Hypercomplex processing of vector-valued seismic signals

• Quaternionic processing of vector-field seismic data

• Author / Creator

  Figueiredo Bahia, Breno

• Vector field data are becoming increasingly more common in several fields of signal processing, such as electrical engineering and geophysics. Processing vector-valued signals, however, has imposed a series of challenges on its practitioners. Many approaches can be taken to carry out vector field data processing, one of which is adopting hypercomplex numbers for its representation. In particular, quaternion signal processing is a growing research area that has been gaining attention among researchers due to its natural ability to represent multicomponent data. In that light, this thesis shows that quaternions offer a consistent way to represent and fully exploit the information in vector field data. It explores how to extend techniques currently used in scalar seismic processing to the case of multicomponent data in a natural way and introduces the augmented second-order statistics of quaternion signals to harness the second-order information within the vector-valued seismic data. Two techniques are developed for processing multicomponent seismic data: the Quaternion Singular Spectrum Analysis (QSSA) and the quaternion frequency-space deconvolution (QFXDECON). These methods have been applied to synthetic and field multicomponent denoising and reconstruction, showing clear gains in their formulation. Finally, denoising methods such as the above can extend their applicability through the Regularization by Denoising (RED) framework. The RED cost function is used to formulate the simultaneous source separation problem and provides one way to leverage high-quality scalar and vector-valued denoising methods in deblending. The software developed in this thesis is mostly based on the Julia language, and it can be found at https://github.com/bbahia-phd/HCDSP.

• Subjects / Keywords

  • Quaternions
  • Vector-data
  • Low-rank
  • Sparsity
  • Deblending

• Graduation date

  Fall 2022

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/r3-8deh-e547

• License

  This thesis is made available by the University of Alberta Library with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.