R. O. Davis

Rational approximation of stress and strain based on downhole acceleration measurements

Recordings from downhole accelerometer arrays offer unique insight into soil behavior and ground response during earthquakes. In this paper we present a scheme for interpolating displacement and acceleration measurements to provide approximations for subsurface shear strain and stress as continuous functions of time. Our suggested interpolating functions are constructed in such a way that the free surface boundary condition will always be satisfied and the interpolated displacement and acceleration remain finite for all depths. We also show how the functions can be adapted to represent layered soil profiles. Depending on the number of instruments in the downhole array, a truncated series of functions can be derived so that each represents a modal shape for the layered soil profile. The resulting approximations for strain and stress are considered more accurate and robust than previous approximations.