Exploring the Concept of Self-Similarity and High-Frequency Decay Kappa-Model and fmax-Model Using Strong-Motion Surface and Borehole Data of Japan: A Statistical Approach

We statistically analyzed the fmax-model, ?-model and stress drop (??) using surface and borehole data of the KIK-NET Japan seismological network. The statistical tests show no contribution of source in the fmax-model and ?-model. The �fmax� values obtained in the present study are 4.2�11.0 Hz and 5�11.0 Hz for surface and borehole data, respectively. The impact of local heterogeneities and wave propagation path is clearly visible on both surface and borehole fmax-models. The same is confirmed by the p-value �t-test�. The multivariate linear regression (MVLR) has been applied for the analysis of dependent variables �?(s)� and �?(w)� w.r.t. independent variables epicentral distance and magnitude. The p-value calculated by t-test indicates the strong dependence of ?(s) and ?(w) on near-surface geology and the physical state of the wave travelling media but almost no contribution of magnitude. The contribution of near-surface geology in kappa values is also confirmed by the �?0� (kappa at epicentral distance = 0). The relationships between the fmax-model and the ?-model have been developed for the study region. The stress drop (??(s)) assessed from surface data is 44.16-65.86 bars with an average value of 53.19 bars and borehole derived stress drop (??(w)) is 46.38-68.13 bars with an average value of 54.16 bars. This study discards the effect of depth; type of earthquake, i.e. normal, reverse and strike-slip; and signal to noise ratio (SNR) on stress drop as there is no huge variation in both ??(s) and ??(w) with the seismic moment and source radius. Therefore, the study supports the concept of self-similarity. � The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.