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

Problems associated with instrument tilts during seismic events

This paper begins with a brief introduction regarding the problems associated with instrument tilts and rotations when recording a seismic event. Most instruments are designed to respond to translational motion along the longitudinal and vertical axes. Tilts in a gravity field introduce a horizontal acceleration component, which is indistinguishable from horizontal acceleration. When the seismometer frame is tilted by a small angle, a torque will be exerted around the hinge and will cause pendulum motion relative to the frame. The effect of this torque is the same as that produced by a horizontal acceleration and leads to baseline shifts in the recorded data. The base line offset of the recorded seismic data makes it difficult to locate the origin. Therefore this base line error should be corrected in order to remove the tilt component embedded in the ground acceleration. Fourier amplitude spectra are applied to vertical and horizontal components of acceleration to measure the difference in high frequency range; the difference is due to the residual tilt present in the horizontal component in the N-S and E-W directions. In this paper we apply independent component analysis (ICA) on simulated tilt data. ICA is a separation technique used in order to recover and hence remove the tilt time series from the acceleration time histories of a near field earthquake source

A brief review of instrument de-convolution of seismic data

Most corrected seismic data assume a 2nd order, single-degree-of-freedom (SDOF) instrument function with which to de-convolve the instrument response from the ground motion. Other corrected seismic data is not explicitly de-convolved, citing as reason insufficient instrument information with which to de-convolve the data. Whereas this latter approach may facilitate ease of processing, the estimate of the ground motion cannot be entirely reliable and therefore methods of deconvolution have been suggested and described in [1, 2, 4 ,5]]. This paper reviews a relatively straightforward implementation of the well-known recursive least squares (RLS) algorithm in the context of a system identification problem [4]. The paper then goes on to discuss the order in which implementation of the RLS algorithm should be applied when correcting seismic data. Noise reduction is typically achieved by de-noising using the discrete wavelet transform [8, 9] or filtering the resulting de-convolved seismic data. De-noising removes only those signals whose amplitudes are below a certain threshold and is not therefore frequency selective. Standard band-pass filtering methods on the other hand are frequency selective, but different cut-off frequencies for band-pass filters are applied in different parts of the world when correcting seismic events. These give rise to substantial differences in power spectral density characteristics of the corrected seismic data

Using ICA for analysis of seismic events

Independent Component Analysis (ICA) is a statistical and computational technique for revealing hidden factors that underlie set of random variables, measurements, or signals. ICA is a general purpose technique which is used to linearly transform the observed random data into components. The ICA can be estimated by using the concept of maximum nonGaussianity, maximum likelihood estimation, or minimisation of mutual information. This paper applies ICA to seismic acceleration time histories in order to locate any hidden components of ground rotational motion or tilts. Normally the three components of seismically induced rotations are not recorded in most of the available seismic instruments, primarily because previous devices did not provide the required sensitivity to observe rotations in a wide frequency band and distance range (the two horizontal components, equal to tilt at the free surface, are generally recorded at low frequencies) Igel et al 2003. From the x, y and z components usually recorded the Extended Generalised Lambda Distributions (EGLD) – ICA model was used to examine whether rotational or tilt trends were embedded within the 3 components. The algorithm tries to fit a matrix from the data which will separate any other trends within the available components. The results show that the EGLDICA separates trends within the 3 components; however these are not yet identified as tilts or rotations