# Performance of a seismicity model for earthquakes in Japan (*M* ≥ 5.0) based on *P*-wave velocity anomalies

- Masajiro Imoto
^{1}Email author

**63**:11

https://doi.org/10.5047/eps.2010.06.005

© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2011

**Received: **8 March 2010

**Accepted: **18 June 2010

**Published: **4 March 2011

## Abstract

We consider *P*-wave perturbations from a standard layered model for Japan, as a predictive parameter that may be useful for assessing regional seismogenesis. To assess the performance of a seismicity model with predictive parameters, we used the Kullback-Leibler statistic in terms of information gain per event (IGpe), which is the distance between two distributions of parameters, the background distribution (parameters over the entire space domain), and the conditional distribution (parameters at earthquake epicenters). We selected 198 epicenters of earthquakes with magnitudes ≥5.0 that occurred between 1961 and 2008 to estimate the conditional distribution. More than 3,000 points were selected at every point on a 0.1 × 0.1° grid for the background distribution. *P*-wave variations were considered at four different depths (10, 15, 20, and 25 km at each point) for both distributions. We compared the two distributions at each depth but found no significant difference in the average value of perturbations between them. As these distributions are well-approximated by normal distributions, IGpe can be estimated directly from the means and standard deviations of both distributions at each depth. We obtained an IGpe of ≤0.03 using a single parameter. However, when multiple parameters with correlations were considered, an IGpe of 0.3 was estimated, which means that the average probability across the 198 earthquakes is 1.35-fold higher than that of a Poisson process model.

### Key words

Seismicity model information gain Kullback-Leibler quantity*P*-wave velocity structure predictive parameters correlation Japan

## 1. Introduction

Seismicity models provide some of the most useful products in earthquake prediction research. The incorporation of various predictive parameters could result in better performing models. Utsu (1977), 1982) and many others (Rhoades and Evison, 1979; Aki, 1981; Hamada, 1983; Grandori et al., 1988) have formulated expressions for earthquake probabilities based on precursory anomalies from a variety of measurements. Imoto (2006, 2007) proposed a method to build models based on multiple predictive parameters in which independence among parameters is not necessarily assumed as it has been in previous studies. His result implies that mutual correlations among predictive parameters for certain conditions could produce a better performance than expected for those cases in which the parameters are independent.

With the development of dense seismic networks and computational power, seismic wave velocity structures have been modeled to higher resolutions than has previously been possible. Seismogenesis must be closely related to the physical properties (e.g., pressure, temperature, and properties of geology) of focal areas. Of these, the *P*-wave velocity is more generally and systematically sampled than any other parameter. Many issues are involved in the relationship between seismic wave velocity perturbations and seismicities, and some of these have been discussed in only limited terms (i.e., AL-Shukri and Mitchell, 1988; Michael, 1988; Kaufmann and Long, 1996; Hauksson and Haase, 1997).

In the 1970s, a large body of literature was published on changes in seismic velocity before earthquakes. A change in *P*-wave velocity was interpreted using the dilatancy theory (hypothesis) that rocks underwent dilatation in the last stage before failure (Nur, 1972; Scholz et al., 1973). To date, systematic and homogeneous measurements detecting such variations have not been obtained. Consequently, in the study reported here, variations in seismic velocity over time are not discussed.

After the Hi-net seismic network was established in Japan (Obara et al., 2005), Matsubara et al. (2008) revealed fine structures of *P*- and *S*-wave velocities in Japan. Some of their remarkable findings are as follows. The high-velocity Pacific plate and Philippine Sea plate are clearly imaged to the depth of 150 km beneath northeastern and the southwestern Japan, respectively. High-*V*_{
p
}/*V*_{
s
} (*P*-wave velocity by *S*-wave velocity) zones are widely distributed beneath the volcanic front where seismic swarm activities, including moderately sized earthquakes, have often been observed. Non-volcanic tremors occur in the high-*V*_{
p
}/*V*_{
s
} zone at depths of 30–40 km beneath southwestern Japan where the oceanic crust of the Philippine Sea plate encounters the wedge mantle of the Eurasian plate.

Matsubara and Obara (2008) reported characteristic features of the perturbations in zones beneath active faults, and this information may be incorporated into the construction of a seismicity model that performs better than any previous model. However, before building such a model, it is necessary to appropriately evaluate the information of each contributing parameter.

In the study reported here, we evaluate model performance in terms of information gain per event (IGpe; Daley and Vere-Jones, 2003; Imoto, 2004) in order to incorporate information on the *P*-wave velocity structure into current seismicity models. The results present a good example of cases in which correlations among predictive parameters increase predictive power more than those without correlations.

## 2. Method

*θ*, which are represented by

*g*(

*θ*)

*dθ*(background density) and

*f*(

*θ*)

*dθ*(conditional density) and which are empirically determined with random samples of cells in the whole study volume and samples conditioned on occurrences of earthquakes in some cells. The hazard function at a space-time point (

*x*), conditioned on a value of

*θ*(

*x*), is given bywhere

*m*

_{0}is the number of earthquakes above the threshold, and

*V*

_{0}is the space-time volume being studied (see Appendix).

*θ*defined,

*R*. The above equation represents the fact that IGpe is equivalent to the Kullback-Leibler quantity of information expressing the distance between two probability distributions. Assuming that

*f*(

*θ*) and

*g*(

*θ*) are normal multivariate distributions, Imoto (2007) derived an analytical equation to estimate the IGpe value.

