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Constructing a statistical model to characterize the physical conditions associated with large earthquake occurrence is crucial for disaster mitigation. With the aim to formulate such a model, we previously developed a statistical evaluation system which assesses the correlation of the spatiotemporal relationship between different kinds of physical quantities with the occurrence times of large inland earthquakes. In this study, we focused on assessing the relationship between geodetic and seismic quantities and attempted to find the pair of related quantities that most likely indicates preparatory processes of large earthquakes in Japan. We assessed the quantities prior to M ≥ 6.0 inland earthquakes for the period of 2001–2007 in terms of probability gains and error diagram. Our system revealed that the pair of absolute value of dilatation rate and seismic energy showed the highest statistical performance. Further validation of this result is required by updating the database of physical quantities.

It is an urgent issue for disaster mitigation to develop a statistical model well reflecting crustal activities, which are expected to include the preparatory processes of large inland earthquakes. Resolution of this issue requires a comprehensive understanding and monitoring of crustal activities through more than one kind of physical observation. Therefore, keeping this in mind, in this study, we focused on examining the spatiotemporal relationships between different physical quantities, at least one of which is time-variable. By determining informative combinations of physical quantities, that is, those having some correlation, we aim to develop a monitoring index/indices in crustal activities which feature the preparatory processes of large inland earthquakes for Japan. Imoto [

As the first step toward formulating a model to capture statistical and physical conditions for the occurrence of large inland earthquakes, we created a database of physical observations with spatially and temporally gridded formats (Figure

Tabulated information on input parameters required at each step of statistical evaluation system. The related schematic explanation should be referred to Figure

No. | Parameter |
---|---|

(1) | Range of region for analysis (inland Japan) |

(2) | Interval between spatial grids (0.05°) |

(3) | Interval between time grids (three month) |

(4) | Time period referred to for calculating physical quantities such as dilatation rate for each time grid (two years) |

(5) | Range of depth (0 ≤ depth ≤ 30 km) |

(6) | Range of magnitude (M ≥ 1.0) |

(7) | Smoothing (weight-adjusting) parameters for obtaining spatially gridded physical quantities (refer to Figure |

(8) | Search radius for applying smoothing parameters to area centered at a calculation grid (Figure |

(9) | Search radius for calculating statistical index for a calculation grid (60 km) |

(10) | Approval method for classifying the temporal change in statistical index |

(11) | Confidence level for statistical approval (95%) |

(12) | Calculation period of total seismic energy released following calculation period of temporal change in statistical index |

(13) | Lower limit of total seismic energy released during period (12) which is regarded as seismically active (Figure |

(14) | Definition of large inland earthquakes (lower limit of magnitudes) (M ≥ 6.0) |

Gridded maps for (a) dilatation rate, (b) maximum shear strain rate, (c) seismic energy [

(a) Schematic explanation on the method of obtaining geodetic quantities (dilatation rate and maximum shear strain rate) and seismic quantities (seismic energy and number of earthquakes) for each grid, which were calculated by relating them to the displacement rates for GPS stations (open triangle) and the magnitudes for hypocenters (open circle) in circular area, respectively. We weighted the observation errors for GPS stations and seismic quantities for hypocenters depending on the distances between the calculation grid (black square) and the other grids in circular area, respectively. The vertical axis of each right figure in which weight curve is delineated shows the distances relative to the calculation grid. (b) Schematic explanation on the approach of obtaining Figures

Here, we actually operated the system to examine the relationship between two physical quantities and the occurrence times of

The statistical evaluation system developed by Kawamura et al. [

We created a database comprising items (a) to (d) in Figure

We here explain the method of making physical quantities (a) to (d) (Figure

To obtain seismic energy (c) and the number of earthquakes (d) for each grid point, the earthquakes within a radius of 60 km of grid point with depths shallower than 30 km and magnitudes ≥1.0 were collected (Figure

Spatial distributions of linear trends of statistical index ^{10} Nm) was radiated during one year after the time period shown in panel (c) and (d). Linear trends of

After the selection of one of the four possible pairs (here, the absolute value of dilatation rate and seismic energy (per two years), maximum shear strain rate and seismic energy, absolute value of dilatation rate and the number of earthquakes (per two years), and maximum shear strain rate and the number of earthquakes), its relationship was examined using scatter diagrams for circular regions, each having 60-km radius centered in 0.05°-by-0.05° spatial grids, over inland Japan; each pair was compared for two-year time windows centered in a three-month-interval time grid.

