1. Progress in phase unwrapping
Marcílio Castro de Matos, Kui Zhang and Kurt J Marfurt
University of Oklahoma
Attribute-Assisted Seismic Processing and Interpretation
Summary
Objectives
Time-frequency 2d Phase unwrapping
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.
Ex: Test signal
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
Morlet CWT Phase
Unwrap
Don’t Unwrap
Compute the phase differences;
Compute the wrapped phase differences;
Initialize the first unwrapped value;
Unwrap by summing the wrapped phase differences.
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
i=0, 1,…n-1
Wrapped phase
Unwrapped phase
Amplitude spectrum
Ex: Filter frequency response
Time-frequency 2d Phase unwrapping
Ex: Seismic instantaneous phase unwrapping
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