Vector interpolation and regularized elastic imaging of multicomponent seismic data

• Author / Creator

  Stanton, Kenneth A

• Historically seismic data processing has relied on the acoustic approximation to process single component data under the simplifying assumption that the recorded wavefield consists mainly of compressional wave modes. With the advancement of multicomponent seismic technology there is an increased need for purpose-built processing tools to improve the quality of the data while considering its vector-elastic nature. Past research in this field resulted in the extension of several key processing steps from the scalar-acoustic to the vector-elastic case. These steps included elastic redatuming, noise attenuation, deconvolution, full waveform inversion and imaging. This thesis is focused on the extension of two other important processing steps to the vector-elastic case: regularization, which compensates for poor spatial sampling of receivers and sources at the earth’s surface, and least squares imaging, which compensates for poor illumination of the earth’s subsurface. These two topics approach the processing of multicomponent seismic data from two very different approaches. In the extension of scalar reconstruction to the vector case a mathematical representation of multicomponent data in the Fourier domain is achieved via hypercomplex numbers; more specifically, the quaternions. Following the algebraic rules of quaternions it is possible for Fourier regularization algorithms to be adapted to the vector case. A different approach is necessary to extend acoustic least squares migration to the elastic case. In this case the acoustic wave equation must be substituted for the elastic wave equation within the single scattering approximation. This allows elastic wave equation modelling and migration linear operators to be built, providing the necessary tools to approach elastic imaging as an inverse problem with the goal that the optimal image of the earth subsurface is one that best explains the data. Both vector regularization and elastic least squares imaging are found to be improvements over their scalar-acoustic counterparts. In the case of vector regularization the quality of the result is found to be insensitive to the orientation of the input measurements, while in elastic least squares imaging the minimization of wavefield crosstalk is improved by minimizing the least squares error between observed and predicted data components.

• Subjects / Keywords

  • Signal processing
  • Migration
  • Geophysics
  • Regularization
  • Least-squares migration
  • Imaging
  • Interpolation
  • Multicomponent
  • Elastic
  • Vector
  • Seismic

• Graduation date

  Fall 2017

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3XD0RB6V

• License

  This thesis is made available by the University of Alberta Libraries 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.