3-D Spatial Variation ofb-Values of Magnitude-Frequency Distribution Beneath the Kanto District, Japan

Abstract

S U M M A R YA method is developed for estimation and interpolation of 6-values in space. A 3-D spline function is considered for the logarithm of the 6-value at each location in the space. Since many parameters for the spline coefficients are required to obtain a sensible estimate of the spatial variation of 6-values, we consider the penalized log-likelihood with the standard roughness penalties for the spline function. Further the error bands of the b-value estimation at each location can be calculated. Using the current method, the spatial distribution of 6-values beneath the Kanto District down to the depth of 100km is determined based on hypocentral data of microearthquakes from the Kanto-Tokai Observational Network of the National Research Center for Disaster Prevention. The stability of the estimated pattern is checked by comparing with the results using alternative cut-off magnitudes. This is further ensured by comparison with the result obtained by an alternative model using equally divided blocks. On the whole, the vertical change in 6-value is greater than the horizontal one. It is high in the crust of the Eurasian plate, especially above the upper boundary of the subducting Pacific plate and in the northwest part, or the volcanic area, in the Kanto District. A steep decrease of the 6-values is seen to take place in perpendicular direction to the subducting Pacific plate boundary. Also, a similar change is seen in the boundary between the Eurasian and Phillippine Sea plates, especially beneath the southern part of the Kanto Plain. The 6-value is low in the upper boundary of the subducting plates, but high in the lower plane of the double seismic zone in the Pacific plate. It appears that, even within a narrow area of aftershocks, the 6-value can change significantly. It is also found that the variation of the 6-value estimate is in good agreement with the structure of seismic wave fractional velocity perturbations. The regions of high and low 6-values correspond, respectively, to the lower and higher parts of the P-wave velocity. The similar relationship is seen with the spatial structure of the seismic wave attenuation.

Properties of the Aftershock Sequence of the 1999 Mw 7.1 Hector Mine Earthquake: Implications for Aftershock Hazard

“…Strong spatial variations of the earthquake size distribution expressed in terms of the b-value, on scales of 1-50 km, have also been determined in different tectonic regimes, ranging from small scales, such as volcanic systems (Wiemer and McNutt, 1997;Wiemer et al, 1998), to regional scales (e.g., Ogata et al, 1991;, Gerstenberger et al, 2001a. Stress is also a factor involved in perturbing the b-value (Urbancic et al, 1992;Wyss, 1973;Lahaie and Grasso, 1999;Wiemer and Wyss, 2000).…”

Significant improvements of the space-time ETAS model for forecasting of accurate baseline seismicity

“…Given a set of data, one seeks to compare the goodness-offit of Bayesian models that have distinct likelihoods or distinct priors and to search for the optimal hyper-parameter values. For instance, Ogata et al (1991) compared the use of different priors for isotropic and anisotropic smoothness constraints, which need two and five hyper-parameters, respectively. For such a purpose, Akaike (1980) justified and developed the Good's method based on the entropy maximization principle (Akaike, 1978) and defined…”

“…However there remain the issues of optimal selection of the number of earthquakes in the disk and evaluation of significance of the b-value changes. function fits better than the bi-cubic B-spline function that was used in Ogata et al (1991). The estimation of the coefficients is undertaken by the penalized log-likelihood, where the penalty is tuned by the similar Bayesian procedure based on the ABIC (see Section 4 and Appendix).…”

“…The exponential with respect to each φ-function is adopted to avoid negative values of the parameter functions. The two dimensional cubic B-spline expansion could be used as in Katsura (1988, 1993) and Ogata et al (1991). However, the spatial distribution of the epicenters such as shown in Fig.…”

Measuring seismicity diversity and anomalies using point process models: case studies before and after the 2016 Kumamoto earthquakes in Kyushu, Japan

“…For these analyses, we use the epidemic-type aftershock sequence (ETAS; Ogata 1985Ogata , 1988) model and its extended versions (Kumazawa and Ogata 2013;Kumazawa et al 2016a, b) for a variety of seismicity patterns in addition to a model for the magnitude frequency changes (Ogata 1989;Ogata et al 1991). For each dataset, we compare the goodness-of-fit of the models for the best fit, as given in the following section.…”