# Global Precedent-Based Extrapolation Estimate of the M8+ Earthquake Hazard (According to USGS Data as of 1 June 2021)

^{*}

## Abstract

**:**

## 1. Introduction

_{x}= C |E

_{x}− E

_{0}|

^{γ}= C |m

_{x}(x′)

^{2}/2 − m

_{x}(x′

_{0})

^{2}/2|

^{γ}. Here, m

_{x}, F

_{x}and E

_{x}are, respectively, the “measure of inertness,” the “force” and the “energy of motion” of the system with respect to parameter x; C is a constant of proportionality; γ is an exponent of nonlinearity and x′ and x′

_{0}are the rates of change of the parameters in the current and stationary states, respectively. This conclusion was transformed into the DSDNP equation [4,5]:

^{λ}− (x′

_{0})

^{λ}|

^{α/}

^{λ},

_{0}) and at a significant distance from it (x′ >> x′

_{0}). The above conclusion about the self-development of natural systems corresponds to DSDNP Equation (1) at λ = 2, α = 2γ and k = Cm

_{x}

^{γ−1}.

^{α}.

## 2. Materials and Methods

#### 2.1. The Model Equation

k = 0 | x = x_{1} + x’(t − t_{1}), x′ = const |

k ≠ 0, α ≠ 1, α ≠ 2 | x = X_{a} + [k(α − 1)(T_{a} − t)]^{(α−2)/(α−1)}/[k(2 − α)],T _{a} = t_{1} + (x′_{1}^{1−}^{α})/[k(α − 1)], X_{a} = x_{1} + (x′_{1}^{2−α})/[k(α − 2)] |

k ≠ 0, α = 1 | x = X_{a} + (x_{1} − X_{a}) exp[k(t − t_{1})], X_{a} = x_{1} − x′_{1}/k |

k ≠ 0, α = 2 | x = x_{1} + ln|(T_{a} − t_{1})/(T_{a} − t)|/k, T_{a} = t_{1} + 1/(kx′_{1}) |

k ≠ 0, α ≠ 1, α ≠ 2 | ln|x − Xa| = c_{1}ln|t − Ta| + c_{0}, c_{1} = (α − 2)/(α − 1),c _{0} = ln|k(α − 1)|(α − 2)/(α − 1) − ln|k(α − 2)| |

k ≠ 0, α = 1 | ln|x − Xa| = c_{1}t + c_{0}, c_{1} = k, c_{0} = ln|x_{1} − X_{a}| − k × t_{1} |

k ≠ 0, α = 2 | x = c_{1}ln|T_{a} − t| + c_{0}, c_{1} = −1/k, c_{0} = x_{1} + ln|T_{a} − t_{1}|/k |

#### 2.2. The Optimization and Its Criteria

_{1}, x′

_{1}and t

_{1}) is complex and requires large computing resources. However, when using solutions from Equation (2) in linear form (conventional or logarithmic), optimization is reduced to the analysis and comparison of several variants of linear regression. In some cases, optimization may also be required with respect to one or two additional parameters: T

_{a}and/or X

_{a}. The optimal values (α, k, x

_{1}, x′

_{1}and t

_{1}) for each variant are easily determined analytically from linearity constants (c

_{0}, c

_{1}) and asymptotes (T

_{a}and/or X

_{a}). This greatly simplifies the optimization procedure and reduces the requirements for computing resources.

_{xt}= {Σ(Δx

_{i}Δt

_{i})/[n(x

_{c}− x

_{s})(t

_{c}− t

_{s})]}

^{0.5}is used as an optimization criterion to ensure the stability of the results. Here, (x

_{c}− x

_{s}) and (t

_{c}− t

_{s}) are the ranges of variations of the factual data for optimization (these ranges normalize the coordinates to a range from 0 to 1), and Δx

_{i}and Δt

_{i}are the deviations of each point of the factual data from the calculated curve along the abscissa and ordinate axes, respectively. In a geometric sense, the bicoordinate deviation corresponds to the side of a square equal in area to a rectangle with sides Δx

_{i}and Δt

_{i}, i.e., the bicoordinate deviation is the geometric mean of these deviations. The bicoordinate root mean square deviation is not the only possible criterion for the stability of the optimization results (optimization by area deviations has been successfully applied before), and moreover, it cannot be argued that this criterion is the best. However, it allows you to get stable results and is adequate for the available computing resources. For greater sensitivity, optimization is performed according to the maximum of the regularity coefficient (the inverse value for bicoordinate deviation): K

_{re}

_{g}= 1/Δ

_{xt}.

#### 2.3. The Processing of Seismic Catalogs

_{reg}< 10 are ignored. From all the test approximations, the three best variants are selected: the first one is based on the maximum K

_{reg}, and the rest are based on the nearest and main maxima of the K

_{reg}/K

_{lin}ratio. The first variant is always determined, the rest depending on the presence and combination of current nonlinear trends. Nonlinearity variants allow you to track new development trends that begin (and, therefore, are still poorly expressed) against the background of the main trends.

#### 2.4. The Estimation of Extrapolation Predictability

_{f},x

_{f}) from the calculated curve along the one normal to it is used. It is calculated on the approximation section of the trend in coordinates normalized to a range from 0 to 1 from the first (t

_{s},x

_{s}) to the last point (t

_{c},x

_{c}):

_{r}− x

_{f})/(x

_{c}− x

_{s})) × ((t

_{r}− t

_{f})/(t

_{c}− t

_{s})))

^{2}/(((x

_{r}− x

_{f})/(x

_{c}− x

_{s}))

^{2}+ ((t

_{r}− t

_{f})/(t

_{c}− t

_{s}))

^{2})]/n}

^{0.5}.

_{f},x

_{f}) to the calculated curve is estimated in the first approximation as the height h of a right triangle (t

_{r},x

_{f})–(t

_{f},x

_{f})–(t

_{f},x

_{r}) lowered by the hypotenuse (t

_{r},x

_{f})–(t

_{f},x

_{r}) from the opposite vertex, which is the factual point (t

_{f},x

_{f}): h = ab/c. As a result, Equation (3) is an expression for the root mean square value of these distances.

_{p},x

_{p}) to the calculated point is in the band of permissible errors ± 3σ, i.e., the ratio is fulfilled:

_{r}− x

_{p})/(x

_{p}− x

_{s})) × ((t

_{r}− t

_{p})/(t

_{p}− t

_{s})))

^{2}/(((x

_{r}− x

_{p})/(x

_{p}− x

_{s}))

^{2}+ ((t

_{r}− t

_{p})/(t

_{p}− t

_{s}))

^{2})]

^{0.5}≤ 3σ.

_{s},x

_{s}) point to the point being tested (t

_{p},x

_{p}), then the average deviation is pre-recalculated to the same normalization range; that is, σ is pre-recalculated on the approximation section of the trend according to Equation (3) with the replacement of t

_{c}and x

_{c}by t

_{p}and x

_{p}.

#### 2.5. Quantitative Estimates in Prediction Precedents for Strong Earthquakes

_{sh_f}− t

_{c})/σ

_{t}.

_{pn}is calculated by the formula:

_{pn}= (Δ

_{x}− Δ

_{t})/(Δ

_{x}+ Δ

_{t}), where Δ

_{x}= (x

_{sh_f}− x

_{s})/(x

_{c}− x

_{s}) − 1, Δ

_{t}= (t

_{sh_f}− t

_{s})/(t

_{c}− t

_{s}) − 1.

_{sh_f}, t

_{sh_f}) are used in retrospective estimates. When predicting by precedent, instead of them, the calculated values (x

_{sh_i}, t

_{sh_i}) for a strong earthquake are used in the Equation (6).

_{pn}corresponds to the sign of the coefficient k in the DSDNP equation, but not in the integer, except in real terms. For extremely nonlinear activation sequences, parameter predictability dominates over time predictability, so the L

_{pn}value is close to 1. As the ratio in the predictability of the trend in terms of parameter and time is leveled, the L

_{pn}value decreases, reaching 0 for sequences close to stationary development. A further shift of the ratios in trend predictability leads to an increasing increase in time predictability compared to parameter predictability, which corresponds to attenuation sequences. L

_{pn}values tend to be −1 for extremely nonlinear attenuation sequences, in which the time predictability significantly exceeds the parameter predictability. Thus, for the activation sequences considered by us (foreshock sequences in case of the completion of activation by a strong earthquake), the L

_{pn}value varies from 0 to 1. As will be shown below on the example of retro-forecasts, the predictive nonlinearity of the L

_{pn}determines the asymmetry of the band of permissible deviations and thereby reflects the stochasticity/determinism of the position (fluctuations) of the main thrust of the predicted trend.

_{c}− x

_{s})/(x

_{sh_f}− x

_{s}) + (t

_{c}− t

_{s})/(t

_{sh_f}− t

_{s})].

_{sh_f},t

_{sh_f}) in Equation (7), calculated values (x

_{sh_i},t

_{sh_i}) for a strong earthquake are also used.

