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

Using seismic mixtures to extract tilts and recover estimates of ground displacements

One of the goals of seismology is to understand the behaviour of the earth’s movements during the occurrence of an earthquake. This research focuses on the recovery of better estimation of the true ground displacements as the tilt components are inherent in recorded acceleration time histories. The raw acceleration time histories recorded in seismograms of the near field earthquake are contaminated by the effects of tilt time histories. The effects of tilt time histories cause non–zero baseline errors in seismic records thereby providing offset in the ground velocity although the final velocity never ends to zero and ground displacement diverges from the constant value. To perform baseline corrections it is therefore necessary to remove the tilt and noise components. Tilt separation was undertaken using a model designated the Tilt Separation – Independent Component Analysis (TS-ICA) model, and an enhanced version of the Extended Generalised Beta Distribution (EGBD) model. Several source distributions such as Normal, Gaussian, Non-Gaussian, Sub and Super Gaussian and skewed distribution with zero kurtosis has been modelled using EGBD and separated using EGBD-ICA. In order to refine the EGBD-ICA model, a randomised mixing matrix was introduced in the existing EGBD-ICA model using MATLAB. With the introduction of the mixing matrix, the consistency of the source separation has improved and particularly tilt separation was convincing for both artificial tilt separation from the Hector Mine earthquake data and real-time tilt separation from the real-time acceleration time histories. The tilt separation and de-noising by the TS-ICA model has given better estimates of ground displacement than the tilt contaminated ground displacement. The estimated tilt angle can provide further scope for seismic scientists and civil engineers to improve their understanding of the tilt behaviour during an earthquake and can add another dimension to their research by making it possible to improve the stability of the building structures in the seismically active regions and areas which are potentially prone to earthquake