The spatial distribution of earthquakes is a fractal, which is characterized by a fractal dimension. However, if a spatial distribution has a heterogeneous fractal structure, a single value of fractal dimension [e.g. Do (capacity dimension) or D2 (correlation dimension)] is not enough to characterize it. From a multifractal viewpoint, we analysed the spatial distribution of microearthquakes in the Kanto region by using a local density function. Generalized dimensions, D,, of the spatial distribution were calculated from the slopes of generalized correlation integrals, C,(r) versus distance r, on a log-log plot, examining the self-similarity of the spatial distribution of microearthquakes. Self-similar structures are held well at scales from 1.26 to 12.6 km. Our results suggest that the spatial distribution of microearthquakes in the Kanto region is not a homogeneous fractal structure but a heterogeneous one with generalized dimensions D2 = 2.2 h D3 2 -. ? D, = 1.7. The value of D,, the lower limit of fractal dimension, is the fractal dimension of the most intensive clustering in the heterogeneous fractal set. The fractal dimension of the most intensive clustering of microearthquakes in the Kanto region is 1.7.
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.
S U M M A R Y Oceanic crusts subducting into the mantle were detected by analyses of mantle earthquakes in the Kanto district, central Japan. Earthquakes in a depth range of 30-80 km in the southwestern Ibaraki prefecture were relocated by a modified method of joint hypocentre determination. We obtained a good distribution map of hypocentres and focal mechanisms. A boundary layer between the Eurasian and Philippine Sea plates was found, where thrust earthquakes with P axes in the NW-SE direction and of which low-angle nodal planes dip northward occurred in a layer with a thickness of about 4 km. The P-wave velocity in this layer is estimated to be less than about 7.0kms-l. Another boundary layer between the Philippine Sea and Pacific plates exists about 15 km beneath the above boundary layer. Thrust earthquakes with P axes in the EW direction and of which low-angle nodal planes dip westward occurred in this layer that also has a thickness of about 4km. Furthermore, normal-faulting earthquakes of which the P axes are almost perpendicular to the boundary layers were found immediately outside the boundary layers. Combining these results, we can conclude that the boundary layers are oceanic crusts that exist at the top of the subducting Philippine Sea and Pacific plates. 'Weak-zone-normal compression' was proposed to result from the existence of low-velocity oceanic crusts at plate boundaries. This hypothesis can be explained, because only stress caused by relative motion of the two plates is consumed inside the weak oceanic crust. The remnant stress after subtracting the above stress from the tectonic one applied at the plate boundary is the stress of which the P axis is normal to the plate boundary.
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