#### 2.6. The Real-Time Predictive Estimation Algorithm

_{sh_f}of the main earthquake to the rate x′

_{sh}of change of the parameter at the point of the extrapolation curve closest to the main earthquake. In retrospective studies, this point is determined in parameter–time coordinates, normalized to a range from 0 to 1 according to the factual values from point (t

_{s},x

_{s}) to point (t

_{sh_f},x

_{sh_f}). If the factual point of a strong earthquake is located within the region of existence of the extrapolation curve (t

_{sh_f}< T

_{a}at α > 1 and x

_{sh_f}< X

_{a}at α > 2), then the distances to the extrapolation curve from the factual point of a strong earthquake are determined by the abscissa (a) and ordinate (b): a = |t

_{sh_f}− t(x

_{sh_f})|, b = |x

_{sh_f}− x(t

_{sh_f})|. Geometrically, these distances correspond to the cathetus of a right triangle with a vertex at the point (t

_{sh_f},x

_{sh_f}) (see Figure 1, assuming that point (t

_{f},x

_{f}) is point (t

_{sh_f},x

_{sh_f}) and point (t

_{i},x

_{i}) is point (t

_{sh_i},x

_{sh_i})). Then, the position of point (t

_{sh_i},x

_{sh_i}) is approximately defined as the intersection of the hypotenuse perpendicular to it from the vertex of the right angle. Based on the proportions existing in a right triangle, we determined the coordinate values for this point: t

_{sh_i}= t

_{sh_f}+ (t(x

_{sh_f}) − t

_{sh_f})/(a + b) and x

_{sh_i}= x

_{sh_f}+ (x(t

_{sh_f}) − x

_{sh_f})/(a + b). Using these coordinates, the rate x′

_{sh}is calculated: x′

_{sh}= [k(α − 1)(T

_{a}− t

_{sh_i})]

^{1/(1−α)}at α ≥ 1.5 or x′

_{sh}= [k(2 − α)(x

_{sh_i}− X

_{a})]

^{1/(2−α)}at α < 1.5.

_{sh_i}= x(t

_{sh_f}) and t

_{sh_i}= t

_{sh_f}or t

_{sh_i}= t(x

_{sh_f}) and x

_{sh_i}= x

_{sh_f}. After that, the rate x′

_{sh}is calculated according to the above formulas. If both coordinates go beyond the limits of the existence of the extrapolation curve (t

_{sh_f}≥ T

_{a}and x

_{sh_f}≥ X

_{a}at α > 2), the asymptotic point (Ta,Xa) turns out to be the closest to the earthquake; therefore, an extremely large value is conditionally assumed as the rate x′

_{sh}.

_{sh}parameter at the point of the extrapolation curve closest to the main earthquake. For this purpose, a database of precedent retrospective predictions is created. This database includes information about the hypocentric radius of the sample, α, k and x′

_{sh}, as well as information about this strong precedent earthquake (magnitude, time and place).

- Search in the catalog for unfinished (not come out of the band of admissible errors at the time of the catalog end) prediction definitions, in which a tendency towards an increase in seismic activity is found.
- Comparison of the type of an activity increase with the database of precedent retrospective predictions alongside the sample radius, exponent α (with an accuracy of 0.01) and coefficient k (when comparing lg k with an accuracy of 0.1). All cases of an activity increase that have no analogs in the database of precedent retrospective predictions are ignored.
- For each precedent retrospective prediction based on the rate of change in the x′
_{sh}parameter, the time t_{sh}and the value of the x_{sh}parameter are calculated, at which, for a given type of an activity increase, its level will correspond to the level of the precedent shock:t_{sh_i}= T_{a}− x′_{sh}^{1−α}/[k(1 − α)] when α ≠ 1 or t_{sh_i}= t_{1}+ ln(x′_{sh}/x′_{1})/k when α = 1,x_{sh_i}= X_{a}− x′_{sh}^{2−α}/[k(2 − α)] when α ≠ 2 or x_{sh_i}= x_{1}+ ln(x′_{sh}/x′_{1})/k when α = 2.Then, the values of L_{pn}, A and σ_{t}are estimated. The definitions, for which the approximation and extrapolation ratio A exceed the maximum value of A_{max}for retro-forecast precedents, are considered as having no precedents. - The revealed precedent retrospective predictions are grouped by the main shock. For each group, the calculated average time of the strong earthquake and its standard deviation σ
_{sh}, as well as the average values of L_{pn}, A and σ_{t}, are determined.

#### 2.7. Initial Data

## 3. Results

#### 3.1. Analysis of Retro-Precedents of Foreshock Forecasting

#### 3.1.1. The Relationship between the Predicted Nonlinearity of the Seismic Energy Flow and the Determinism of Strong Earthquakes

_{pn}are shown in Figure A2. Table A1 contains data on the main shock, sample and some characteristics of the foreshock trend corresponding to these examples. It can be seen in Figure A2 that, for a low predicted nonlinearity L

_{pn}(graph in Figure A2a), the position of the strong earthquake step in the energy flux is weakly determined by the band of admissible deviations. A strong earthquake in this band could have occurred both much earlier and much later than its factual time, i.e., the stochasticity of a strong shock time increases with decreasing the predicted nonlinearity. The latter is typical for the sequences of activation close to stationary development. On the contrary, with an increase in the predicted nonlinearity (graphs in Figure A2b–f), the asymmetry of the band of admissible deviations by the parameter and time increases. As a result, the step of a strong earthquake, requiring a large admissible deviation by the parameter, is more and more rigidly determined by a reduction of the time interval, in which a strong shock can occur. This variability of stochasticity/determinacy of the process, depending on the level of predicted nonlinearity L

_{pn}, has to be taken into account in predictive extrapolation calculations of the time of strong earthquakes.

#### 3.1.2. Statistics of Lead Time, Relative Accuracy and Approximation-Extrapolation Ratio in Retro-Forecasts of Strong Earthquakes

_{average}= 3.26, Table A3). However, a high lead time in the range of 3 years or more leads to an increase in the average relative accuracy of forecasting to a quantitative level (Δ

_{average}= 5.69 for (t

_{sh_f}− t

_{c}) > 1000 days; see Table A3). There is also a general tendency to further increase the average relative accuracy for the most deterministic earthquakes (with the highest level of predictive nonlinearity, L

_{pn}).

_{sh_f}− t

_{c}) < 10 days. Nevertheless, against the general background of this decline, retro-forecasts with a quantitative level of accuracy are noted at all time ranges. Thus, the distribution of retro-forecast definitions by their lead time and accuracy indicates the possibility of, at least, medium long-term quantitative predictions of strong earthquakes with the prospect of quantitative forecasting at all ranges of lead time.

_{max}= 2.50. It follows from this that, for sequences with weakly expressed predictive nonlinearity (and, accordingly, approximately proportional increments in the predictive part of the parameter and time), the time extrapolation cannot exceed the duration of the approximation component of the trend by more than 1.5 times. For extremely nonlinear sequences, in which almost all the increments of the parameter fall on the forecast part of the trend, the extrapolation possibilities are reduced in time and are limited to 20% of the duration of the approximation component of the foreshock trend. In addition, the data in Table A4 indicate that both the maximum and average values of the approximation–extrapolation ratio A tend to increase with the increasing lead time and predictive nonlinearity of retro-forecasts.

#### 3.2. Precedent-Based Extrapolation Estimation of Seismic Hazard in Retrospect

_{pn}≥ 0.9. Seven strong earthquakes used as precedents according to the USGS catalog have 597 precedent forecasts. This corresponds to 20% of the number of precedent earthquakes and 79.5% of the number of precedent forecasts based on the results of processing the USGS catalog. These earthquakes are used to retrospectively adjust the algorithm of precedent-based extrapolation estimations (see Appendix B): M8.0 earthquake on 16 November 2000 (−3.980° latitude, 152.169° longitude, 33-km depth)—30 precedent forecasts; M8.1 earthquake on 13 January 2007 (46.243°, 154.524°, 10)—52 precedent forecasts; M8.4 earthquake on 12 September 2007 (−4.438°, 101.367°, 34)—178 precedent forecasts; M9.1 earthquake on 11 March 2011 (38.297°, 142.373°, 29)—39 precedent forecasts; M8.0 earthquake on 6 February 2013 (−10.799°, 165.114°, 24)—34 precedent forecasts; M8.2 earthquake on 1 April 2014 (−19.610°, −70.769°, 25)—244 precedent forecasts and M8.0 earthquake on 26 May 2019 (−5.812°, −75.270°, 122)—20 precedent forecasts.

_{err}(the distance between their factual and calculated positions) are given in Table A5, Table A6, Table A7, Table A8, Table A9, Table A10 and Table A11.

#### 3.3. Precedent-Based Extrapolation Estimation of Seismic Hazard in Real-Time

## 4. Discussion

_{max}).