*θ*

_{1}, the IGpe(

*θ*

_{1}) can be represented aswhere

*μ*

_{1}is the mean, and is the variance of

*f*(

*θ*

^{1}), and those of

*g*(

*θ*

^{1}) are scaled to be 0 (mean) and 1 (variance).

*n*variables

*θ*

_{1},

*θ*

_{2},…

*θ*

_{ n }as possessing joint density distributions

*f*(

*θ*

_{1},

*θ*

_{2}, …

*θ*

_{ n }) and

*g*(

*θ*

_{1},

*θ*

_{2}, …

*θ*

_{ n }), and their marginal distributions of

*θ*

_{ i }are noted as

*f*

_{ i }(

*θ*

_{ i }) for the conditional distribution and

*g*

_{ i }(

*θ*

_{ i }) for the background distribution. If variables

*θ*

_{1},

*θ*

_{2}, …

*θ*

_{ n }are mutually independent in both distributions and are normally distributed with the mean

*μ*

_{ i }, and variance for the conditional distribution and 0 and 1 for the background distribution, the IGpe can be represented as follows.We assume here that the correlation among the

*n*variables

*θ*

_{1},

*θ*

_{2}, …

*θ*

_{ n }only occurs in the conditional density distribution

*f*(

*θ*

_{1},

*θ*

_{2}, …

*θ*

_{ n }):where the superscript −1 refers to the inverse of a matrix, and the covariance matrix

**C**can be expressed aswhere

*ρ*

_{ ij }is the correlation coefficient between

*θ*

_{ i }and

*θ*

_{ j }.

*θ*) coordinate system with an orthogonal matrix, the covariance matrix can be expressed as a diagonal matrix. At the same time, the vector μ is transformed into μ′ with the same orthogonal matrix. Referring to the previous case, the IGpe is represented bywhere trace denotes the sum of the diagonal elements and is an invariant parameter for a unitary transformation, and represent the eigenvalues of

**C**. Comparing Eqs. (7) and (4), the first term in the right side of Eq. (7) exceeds that of Eq. (4) unless every

*ρ*

_{ ij }is zero. The other three terms have the same values in both equations. Therefore, the IGpe for a conditional distribution of correlated variables always exceeds that with no correlation.

In general, some correlations among parameters may be observed in both distributions. The procedure from Eq. (5) to Eq. (7) could be applied after the covariance matrix for the background distribution is changed into the identity matrix by transformations of the coordinate system with an orthogonal matrix and a diagonal matrix.

Once we have estimated the means and variances of the parameters together with the correlation matrices for both the conditional and the background distributions, we can represent them by *f* (*θ*) and *g*(*θ*) and thus calculate the hazard function of Eq. (1). This function estimates the hazard rate at any point of interest conditioned on the parameter values observed at that point.

## 3. Data

We consider a seismicity model for earthquakes *M* ≥ 5.0 in Japan based on *P*-wave velocity perturbation data. We use the hypocenter parameters for 1961–2008 determined by the Japan Meteorological Agency (JMA). This period is selected to balance both the number of earthquakes and the accuracy of estimated locations. In terms of the complex tectonic setting in and around Japan, we restricted ourselves to earthquakes shallower than 30 km.

Matsubara et al. (2008) constructed three-dimensional *P*- and *S*-wave velocity models beneath all of Japan at depths of 0–40 km, with a 0.2° grid spacing in the horizontal direction and a 5- to 10-km spacing in the vertical direction. They also constructed a velocity model down to the depth of 400 km with less densely spaced grids. In general, velocity variations from a standard velocity model are estimated since *P*- and *S*-wave velocities strongly depend on depth. Therefore, comparing variations at the same depth may be useful for obtaining characteristic seismogenic features of a focal area.

*P*-wave velocity differences at four different depths (10, 15, 20, and 25 km) for each point are used. We consider that a set of these four parameters plays important roles as predictive parameters. More than 3,000 points with reliable velocity anomalies are selected at every point of a 0.1 × 0.1° grid for the background distributions, which mostly cover inland parts of Japan, with the exception of Hokkaido Island. To estimate the conditional distributions, we select 198 epicenters of earthquakes (Table 1) with magnitudes >5.0 that occurred between 1961 and 2008.

List of target earthquakes used for the conditional distribution.

YMD | HH | MM | Lat | Long | Depth | Mag | Gain | Ln (Gain) |
---|---|---|---|---|---|---|---|---|

