Taming waveform inversion non-linearity through phase unwrapping of the model and objective functions
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Alkhalifah, Tariq Ali
Choi, Yun Seok
KAUST Department
Earth Science and Engineering ProgramPhysical Science and Engineering (PSE) Division
Seismic Wave Analysis Group
Date
2012-12Permanent link to this record
http://hdl.handle.net/10754/555750
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Traveltime inversion focuses on the geometrical features of the waveform (traveltimes), which is generally smooth, and thus, tends to provide averaged (smoothed) information of the model. On other hand, general waveform inversion uses additional elements of the wavefield including amplitudes to extract higher resolution information, but this comes at the cost of introducing non-linearity to the inversion operator, complicating the convergence process. We use unwrapped phase-based objective functions in waveform inversion as a link between the two general types of inversions in a domain in which such contributions to the inversion process can be easily identified and controlled. The instantaneous traveltime is a measure of the average traveltime of the energy in a trace as a function of frequency. It unwraps the phase of wavefields yielding far less non-linearity in the objective function than that experienced with conventional wavefields, yet it still holds most of the critical wavefield information in its frequency dependency. However, it suffers from non-linearity introduced by the model (or reflectivity), as reflections from independent events in our model interact with each other. Unwrapping the phase of such a model can mitigate this non-linearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced non-linearity and, thus, make the inversion more convergent. Simple numerical examples demonstrate these assertions.Citation
Alkhalifah, Tariq, and Yunseok Choi. "Taming waveform inversion non-linearity through phase unwrapping of the model and objective functions." Geophysical Journal International 191, no. 3 (2012): 1171-1178.Publisher
Oxford University Press (OUP)Additional Links
http://gji.oxfordjournals.org/content/191/3/1171.shortae974a485f413a2113503eed53cd6c53
10.1111/j.1365-246X.2012.05699.x