_{sh}values, especially against the background of low σ

_{t}values. In particular, for cluster 17, the standard deviation of the estimated earthquake time (σ

_{sh}) is 4.5 years, with only a daily expected average deviation in time of the actual data from the calculated curve (σ

_{t}). This indicates the presence of several alternatives (or their ‘fans’) for the further development of the hazard with significant discrepancies between them. The number of clusters with similar large σ

_{sh}values is a significant part of their total number, which requires additional research to solve this problem.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

M | earthquake magnitude |

x_{1}, x′_{1}, t_{1} | initial conditions (the values of the parameter and its rate of change at certain time points) |

T_{a}, X_{a} | values of the asymptotes with respect to time and parameter |

c_{0}, c_{1} | linear dependence constants |

Δ_{xt} | bicoordinate root-mean-square deviation |

n | number of points in the optimized data |

x_{s}, t_{s} | values of x and t at the first point of the factual data for optimization (the beginning of the approximated part of the sequence) |

x_{c}, t_{c} | values of x and t at the end point of the factual data for optimization (the end of the approximated part of the sequence and the beginning of extrapolation in the factual data) |

K_{reg} | regularity coefficient (the inverse value for bicoordinate deviation) |

K_{lin} | regularity coefficient in the case of linear approximation |

σ | mean deviation of the factual points from the calculated curve along the normal to it |

x_{p}, t_{p} | factual values of x and t at the end of the extrapolation (at the last predicted point in the sequence) |

x_{f}, t_{f} | factual values of x and t |

x_{r} = x(t_{f}), t_{r} = t(x_{f}) | calculated values of x and t |

x_{i}, t_{i} | coordinates of the point on the calculated curve closest to the factual point |

x_{sh_f}, t_{sh_f} | factual values of x and t for a strong earthquake |

x_{sh_i}, t_{sh_i} | coordinates of the point on the calculated curve closest to the factual point of a strong earthquake/calculated values of x and t for a strong earthquake in the prediction by precedent |

σ_{t} | expected average deviation in time of the factual data from the calculated curve at its closest point to the strong earthquake |

σ_{sh} | rms deviation of the estimated time for the earthquake similar in power to the precedent earthquake |

Δ | relative accuracy of precedent predictions in time |

L_{pn} | predicted nonlinearity |

A | approximation and extrapolation ratio |

A_{max} | maximum value of A detected in retro-forecasts |

x′_{sh} | rate of change of the parameter x at the point of the extrapolation curve closest to the strong earthquake |

N_{sh} | number of strong earthquakes used as precedents |

N_{pr} | number of precedent predictions of strong earthquakes |

D_{err} | error in determining the hypocenter (the distance between factual and calculated position) |

z | number of zones in the cluster |

n_{a} | number of unfinished predictive extrapolations in the cluster |

n_{pr} | number of precedent time calculations |

## Appendix A. Statistics on the Predictability of the Seismic Energy Flux and Strong Earthquakes in It

**Figure A1.**(

**a**) Distribution of the specific weight of predictability w

_{p}for activating the seismic energy flux, (

**b**) foreshock predictability of strong earthquakes and (

**c**) their combination in the coordinates of the α–lg k parameters of the DSDNP equation, according to Reference [24]. M is the magnitude of predicted strong earthquakes.

_{1}× W

_{2}× W

_{3})

^{1/3}is the geometric mean of three independent weight characteristics. The first weight component characterizes the forecast range: W

_{1}= [(x

_{p}− x

_{s})/(x

_{c}− x

_{s}) + (t

_{p}− t

_{s})/(t

_{c}− t

_{s})]/2 − 1. The second weighting component characterizes the nonlinearity of the forecast: W

_{2}= exp|ln[(x

_{p}− x

_{s})/(x

_{c}− x

_{s}))/((t

_{p}− t

_{s})/(t

_{c}− t

_{s})]| − 1. The third weighting component characterizes the quality of the forecast, i.e., the correspondence of the factual data to the calculated approximation–extrapolation curve: W

_{3}= 0.1/σ − 1; all predictive extrapolations with σ > 0.1 are considered low-quality and rejected. The analysis of the weight distribution of predictive extrapolations by the parameters of the DSDNP equation α and k is carried out with rounding by α with an accuracy of 0.01 and by lg k − up to 0.1. The weights of forecast extrapolations having the same rounded values α and lg k are summed and divided by the total weight of all the forecast extrapolations. Further, these specific weights for all available combinations of α and lg k are sorted in descending order and then summed from smaller values to larger ones. Thus, we obtained a cumulative characteristic of the distribution of a specific weight of w

_{p}predictive extrapolations, depending on the combinations of α and lg k: w

_{p}(α, lg k) = Σ

_{α}

_{, lg k}(ΣW(α, lg k)/ΣW). w

_{p}has values close to 1 at the points of the maximum specific gravity of the forecast extrapolations and close to 0 for combinations of α and lg k that are insignificant from the point of view of the forecast.

**Figure A2.**Examples of some foreshock extrapolations of the energy flux. Figures in circles: 1—factual data curve, 2—calculated curve, 3—errors band (±3σ), 4—retrospective prediction moment and 5—strong earthquake. The graphs correspond to the data in Table A1. The intersection of the vertical and horizontal dotted lines on the graphs corresponds to the ‘current’ values of time and parameter, there is the ‘past’ to the left and below this intersection and the ‘future’ to the right and above.

_{pn}, but do not prove this statement. Nevertheless, the graphs of all other (27,673—USGS data, 116,420—all catalogs) precedents of the predictability of strong earthquakes demonstrate a similar relationship between L

_{pn}and the band of permissible deviations. All these results (data for graphs) were obtained automatically during catalog processing (see Section 2.3). That is, we did not choose the forecast moments for the graphs in Figure A2. When processing the catalog for each radius of formation of the hypocentral samples, we totally checked all the catalog events. In each case, the event was considered as the ‘current time’ for test approximations and subsequent predictive extrapolations. Among these extrapolations, trends corresponding to successful forecasts of strong earthquakes were automatically detected, including those shown in Figure A2. This made possible and objective the subsequent analysis of the predictability of strong earthquakes. In total, the analysis of the USGS catalog revealed ~18.8 million ‘current’ activation trends. For this purpose, two to three decimal orders of magnitude more test approximations were performed, the results of which were not logged to save computing resources. At the same time, only in 27,673 cases, among the main “current” activation trends, the fact that M7+ earthquakes hit the band of permissible deviations of the extrapolation (prediction) part of the trend was established. We do not consider it necessary to evaluate this result as ‘good’ or ‘bad’. We consider it as an objective reality that can and should be used to identify hazardous activation trends (as it is shown, for example, in Figure A1). The examples for Figure A2 were selected (also automatically) from all other cases of the predictability of strong earthquakes only because each of them has the maximum predictability (by the magnitude of the ratio A) among the forecasts of a certain level of nonlinearity L

_{pn}: Figure A2a—0 < L

_{pn}≤ 0.5, Figure A2b—0.5 < L

_{pn}≤ 0.8, Figure A2c—0.9 < L

_{pn}≤ 0.95, Figure A2d—0.95 < L

_{pn}≤ 0.98, Figure A2e—0.98 < L

_{pn}≤ 0.99 and Figure A2c—0.99 < L

_{pn}≤ 1.0. This corresponds to the sections of the statistical tables. Therefore, examples of Figure A2 can be considered as additional illustrations to Table A2, Table A3 and Table A4. Additionally, when carefully examining the graphs in Figure A2. it can be noticed that the line of actual data in the forecast part of the graphs before a strong earthquake, as a rule, goes beyond the band of permissible deviations and returns to it at the time of the earthquake. This effect is due to the extrapolation estimation algorithm used in the work (see Section 2.4), according to which each of the actual points in the forecast part is consistently monitored for falling into the band of permissible deviations according to the ratio (4). In this case, a variable (increasing) range of rationing is used. Therefore, points that have previously passed the control by the ratio (4) may be outside the tolerance band of subsequent points. The tolerance band for the upper (terminal) point of a strong earthquake is shown in the graphs of Figure A2.

**Table A1.**Data on the main shock, sample and some characteristics of the foreshock trend for the examples of retrospective prediction extrapolations given in Figure A2.

(a) | (b) | (c) | (d) | (e) | (f) | ||
---|---|---|---|---|---|---|---|

Earthquake | date | 1992 10 11 | 1991 09 30 | 1993 06 08 | 1989 05 23 | 1982 06 07 | 2016 12 08 |

time | 19:24:26 | 00:21:46 | 13:03:36 | 10:54:46 | 10:59:40 | 17:38:46 | |

M | 7.4 | 7.0 | 7.5 | 8.0 | 7.0 | 7.8 | |

latitude | −19.247 | −20.878 | 51.218° | −52.341 | 16.558 | −10.681 | |

longitude | 168.948 | −178.591 | 157.829 | 158.824 | −98.358 | 161.327 | |

depth, km | 129 | 566.4 | 70.6 | 10 | 33.8 | 40 | |

Sample | radius, km | 150 | 60 | 300 | 300 | 150 | 150 |

latitude | −19.604 | −20.797 | 51.176 | −52.941 | 16.931 | −9.802 | |

longitude | 168.541 | −178.846 | 159.677 | 158.824 | −97.285 | 160.861 | |

depth, km | 0 | 600 | 0 | 0 | 100 | 100 | |

Foreshock trend | t_{sh_f} − t_{c}, days | 8245 | 6001 | 766 | 3312 | 689 | 73.36 |

Δ = (t_{sh_f} − t_{c})/σ_{t} | 15.90 | 27.34 | 20.33 | 35.32 | 36.28 | 89.22 | |

L_{pn} | 0.2313 | 0.7852 | 0.9435 | 0.9757 | 0.9890 | 0.9986 | |

A | 1.6309 | 2.3451 | 1.9442 | 2.4337 | 2.2048 | 2.1360 | |

α | 1.0000 | 2.0000 | 2.0000 | 2.0000 | 2.0000 | 2.0000 | |

lg k | −4.6110 | −15.0095 | −15.2064 | −15.3332 | −13.7995 | −14.0278 |

**Table A2.**Distribution of the precedents of foreshock retro-forecasts depending on the sample radius R, predictive nonlinearity L

_{pn}and forecast lead time.

