Full Waveform Inversion (FWI) is a highly promising but far from robust and stable optimisation for computing the subsurface velocity model from seismic data acquired with long offsets and low frequencies. Mathematically, it solves the non-linear problem of matching model-predicted data to observed data with an iterative localised minimisation of the misfit. Therefore it is necessarily restricted by the need for an accurate starting model. In this thesis, we look at being able to relax the constraints on the starting model in FWI, obtain lower wavenumber updates from FWI, and in the process distinguish between adequate and inadequate starting models. Our approach here is to precede the conventional Born-based iterations with Rytov-based iterations which isolate discrete frequency phase. Here the misfit function being minimised is the norm of the phase residual which measures the difference in phase between observed and predicted data. Our treatment of the phase residual differs from previous work in two specific ways: i) we define the time-weighted phase residual, ii) we unwrap the residual thereby accounting for errors greater than half a cycle or 'cycle-skipped'. Previous work did (i) using the Laplace-Fourier domain i.e. using an exponential function. Here we use a more versatile time window which prepares the residual for (ii). Previous work in the context of FWI did not attempt (ii) at all. We find it is the combination of (i) and (ii) that provides the solution we are looking for. In this thesis we formulate the theory for inverting the time-weighted phase residual. We find this mismatch measure meets the requirement of being able to distinguish between adequate and inadequate starting models. Finally, we demonstrate that an 'unwrapped' solution deals with the latter. The unwrapped solution is shown to correctly invert cycle-skipped data and successfully update longer wavelengths than possible with conventional inversion when wide-angle data is available. This leads to a multi-scale approach which ends with conventional inversion but begins with phase-unwrapped inversion at the lowest useable frequency. It finds the global minimum solution to the full wavefield inverse problem down to a depth governed by the offset range of the survey using only a simple starting model.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:656419 |
| Date | January 2013 |
| Creators | Shah, Nikhil |
| Contributors | Warner, Mike; Morgan, Joanna |
| Publisher | Imperial College London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/10044/1/24849 |
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