Seismic Correction in the Wavelet Domain

This thesis summarises novel approaches and methods in the wavelet domain
employed and published in the literature by the author for the correction and
processing of time-series data from recorded seismic events, obtained from strong
motion accelerographs. Historically, the research developed to first de-convolve the
instrument response from legacy analogue strong-motion instruments, of which there
are a large number. This was to make available better estimates of the acceleration
ground motion before the more problematic part of the research that of obtaining
ground velocities and displacements. The characteristics of legacy analogue strongmotion
instruments are unfortunately in most cases not available, making it difficult
to de-couple the instrument response. Essentially this is a system identification
problem presented and summarised therein with solutions that are transparent to this
lack of instrument data. This was followed by the more fundamental and problematic
part of the research that of recovering the velocity and displacement from the
recorded data. In all cases the instruments are tri-axial, i.e. translation only. This is a
limiting factor and leads to distortions manifest by dc shifts in the recorded data as a
consequence of the instrument pitching, rolling and yawing during seismic events.
These distortions are embedded in the translation acceleration time–series, their
contributions having been recorded by the same tri-axial sensors. In the literature this
is termed ‘baseline error’ and it effectively prevents meaningful integration to
velocity and displacement. Sophisticated methods do exist, which recover estimates of
velocity and displacement, but these require a good measure of expertise and do not
recover all the possible information from the recorded data. A novel, automated
wavelet transform method developed by the author and published in the earthquake
engineering literature is presented. This surmounts the problem of obtaining the
velocity and displacement and in addition recovers both a low-frequency pulse called
the ‘fling’, the displacement ‘fling-step’ and the form of the baseline error, both
inferred in the literature, but hitherto never recovered. Once the acceleration fling
pulse is recovered meaningful integration becomes a reality. However, the necessity
of developing novel algorithms in order to recover important information emphasises
the weakness of modern digital instruments in that they are all tri- rather than sextaxial
instruments.