Analysis of records from downhole arrays

Abstract

The paper presents an approach to identify characteristics of layered soil media from the records of vertical downhole arrays. It is assumed that the behavior of soil is linear and it is subjected to vertically propagating shear waves. The approach is based on discrete time formulation of wave propagation in terms of up-going and down-going waves in the layers. It is shown that the upgoing and downgoing waves in any layer can be expressed as a linear combination of the time-shifted and scaled forms of the excitation. For identification, we first model the surface record as the response of an IIR filter (i.e., an auto-regressive random process) subjected to Gaussian white-noise input. We convert the IIR filter into a lattice filter, defined by its reflection coefficients. We then divide the soil into fictional thin layers, whose two-way travel times are equal to the sampling interval. Starting from the top layer next to the surface, we calculate the motions at each fictional layer interface by using the surface record and the reflection coefficients. When the calculated interface response matches the recorded response by one of the downhole sensors, we conclude that the layers above the matching interface represent the layers between the surface and the downhole sensor.