1961/2/2 | 3 | 39 | 37.45 | 138.84 | 0 | 5.2 | 1.59 | 0.47 |

1961/3/16 | 7 | 16 | 32.02 | 130.69 | 0 | 5.3 | 1.66 | 0.51 |

1961/3/18 | 15 | 22 | 31.99 | 130.77 | 3.1 | 5.1 | 1.69 | 0.53 |

1961/5/7 | 21 | 14 | 35.05 | 134.51 | 23 | 5.9 | 1.85 | 0.62 |

1961/8/19 | 14 | 33 | 36.11 | 136.7 | 10 | 7 | 0.70 | −0.36 |

1961/8/19 | 22 | 24 | 36.54 | 137.68 | 0 | 5 | 1.87 | 0.63 |

1962/3/13 | 15 | 7 | 37.07 | 139.13 | 3 | 5.1 | 2.44 | 0.89 |

1962/4/30 | 11 | 26 | 38.74 | 141.14 | 19 | 6.5 | 1.31 | 0.27 |

1962/12/10 | 6 | 16 | 39.8 | 140.87 | 16 | 5 | 0.66 | −0.42 |

1963/1/28 | 13 | 5 | 43.59 | 144.71 | 10 | 5.3 | 1.52 | 0.42 |

1963/2/9 | 12 | 53 | 36.35 | 137.69 | 0 | 5.4 | 1.86 | 0.62 |

1963/3/27 | 6 | 34 | 35.81 | 135.79 | 13.1 | 6.9 | 1.57 | 0.45 |

1963/3/31 | 21 | 26 | 35.13 | 132.42 | 12 | 5.1 | 1.55 | 0.44 |

1963/4/21 | 22 | 2 | 35.26 | 137.61 | 4.1 | 5 | 1.41 | 0.35 |

1963/7/24 | 20 | 50 | 35.84 | 137.01 | 7 | 5 | 1.61 | 0.48 |

1963/7/30 | 17 | 27 | 33.86 | 135 | 8.1 | 5.2 | 0.78 | −0.25 |

1963/8/11 | 16 | 37 | 38.72 | 141.15 | 8 | 5.2 | 1.17 | 0.15 |

1964/6/16 | 13 | 17 | 38.65 | 139.52 | 0 | 6.1 | 1.71 | 0.54 |

1964/6/16 | 15 | 52 | 38.02 | 139.01 | 15.1 | 5.6 | 0.57 | −0.56 |

1964/11/3 | 20 | 9 | 34.74 | 138.84 | 0 | 5.3 | 0.93 | −0.07 |

1965/1/13 | 17 | 40 | 38.72 | 141.13 | 0 | 5.2 | 1.19 | 0.18 |

1965/2/26 | 15 | 42 | 35.27 | 132.73 | 20 | 5.1 | 1.41 | 0.35 |

1965/4/20 | 8 | 41 | 34.88 | 138.3 | 20 | 6.1 | 3.02 | 1.11 |

1965/8/31 | 16 | 48 | 43.48 | 144.43 | 0 | 5.1 | 0.93 | −0.07 |

1965/9/9 | 13 | 39 | 43.47 | 144.3 | 0 | 5.1 | 1.55 | 0.44 |

1965/11/23 | 2 | 57 | 36.52 | 138.23 | 0 | 5 | 2.07 | 0.73 |

1966/1/9 | 7 | 39 | 37.15 | 138.55 | 0 | 5.2 | 0.42 | −0.86 |

1966/1/23 | 20 | 15 | 36.52 | 138.22 | 0 | 5.1 | 2.10 | 0.74 |

1966/4/5 | 17 | 51 | 36.58 | 138.32 | 0 | 5.4 | 2.09 | 0.74 |

1966/5/6 | 19 | 8 | 36.52 | 138.25 | 0 | 5 | 2.06 | 0.72 |

1966/5/26 | 7 | 49 | 35.35 | 136.5 | 20 | 5.1 | 1.75 | 0.56 |

1966/5/28 | 14 | 21 | 36.57 | 138.22 | 0 | 5.3 | 2.84 | 1.04 |

1966/6/12 | 9 | 43 | 36.53 | 138.32 | 0 | 5 | 2.04 | 0.71 |

1966/6/26 | 16 | 34 | 36.55 | 138.35 | 0 | 5 | 1.77 | 0.57 |

1966/8/3 | 3 | 48 | 36.47 | 138.2 | 0 | 5.3 | 2.02 | 0.7 |

1966/8/8 | 9 | 37 | 36.53 | 138.32 | 0 | 5.1 | 2.04 | 0.71 |

1966/8/28 | 13 | 9 | 36.47 | 138.13 | 0 | 5.3 | 1.43 | 0.36 |

1966/8/29 | 0 | 36 | 36.57 | 138.25 | 0 | 5.1 | 2.52 | 0.92 |

1966/9/14 | 10 | 14 | 36.57 | 138.25 | 0 | 5 | 2.52 | 0.92 |

1966/10/26 | 3 | 4 | 36.55 | 138.37 | 0 | 5.3 | 1.58 | 0.46 |

1966/11/12 | 21 | 1 | 33.07 | 130.27 | 20 | 5.5 | 1.54 | 0.43 |

1966/12/5 | 16 | 23 | 32.33 | 131.82 | 0 | 5 | 1.11 | 0.11 |

1967/1/16 | 12 | 32 | 36.48 | 138 | 0 | 5.2 | 2.32 | 0.84 |

1967/2/3 | 17 | 17 | 36.43 | 138.07 | 0 | 5.4 | 1.40 | 0.34 |

1967/3/2 | 3 | 39 | 36.5 | 138.3 | 0 | 5.1 | 1.87 | 0.62 |

1967/5/5 | 8 | 25 | 36.4 | 138.05 | 10 | 5.2 | 1.15 | 0.14 |

1967/9/14 | 19 | 38 | 36.43 | 138.15 | 10 | 5.1 | 1.58 | 0.46 |

1967/10/14 | 4 | 48 | 36.53 | 138.2 | 10 | 5.3 | 2.41 | 0.88 |

1967/11/4 | 23 | 30 | 43.48 | 144.27 | 20 | 6.5 | 1.53 | 0.42 |

1968/1/26 | 16 | 55 | 36.52 | 138.15 | 0 | 5.3 | 1.71 | 0.53 |

1968/2/21 | 10 | 44 | 32.02 | 130.72 | 0 | 6.1 | 1.78 | 0.57 |

1968/3/25 | 0 | 58 | 32.02 | 130.72 | 0 | 5.7 | 1.78 | 0.57 |

