2D nonlinear inversion of bedrock motion from the surface motion of a layered half-space

This paper proposes a method for two-dimensional (2D) nonlinear inversion of bedrock earthquake motion from the surface motion of a layered half-space. The exact dynamic-stiffness matrices of soil layer and half-space are used for the inversion of bedrock motion and incident angle from both the surface horizontal motion and vertical motion, and the equivalent linearization approach is used to consider the nonlinearity of the soil layers. The method of inversion is verified by an example of obliquely incident El Centro Earthquake record at bedrock. It is shown that, the bedrock motion and incident angle can be accurately inversed from both the horizontal motion and vertical motion. The one-dimensional (1D) traditional inversion of bedrock horizontal motion from only surface horizontal motion in literatures may cause large error due to ignoring wave mode conversion, because there is vertical motion accompanying two surface horizontal motions in real earthquake records anyway. The error in 10 inversion depends on the ratio of surface vertical motion to horizontal motion, and the larger the surface vertical motion, the larger the error.