SEISMIC PHASE UNWRAPPING: METHODS, RESULTS, PROBLEMS¹

Abstract

SHATILO, A.P., 1992. Seismic phase unwrapping: methods, results, problems. Geophysical Prospecting 40, 21 1-225.Six known methods of seismic phase unwrapping (or phase restoration) are compared. All the methods tested unwrap the phase satisfactorily if the initial function is a simple theoretical wavelet. None of the methods restore the phase of a synthetic trace exactly.An initial validity test of the phase-unwrapping method is that the sum of the restored wavelet phase spectrum and the restored pulse-trace phase spectrum (assuming the convolutional model for the seismic trace) must be equal to the restored phase spectrum of the synthetic trace. Results show that none of the tested methods satisfy this test. Quantitative estimation of the phase-unwrapping accuracy by correlation analysis of the phase deconvolution results separated these methods, according to their efficiency, into three groups. The first group consists of methods using a priori wavelet information. These methods make the wavelet phase estimation more effective than the minimum-phase approach, if the wavelet is non-minimum-phase. The second group consists of methods using the phase increment A4(Au) between two adjacent frequencies. These methods help to decrease the time shift of the initial synthetic trace relative to the model of the medium. At the same time they degrade the trace .correlation with the medium model. The third group consists of methods using an integration of the phase derivative. These methods do not lead to any improvement of the initial seismic trace.The main problem in the phase unwrapping of a seismic trace is the random character of the pulse trace. For this reason methods based on an analysis of the value of A+(Aw) only, or using an adaptive approach (i.e. as Am decreases) are not effective. In addition, methods based on integration of the phase derivative are unreliable, due to errors in numerical integration and differentiation.

Accurate High-Resolution Measurements of 3-D Tissue Dynamics With Registration-Enhanced Displacement Encoded MRI

“…Consequently, a major part of displacement measurement via DENSE is the postprocessing of phase wrapped images, which involves two critical steps: first, the phase is unwrapped to eliminate discontinuities in phase images, and second, the resulting continuous phase maps is matched to true displacements by correcting for the phase offsets at selected pixels (known as “seed,” “true phase,” or “reference” points). Although phase unwrapping has been well studied from its association with other fields like radar interferometry [46], [47] and geophysics [48], [49], matching the results to underlying displacements is more unique to DENSE reconstruction, which continues as an active area of research [29], [45], [50]. …”

Research Note: Full‐waveform inversion of the unwrapped phase of a model

“…There are many ways to unwrap the phase of a signal. Many of the existing methods are based numerically on conditional statements in the algorithm (Shatilo ). An explicit way to unwrap the phase was suggested by Stoffa, Buhl and Bryan () and we write it in terms of traveltime (we refer to it as instantaneous traveltime) instead of phase, as follows: where u is the wavefield in the frequency domain, ω is the angular frequency and ℑ stands for the imaginary part.…”

Seismic inversion for coal‐seam thicknesses: trials from the Belvoir coalfield, England

“…We can either keep this estimated wavelet fixed when inverting for the earth model, or parametrize it in the frequency domain. After unwrapping the phase spectrum of this wavelet, as described by Shatilo (1992), the wavelet can be conveniently expressed in the frequency domain using up to eight parameters. These are: four frequencies defining a flat, band-limited amplitude spectrum with cosine tapers, up to three phase parameters and an amplitude scaler.…”