1968/3/30 | 4 | 4 | 34.17 | 135.17 | 0 | 5 | 1.98 | 0.68 |

1968/4/4 | 19 | 54 | 36.57 | 138.18 | 0 | 5.1 | 2.78 | 1.02 |

1968/6/15 | 11 | 14 | 37.15 | 138.67 | 10 | 5 | 0.66 | −0.42 |

1968/8/18 | 16 | 12 | 35.22 | 135.38 | 0 | 5.6 | 1.58 | 0.46 |

1968/9/21 | 7 | 25 | 36.82 | 138.27 | 10 | 5.3 | 0.42 | −0.88 |

1969/9/2 | 21 | 7 | 36.2 | 137.72 | 0 | 5 | 1.68 | 0.52 |

1969/9/9 | 14 | 15 | 35.78 | 137.07 | 0 | 6.6 | 3.03 | 1.11 |

1970/2/27 | 19 | 13 | 36.97 | 137.65 | 0 | 5.1 | 0.90 | −0.11 |

1970/4/9 | 1 | 43 | 36.43 | 138.1 | 0 | 5 | 1.11 | 0.1 |

1970/10/16 | 14 | 26 | 39.2 | 140.75 | 0 | 6.2 | 2.14 | 0.76 |

1971/2/26 | 4 | 27 | 37.13 | 138.35 | 0 | 5.5 | 2.00 | 0.69 |

1971/7/23 | 7 | 7 | 35.55 | 138.97 | 10 | 5.3 | 1.00 | 0 |

1972/4/14 | 4 | 29 | 34.9 | 132.93 | 10 | 5.2 | 0.64 | −0.45 |

1972/8/20 | 19 | 9 | 38.6 | 139.95 | 20 | 5.3 | 1.69 | 0.52 |

1972/8/31 | 16 | 54 | 35.28 | 135.62 | 10 | 5.1 | 1.65 | 0.5 |

1972/8/31 | 17 | 7 | 35.88 | 136.77 | 10 | 6 | 2.45 | 0.9 |

1972/9/6 | 20 | 42 | 32.75 | 130.43 | 10 | 5.2 | 1.13 | 0.12 |

1973/2/25 | 19 | 9 | 34.73 | 132.42 | 0 | 5 | 1.01 | 0.01 |

1973/9/21 | 11 | 21 | 35.1 | 134.52 | 10 | 5.1 | 2.53 | 0.93 |

1973/10/27 | 13 | 44 | 35.2 | 133.27 | 10 | 5.1 | 2.99 | 1.1 |

1974/5/9 | 8 | 33 | 34.57 | 138.8 | 10 | 6.9 | 0.81 | −0.21 |

1975/1/23 | 23 | 19 | 33 | 131.13 | 0 | 6.1 | 1.83 | 0.6 |

1975/4/21 | 2 | 35 | 33.13 | 131.33 | 0 | 6.4 | 1.89 | 0.64 |

1976/6/16 | 7 | 36 | 35.5 | 139 | 20 | 5.5 | 2.04 | 0.72 |

1976/8/18 | 2 | 18 | 34.78 | 138.95 | 0 | 5.4 | 0.33 | −1.11 |

1977/5/2 | 1 | 23 | 35.15 | 132.7 | 10 | 5.6 | 1.17 | 0.16 |

1977/6/28 | 11 | 46 | 32.9 | 130.72 | 10 | 5.3 | 1.54 | 0.43 |

1978/1/15 | 7 | 31 | 34.83 | 138.88 | 20 | 5.8 | 0.06 | −2.73 |

1978/6/4 | 5 | 3 | 35.08 | 132.7 | 0 | 6.1 | 1.07 | 0.07 |

1978/10/7 | 5 | 44 | 35.78 | 137.5 | 0 | 5.4 | 5.29 | 1.67 |

1978/11/23 | 10 | 43 | 34.77 | 139.02 | 0 | 5.1 | 1.19 | 0.17 |

1978/12/3 | 22 | 15 | 34.88 | 139.18 | 20 | 5.5 | 2.31 | 0.84 |

1979/3/17 | 12 | 26 | 31.95 | 130.57 | 20 | 5 | 1.41 | 0.35 |

1979/8/17 | 15 | 0 | 38.12 | 139.25 | 20 | 5 | 0.90 | −0.11 |

1979/10/16 | 7 | 45 | 35.28 | 135.88 | 10 | 5 | 2.33 | 0.85 |

1979/12/28 | 23 | 54 | 34.92 | 134.37 | 20 | 5 | 1.31 | 0.27 |

1980/1/25 | 20 | 11 | 38.58 | 141.7 | 0 | 5.1 | 1.38 | 0.32 |

1980/6/29 | 16 | 20 | 34.92 | 139.23 | 10 | 6.7 | 1.52 | 0.42 |

1980/7/31 | 10 | 13 | 38.7 | 141.2 | 0 | 5 | 1.09 | 0.09 |

1981/1/30 | 6 | 19 | 32.43 | 129.85 | 0 | 5.3 | 1.18 | 0.17 |

1981/5/19 | 0 | 31 | 37.08 | 137.7 | 0 | 5 | 1.39 | 0.33 |

1982/1/8 | 5 | 37 | 40.02 | 140.48 | 0 | 5.2 | 1.51 | 0.41 |

1983/3/6 | 6 | 32 | 35.69 | 136.02 | 8 | 5 | 1.03 | 0.03 |

1983/8/8 | 12 | 47 | 35.52 | 139.02 | 22 | 6 | 1.63 | 0.49 |

1983/10/16 | 19 | 39 | 37.14 | 137.97 | 15 | 5.3 | 0.45 | −0.79 |

1983/10/31 | 1 | 51 | 35.42 | 133.92 | 15 | 6.2 | 1.07 | 0.06 |

1984/2/14 | 1 | 53 | 35.59 | 139.1 | 25 | 5.4 | 1.25 | 0.22 |

1984/5/30 | 9 | 39 | 34.96 | 134.59 | 17 | 5.6 | 1.10 | 0.09 |

1984/6/25 | 6 | 29 | 34.76 | 132.58 | 12 | 5.3 | 1.29 | 0.26 |

1984/8/6 | 17 | 30 | 32.76 | 130.18 | 7 | 5.7 | 1.92 | 0.65 |

1984/9/14 | 8 | 48 | 35.83 | 137.56 | 2 | 6.8 | 1.23 | 0.2 |

1984/10/3 | 9 | 12 | 35.83 | 137.62 | 5 | 5.4 | 0.07 | −2.69 |

