A robust seismic phase unwrapping method

One of the difficulties in seismic phase unwrapping occurs at the frequency components with energy close to zero, where the final. unwrapped phase fun ction should have +/-pi discontinuities. At those frequency components, pri ncipal values of the wrapped phase spectrum and in turn the values of the f inal unwrapped phase function are contaminated severely by numerical errors . These errors also propagate along the frequency axis as the unwrapped pha se function is calculated recursively. This paper presents a robust phase u nwrapping method. Unwrapped phase function is defined as the sum of phase i ncrements, where the phase increment of adjacent frequency components is ev aluated in terms of the difference of principal values of the wrapped phase spectrum. In the vicinity of +/-pi discontinuities, appropriate treatment of phase increments is required, preventing the numerical errors from propa gating along the frequency axis.