Full-waveform inversion with the reconstructed wavefield method

Abstract

Over the last decade, conventional full waveform inversion (FWI) has been widely applied to real seismic data for both production and research purposes. The underlying theory has been well established and produces high resolution subsurface models by minimizing the misfit between the seismic data and simulated seismograms obtained by solving the wave equation exactly. However, in practice, it is still a challenging inversion method for updating the model parameters. A local optimization scheme is used to solve the minimization problem and it does not prevent convergence towards local minima because of the nonlinearity and ill-posedness of the problem. For example, FWI may converge to a local minimum because of the lack of low frequencies in the recorded data or an inaccurate starting model. We propose a novel approach to time domain full waveform inversion with the reconstructed wavefield method (RFWI). RFWI relaxes the constraint that the forward modeled data exactly solve the wave equation as in conventional FWI, and instead uses an 2 approximate solution. RFWI estimates earth models and jointly reconstructs the forward wavefield by minimizing an objective function that includes penalties for both the data misfit and wave equation error. By extending the search space, RFWI offers potential benefits of avoiding cycle skipping and overcoming some of the problems with local minima. This paper first presents the theory and implementation of time domain RFWI. It also discusses the differences and similarities between conventional FWI and RFWI. The benefits of RFWI over conventional FWI are demonstrated using a 2D synthetic example. Finally, the applicability of RFWI on field data is illustrated on a 2D streamer data set from offshore Congo and a 3D ocean bottom seismic data set from the Gulf of Mexico.

Efficient Wavefield Inversion With Outer Iterations and Total Variation Constraint

“…This allows for a larger searchspace over both the wavefields and the model [26], [27]. By extending the source function beyond a point source, reconstructed wavefields are able to fit the recorded data better than the original WRI [28], [29], [30]. In WRI (or modified WRI), the velocity is updated at every iteration, which consequently means an updated wave equation operator.…”

Full-waveform inversion via source-receiver extension

“…Other source extension concepts have also been productive. Waveform reconstruction inversion as described by van Leeuwen and Herrmann (2013) is roughly equivalent to introducing artificial sources "everywhere" (for discussion of other related algorithms, see Huang and Symes, 2016a;Wang and Yingst, 2016). Contrast source inversion, described, for example, by Abubakar et al (2011), may also be regarded as a source extension approach.…”

Seismic wavefield imaging of Earth’s interior across scales

“…The cycle-skipping problem 106,117,118 , in which observed and simulated waveforms are misaligned by one cycle or more, renders incorrect misfit measurements and hinders convergence. This issue has motivated reformulations of the inverse problem that are less sensitive to cycle skipping, including adaptive waveform inversion 117 , source-receiver extension 119 , extension through time lag 120 , the use of optimal transport distance 106,121-123 and wavefield-reconstruction inversion 124,125 .…”