R, km | L_{pn} | Forecast Lead Time, t_{sh_f}–t_{c}, Days | Total | ||||
---|---|---|---|---|---|---|---|

<1 | 1–10 | 10–100 | 100–1000 | >1000 | |||

300 | 0.99–1.00 | 1705 | 693 | 1671 | 494 | 2 | 4565 |

0.98–0.99 | 2 | 135 | 987 | 1241 | 33 | 2398 | |

0.95–0.98 | 1 | 147 | 1752 | 3426 | 406 | 5732 | |

0.90–0.95 | 0 | 1 | 1572 | 3281 | 291 | 5145 | |

0.80–0.90 | 0 | 0 | 362 | 8819 | 1141 | 10,322 | |

0.50–0.80 | 0 | 0 | 14 | 9784 | 6219 | 16,017 | |

0.00–0.50 | 0 | 0 | 0 | 401 | 261 | 662 | |

subtotal | 1708 | 976 | 6358 | 27,446 | 8353 | 44,841 | |

150 | 0.99–1.00 | 2072 | 1361 | 1525 | 443 | 10 | 5411 |

0.98–0.99 | 2 | 662 | 708 | 914 | 148 | 2434 | |

0.95–0.98 | 0 | 983 | 810 | 3085 | 696 | 5574 | |

0.90–0.95 | 0 | 249 | 707 | 2773 | 2220 | 5949 | |

0.80–0.90 | 0 | 0 | 737 | 4029 | 3099 | 7865 | |

0.50–0.80 | 0 | 0 | 1 | 2575 | 3870 | 6446 | |

0.00–0.50 | 0 | 0 | 0 | 20 | 252 | 272 | |

subtotal | 2074 | 3255 | 4488 | 13,839 | 10,295 | 33,951 | |

60 | 0.99–1.00 | 3306 | 4775 | 5501 | 858 | 131 | 14,571 |

0.98–0.99 | 0 | 18 | 249 | 1186 | 26 | 1479 | |

0.95–0.98 | 0 | 13 | 67 | 1559 | 209 | 1848 | |

0.90–0.95 | 0 | 0 | 2 | 1384 | 790 | 2176 | |

0.80–0.90 | 0 | 0 | 0 | 856 | 1276 | 2132 | |

0.50–0.80 | 0 | 0 | 0 | 608 | 897 | 1505 | |

0.00–0.50 | 0 | 0 | 0 | 0 | 11 | 11 | |

subtotal | 3306 | 4806 | 5819 | 6451 | 3340 | 23,722 | |

30 | 0.99–1.00 | 3496 | 2494 | 1751 | 738 | 60 | 8539 |

0.98–0.99 | 0 | 0 | 7 | 475 | 229 | 711 | |

0.95–0.98 | 0 | 0 | 2 | 533 | 313 | 848 | |

0.90–0.95 | 0 | 0 | 0 | 114 | 49 | 163 | |

0.80–0.90 | 0 | 0 | 0 | 160 | 44 | 204 | |

0.50–0.80 | 0 | 0 | 0 | 1 | 8 | 9 | |

subtotal | 3496 | 2494 | 1760 | 2021 | 703 | 10,474 | |

15 | 0.99–1.00 | 1305 | 1202 | 566 | 119 | 20 | 3212 |

0.98–0.99 | 1 | 0 | 0 | 0 | 14 | 15 | |

0.95–0.98 | 0 | 0 | 0 | 0 | 2 | 2 | |

0.90–0.95 | 0 | 0 | 0 | 0 | 2 | 2 | |

0.80–0.90 | 0 | 0 | 0 | 0 | 1 | 1 | |

subtotal | 1306 | 1202 | 566 | 119 | 39 | 3232 | |

7.5 | 0.99–1.00 | 468 | 9 | 0 | 3 | 0 | 480 |

total | 12,358 | 12,742 | 18,991 | 49,879 | 22,730 | 116,700 |

**Table A3.**The maximum (average) relative accuracy Δ of foreshock retro-forecasts depending on the sample radius R, predictive nonlinearity L

_{pn}and forecast lead time.

R, km | L_{pn} | Forecast Lead Time, t_{sh_f}–t_{c}, Days | Total | ||||
---|---|---|---|---|---|---|---|

<1 | 1–10 | 10–100 | 100–1000 | >1000 | |||

300 | 0.99–1.00 | 20.58 (2.38) | 18.63 (1.59) | 27.45 (3.39) | 40.92 (2.67) | 8.63 (8.42) | 40.92 (2.66) |

0.98–0.99 | 3.25 (3.24) | 9.89 (3.25) | 25.80 (2.97) | 25.88 (3.22) | 24.53 (15.14) | 25.88 (3.28) | |

0.95–0.98 | 4.53 (4.53) | 6.53 (1.98) | 20.27 (2.57) | 22.94 (3.45) | 35.32 (6.43) | 35.32 (3.35) | |

0.90–0.95 | 7.63 (7.63) | 8.80 (1.63) | 20.33 (2.75) | 36.33 (5.58) | 36.33 (2.57) | ||

0.80–0.90 | 7.51 (1.48) | 18.53 (3.03) | 18.56 (6.60) | 18.56 (3.37) | |||

0.50–0.80 | 5.18 (3.75) | 12.51 (3.95) | 23.44 (6.85) | 23.44 (5.08) | |||

0.00–0.50 | 8.88 (6.04) | 15.44 (5.46) | 15.44 (5.81) | ||||

subtotal | 20.58 (2.38) | 18.63 (1.88) | 27.45 (2.55) | 40.92 (3.43) | 36.33 (6.74) | 40.92 (3.85) | |

150 | 0.99–1.00 | 24.72 (1.60) | 71.51 (1.71) | 89.22 (3.53) | 37.67 (3.86) | 91.27 (33.64) | 91.27 (2.42) |

0.98–0.99 | 3.46 (3.32) | 9.17 (0.51) | 16.25 (3.02) | 36.28 (3.50) | 36.27 (8.27) | 36.28 (2.84) | |

0.95–0.98 | 3.32 (0.53) | 10.39 (1.89) | 17.18 (4.89) | 29.12 (4.68) | 29.12 (3.66) | ||

0.90–0.95 | 2.86 (1.08) | 5.88 (1.79) | 15.36 (2.73) | 16.46 (4.39) | 16.46 (3.17) | ||

0.80–0.90 | 5.87 (2.77) | 16.09 (3.20) | 22.01 (5.09) | 22.01 (3.90) | |||

0.50–0.80 | 4.55 (4.55) | 10.36 (3.78) | 20.17 (5.35) | 20.17 (4.72) | |||

0.00–0.50 | 4.82 (4.47) | 15.90 (4.57) | 15.90 (4.56) | ||||

subtotal | 24.72 (1.60) | 71.51 (1.06) | 89.22 (2.75) | 37.67 (3.63) | 91.27 (5.07) | 91.27 (3.58) | |

60 | 0.99–1.00 | 21.79 (1.03) | 10.96 (0.97) | 22.18 (2.20) | 59.51 (4.01) | 18.73 (12.20) | 59.51 (1.73) |

0.98–0.99 | 2.72 (1.70) | 6.66 (1.87) | 19.29 (2.14) | 17.80 (9.49) | 19.29 (2.22) | ||

0.95–0.98 | 2.88 (2.47) | 5.43 (2.32) | 16.69 (2.91) | 18.06 (6.11) | 18.06 (3.25) | ||

0.90–0.95 | 1.79 (1.39) | 9.37 (1.84) | 16.37 (5.41) | 16.37 (3.13) | |||

0.80–0.90 | 8.98 (2.34) | 18.78 (3.73) | 18.78 (3.17) | ||||

0.50–0.80 | 6.75 (3.13) | 28.61 (4.75) | 28.61 (4.10) | ||||

0.00–0.50 | 7.53 (4.43) | 7.53 (4.43) | |||||

subtotal | 21.79 (1.03) | 10.96 0.97) | 22.18 (2.19) | 59.51 (2.63) | 28.61 (4.93) | 59.51 (2.29) | |

30 | 0.99–1.00 | 8.61 (1.16) | 12.97 (1.26) | 13.85 (3.75) | 658.60 (3.86) | 22.43 (10.83) | 658.60 (2.02) |

0.98–0.99 | 1.53 (0.78) | 8.57 (2.19) | 14.07 (5.68) | 14.07 (3.30) | |||

0.95–0.98 | 5.78 (5.76) | 8.35 (2.77) | 11.56 (4.83) | 11.56 (3.53) | |||

0.90–0.95 | 9.04 (2.84) | 15.46 (5.84) | 15.46 (3.74) | ||||

0.80–0.90 | 6.61 (4.08) | 8.33 (5.46) | 8.33 (4.38) | ||||

0.50–0.80 | 5.10 (5.10) | 8.18 (5.68) | 8.18 (5.61) | ||||

subtotal | 8.61 (1.16) | 12.97 (1.26) | 13.85 (3.74) | 658.60 (3.14) | 22.43 (5.74) | 658.60 (2.31) | |

15 | 0.99–1.00 | 10.09 (0.83) | 18.41 (1.40) | 10.13 (5.05) | 31.75 (7.79) | 37.18 (11.34) | 37.18 (2.11) |

0.98–0.99 | 5.62 (5.62) | 12.87 (7.02) | 12.87 (6.92) | ||||

0.95–0.98 | 12.40 (9.97) | 12.40 (9.97) | |||||

0.90–0.95 | 2.40 (2.26) | 2.40 (2.26) | |||||

0.80–0.90 | 5.22 (5.22) | 5.22 (5.22) | |||||

subtotal | 10.09 (0.83) | 18.41 (1.40) | 10.13 (5.05) | 31.75 (7.79) | 37.18 (9.09) | 37.18 (2.14) | |

7.5 | 0.99–1.00 | 7.64 (2.00) | 5.77 (3.85) | 9.77 (7.47) | 9.77 (2.07) | ||

total | 24.72 (1.36) | 71.51 (1.16 | 89.22 (2.67) | 658.60 (3.38) | 91.27 (5.69) | 658.60 (3.26) |

**Table A4.**The maximum (average) approximation–extrapolation relation A of foreshock retro-forecasts depending on the sample radius R, predictive nonlinearity L

_{pn}and forecast lead time.

