to the overall changes allocated to the V (T) depends on the intensity of the voids/connections associated with it and its special sizes. For simplicity, we take the average of all Vτ system's dynamics in the system:

$$ V

(6)

To show the logarithmic development of our work frame, we now derive an expression of (5) solution for the initial state V0 = v (0)

$ thread W

(7)

Who in turn leads

$ thread } {\ Tau}. $$

(8)

LHS can be expressed for the screen above

$ thread {1} {w} \ right) dw = {\ left[\log \left(\frac{w-1}{w}\right)\right]} _ {0}^{t} = \ log

(9)

Leave ξ0 = (W (0) – 1)/W (0), we finally find that w

(10)

Using this frame, we calculated the differences in the synthetic seismic speed shown in Figure 3, which extends 10,000 days (about 27 years). First, we arbitrarily determine the Logaretami range of relaxation times τ from 10 to 4999 days (all values ​​in Figure 3). For each of these values ​​τ, the goal is to estimate a Vτ (T) time chain that corresponds to the relaxation phenomenon determined by the time range τ. We repair V∞ to 0 to get the capacity of speed disorders (Vτ (T) to δvτ (T)) and decrease 5 consecutive speed δ (−8, −2, −1, −1 and −5 M/S at 500, 620, 1300, 5000, 7000 days in the time chain). Finally, we reform the V* to 1000 m/s for all δvτ (T). Using these values, the equation (5) can be incorporated to obtain the time chains shown in Figure 3A.

In the last step, we have made the average of all disorders δvτ (T) after the equation (6) and we added the value v∞ = 1500 m/s (reference value on our site) to the time chain to obtain Figure 3B.

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