L. Guasch

Adaptive Waveform Inversion - FWI Without Cycle Skipping - Theory

Conventional FWI minimises the direct differences between observed and predicted seismic datasets. Because seismic data are oscillatory, this approach will suffer from the detrimental effects of cycle skipping if the starting model is inaccurate. We reformulate FWI so that it instead adapts the predicted data to the observed data using Wiener filters, and then iterates to improve the model by forcing the Wiener filters towards zero-lag delta functions. This adaptive FWI scheme is demonstrated on synthetic data where it is shown to be immune to cycle skipping, and is able to invert successfully data for which conventional FWI fails entirely. The new method does not require low frequencies or a highly accurate starting model to be successful. Adaptive FWI has some features in common with wave-equation migration velocity analysis, but it works for all types of arrivals including multiples and refractions, and it does not have the high computational costs of WEMVA in 3D.

A Strategy for Waveform Inversion without an Accurate Starting Model

SUMMARY A key limitation of waveform inversion as currently implemented is the need for a starting model of high accuracy or field data with low frequencies. Here we present a new approach - staged waveform inversion - designed to mitigate this need and thereby permit the application of waveform inversion to a much wider range of datasets.

Total Variation Regularization Strategies in Full-Waveform Inversion

We propose an extended full-waveform inversion formulation that includes general convex constraints on the model. Though the full problem is highly nonconvex, the overarching optimization scheme arrives at geologically plausible results by solving a sequence of relaxed and warm-started constrained convex subproblems. The combination of box, total variation, and successively relaxed asymmetric total variation constraints allows us to steer free from parasitic local minima while keeping the estimated physical parameters laterally continuous and in a physically realistic range. For accurate starting models, numerical experiments carried out on the challenging 2004 BP velocity benchmark demonstrate that bound and total variation constraints improve the inversion result significantly by removing inversion artifacts, related to source encoding, and by clearly improved delineation of top, bottom, and flanks of a high-velocity high-contrast salt inclusion. The experiments also show that for poor starting models t...

A Phase-unwrapped Solution for Overcoming a Poor Starting Model in Full-wavefield Inversion

We present a new phase-unwrapped full-wavefield inversion (FWI) methodology for applying the technique to seismic data directly from a poor or simple starting model in an automated, robust manner. The well-known difficulty that arises with a poor starting model is a ‘cycle-skipped’ relationship between predicted and observed data at useable inversion frequencies. The local minimum convergence of cycle-skipped data is one of the root causes for inaccurately recovered models in practical applications of FWI. Further it is why practical applications to date have focussed on favourable datasets possessing very low frequencies and an accurate velocity model already known prior to applying FWI. Here we tackle the cycle-skipping problem by inverting the lowest useable frequency of the data using an unwrapped phase-only objective function. We minimise a smooth, phase-unwrapped residual, extracted from the data by exploiting the spatial continuity existing between adjacent traces. The majority of field datasets acquired today are spatially well enough sampled to be manipulated in this way. An application to highly cycle-skipped synthetic data from the Marmousi model shows the benefit of applying phase-unwrapped inversion to a dataset prior to starting conventional FWI.

Which Physics for Full-wavefield Seismic Inversion?

Full waveform seismic inversion, as currently commercially available in 3D, uses the acoustic approximation to the wave equation, and generally ignores the effects of elasticity, attenuation and anomalous density variations. We examine the consequences of these practical compromises by inverting 3D synthetic seismic data using different approximations to the physics of wave propagation in the forward and inverse modelling. We also invert using different portions of the data, and examine the effects of data amplitudes. We conclude that current FWI practice works well if amplitudes and reflected energy are suppressed in the inversion, but that a more-complete description of the physics is required in order to extract quantitative physical properties from amplitudes and reflections.

Adaptive Waveform Inversion - FWI Without Cycle Skipping - Applications

Conventional FWI suffers from cycle skipping if the starting model is inadequate at the lowest frequencies present in a dataset. The newly developed technique of adaptive FWI overcomes cycle skipping, and is able to invert normal bandwidth data beginning from an inaccurate velocity model. Here we apply the method to data extracted from a 3D field model, and show that the new method outperforms conventional FWI when starting at higher frequencies than have previously been used to invert this field dataset. We also apply the new methodology to a synthetic dataset that is not cycle skipped, but that is dominated by reflected rather than refracted arrivals. In this case, we show that adaptive FWI also produces a superior result because it has enhanced sensitivity to reflection data, and is able to update the velocity macro-model successfully using reflection-only data.

Waveform inversion of surface seismic data without the need for low frequencies

Summary Waveform inversion is a technique with capability of generating velocity models with unprecedented resolution and clarity from seismic data. However it often requires unrealistically low frequencies in the data to achieve this. We propose a scheme designed to mitigate this need ‐ a necessary key step for realising the potential of the technique in a far wider range of datasets and targets than currently possible. The scheme operates by preceding the inversion of the field data by inversion of intermediate datasets ‐ synthesised by extracting the irrotational component of the phase mismatch at the lowest useable frequency. We demonstrate its effectiveness over the corresponding conventional approach by inverting data from the Marmousi model with a minimum frequency of 5Hz.

Adaptive Waveform Inversion Using Incomplete Physics, Imperfect Data, and an Incorrect Source

Adaptive waveform inversion (AWI) provides a means of performing full-waveform inversion (FWI) that appears to be immune to the effects of cycle skipping. However, the form of the AWI algorithm suggests that it could have increased sensitivity to errors in the assumed source wavelet, to noise in the field data, and to inadequacies in the physics used to simulate wave propagation. We examine each of these for a synthetic model. We show that AWI is in fact less sensitive than FWI to errors in the source wavelet, and is no more sensitive to errors in the data and in the modelling than is FWI. It appears likely that the immunity that AWI displays to cycle skipping also contributes to its reduced sensitivity to errors in the assumed source wavelet.

Imaging Beneath a Gas Cloud in the North Sea without Conventional Tomography

To reduce sensitivity of full-waveform inversion to cycle skipping, new objective functions have been introduced in the last couple of years. We here investigate the capability of adaptive waveform inversion (AWI) based on Wiener coefficients which we apply to a gas cloud field in the North Sea. The objective of this work is to evaluate if AWI can start from a simple 1D like initial velocity model and produce reasonable migrated images. To do so we compare the results from FWI starting from a well-defined reflection tomography model with the results derived from AWI starting from a simple 1D initial model. The quality of the results is evaluated using RMO cubes derived from 3D Kirchhoff PSDM common image gathers. We here demonstrate that, in this gas-cloud context, AWI is able to reconstruct a well resolved velocity in the gas cloud starting from the 1D like model. The quality of the P-wave velocity model is better than the velocity model derived from tomography and similar to the one derived by tomography plus FWI. For this case, we show that AWI could replace tomography for model building thus reducing the project duration.

Convergence Regions for AWI and FWI

Cycle-skipping is the most significant local minimum FWI suffers in practice, while adaptive waveform inversion (AWI) provides a new waveform-inversion scheme which is robust against cycle-skipping. In this paper, we present an extensive test exploring the convergence properties of both FWI and AWI against cycle-skipping. A set of 1300 initial models are designed by progressively smoothing the Marmousi model and by bulk shifting its mean slowness. The convergence regions of FWI and AWI are mapped based on the recovered models of both approaches. AWI shows a convergence region broader than FWI. It succeeds refining the initial models to the global minimum which FWI cannot.