Adaptive waveform inversion: Practice

Abstract

Adaptive waveform inversion (AWI) reformulates the misfit function used to perform full-waveform inversion (FWI), so that it no longer contains local minima related to cycle skipping. It does this by finding a model that drives the ratio of the predicted and observed data sets to unity rather than driving the difference between these two data sets to zero as is the case for conventional FWI. We apply AWI to a 3D field data set acquired over a pervasive gas cloud in the North Sea, comparing its performance with that of conventional FWI in a variety of circumstances. When starting inversion from 3 Hz, and using a good starting model obtained from reflection tomography, FWI and AWI generate similar models although the FWI result contains edge artifacts that are not produced by AWI. However, when the starting frequency is increased to approximately 6 Hz, or when the starting model is less accurate, FWI fails to recover a good model whereas AWI continues to converge. When both of these conditions apply, FWI fails comprehensively, leading to a model that is significantly worse than the starting model, whereas the AWI result remains largely unaffected. We applied Kirchhoff depth migration to the fully-processed data using the FWI result obtained following reflection tomography, and using the AWI result obtained from a simple one-dimensional starting model. We use the resulting migrated volumes, together with measures of residual moveout throughout the volume, to show that the AWI result from a simple starting model is at least as good as the FWI result obtained following tomography. We conclude that AWI is robust in the presence of cycle skipping on this 3D field data set, and can proceed successfully from a less-accurate starting model, and from a higher starting frequency, in circumstances in which FWI fails completely.

A review on reflection-waveform inversion

“…Consequently, solving cycle skipping turns into an important topic in FWI studies. Currently, the first category of proposed methods for cycle skipping is to introduce objective functions that have wider convex region; for example, the objective function based on penalizing the nonzero lags of cross-correlation or deconvolution [e.g., Adaptive Waveform Inversion-AWI (Warner and Guasch 2016;Guasch et al 2019;van Leeuwen and Mulder 2010;Luo and Sava 2011;Zhu and Fomel 2016)], optimal transport distance functions (Métivier et al 2016;, Wavefield Reconstruction Inversion-RWI (van Leeuwen and Herrmann 2013; da Silva and Yao 2017), etc.…”

Full-waveform inversion imaging of the human brain

“…Now the attempt at recovering a reasonable starting model for the skull purely from the data succeeds even though no a-priori model of the skull is assumed. Adaptive waveform inversion has immunity to cycle skipping, which is otherwise a common problem for conventional FWI [27], as well as an increased ability to recover sound-speed information from strong reflections such as those generated by the bones of the skull. We suspect that both of these characteristics may play a role in explaining the improvement of In practice, we suspect that such solutions may not actually be required in a clinical setting, and we have not pursued them further here.…”

“…Adaptive waveform inversion (AWI) is a form of FWI that has immunity to cycle skipping [26,27]. In conventional FWI, the algorithm seeks to drive the sample-by-sample difference between the predicted and observed data to zero.…”

“…Since division in the frequency domain represents deconvolution in the time domain, the AWI algorithm effectively deconvolves one dataset by the other and then attempts to drive the result of that deconvolution towards a unit-amplitude delta function at zero temporal lag. The mathematical details are given on [26], and practical details are given in [27].…”

Full-waveform inversion imaging of the human brain

“…FWI combines this moreaccurate description of the physics with an appropriate non-linear inversion scheme, and a suitable data acquisition geometry, so that it is able to recover fine-scale heterogeneity throughout the model. Adaptive waveform inversion (AWI) 3,19 is a modification of FWI that is better able to begin from a poor starting model; here we use it as a preconditioner for FWI so that inversion can begin successfully without any a priori information about the skull. Figure 1 outlines the geometry of the method.…”