複雑な3次元波動場のP, SV及びSH波への地表面地震動を用いた分離

数値実験に基づく時間－空間領域における手法の評価

抄録

 In recent years, synthesis of strong ground-motion waveforms has increasingly been performed by finite-difference methods (FDM) in strong ground-motion prediction using models of subsurface velocity structures with irregular sediment-bedrock interfaces and incident waves from complex source processes. It is known that the seismic motions in the simulations of these complex subsurface velocity structure models exhibit remarkable temporal and spatial variations due to interference between waves (including transforms between P- and S-waves and between body and surface waves) dispersed by irregular sediment-bedrock interfaces. The characteristics of these variations can be investigated in more detail if these complex wavefields can be separated into P- and S-waves and the S-waves can further be separated into SV- and SH-waves.

 In this article, in the spatial domain, we have presented a procedure for the separation of waves in an irregular subsurface structure model into P-, SH-, and SV-waves based on the ground surface displacement (or velocity or acceleration) induced by the seismic motion (or velocity or acceleration) synthesized by FDM or other method or taken from high-density array earthquake observation recordings, and applied the procedure to the synthetic seismic motion response induced by a dislocation point source in a three-dimensional sedimentary-basin model (Figs. 1 and 2) to derive the acceleration waveforms corresponding to the P-, SH-, and SV-wave potentials. This enabled clear identification of the radiation characteristics of the body waves by the potentials corresponding to the point source mechanism, together with clear identification of a wave group (Rayleigh waves) formed by coupling of P- and SV-waves, and a wave group (Love waves) solely of SH-waves travelling horizontally in the sedimentary layer (Figs. 7 and 8).

 As given in Chapter 2, we have in particular presented a procedure for considering the expression (Eqs. 1(a)-(c)) of relations between the three-component displacements {u, v, w} and the P-, SV-, and SH-wave potentials {φ, χ, ψ} while assuming stress-free conditions (Eqs. 7(a)-(c)) at the ground surface, and thereby deriving their potentials in the spatial domain solely from the displacement vectors of the full wavefield at the ground surface. Using this procedure, we derived the P-wave potential (Eq. 8a) and the vertical displacement component (Eq. 8b) induced by this potential without performing partial differentiation of the ground surface displacement vectors in the vertical direction, and next derived the SH-wave potential as the solution of the two-dimensional Poisson equation (Eq. 3) at the ground surface. The three-component displacement induced by the SV-wave potential were obtained by subtracting the previously obtained components of displacement induced by the P-wave potential and the SH-wave potential from the three-component displacement induced by the given full wavefield (Eqs. 11(a)-(c)). To investigate the separation accuracy of the finite-difference approximation (Eqs. 12, 13 and 14) of the partial derivatives with respect to space, we compared the results with the three-directional acceleration waveforms induced by the potentials obtained by the near-field three-dimensional Aki and Larner method (NF3DALM)^{ref. 16)} (Fig. 3). The results showed that good accuracy is obtained by the finite-difference approximation with a grid spacing that is approximately one-fourth or less the shortest wavelength of waves travelling horizontally in the sedimentary layer (Fig. 6).