Seismic Input Motion Determined from a Surface–Downhole Pair of Sensors: A Constrained Deconvolution Approach

Abstract We apply a deconvolution approach to the problem of determining the input motion at the base of an instrumented borehole using only a pair of recordings, one at the borehole surface and the other at its bottom. To stabilize the bottom-to-surface spectral ratio, we apply an iterative regularization algorithm that allows us to constrain the solution to be positively defined and to have a finite time duration. Through the analysis of synthetic data, we show that the method is capable of retrieving reliable input motion, suppressing the effect of the negative interference generated by the downgoing waves. Results obtained by applying the methodology to weak earthquakes recorded at the Atakoy (Istanbul) vertical array are also presented and show that removing the effect of the downgoing waves is remarkable, even considering the recording at a depth of 140 m.