Quantification of the relationship between geodetic and seismic quantities requires us to define an index well characterizing the relationship. We here define the index as a statistical index

For a particular circular region centered in a spatial grid and for a two-year time window centered in a time grid, the mean of the absolute value of dilatation rate or the maximum shear strain rate was calculated from the grids ranking in the top 20% in terms of seismic energy or number of earthquakes. We defined this parameter as statistical index

Process (1) was carried out for each time window which is moved by three months. The linear trend of

Processes (1) and (2) are carried out for every spatial grid with an interval of 0.05°.

The relationship between the occurrence times of large inland mainshocks and different types of statistical index

the number of cases in which physical events of interest occur during the period of

the number of cases in which physical events did not occur during the period of

the number of cases in which physical events of interest occur during the period of

the number of cases in which physical events did not occur during the period of

Model contingency table for explaining the relationship between potential conditions for/against the occurrence of physical events such as large inland earthquakes and their actual occurrence. The relation can be classified into the following four elements:

Potential condition for event occurrence | Event occurrence | |

Yes | No | |

Positive | ||

Negative |

By this definition,

Total number of the periods of

Total number of periods in which physical events of interest occurred.

If an event occurs during the time period of

We here focused on time variations of spatial grid counts which are accompanied by one-year release of total seismic energy larger than or equal to M4.0 earthquake (6.0 × 10^{10} Nm); the seismically active grid counts are specifically defined as no. PTN1 for those of significant decrease in

Contingency table showing the relationship between proposed potential conditions associated with the occurrence of M ≥ 6.0 inland mainshocks for four pairs of geodetic and seismic quantities and their actual occurrence times. The four figures for each element correspond to the following four pairs of geodetic and seismic quantities from left: the absolute value of dilatation rate and seismic energy, maximum shear strain rate and seismic energy, absolute value of dilatation rate and the number of earthquakes, and maximum shear strain rate and the number of earthquakes. A proposed potential condition occurring prior to the occurrence of inland mainshocks, Δ(no. PTN1/no. PTN2)<0, implies that the trend of no. PTN1/no. PTN2 is negative (Figure

Occurrence of inland earthquakes (M ≥ 6) | Nonoccurrence | Alarm rate | |
---|---|---|---|

5/5/4/3 | 7/12/7/10 | 0.417/0.294/0.364/0.231 | |

0/0/1/2 | 13/8/13/10 | ||

Success rate | 1.00/1.00/0.80/0.60 |

Probability gains of AR and SR: 3.56/2.49/3.00/1.97 and 3.58/3.49/2.73/2.13.

Temporal variation in no. PTN1, no. PTN2, and no. PTN3 (ref. Figure

Temporal variation in the ratio of no. PTN1 to no. PTN2 (ref. Figure

Statistical evaluation process at

We applied the bootstrap method to shuffle the spatial distributions of no. PTNs1–3 grids and their corresponding seismically inactive grids for a particular time window.

Process (1) was carried out by moving the time window with its beginning time grid fixed. By repeating this, we obtained the temporal variation of the shuffled spatial distributions.

We applied the bootstrap method to shuffle the temporal variation obtained in process (2).

Processes (1) to (3) were repeated 100 times.

The 100 ARs and SRs obtained were averaged.

Thus, calculated references AR and SR were considered as being due to a random phenomenon.

Among the four pairs of geodetic and seismic quantities examined, the pair comprising the absolute value of dilatation rate and seismic energy was found to be the most closely related in terms of probability gains of both alarm rate (AR) and success rate (SR) for M ≥ 6.0 inland mainshocks (3.56 and 3.58, resp.) (Table

Error diagram (Molchan diagram) for evaluating the significance of the performance of a proposed potential condition for the occurrence of large inland earthquakes.

On the assumption that this tendency holds for even a small region influenced by a change in Coulomb failure stress (

Based on the notion that there are some correlations between different kinds of observations that may represent different aspects of crustal phenomena, we began with creating a database of various physical quantities and further constructed a basic system for statistically evaluating and validating a monitoring index which would reflect crustal activities associated with the occurrence of physical events such as large inland earthquakes. We have indicated that the most informative pair of geodetic and seismic quantities comprises the absolute value of dilatation rate and seismic energy in terms of probability gains of alarm rate (AR) and success rate (SR) and error diagram for M ≥ 6.0 inland mainshocks. The probability gains were calculated on the basis of contingency tables which show the relationship between the temporal changes in linear trends of statistical index

The authors deeply acknowledge valuable comments provided by two anonymous reviewers, which highly contributed to the improvement of the manuscript. They are also grateful to Geospatial Information Authority of Japan, and Japan Meteorological Agency for letting them utilize GEONET (GPS Earth Observation NETwork) data and unified hypocenter catalog, respectively.