APPLICATION OF QUATERNION TRANSFORM IN EARTH SCIENCES

Abstract

Quaternion Transform has been used in image processing for quite a while now. The reason it intrigued me was because it processes all the components of the image namely its color values for red, green and blue colors which constitute the whole image, simultaneously instead of taking Fourier Transform of each component individually. Now in an earthquake record we also have three different components recorded at a particular station namely East- West, North-South and Up-Down components. And we use Fourier Transform of each component individually to obtain the frequency spectrum of the earthquake, so why not use a Quaternion Fourier Transform to do so in one go. This is exactly what I have tried to do in this particular work, to find an application of Quaternion Fourier Transform in Earth Sciences or Seismology in particular. In this work I have used two different types of Quaternion Fourier Transforms one of them being the OFT of type 2 while other is Local Quaternion Fourier Transform or QS Transform. The QFT results in a quaternion function whose magnitude when plotted against frequency gives the frequency spectrum of the entire earthquake record. While the power map of the QS Transform gives the reconstructed earthquake record with significant events from each of its components in a single record.