R, km | L_{pn} | Forecast Lead Time, t_{sh_f}–t_{c}, Days | Total | ||||
---|---|---|---|---|---|---|---|

<1 | 1–10 | 10–100 | 100–1000 | >1000 | |||

300 | 0.99–1.00 | 2.05 (1.82) | 2.26 (1.58) | 2.24 (1.68) | 2.23 (1.60) | 2.06 (2.00) | 2.26 (1.71) |

0.98–0.99 | 1.56 (1.56) | 2.15 (1.57) | 2.13 (1.57) | 2.29 (1.61) | 2.18 (2.04) | 2.29 (1.60) | |

0.95–0.98 | 1.42 (1.42) | 1.75 (1.47) | 2.12 (1.42) | 2.31 (1.52) | 2.43 (1.83) | 2.43 (1.51) | |

0.90–0.95 | 1.60 (1.60) | 1.87 (1.25) | 2.15 (1.36) | 2.36 (1.67) | 2.36 (1.34) | ||

0.80–0.90 | 1.68 (1.18) | 2.19 (1.29) | 2.16 (1.53) | 2.19 (1.31) | |||

0.50–0.80 | 1.39 (1.26) | 1.84 (1.24) | 2.25 (1.41) | 2.25 (1.30) | |||

0.00–0.50 | 1.49 (1.24) | 1.92 (1.23) | 1.92 (1.24) | ||||

subtotal | 2.05 (1.82) | 2.26 (1.56) | 2.24 (1.46) | 2.31 (1.33) | 2.43 (1.45) | 2.43 (1.39) | |

150 | 0.99–1.00 | 2.07 (1.79) | 2.17 (1.61) | 2.22 (1.75) | 2.37 (1.84) | 2.47 (2.21) | 2.47 (1.74) |

0.98–0.99 | 1.59 (1.57) | 1.98 (1.24) | 2.15 (1.48) | 2.42 (1.72) | 2.35 (2.07) | 2.42 (1.54) | |

0.95–0.98 | 1.54 (1.19) | 2.10 (1.31) | 2.41 (1.67) | 2.27 (1.74) | 2.41 (1.54) | ||

0.90–0.95 | 1.32 (1.16) | 1.73 (1.22) | 2.08 (1.40) | 2.40 (1.63) | 2.40 (1.46) | ||

0.80–0.90 | 1.70 (1.33) | 2.22 (1.34) | 2.30 (1.53) | 2.30 (1.41) | |||

0.50–0.80 | 1.39 (1.39) | 1.71 (1.26) | 2.06 (1.39) | 2.06 (1.34) | |||

0.00–0.50 | 1.36 (1.33) | 1.67 (1.23) | 1.67 (1.23) | ||||

subtotal | 2.07 (1.78) | 2.17 (1.37) | 2.22 (1.48) | 2.42 (1.45) | 2.47 (1.51) | 2.47 (1.49) | |

60 | 0.99–1.00 | 2.00 (1.82) | 2.03 (1.74) | 2.19 (1.77) | 2.24 (1.77) | 2.33 (2.16) | 2.33 (1.77) |

0.98–0.99 | 1.75 (1.57) | 1.84 (1.44) | 2.11 (1.59) | 2.30 (2.06) | 2.30 (1.58) | ||

0.95–0.98 | 1.56 (1.54) | 1.67 (1.42) | 2.24 (1.53) | 2.50 (1.85) | 2.50 (1.56) | ||

0.90–0.95 | 1.47 (1.36) | 2.01 (1.36) | 2.22 (1.59) | 2.22 (1.44) | |||

0.80–0.90 | 1.80 (1.33) | 2.11 (1.46) | 2.11 (1.41) | ||||

0.50–0.80 | 1.60 (1.20) | 2.35 (1.29) | 2.35 (1.25) | ||||

0.00–0.50 | 1.61 (1.33) | 1.61 (1.33) | |||||

subtotal | 2.00 (1.82) | 2.03 (1.74) | 2.19 (1.75) | 2.24 (1.48) | 2.50 (1.50) | 2.50 (1.65) | |

30 | 0.99–1.00 | 2.00 (1.84) | 2.02 (1.86) | 2.07 (1.86) | 2.27 (1.81) | 2.19 (2.05) | 2.27 (1.85) |

0.98–0.99 | 1.59 (1.36) | 2.06 (1.65) | 2.17 (1.89) | 2.17 (1.73) | |||

0.95–0.98 | 1.33 (1.33) | 2.05 (1.62) | 2.15 (1.78) | 2.15 (1.68) | |||

0.90–0.95 | 1.84 (1.45) | 2.37 (1.73) | 2.37 (1.53) | ||||

0.80–0.90 | 1.69 (1.42) | 1.79 (1.50) | 1.79 (1.44) | ||||

0.50–0.80 | 1.47 (1.47) | 1.75 (1.45) | 1.75 (1.45) | ||||

subtotal | 2.00 (1.84) | 2.02 (1.86) | 2.07 (1.85) | 2.27 (1.67) | 2.37 (1.82) | 2.37 (1.81) | |

15 | 0.99–1.00 | 2.00 (1.87) | 2.00 (1.97) | 2.01 (1.98) | 2.19 (1.98) | 2.45 (2.07) | 2.45 (1.93) |

0.98–0.99 | 1.70 (1.70) | 2.16 (1.93) | 2.16 (1.91) | ||||

0.95–0.98 | 2.13 (2.05) | 2.13 (2.05) | |||||

0.90–0.95 | 1.44 (1.41) | 1.44 (1.41) | |||||

0.80–0.90 | 1.54 (1.54) | 1.54 (1.54) | |||||

subtotal | 2.00 (1.87) | 2.00 (1.97) | 2.01 (1.98) | 2.19 (1.98) | 2.45 (1.97) | 2.45 (1.93) | |

7.5 | 0.99–1.00 | 2.00 (1.92) | 2.01 (2.00) | 2.01 (2.00) | 2.01 (1.92) | ||

total | 2.05 (1.82) | 2.26 (1.68) | 2.24 (1.60) | 2.42 (1.40) | 2.50 (1.50) | 2.26 (1.71) |

## Appendix B. Retrospective Cluster Estimates of the Seismic Energy Flux before Some M8+ Earthquakes

**Figure A3.**Zones of factual predictability for the earthquake of 16 November 2000 (

**a**), identified zones with similar development according to the parameters of the DSDNP equation (

**b**) and a cluster of zones of the greatest activity (

**c**) used to calculate the time and place of a precedent earthquake. The circles show the position of the zones in which potentially hazardous activity is detected; the thickness of the circle line reflects the number of potentially hazardous trends detected. A double circle with a crosshair is the factual (black) and calculated (blue) positions of the precedent earthquake. The calculated cluster is shown by a solid fill. The cluster color corresponds to the number (the more, the redder) of potentially hazardous unfinished extrapolations found in the cluster. A cluster of predictability of another earthquake (M8.1, 1 April 2007) with a similar foreshock preparation was also found. The size of the maps is 2222 × 2222 km (±10° latitude from the epicenter of the earthquake). The smaller map to the right of each geographical map is a north–south cross-section with a depth of 750 km.

**Figure A4.**Retro predictability of the earthquake on 16 November 2000 in the zone with the highest (at the estimate date, see Figure A3, column ‘a’) number of successful predictive extrapolations. 1—factual data, 2—approximations, 3—the moment of retro-prediction, 4—extrapolations, 5—the earthquake of 16 November 2000 in factual data and 6—calculation position for the earthquake of 16 November 2000.

**Table A5.**Retro estimation of the place and time of earthquakes by clusters of the precedent activity for earthquake 16 November 2000.

Estimate Date | z | n_{a} | n_{pr} | Calculated Date | Time Error | D_{err}, km | |
---|---|---|---|---|---|---|---|

Days | % | ||||||

M8.0 earthquake on 16 November 2000 | |||||||

2000.02.01 | 1 | 2 | 2 | 2000.06.23 | 146 | >50 | 126 |

2000.03.01 | 6 | 7 | 7 | 2000.07.05 | 134 | >50 | 96 |

2000.04.01 | 8 | 10 | 10 | 2000.08.19 | 89 | 38.77 | 113 |

2000.05.01 | 8 | 12 | 12 | 2000.09.16 | 60 | 30.23 | 119 |

2000.06.01 | 11 | 16 | 16 | 2000.10.28 | 19 | 11.12 | 105 |

2000.07.01 | 11 | 21 | 27 | 2000.12.12 | 27 | 16.23 | 109 |

2000.08.01 | 12 | 26 | 32 | 2001.01.17 | 62 | 36.69 | 125 |

2000.09.01 | 10 | 27 | 35 | 2001.02.23 | 99 | >50 | 121 |

2000.10.01 | 10 | 27 | 35 | 2001.03.06 | 110 | >50 | 122 |

2000.11.16 | 10 | 32 | 40 | 2001.03.03 | 107 | >50 | 121 |

M8.1 earthquake on 1 April 2007 (20:39:58, −8.466°, 157.043°, 24 km) | |||||||

2000.02.01 | 3 | 11 | 11 | 2005.04.18 | 713 | 27.26 | 62 |

2000.03.01 | 3 | 11 | 11 | 2005.04.18 | 713 | 27.57 | 62 |

2000.04.01 | 3 | 11 | 11 | 2005.04.18 | 713 | 27.90 | 62 |

2000.05.01 | 3 | 11 | 11 | 2005.04.18 | 713 | 28.23 | 62 |

2000.06.01 | 3 | 11 | 11 | 2005.04.18 | 713 | 28.58 | 62 |

2000.07.01 | 3 | 11 | 11 | 2005.04.18 | 713 | 28.93 | 62 |

2000.08.01 | 1 | 9 | 9 | 2006.08.30 | 214 | 8.79 | 61 |

2000.09.01 | 1 | 9 | 9 | 2006.08.30 | 214 | 8.91 | 61 |

2000.10.01 | 1 | 9 | 9 | 2006.08.30 | 214 | 9.02 | 61 |

2000.11.16 | 3 | 11 | 11 | 2005.04.18 | 713 | 30.64 | 62 |

_{a}—the number of unfinished predictive extrapolations in the cluster and n

_{pr}—the number of precedent time calculations.