1985/2/26 | 19 | 53 | 35.84 | 137.58 | 7.1 | 5.2 | 0.42 | −0.88 |

1985/3/28 | 16 | 13 | 38.88 | 140.73 | 5.1 | 5.3 | 1.12 | 0.12 |

1985/7/2 | 13 | 20 | 35.38 | 133.61 | 13.1 | 5.1 | 1.60 | 0.47 |

1985/10/3 | 20 | 57 | 35.18 | 135.86 | 8 | 5.3 | 0.99 | −0.01 |

1985/11/27 | 9 | 1 | 35.62 | 135.75 | 11 | 5.2 | 1.43 | 0.36 |

1986/3/7 | 3 | 25 | 36.03 | 137.5 | 4 | 5.1 | 2.83 | 1.04 |

1986/5/26 | 11 | 59 | 40.08 | 141.2 | 10 | 5 | 1.24 | 0.22 |

1986/6/27 | 20 | 18 | 39.04 | 140.95 | 11.1 | 5 | 1.39 | 0.33 |

1986/7/28 | 9 | 43 | 32.47 | 130.48 | 13 | 5.1 | 2.31 | 0.84 |

1986/12/30 | 9 | 38 | 36.64 | 137.92 | 3 | 5.9 | 1.03 | 0.03 |

1987/5/9 | 12 | 54 | 34.15 | 135.4 | 8 | 5.6 | 2.08 | 0.73 |

1987/5/28 | 6 | 3 | 35 | 135.53 | 16.1 | 5 | 2.02 | 0.7 |

1987/11/18 | 0 | 57 | 34.24 | 131.46 | 8 | 5.4 | 1.27 | 0.24 |

1988/7/31 | 8 | 40 | 34.97 | 139.21 | 5 | 5.2 | 1.00 | 0 |

1988/9/29 | 17 | 23 | 35.92 | 139.19 | 15 | 5.1 | 0.25 | −1.39 |

1989/7/9 | 11 | 9 | 34.99 | 139.11 | 3 | 5.5 | 1.70 | 0.53 |

1989/10/27 | 7 | 41 | 35.26 | 133.37 | 13 | 5.3 | 3.99 | 1.38 |

1989/11/2 | 4 | 57 | 35.26 | 133.37 | 14.1 | 5.5 | 4.01 | 1.39 |

1990/1/11 | 20 | 10 | 35.11 | 135.98 | 11 | 5 | 1.34 | 0.29 |

1990/2/20 | 15 | 53 | 34.76 | 139.23 | 5.1 | 6.5 | 1.66 | 0.51 |

1990/8/5 | 16 | 13 | 35.21 | 139.09 | 13.1 | 5.3 | 1.61 | 0.47 |

1990/9/29 | 7 | 57 | 34.99 | 134.29 | 11 | 5.4 | 1.56 | 0.44 |

1990/11/11 | 4 | 5 | 44.28 | 142.13 | 0 | 5 | 1.50 | 0.41 |

1990/11/21 | 10 | 44 | 35.28 | 133.34 | 13.1 | 5.1 | 2.82 | 1.04 |

1990/11/23 | 19 | 33 | 35.27 | 133.36 | 14 | 5.2 | 3.61 | 1.28 |

1990/12/1 | 20 | 23 | 35.28 | 133.34 | 12 | 5.1 | 2.70 | 0.99 |

1990/12/7 | 18 | 38 | 37.21 | 138.56 | 14.1 | 5.4 | 0.61 | −0.49 |

1991/8/28 | 10 | 29 | 35.32 | 133.19 | 13 | 5.9 | 0.74 | −0.3 |

1991/10/28 | 10 | 9 | 33.92 | 131.16 | 18 | 6 | 1.17 | 0.16 |

1992/5/20 | 12 | 29 | 36.12 | 135.95 | 9.1 | 5 | 1.63 | 0.49 |

1993/4/2 | 19 | 5 | 37.59 | 137.45 | 5 | 5 | 1.66 | 0.51 |

1993/4/23 | 5 | 18 | 35.81 | 137.5 | 7.1 | 5.1 | 3.87 | 1.35 |

1993/5/7 | 4 | 57 | 37.62 | 137.4 | 20 | 5 | 1.57 | 0.45 |

1993/7/20 | 0 | 10 | 36.35 | 137.65 | 4 | 5 | 1.78 | 0.58 |

1994/2/13 | 2 | 6 | 32.08 | 130.49 | 5 | 5.7 | 1.28 | 0.25 |

1994/5/8 | 17 | 2 | 34.08 | 135.12 | 10.1 | 5 | 0.75 | −0.29 |

1994/9/7 | 12 | 54 | 32.01 | 131.15 | 19 | 5.3 | 4.67 | 1.54 |

1994/12/18 | 20 | 7 | 37.29 | 139.89 | 6 | 5.5 | 2.13 | 0.75 |

1995/1/17 | 5 | 46 | 34.6 | 135.04 | 16.1 | 7.3 | 1.12 | 0.11 |

1995/1/17 | 7 | 38 | 34.79 | 135.44 | 12 | 5.4 | 1.47 | 0.39 |

1995/1/25 | 23 | 15 | 34.79 | 135.3 | 14.8 | 5.1 | 0.78 | −0.25 |

1995/2/18 | 21 | 37 | 34.44 | 134.81 | 15.9 | 5 | 1.67 | 0.51 |

1995/3/17 | 0 | 8 | 35.74 | 137.56 | 10.4 | 5.3 | 1.29 | 0.26 |

1995/4/1 | 12 | 49 | 37.89 | 139.25 | 16.2 | 5.6 | 0.48 | −0.74 |

1995/10/1 | 20 | 48 | 34.95 | 139.15 | 0 | 5 | 1.50 | 0.41 |

1996/2/7 | 10 | 33 | 35.94 | 136.62 | 12.1 | 5.3 | 1.23 | 0.21 |

1996/3/6 | 23 | 35 | 35.47 | 138.95 | 19.6 | 5.5 | 2.67 | 0.98 |

1996/8/11 | 3 | 12 | 38.91 | 140.63 | 8.6 | 6.1 | 0.63 | −0.47 |

1997/3/4 | 12 | 51 | 34.96 | 139.17 | 2.6 | 5.9 | 1.39 | 0.33 |

1997/3/26 | 17 | 31 | 31.97 | 130.36 | 11.9 | 6.6 | 1.30 | 0.26 |

1997/4/3 | 4 | 33 | 31.97 | 130.32 | 14.8 | 5.7 | 1.54 | 0.43 |

