An auxiliary plane method for harmonic function transformation between two skew cylindrical coordinate systems

Aiming at the coordinate transformation in studying a 3-D seismic response with wave function expansion method, this paper presents an auxiliary plane method for harmonic function transformation between two skew cylindrical coordinate systems. By creating a series of auxiliary plane corresponding to spatial points, the 3-D harmonic wave function is transformed from cylindrical coordinate system to planar polar coordinate. Then the wave function under a cylindrical coordinate system is transformed into another one, which is skew to the former, by using the Grafrsquo;s addition formula on the auxiliary plane. Thus the 3-D problem is turned into two-dimensional. Finally, the coordinate transformation formula between two skew cylindrical coordinate systems is given.