**Figure A5.**Zones of factual predictability for the earthquake of 13 January 2007 (

**a**), identified zones with similar development according to the parameters of the DSDNP equation (

**b**) and a cluster of zones of the greatest activity (

**c**) used to calculate the time and place of a precedent earthquake (see Figure A3 for explanations).

**Table A6.**Retro estimation of the place and time of the earthquake on 13 January 2007 by the cluster of its precedent activity.

Estimate Date | z | n_{a} | n_{pr} | Calculated Date | Time Error | D_{err}, km | |
---|---|---|---|---|---|---|---|

Days | % | ||||||

2006.12.01 | 2 | 3 | 3 | 2006.11.30 | 44 | >50 | 34 |

2006.12.16 | 13 | 21 | 34 | 2006.12.12 | 32 | >50 | 14 |

2007.01.01 | 10 | 31 | 55 | 2006.12.27 | 16 | >50 | 40 |

2007.01.13 | 13 | 38 | 66 | 2006.12.30 | 13 | >50 | 41 |

**Figure A7.**Zones of factual predictability for the earthquake of 12 September 2007 (

**a**), identified zones with similar development according to the parameters of the DSDNP equation (

**b**) and a cluster of zones of the greatest activity (

**c**) used to calculate the time and place of a precedent earthquake (see Figure A3 for explanations).

**Table A7.**Retro estimation of the place and time of the earthquake on 12 September 2007 by the cluster of its precedent activity.

Estimate Date | z | n_{a} | n_{pr} | Calculated Date | Time Error | D_{err}, km | |
---|---|---|---|---|---|---|---|

days | % | ||||||

2002.07.01 | 6 | 19 | 30 | 2003.07.02 | 1533 | >50 | 124 |

2003.01.01 | 12 | 34 | 108 | 2004.07.24 | 1145 | >50 | 97 |

2004.01.01 | 15 | 90 | 299 | 2005.10.30 | 682 | >50 | 131 |

2005.01.01 | 17 | 139 | 605 | 2007.01.09 | 246 | 25.02 | 129 |

2006.01.01 | 18 | 147 | 656 | 2007.02.11 | 213 | 34.44 | 106 |

2007.01.01 | 19 | 151 | 584 | 2007.01.12 | 243 | >50 | 121 |

2007.09.12 | 21 | 177 | 764 | 2007.02.17 | 207 | >50 | 90 |

**Figure A9.**Zones of factual predictability for the earthquake of 11 March 2011 (

**a**), identified zones with similar development according to the parameters of the DSDNP equation (

**b**) and a cluster of zones of the greatest activity (

**c**) used to calculate the time and place of a precedent earthquake (see Figure A3 for explanations).

**Table A8.**Retro estimation of the place and time of the earthquake on 11 March 2011 by the cluster of its precedent activity.

Estimate Date | z | n_{a} | n_{pr} | Calculated Date | Time Error | D_{err}, km | |
---|---|---|---|---|---|---|---|

days | % | ||||||

2007.07.01 | 1 | 1 | 9 | 2010.06.30 | 253 | 18.78 | 261 |

2008.01.01 | 1 | 9 | 81 | 2011.01.13 | 56 | 4.85 | 261 |

2009.01.01 | 2 | 13 | 109 | 2011.04.01 | 21 | 2.58 | 263 |

2010.01.01 | 1 | 12 | 108 | 2011.04.08 | 28 | 6.15 | 261 |

2011.01.01 | 1 | 12 | 99 | 2011.04.27 | 47 | 40.39 | 261 |

2011.03.01 | 1 | 12 | 93 | 2011.05.02 | 53 | >50 | 261 |

2011.03.11 | 7 | 31 | 115 | 2011.04.22 | 43 | >50 | 126 |

**Figure A11.**Zones of factual predictability for the earthquake of 6 February 2013 (

**a**), identified zones with similar development according to the parameters of the DSDNP equation (

**b**) and a cluster of zones of the greatest activity (

**c**) used to calculate the time and place of a precedent earthquake (see Figure A3 for explanations). Clusters of predictability of other earthquakes (9 January 2001 M7.1, 1 April 2007 M8.1 and 10 August 2010 M7.3) were also found with similar preparations.

**Figure A12.**Retro predictability of the earthquake on 6 February 2013 in the zone with the highest (at the estimate date; see Figure A11, column ‘a’) number of successful predictive extrapolations (see Figure A4 for explanations).

**Table A9.**Retro estimation of the place and time of earthquakes by clusters of precedent activity for earthquake 6 February 2013.

Estimate Date | z | n_{a} | n_{pr} | Calculated Date | Time Error | D_{err}, km | |
---|---|---|---|---|---|---|---|

Days | % | ||||||

M8.0 earthquake on 6 February 2013 | |||||||

2001.01.01 | 3 | 4 | 6 | 2005.10.07 | 132 | >50 | 2679 |

2002.01.01 | 3 | 4 | 6 | 2005.10.07 | 132 | >50 | 2679 |

2003.01.01 | 3 | 4 | 6 | 2005.10.07 | 132 | >50 | 2679 |

2004.01.01 | 2 | 3 | 5 | 2006.04.26 | 132 | >50 | 2477 |

2005.01.01 | 3 | 3 | 4 | 2009.07.23 | 80 | 43.72 | 1293 |

2006.01.01 | 4 | 3 | 4 | 2009.07.23 | 80 | 49.87 | 1293 |

2007.01.01 | 2 | 2 | 2 | 2012.12.22 | 33 | 2.05 | 46 |

2008.01.01 | 2 | 2 | 2 | 2012.12.22 | 33 | 2.45 | 46 |

2009.01.01 | 2 | 2 | 2 | 2012.12.22 | 33 | 3.05 | 46 |

2010.01.01 | 2 | 2 | 2 | 2012.12.22 | 33 | 4.03 | 46 |

2011.01.01 | 1 | 1 | 1 | 2015.07.29 | 27 | >50 | 904 |

2012.01.01 | 2 | 3 | 6 | 2013.01.21 | 112 | 3.86 | 16 |

2013.01.01 | 3 | 5 | 11 | 2013.10.05 | 102 | >50 | 241 |

2013.02.06 | 11 | 17 | 23 | 2013.06.01 | 28 | >50 | 116 |

M7.1 earthquake on 9 January 2001 (16:49:28, −14.928°, 167.170°, 103 km) | |||||||

2001.01.01 | 1 | 2 | 3 | 2000.09.03 | 176 | >50 | 129 |

M8.1 earthquake on 1 April 2007 (20:39:58, −8.466°, 157.043°, 24 km) | |||||||

2001.01.01 | 2 | 8 | 16 | 2005.08.19 | 171 | 25.86 | 590 |

2002.01.01 | 3 | 9 | 17 | 2005.06.02 | 188 | 34.86 | 668 |

2003.01.01 | 2 | 8 | 16 | 2005.08.19 | 171 | 38.03 | 590 |

2004.01.01 | 2 | 7 | 14 | 2005.11.25 | 162 | 41.50 | 492 |

2005.01.01 | 2 | 7 | 14 | 2005.11.25 | 162 | >50 | 492 |

2006.01.01 | 2 | 6 | 12 | 2005.12.15 | 151 | >50 | 473 |

2007.01.01 | 2 | 4 | 8 | 2006.07.11 | 158 | >50 | 264 |

M7.3 earthquake on 10 August 2010 (05:23:44, −17.541°, 168.069°, 25 km) | |||||||

2003.01.01 | 2 | 4 | 5 | 2005.03.18 | 71 | >50 | 1971 |

2004.01.01 | 3 | 12 | 13 | 2005.10.15 | 37 | >50 | 1760 |

2005.01.01 | 4 | 18 | 18 | 2006.05.23 | 24 | >50 | 1540 |

2006.01.01 | 4 | 18 | 18 | 2006.05.23 | 24 | >50 | 1540 |

**Figure A13.**Zones of factual predictability for the earthquake of 1 April 2014 (

**a**), identified zones with similar development according to the parameters of the DSDNP equation (

**b**) and a cluster of zones of the greatest activity (

**c**) used to calculate the time and place of a precedent earthquake (see Figure A3 for explanations).

**Figure A14.**Retro predictability of the earthquake on 1 April 2014 in the zone with the highest (at the estimate date; see Figure A13, column ‘a’) number of successful predictive extrapolations (see Figure A4 for explanations).

**Table A10.**Retro estimation of the place and time of the earthquake on 1 April 2014 by the cluster of its precedent activity.