1997/5/13 | 14 | 38 | 31.95 | 130.3 | 9.2 | 6.4 | 1.40 | 0.33 |

1997/5/24 | 2 | 50 | 34.5 | 137.5 | 23.1 | 6 | 0.45 | −0.8 |

1997/6/25 | 18 | 50 | 34.44 | 131.66 | 8.3 | 6.6 | 1.62 | 0.48 |

1997/9/4 | 5 | 15 | 35.26 | 133.38 | 8.9 | 5.5 | 4.01 | 1.39 |

1998/2/21 | 9 | 55 | 37.27 | 138.79 | 19.1 | 5.2 | 1.53 | 0.43 |

1998/4/22 | 20 | 32 | 35.17 | 136.56 | 7.8 | 5.5 | 1.42 | 0.35 |

1998/4/26 | 7 | 37 | 34.96 | 139.17 | 6.1 | 5 | 1.28 | 0.25 |

1998/5/3 | 11 | 9 | 34.96 | 139.18 | 4.7 | 5.9 | 1.32 | 0.27 |

1998/7/1 | 2 | 22 | 36.62 | 137.91 | 8.9 | 5 | 1.20 | 0.19 |

1998/8/3 | 20 | 9 | 37.21 | 139.99 | 7.6 | 5.2 | 0.38 | −0.97 |

1998/8/12 | 15 | 13 | 36.24 | 137.63 | 2.8 | 5 | 2.52 | 0.93 |

1998/8/16 | 3 | 31 | 36.33 | 137.62 | 3.2 | 5.6 | 1.83 | 0.6 |

1998/9/3 | 16 | 58 | 39.81 | 140.9 | 7.9 | 6.2 | 0.98 | −0.02 |

1998/9/15 | 16 | 24 | 38.28 | 140.76 | 13.2 | 5.2 | 0.80 | −0.22 |

1999/2/26 | 14 | 18 | 39.15 | 139.84 | 20.6 | 5.3 | 0.30 | −1.21 |

1999/3/16 | 16 | 43 | 35.28 | 135.93 | 11.6 | 5.2 | 2.05 | 0.72 |

1999/11/7 | 3 | 34 | 36.06 | 135.79 | 15 | 5 | 1.44 | 0.37 |

2000/6/8 | 9 | 32 | 32.69 | 130.76 | 10.3 | 5 | 1.61 | 0.47 |

2000/10/6 | 13 | 30 | 35.27 | 133.35 | 9 | 7.3 | 3.18 | 1.16 |

2001/1/4 | 13 | 18 | 36.96 | 138.77 | 11.2 | 5.3 | 2.35 | 0.85 |

2001/1/12 | 8 | 0 | 35.47 | 134.49 | 10.6 | 5.6 | 1.32 | 0.28 |

2001/3/31 | 6 | 9 | 36.82 | 139.38 | 4.7 | 5.2 | 2.27 | 0.82 |

2001/8/25 | 22 | 21 | 35.15 | 135.66 | 8.2 | 5.4 | 2.70 | 0.99 |

2002/9/16 | 10 | 10 | 35.37 | 133.74 | 9.6 | 5.5 | 1.82 | 0.6 |

2003/7/26 | 7 | 13 | 38.4 | 141.17 | 11.9 | 6.4 | 0.00 | −6.24 |

2004/10/23 | 17 | 56 | 37.29 | 138.87 | 13.1 | 6.8 | 1.25 | 0.22 |

2004/10/27 | 10 | 40 | 37.29 | 139.03 | 11.6 | 6.1 | 3.23 | 1.17 |

2004/11/1 | 4 | 35 | 37.21 | 138.9 | 8.5 | 5 | 2.22 | 0.8 |

2004/11/4 | 8 | 57 | 37.43 | 138.91 | 18 | 5.2 | 1.14 | 0.13 |

2004/11/8 | 11 | 15 | 37.4 | 139.03 | 0 | 5.9 | 1.04 | 0.04 |

2004/12/14 | 14 | 56 | 44.08 | 141.7 | 8.6 | 6.1 | 4.01 | 1.39 |

2004/12/28 | 18 | 30 | 37.32 | 138.98 | 8 | 5 | 1.56 | 0.44 |

2005/3/20 | 10 | 53 | 33.74 | 130.18 | 9.2 | 7 | 2.03 | 0.71 |

2005/4/10 | 20 | 34 | 33.67 | 130.28 | 4.7 | 5 | 2.41 | 0.88 |

2005/4/20 | 6 | 11 | 33.68 | 130.29 | 13.5 | 5.8 | 2.74 | 1.01 |

2005/5/2 | 1 | 23 | 33.67 | 130.32 | 11.4 | 5 | 2.99 | 1.1 |

2005/6/20 | 13 | 3 | 37.23 | 138.59 | 14.5 | 5 | 0.60 | −0.51 |

2005/8/21 | 11 | 29 | 37.3 | 138.71 | 16.7 | 5 | 0.91 | −0.09 |

2006/4/21 | 2 | 50 | 34.94 | 139.2 | 7.1 | 5.8 | 1.63 | 0.49 |

2007/4/15 | 12 | 19 | 34.79 | 136.41 | 16 | 5.4 | 0.63 | −0.45 |

2007/7/16 | 10 | 13 | 37.56 | 138.61 | 16.8 | 6.8 | 1.25 | 0.22 |

2007/8/18 | 16 | 55 | 35.34 | 140.35 | 20.2 | 5.2 | 0.13 | −2 |

2008/6/14 | 8 | 43 | 39.03 | 140.88 | 7.8 | 7.2 | 2.36 | 0.86 |

## 4. Information Gain per Event

The chi square-test for goodness-of-fit was performed within the framework of the null hypothesis that *P*-wave velocity differences at each depth possess a normal distribution. The hypothesis for samples at either 10 or 15 km is accepted at the 10% level of significance. The hypothesis for samples at either 20 or at 25 km is accepted at the 1% level of significance, which may appear higher than usual but is assessed to be adequate for fitting with a function of two parameters.

