Fast Stacking and Phase Corrections of Shear Wave Signals in a Noisy Environment

Abstract

Hardware, software, and analysis of transient response of sources and receivers are presented for a piezoelectric bender element system designed to measure shear wave velocities in noisy environments. Signal-to-noise ratio is improved by signal stacking, wherein data vectors from many pulses are summed. A new fast-stacking algorithm enables signal quality to be improved much more rapidly than conventional stacking. Conventional stacking is accomplished by repeatedly sending an excitation pulse to a source, waiting for the signal and secondary reflections to pass the receiver and then introducing a subsequent excitation pulse. Using conventional stacking, it is important to wait for the signal and secondary reflections to die out before exciting subsequent pulses. In the new fast-stacking algorithm, a varied interval between consecutive pulses is used so that high quality signals can be obtained even if consecutive pulses are excited in rapid succession. Transient behavior of soil–bender interaction was characterized using closed-form analytical solutions of single-degree-of-freedom oscillators, numerical solutions using a beam-on-springs method, and measurements from an array of bender elements in a sand model. The time delay caused by soil–bender interaction was calculated to be half of the natural period of the bender element, and this theoretical time delay was supported by experimental data. This system makes it feasible to rapidly collect accurate shear wave velocity information so that transient changes in shear wave velocity can be monitored even if background noise is large.