Estimate Date | z | n_{a} | n_{pr} | Calculated Date | Time Error | D_{err}, km | |
---|---|---|---|---|---|---|---|

Days | % | ||||||

2005.01.01 | 6 | 12 | 15 | 2006.12.27 | 2653 | >50 | 50 |

2006.01.01 | 5 | 33 | 60 | 2016.01.16 | 655 | 17.85 | 218 |

2007.01.01 | 6 | 36 | 66 | 2016.06.28 | 818 | 23.60 | 215 |

2008.01.01 | 4 | 26 | 126 | 2008.10.14 | 1995 | >50 | 288 |

2009.01.01 | 9 | 50 | 310 | 2009.03.28 | 1831 | >50 | 271 |

2010.01.01 | 6 | 57 | 180 | 2009.09.23 | 1652 | >50 | 258 |

2011.01.01 | 11 | 117 | 485 | 2011.10.14 | 900 | >50 | 153 |

2012.01.01 | 12 | 142 | 601 | 2012.08.31 | 579 | >50 | 152 |

2013.01.01 | 10 | 132 | 613 | 2013.01.04 | 453 | >50 | 139 |

2014.01.01 | 7 | 121 | 509 | 2014.06.10 | 70 | 43.45 | 110 |

2014.04.01 | 18 | 164 | 651 | 2014.06.14 | 74 | >50 | 76 |

**Figure A15.**Zones of factual predictability for the earthquake of 26 May 2019 (

**a**), identified zones with similar development according to the parameters of the DSDNP equation (

**b**) and a cluster of zones of the greatest activity (

**c**) used to calculate the time and place of a precedent earthquake (see Figure A3 for explanations).

**Figure A16.**Retro predictability of the earthquake on 26 May 2019 in the zone with the highest (at the estimate date; see Figure A15, column ‘a’) number of successful predictive extrapolations (see Figure A4 for explanations).

**Table A11.**Retro estimation of the place and time of the earthquake on 26 May 2019 by the cluster of its precedent activity.

Estimate Date | z | n_{a} | n_{pr} | Calculated Date | Time Error | D_{err}, km | |
---|---|---|---|---|---|---|---|

Days | % | ||||||

2006.01.01 | 4 | 22 | 42 | 2009.04.12 | 3696 | >50 | 405 |

2007.01.01 | 4 | 21 | 41 | 2009.06.19 | 3628 | >50 | 407 |

2008.01.01 | 6 | 21 | 45 | 2009.12.06 | 3458 | >50 | 382 |

2009.01.01 | 5 | 25 | 55 | 2010.03.17 | 3356 | >50 | 376 |

2010.01.01 | 4 | 25 | 61 | 2011.09.02 | 2823 | >50 | 336 |

2011.01.01 | 7 | 26 | 66 | 2012.10.22 | 2407 | >50 | 330 |

2012.01.01 | 7 | 23 | 59 | 2013.04.25 | 2222 | >50 | 320 |

2013.01.01 | 7 | 29 | 75 | 2015.08.25 | 1369 | >50 | 287 |

2014.01.01 | 6 | 34 | 93 | 2016.04.21 | 1130 | >50 | 287 |

2015.01.01 | 9 | 31 | 83 | 2015.04.29 | 1487 | >50 | 305 |

2016.01.01 | 9 | 29 | 79 | 2017.07.12 | 683 | >50 | 269 |

2017.01.01 | 9 | 22 | 62 | 2018.09.27 | 241 | 27.50 | 267 |

2018.01.01 | 8 | 16 | 46 | 2020.02.03 | 253 | 33.12 | 240 |

2019.01.01 | 8 | 15 | 42 | 2020.11.14 | 539 | >50 | 246 |

2019.05.26 | 9 | 19 | 45 | 2021.03.09 | 653 | >50 | 195 |

## Appendix C. Current Cluster Estimates of the Potential Hazard of Seismic Energy Flux

**Figure A17.**Cluster estimates of the potential hazard of seismic energy flux: 1 January 2020 (

**a**), 1 July 2020 (

**b**), 1 January 2021 (

**c**) and 1 June 2021 (

**d**). The cluster color corresponds to the number (the more, the redder) of potentially hazardous unfinished extrapolations found in the cluster. Circles with a crosshair are M7+ earthquakes that occurred after the hazard assessment date before 1 June 2021: black—in identified activity clusters and within the error band of predicted trends (full predictability, Table A12), green—in identified activity clusters with a violation of the error band of trends in the cluster (partially predictability) and blue—unrelated to clusters of potentially hazardous activity (lack of predictability).

**Table A12.**M7+ earthquakes that occurred during the period after the hazard estimation until 1 June 2021 in accordance with the extrapolation of trends in the identified clusters.

Earthquake | Number of Successful Extrapolations | ||||||
---|---|---|---|---|---|---|---|

Date | Latitude | Longitude | Depth | M | 1 January 2020 | 1 July 2020 | 1 January 2021 |

2020.07.22 | 55.072 | −158.596 | 28.0 | 7.8 | 4 | 4 | |

2020.10.30 | 37.897 | 26.784 | 21.0 | 7.0 | 3 | 3 | |

2021.02.10 | −23.051 | 171.657 | 10.0 | 7.7 | 9 | 12 | 15 |

2021.02.13 | 37.727 | 141.775 | 44.0 | 7.1 | 13 | 13 | 12 |

2021.03.04 | −37.479 | 179.458 | 10.0 | 7.3 | 11 | 11 | 11 |

2021.03.04 | −29.677 | −177.840 | 43.0 | 7.4 | 2 | 3 | |

2021.03.04 | −29.723 | −177.279 | 28.9 | 8.1 | 2 | 2 | 2 |

No. | Localization | Precedent Earthquake | Extrapolation Calculations | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Latitude | Longitude | Depth | R, km | Catalogue | M | Date | Latitude | Longitude | Depth | z | n_{a} | n_{pr} | Date | σ_{sh} | σ_{t} | |

1 | 60.778 | −150.661 | 29 | 156.8 | JMA | 8.2 | 2007.01.13 | 46.938 | 155.052 | 30.0 | 9 | 659 | 1591 | 2021.10.11 | 339 | 78 |

2 | 35.703 | −118.052 | 0 | 150.0 | JMA | 8.2 | 2007.01.13 | 46.938 | 155.052 | 30.0 | 3 | 632 | 2089 | 2021.04.22 | 84 | 107 |

3 | 62.373 | −149.723 | 23 | 300.0 | USGS | 8.3 | 1994.10.04 | 43.773 | 147.321 | 14.0 | 3 | 174 | 174 | 2023.03.07 | 205 | 21 |

4 | 36.315 | −97.421 | 0 | 300.0 | JMA | 8.2 | 1994.10.04 | 43.375 | 147.673 | 28.0 | 3 | 166 | 166 | 2023.06.09 | 184 | 4 |

5 | 56.168 | −149.196 | 0 | 152.1 | USGS | 8.0 | 2000.11.16 | −3.980 | 152.169 | 33.0 | 3 | 144 | 144 | 2018.10.31 | 99 | 353 |

6 | 63.315 | −150.986 | 33 | 271.3 | USGS | 8.0 | 2000.11.16 | −3.980 | 152.169 | 33.0 | 5 | 142 | 142 | 2023.04.20 | 298 | 79 |

7 | 60.135 | −152.369 | 66 | 150.0 | USGS | 8.6 | 2005.03.28 | 2.085 | 97.108 | 30.0 | 4 | 134 | 134 | 2023.03.05 | 517 | 47 |

8 | 60.000 | −146.939 | 0 | 300.0 | JMA | 8.0 | 2003.09.26 | 41.779 | 144.078 | 45.1 | 1 | 120 | 1048 | 2020.11.02 | 77 | 107 |

9 | 56.379 | −150.343 | 0 | 300.0 | USGS | 8.0 | 2019.05.26 | −5.812 | −75.270 | 122.6 | 2 | 115 | 293 | 2021.01.15 | 183 | 1742 |

10 | 56.497 | −150.340 | 1 | 295.1 | USGS | 8.2 | 2014.04.01 | −19.610 | −70.769 | 25.0 | 3 | 111 | 1535 | 2021.03.04 | 193 | 1351 |

11 | 60.000 | −150.612 | 4 | 300.0 | JMA | 8.2 | 1994.10.04 | 43.375 | 147.673 | 28.0 | 2 | 106 | 107 | 2022.07.19 | 224 | 82 |

12 | 56.105 | −149.212 | 0 | 150.0 | USGS | 8.1 | 2007.04.01 | −8.466 | 157.043 | 24.0 | 3 | 105 | 105 | 2018.11.22 | 30 | 346 |

13 | −21.176 | −178.075 | 600 | 300.0 | USGS | 9.1 | 2011.03.11 | 38.297 | 142.373 | 29.0 | 1 | 78 | 524 | 2046.08.20 | 1647 | 182 |

14 | 59.933 | −137.822 | 0 | 196.8 | JMA | 8.2 | 2007.01.13 | 46.938 | 155.052 | 30.0 | 5 | 77 | 311 | 2024.08.25 | 764 | 10 |

15 | 35.692 | −97.186 | 0 | 150.0 | USGS | 8.1 | 2007.01.13 | 46.243 | 154.524 | 10.0 | 3 | 73 | 73 | 2023.05.31 | 100 | 4 |

16 | 60.000 | −154.235 | 197 | 300.0 | USGS | 8.0 | 1989.05.23 | −52.341 | 160.568 | 10.0 | 2 | 72 | 72 | 2020.09.12 | 157 | 221 |

17 | 39.420 | −122.955 | 0 | 117.9 | USGS | 8.1 | 2007.01.13 | 46.243 | 154.524 | 10.0 | 3 | 70 | 78 | 2025.05.19 | 1635 | 1 |

18 | 60.129 | −152.069 | 81 | 150.0 | USGS | 8.0 | 1972.12.02 | 6.405 | 126.640 | 60.0 | 3 | 69 | 69 | 2024.03.17 | 435 | 208 |

19 | 35.581 | −117.783 | 0 | 60.0 | USGS | 8.0 | 2000.11.16 | −3.980 | 152.169 | 33.0 | 3 | 65 | 65 | 2021.04.06 | 68 | 235 |

