Surface motion of multiple alluvial valleys for incident plane SH-waves by using a semi-analytical approach

摘要: Abstract In this paper, the degenerate kernels and Fourier series expansions are adopted in null-field integral equation to solve exterior Helmholtz problems with alluvial valleys. The main gain of using equations is free calculating principal values for singular integrals by locating point exactly on real boundary. An adaptive observer system addressed fully employ property circular boundaries polar coordinate. Image concept technique decomposition utilized half-plane problems. After moving boundary matching conditions, a linear algebraic obtained without discretization. unknown coefficients can be easily determined. present method treated as “semi-analytical” solution since error only attributes truncation series. Earthquake analysis site response valley or canyon subject incident SH-wave concern. Numerical examples including single successive valleys given test our program. Limiting cases two canyons also addressed. Amplification soft basin observed study. validity semi-analytical verified. Our advantages, well-posed model, value free, elimination boundary-layer effect exponential convergence mesh-free, achieved.