Terms of normal distributions for each parameter and its IGpe value.

Background | Conditional | IGpe | |||
---|---|---|---|---|---|

Av | Std | Av | Std | ||

10 km | 6.039 | 0.169 | 6.066 | 0.163 | 0.014 |

15 km | 6.254 | 0.183 | 6.243 | 0.187 | 0.002 |

20 km | 6.500 | 0.195 | 6.467 | 0.196 | 0.015 |

25 km | 6.764 | 0.225 | 6.720 | 0.204 | 0.028 |

*f*(

*θ*)/

*g*(

*θ*) by an average rate (Poisson rate). Using the formula developed by Imoto (2007), we can estimate an IGpe of 0.30 for the seismicity model of this hazard function. This value is equivalent to a probability gain of 1.35 across all target earthquakes.

Correlation matrices. Lower left: Observed in background distribution. Upper right: Observed in conditional distribution.

10 km | 15 km | 20 km | 25 km | |
---|---|---|---|---|

10 km | — | 0.877 | 0.679 | 0.498 |

15 km | 0.829 | — | 0.887 | 0.681 |

20 km | 0.451 | 0.817 | — | 0.901 |

25 km | 0.103 | 0.437 | 0.808 | — |

## 5. Discussion and Conclusions

Matsubara and Obara (2008) studied the relationship between the seismic velocity structure and the active tectonic faults in the Japan Islands. They first estimated velocity variations at depths of 5, 10, 15, and 20 km and then they compared the values beneath the fault zones with the nationwide averages. They found that velocity becomes higher than the average velocity in the shallow part beneath the fault zones but becomes lower than the average velocity in the deeper part. Based on this finding, they suggested that seismic velocity anomaly could contribute to the detection of blind active faults. Although their finding has not been examined quantitatively, it implies that a *P*-wave velocity model could contribute to the assessments of the seismoge-nesis of shallow earthquakes of moderate and large magnitude.

Taking into account the close relationship between large earthquakes and active faults, we focus on epicenters of earthquakes with a magnitude ≥5.0 at a shallow depth as the conditional group. It may be possible to adopt fault zones as a conditional group, but epicenters of earthquakes are more exactly defined and more easily selected than fault zones. Even with these simple selections, we are able to construct a seismicity model that could possibly assess the seismogenesis of shallow earthquakes. It may be possible to propose more effective models after various predictive parameters have been examined. However, how such models would perform remains to be seen.

*m*

_{0}/

*V*

_{0}), which becomes equal to the

*f*(

*θ*)/

*g*(

*θ*) value in the present case. Although the map indicates some parts of high probability gain up to 2.0, an average over the values at 198 epicenters (Table 1) becomes 1.35. Imoto and Rhoades (2010) combined two models, namely, the Every Earthquake a Precursor According to Scale model (EEPAS, Rhoades and Evison, 2006) and a three-parameter model (Imoto, 2008), into a better performance model in which the hazard rate of the EEPAS model is treated as a surrogate precursor. In a similar way, we can combine the present parameters and an appropriate seismicity model into a better performance model. A study focusing on this point will be conducted in the future.