20 | 61.765 | −149.032 | 0 | 300.0 | USGS | 8.3 | 2013.05.24 | 54.892 | 153.221 | 598.1 | 1 | 58 | 59 | 2023.04.23 | 37 | 27 |

21 | 38.014 | −117.949 | 1 | 60.0 | USGS | 8.2 | 2014.04.01 | −19.610 | −70.769 | 25.0 | 3 | 56 | 380 | 2021.06.27 | 8 | 28 |

22 | −15.882 | −173.658 | 4 | 300.0 | USGS | 9.1 | 2011.03.11 | 38.297 | 142.373 | 29.0 | 3 | 55 | 480 | 2021.07.05 | 439 | 420 |

23 | −6.991 | 106.003 | 35 | 300.0 | USGS | 8.2 | 2014.04.01 | −19.610 | −70.769 | 25.0 | 4 | 52 | 579 | 2047.08.28 | 1178 | 166 |

24 | 44.446 | −114.974 | 0 | 60.0 | USGS | 8.1 | 2007.01.13 | 46.243 | 154.524 | 10.0 | 2 | 45 | 46 | 2021.05.24 | 49 | 56 |

25 | 60.000 | −150.612 | 0 | 300.0 | USGS | 8.2 | 2017.09.08 | 15.022 | −93.899 | 47.4 | 1 | 40 | 40 | 2024.01.11 | 139 | 133 |

26 | −7.059 | 148.782 | 0 | 300.0 | USGS | 9.1 | 2011.03.11 | 38.297 | 142.373 | 29.0 | 2 | 39 | 288 | 2047.03.29 | 1005 | 159 |

27 | 56.471 | −151.969 | 0 | 300.0 | USGS | 8.4 | 2001.06.23 | −16.265 | −73.641 | 33.0 | 2 | 39 | 42 | 2020.05.30 | 318 | 518 |

28 | −55.436 | −28.624 | 11 | 243.2 | USGS | 8.0 | 2013.02.06 | −10.799 | 165.114 | 24.0 | 6 | 37 | 68 | 2027.10.11 | 1569 | 390 |

29 | 56.507 | −150.391 | 1 | 293.1 | USGS | 8.0 | 2013.02.06 | −10.799 | 165.114 | 24.0 | 2 | 35 | 35 | 2021.11.07 | 38 | 1669 |

30 | 60.000 | −150.612 | 0 | 300.0 | USGS | 9.1 | 2004.12.26 | 3.295 | 95.982 | 30.0 | 1 | 35 | 35 | 2021.11.23 | 14 | 5 |

31 | 40.791 | −122.997 | 0 | 260.9 | USGS | 8.2 | 2014.04.01 | −19.610 | −70.769 | 25.0 | 5 | 33 | 209 | 2039.12.25 | 2661 | 515 |

32 | −20.802 | 171.203 | 0 | 300.0 | USGS | 9.1 | 2011.03.11 | 38.297 | 142.373 | 29.0 | 3 | 33 | 182 | 2044.06.24 | 3548 | 177 |

33 | 51.386 | −178.552 | 0 | 150.0 | USGS | 8.0 | 1985.03.03 | −33.135 | −71.871 | 33.0 | 2 | 33 | 33 | 2024.07.08 | 58 | 14 |

34 | 18.363 | 145.800 | 191 | 187.5 | USGS | 8.4 | 2007.09.12 | −4.438 | 101.367 | 34.0 | 6 | 32 | 61 | 2024.10.17 | 795 | 412 |

35 | −55.336 | −28.189 | 0 | 300.0 | USGS | 8.2 | 2014.04.01 | −19.610 | −70.769 | 25.0 | 4 | 28 | 356 | 2026.01.31 | 1035 | 361 |

36 | −30.843 | −71.904 | 15 | 238.9 | USGS | 8.4 | 2007.09.12 | −4.438 | 101.367 | 34.0 | 5 | 27 | 47 | 2019.09.01 | 344 | 479 |

37 | −22.277 | −68.410 | 100 | 150.0 | USGS | 8.1 | 2007.04.01 | −8.466 | 157.043 | 24.0 | 1 | 25 | 46 | 2039.10.29 | 540 | 151 |

38 | 22.426 | 143.047 | 38 | 290.0 | USGS | 8.2 | 2014.04.01 | −19.610 | −70.769 | 25.0 | 4 | 24 | 51 | 2025.01.24 | 1611 | 796 |

39 | −3.529 | −77.411 | 67 | 300.0 | USGS | 8.2 | 2014.04.01 | −19.610 | −70.769 | 25.0 | 5 | 24 | 276 | 2023.10.28 | 1329 | 602 |

40 | −18.713 | −174.459 | 0 | 150.0 | USGS | 8.0 | 2000.11.16 | −3.980 | 152.169 | 33.0 | 2 | 24 | 24 | 2035.01.22 | 1189 | 83 |

41 | 37.649 | −119.053 | 0 | 60.0 | JMA | 9.0 | 2011.03.11 | 38.103 | 142.861 | 23.7 | 2 | 24 | 46 | 2022.02.16 | 79 | 0 |

42 | 36.215 | −118.069 | 0 | 60.0 | USGS | 8.2 | 2014.04.01 | −19.610 | −70.769 | 25.0 | 1 | 23 | 59 | 2027.03.15 | 256 | 1 |

43 | 65.971 | −157.210 | 2 | 139.6 | USGS | 8.2 | 2014.04.01 | −19.610 | −70.769 | 25.0 | 3 | 23 | 27 | 2022.01.12 | 73 | 1 |

44 | 7.355 | 92.847 | 26 | 289.6 | USGS | 8.2 | 2014.04.01 | −19.610 | −70.769 | 25.0 | 7 | 23 | 97 | 2031.01.09 | 1262 | 534 |

45 | 38.320 | −117.931 | 0 | 60.0 | USGS | 8.1 | 2007.01.13 | 46.243 | 154.524 | 10.0 | 4 | 23 | 23 | 2021.05.02 | 70 | 37 |

46 | 62.376 | −150.652 | 0 | 150.0 | USGS | 8.0 | 1985.03.03 | −33.135 | −71.871 | 33.0 | 1 | 23 | 23 | 2022.02.16 | 13 | 129 |

47 | 52.645 | −168.533 | 48 | 288.6 | USGS | 8.2 | 2014.04.01 | −19.610 | −70.769 | 25.0 | 4 | 21 | 225 | 2027.04.03 | 878 | 290 |

48 | −28.600 | −71.601 | 10 | 150.0 | USGS | 8.0 | 2000.11.16 | −3.980 | 152.169 | 33.0 | 4 | 21 | 21 | 2023.08.25 | 1210 | 244 |

49 | 19.574 | −66.403 | 27 | 145.5 | JMA | 8.2 | 2007.01.13 | 46.938 | 155.052 | 30.0 | 3 | 20 | 44 | 2023.03.22 | 447 | 11 |

50 | 18.150 | 145.949 | 189 | 279.0 | USGS | 8.2 | 2014.04.01 | −19.610 | −70.769 | 25.0 | 7 | 20 | 24 | 2025.06.23 | 522 | 491 |

51 | 34.853 | −120.095 | 0 | 300.0 | JMA | 8.0 | 2003.09.26 | 41.779 | 144.078 | 45.1 | 2 | 20 | 48 | 2021.05.14 | 63 | 88 |

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**Figure 1.**Geometric constructions used to calculate the shortest distance h from the factual point (t

_{f},x

_{f}) to the calculated curve and determine the coordinates of the point (t

_{i},x

_{i}) on the calculated curve closest to this factual point. For explanations, see the text.

**Table 1.**Distribution of the number of strong earthquakes used as precedents and their retro-forecasts by magnitude M and catalogs.

M | JMA Catalog | USGS Catalog | Total | |||
---|---|---|---|---|---|---|

N_{sh} | N_{pr} | N_{sh} | N_{pr} | N_{sh} | N_{pr} | |

9.5 | 1 | 1 | 1 | 1 | ||

9.1 | 2 | 40 | 2 | 40 | ||

9.0 | 1 | 150 | 1 | 150 | ||

8.6 | 2 | 7 | 2 | 7 | ||

8.5 | 1 | 2 | 1 | 2 | ||

8.4 | 3 | 197 | 3 | 197 | ||

8.3 | 3 | 19 | 3 | 19 | ||

8.2 | 2 | 253 | 6 | 275 | 8 | 528 |

8.1 | 2 | 5 | 4 | 69 | 6 | 74 |

8.0 | 2 | 405 | 13 | 141 | 15 | 546 |

total | 7 | 813 | 35 | 751 | 42 | 1564 |

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**MDPI and ACS Style**

Malyshev, A.; Malysheva, L. Global Precedent-Based Extrapolation Estimate of the M8+ Earthquake Hazard (According to USGS Data as of 1 June 2021). *GeoHazards* **2022**, *3*, 16-53.
https://doi.org/10.3390/geohazards3010002

**AMA Style**

Malyshev A, Malysheva L. Global Precedent-Based Extrapolation Estimate of the M8+ Earthquake Hazard (According to USGS Data as of 1 June 2021). *GeoHazards*. 2022; 3(1):16-53.
https://doi.org/10.3390/geohazards3010002

**Chicago/Turabian Style**

Malyshev, Aleksandr, and Lidiia Malysheva. 2022. "Global Precedent-Based Extrapolation Estimate of the M8+ Earthquake Hazard (According to USGS Data as of 1 June 2021)" *GeoHazards* 3, no. 1: 16-53.
https://doi.org/10.3390/geohazards3010002