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Frequency-dependent model of the apparent radiation pattern has been extensively incorporated into engineering and scientific applications for high-frequency seismic waves, but distance-dependent properties have not yet been fully taken into account. We investigated the unified characteristics of frequency and distance dependences in both apparent P- and S-wave radiation patterns during local crustal earthquakes. Observed distortions of the apparent P- and S-wave radiation patterns could be simply modeled by using a function of the normalized hypocentral distance, which is a product of the wave number and hypocentral distance. This behavior suggests that major cause of distortion of the apparent radiation pattern is seismic wave scattering and diffraction within the heterogeneous crust. On the basis of observed normalized hypocentral distance dependency, we proposed a method for prediction of spatial distributions of maximum P- and S-wave amplitudes. Our method incorporating normalized hypocentral distance dependence of the apparent radiation pattern reproduced the observed spatial distributions of maximum P- and S-wave amplitudes over a wide frequency and distance ranges successfully.Graphical abstract.

earth, planets and space

Prediction of maximum P- and S-wave amplitude distributions incorporating frequency- and distance-dependent characteristics of the observed apparent radiation patterns