Progress in phase unwrapping

1. Progress in phase unwrapping Marcílio Castro de Matos, Kui Zhang and Kurt J Marfurt University of Oklahoma Attribute-Assisted Seismic Processing and Interpretation http://geology.ou.edu/aaspi/ Summary Objectives Time-frequency 2d Phase unwrapping Ex: Test signal Phase unwrapping is still a very important signal processing research topic specially when applied to SAR radar images, optical fringe-pattern analysis (Ghiglia and Pritt, 1998), and to seismic instantaneous phase (Stark, 2003). This poster shows preliminary results we obtained from the time-frequency phase unwrapping algorithm we have implemented. We are planning to use it as a tool to seismic trace Q-compensation and seismic cepstrum analysis. Morlet CWT absolute value • Develop 2d phase unwrapping algorithms • Develop time-frequency phase unwrapping • Use the time-frequency phase unwrapping to seismic Q compensation algorithm • Extend to 3d Ex: Wedge model 1d Phase unwrapping 1- Classic Phase unwrapping 2- Z-plane Phase unwrapping 3- Itoh’s Phase unwrapping Ex: Filter frequency response Morlet CWT Phase Compute the phase differences; Compute the wrapped phase differences; Initialize the first unwrapped value; Unwrap by summing the wrapped phase differences. Wrapped phase Φ is the unwrapped phase Ψ is the wrapped phase c indicates the unwrapping amount. It’s an integer. n indicates where the phase is unwrapped Unwrap Unwrap Don’t Unwrap i=0, 1,…n-1 Unwrapped phase Time-frequency 2d Phase unwrapping Ex: Seismic instantaneous phase unwrapping Amplitude spectrum Time-frequency 1d Phase unwrapping 2d Unwrapped phase Unwrapped phase detrended by 2pift CWT phase Ex: Real seismic 2d line Ex: Test signal Unwrapping each frequency trace Morlet CWT phase 2d Phase unwrapping • Path dependent • Quality path • Least square Two dimensional phase unwrapping is embodied in the solution of the line integral: Main methods • Main references: • Ghiglia, D. C., and M. D. Pritt, 1998, Two-dimensional Phase Unwrapping: Theory, algorithms, and software: Willey New York. • Stark, T., 2003, Unwrapping instantaneous phase to generate a relative geologic time volume: SEG, Expanded Abstracts The CWT and the phase unwrapping algorithms have been implemented using Fortran 90 language and the SEG-Y data have been read using the Madagascar RSF Fortran 90 API. Itoh’s Phase unwrapping