In summary, we have attempted to assess the performance of a seismicity model for shallow earthquakes in Japan based on a *P*-wave velocity model. Applying the formula derived by Imoto (2007) to the *P*-wave velocity data, we assessed that IGpe of the model is 0.3 units, after incorporating the correlations among the parameters. The bootstrap method suggests that this IGpe value could not be obtained by chance from the background distribution.

## Declarations

### Acknowledgments

The author would like to express his thanks to M. Matsubara for providing a convenient tool to use their *P*-wave velocity data. He also thanks Euan Smith and Masashi Kawamura for their detailed reviews of this article and their valuable comments.

## Authors’ Affiliations

## References

- Aki, K., A probabilistic synthesis of precursory phenomena, in
*Earthquake Prediction*, edited by D. W. Simpson and P. G. Richards, 566–574, AGU, 1981.Google Scholar - AL-Shukri, H. J. and B. J. Mitchell, Reduced seismic velocities in the source zone of New Madrid earthquakes,
*Bull. Seismol. Soc. Am*.,**78**, 1491–1509, 1988.Google Scholar - Daley, D. J. and D. Vere-Jones,
*An Introduction to the Theory of Point Processes*, vol 1, Elementary theory and methods, Second edition, 469 pp, Springer, New York, 2003.Google Scholar - Grandori, G., E. Guagenti, and F. Perotti, Alarm systems based on a pair of short-term earthquake precursors,
*Bull. Seismol. Soc. Am*.,**78**, 1538–1549, 1988.Google Scholar - Hamada, K., A probability model for earthquake prediction,
*Earthq. Predict. Res*.,**2**, 227–234, 1983.Google Scholar - Hauksson, E. and J. S. Haase, Three-dimensional Vp and Vp/Vs velocity models of the Los Angeles basin and central Transverse Ranges, California,
*J. Geophys. Res*.,**102**, 5423–5453, 1997.View ArticleGoogle Scholar - Imoto, M., Probability gains expected for renewal process models,
*Earth Planets Space*,**56**, 563–571, 2004.View ArticleGoogle Scholar - Imoto, M., Earthquake probability based on multidisciplinary observations with correlations,
*Earth Planets Space*,**57**, 1447–1454, 2006.View ArticleGoogle Scholar - Imoto, M., Information gain of a model based on multidisciplinary observations with correlations,
*J. Geophys. Res*.,**112**, B05306, doi:10.1029/ 2006JB004662, 2007.Google Scholar - Imoto, M., Performance of a seismicity model based on three parameters for earthquakes (M≥5.0) in Kanto, central Japan,
*Ann. Geophys*.,**51**(4), 727–736, 2008.Google Scholar - Imoto, M. and D. Rhoades, Seismicity models of moderate earthquakes in Kanto, Japan utilizing multiple predictive parameters,
*Pure Appl. Geophys*.,**167**, 831–843, doi 10.1007/s00024-010-0066-4, 2010.View ArticleGoogle Scholar - Kaufmann, R. D. and L. T. Long, Velocity structure and seismicity of southeastern Tennessee,
*J. Geophys. Res*.,**101**, 8531–8542, 1996.View ArticleGoogle Scholar - Matsubara, M. and K. Obara, Relationship between the seimic velocity structure and the active tectonic faults in the crust beneath Japan islands,
*Eos Trans. AGU*,**89**(53), Fall Meet. Suppl., Abstract T53C-1954, 2008.View ArticleGoogle Scholar - Matsubara, M., K. Obara, and K. Kasahara, Three-dimensional P- and S-wave velocity structures beneath the Japan Islands obtained by high-density seismic stations by seismic tomography,
*Tectonophysics*,**454**, 86–103, 2008.View ArticleGoogle Scholar - Michael, A. J., Effects of three-dimensional velocity structure on the seis-micity of the 1984 Morgan Hill, California, aftershock sequence,
*Bull. Seismol. Soc. Am*.,**78**, 1199–1221, 1988.Google Scholar - Nur, A., Dilatancy, pore fluids and premonitory variations of ts/tp travel times,
*Bull. Seismol. Soc. Am*.,**62**, 1217–1222, 1972.Google Scholar - Obara, K., K. Kasahara, S. Hori, and Y. Okada, A densely distributed high-sensitivity seismograph network in Japan: Hi-net by National Research Institute for Earth Science and Disaster Prevention,
*Rev. Sci. Instrum*.,**76**, 021301, 2005.View ArticleGoogle Scholar - Rhoades, D. and F. Evison, Long-range earthquake forecasting based on a single predictor,
*Geophys. J. R. Astron. Soc*.,**59**, 43–56, 1979.View ArticleGoogle Scholar - Rhoades, D. and F. Evison, The EEPAS forecasting model and the probability of moderate-to-large earthquakes in central Japan,
*Tectonophysics*,**417**, 119–130, 2006.View ArticleGoogle Scholar - Scholz, C., L. R. Sykes, and Y. P. Aggarwal, Earthquake prediction: a physical basis,
*Science*,**181**, 803–810, 1973.View ArticleGoogle Scholar - Utsu, T., Probabilities in earthquake prediction,
*Zisin II*,**30**, 179–185, 1977 (in Japanese).Google Scholar - Utsu, T., Probabilities in earthquake prediction (the second paper),
*Bull. Earthq. Res. Inst*.,**57**, 499–524, 1982 (in Japanese).Google Scholar