Theoretical study of multipoint ground motion characteristics under V-shaped site induced P1 wave

An advanced analytical technique known as the Oblique Coordinate Wave Function Integral Method builds on Biot’s wave theory for saturated porous material, has been developed to address seismic wave scattering in irregular media. This method employs an integral representation of scattered waves, solved by using an oblique coordinate transformation within a rectangular coordinate system with wave function series expansion methods. The inverse transformation between rectangular and cylindrical coordinate systems frequently presents convergence issues, this method effectively resolves these issues. Moreover, using a Cartesian coordinate system to solve the scattered wave field, overcomes the limitations of earlier methods. Such as the large arc assumption in wave function series expansion, that often did not meet boundary conditions precisely. In addition, this method’s scattering analytical solutions are used to derive the coherence function of multi-point ground motion from the second-moment correlation function of a random process. Lastly, a sensitivity analysis of key parameters, such as canyon depth, incident frequency, and soil porosity, is performed to assess the robustness of the method.