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Full waveform inversion (FWI) aims to reconstruct high-resolution subsurface models from the full wavefield, which includes diving waves, post-critical reflections and short-spread reflections. Most successful applications of FWI are driven by the information carried by diving waves and post-critical reflections to build the long-to-intermediate wavelengths of the velocity structure. Alternative approaches, referred to as reflection waveform inversion (RWI), have been recently revisited to retrieve these long-to-intermediate wavelengths from shortspread reflections by using some prior knowledge of the reflectivity and a scale separation between the velocity macromodel and the reflectivity. This study presents a unified formalism of FWI, named as Joint FWI, whose aim is to efficiently combine the diving and reflected waves for velocity model building. The two key ingredients of Joint FWI are, on the data side, the explicit separation between the short-spread reflections and the wide-angle arrivals and, on the model side, the scale separation between the velocity macromodel and the shortscale impedance model. The velocity model and the impedance model are updated in an alternate way by Joint FWI and waveform inversion of the reflection data (least-squares migration), respectively. Starting from a crude velocity model, Joint FWI is applied to the streamer seismic data computed in the synthetic Valhall model. While the conventional FWI is stuck into a local minimum due to cycle skipping, Joint FWI succeeds in building a reliable velocity macromodel. Compared with RWI, the use of diving waves in Joint FWI improves the reconstruction of shallow velocities, which translates into an improved imaging at deeper depths. The smooth velocity model built by Joint FWI can be subsequently used as a reliable initial model for conventional FWI to increase the high-wavenumber content of the velocity model. [ABSTRACT FROM AUTHOR]

Full waveform inversion (FWI) of 3-D data sets has recently been possible thanks to the development of high performance computing. However, FWI remains a computationally intensive task when high frequencies are injected in the inversion or more complex wave physics (viscoelastic) is accounted for. The highest computational cost results from the numerical solution of the wave equation for each seismic source. To reduce the computational burden, one well-known technique is to employ a random linear combination of the sources, rather that using each source independently. This technique, known as source encoding, has shown to successfully reduce the computational cost when applied to real data. Up to now, the inversion is normally carried out using gradient descent algorithms. With the idea of achieving a fast and robust frequency-domain FWI, we assess the performance of the random source encoding method when it is interfaced with second-order optimization methods (quasi-Newton l-BFGS, truncated Newton). Because of the additional seismic modelings required to compute the Newton descent direction, it is not clear beforehand if truncated Newton methods can indeed further reduce the computational cost compared to gradient algorithms. We design precise stopping criteria of iterations to fairly assess the computational cost and the speed-up provided by the source encoding method for each optimization method. We perform experiment on synthetic and real data sets. In both cases, we confirm that combining source encoding with second-order optimization methods reduces the computational cost compared to the case where source encoding is interfaced with gradient descent algorithms. For the synthetic data set, inspired from the geology of Gulf of Mexico, we show that the quasi-Newton l-BFGS algorithm requires the lowest computational cost. For the real data set application on the Valhall data, we show that the truncated Newton methods provide the most robust direction of descent. [ABSTRACT FROM AUTHOR]

Multiparameter full waveform inversion (FWI) is a challenging quantitative seismic imaging method for lithological characterization and reservoir monitoring. The difficulties in multiparameter FWI arise from the variable influence of the different parameter classes on the phase and amplitude of the data, and the trade-off between these. In this framework, choosing a suitable parametrization of the subsurface and designing the suitable FWI workflow are two key methodological issues in non-linear waveform inversion. We assess frequency-domain visco-acoustic FWI to reconstruct the compressive velocity (VP), the density (ρ) or the impedance (IP) and the quality factor (QP), from the hydrophone component, using a synthetic data set that is representative of the Valhall oil field in the North Sea. We first assess which of the (VP, ρ) and (VP, IP) parametrizations provides the most reliable FWI results when dealing with wide-aperture data. Contrary to widely accepted ideas, we show that the (VP, ρ) parametrization allows a better reconstruction of both the VP, ρ and IP parameters, first because it favours the broad-band reconstruction of the dominant VP parameter, and secondly because the trade-off effects between velocity and density at short-to-intermediate scattering angles can be removed by multiplication, to build an impedance model. This allows for the matching of the reflection amplitudes, while the broad-band velocity model accurately describes the kinematic attributes of both the diving waves and reflections. Then, we assess different inversion strategies to recover the quality factor QP, in addition to parameters VP and ρ. A difficulty related to attenuation estimation arises because, on the one hand the values of QP are on average one order of magnitude smaller than those of VP and ρ, and on the other hands model perturbations relative to the starting models can be much higher for QP than for VP and ρ during FWI. In this framework, we show that an empirical tuning of the FWI regularization, which is adapted to each parameter class, is a key issue to correctly account for the attenuation in the inversion. We promote a hierarchical approach where the dominant parameter VP is reconstructed first from the full data set (i.e. without any data preconditioning) to build a velocity model as kinematically accurate as possible before performing the joint update of the three parameter classes during a second step. This hierarchical imaging of compressive wave speed, density and attenuation is applied to a real wide-aperture ocean-bottom-cable data set from the Valhall oil field. Several geological features, such as accumulation of gas below barriers of claystone and soft quaternary sediment are interpreted in the FWI models of density and attenuation. The models of VP, ρ and QP that have been developed by visco-acoustic FWI of the hydrophone data can be used as initial models to perform visco-elastic FWI of the geophone data for the joint update of the compressive and shear wave speeds. [ABSTRACT FROM AUTHOR]