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ABSTRACT Full-waveform inversion is re-emerging as a powerful data-fitting procedure for quantitative seismic imaging of the subsurface from wide-azimuth seismic data. This method is suitable to build high-resolution velocity models provided that the targeted area is sampled by both diving waves and reflected waves. However, the conventional formulation of full-waveform inversion prevents the reconstruction of the small wavenumber components of the velocity model when the subsurface is sampled by reflected waves only. This typically occurs as the depth becomes significant with respect to the length of the receiver array. This study first aims to highlight the limits of the conventional form of full-waveform inversion when applied to seismic reflection data, through a simple canonical example of seismic imaging and to propose a new inversion workflow that overcomes these limitations. The governing idea is to decompose the subsurface model as a background part, which we seek to update and a singular part that corresponds to some prior knowledge of the reflectivity. Forcing this scale uncoupling in the full-waveform inversion formalism brings out the transmitted wavepaths that connect the sources and receivers to the reflectors in the sensitivity kernel of the full-waveform inversion, which is otherwise dominated by the migration impulse responses formed by the correlation of the downgoing direct wavefields coming from the shot and receiver positions. This transmission regime makes full-waveform inversion amenable to the update of the long-to-intermediate wavelengths of the background model from the wide scattering-angle information. However, we show that this prior knowledge of the reflectivity does not prevent the use of a suitable misfit measurement based on cross-correlation, to avoid cycle-skipping issues as well as a suitable inversion domain as the pseudo-depth domain that allows us to preserve the invariant property of the zero-offset time. This latter feature is useful to avoid updating the reflectivity information at each non-linear iteration of the full-waveform inversion, hence considerably reducing the computational cost of the entire workflow. Prior information of the reflectivity in the full-waveform inversion formalism, a robust misfit function that prevents cycle-skipping issues and a suitable inversion domain that preserves the seismic invariant are the three key ingredients that should ensure well-posedness and computational efficiency of full-waveform inversion algorithms for seismic reflection data. [ABSTRACT FROM AUTHOR]

ABSTRACT Building an accurate initial velocity model for full waveform inversion (FWI) is a key issue to guarantee convergence of full waveform inversion towards the global minimum of a misfit function. In this study, we assess joint refraction and reflection stereotomography as a tool to build a reliable starting model for frequency-domain full waveform inversion from long-offset ( i.e., wide-aperture) data. Stereotomography is a slope tomographic method that is based on the inversion of traveltimes and slopes of locally-coherent events in a data cube. One advantage of stereotomography compared to conventional traveltime reflection tomography is the semi-automatic picking procedure of locally-coherent events, which is easier than the picking of continuous events, and can lead to a higher density of picks. While conventional applications of stereotomography only consider short-offset reflected waves, we assess the benefits provided by the joint inversion of reflected and refracted arrivals. Introduction of the refracted waves allows the construction of a starting model that kinematically fits the first arrivals, a necessary requirement for full waveform inversion. In a similar way to frequency-domain full waveform inversion, we design a multiscale approach of stereotomography, which proceeds hierarchically from the wide-aperture to the short-aperture components of the data, to reduce the non-linearity of the stereotomographic inversion of long-offset data. This workflow which combines stereotomography and full waveform inversion, is applied to synthetic and real data case studies for the Valhall oil-field target. The synthetic results show that the joint refraction and reflection stereotomography for a 24-km maximum offset data set provides a more reliable initial model for full waveform inversion than reflection stereotomography performed for a 4-km maximum offset data set, in particular in low-velocity gas layers and in the deep part of a structure below a reservoir. Application of joint stereotomography, full waveform inversion and reverse-time migration to real data reveals that the FWI models and the reverse-time migration images computed from the stereotomography model shares several features with FWI velocity models and migrated images computed from an anisotropic reflection-traveltime tomography model, although stereotomography was performed in the isotropic approximation. Implementation of anisotropy in joint refraction and reflection stereotomography of long-offset data is a key issue to further improve the accuracy of the method. [ABSTRACT FROM AUTHOR]

ABSTRACT We present a parallel domain decomposition method based on a hybrid direct-iterative solver for 3D frequency-domain modelling of visco-acoustic waves. The method is developed as a modelling engine for frequency-domain full waveform inversion. Frequency-domain seismic modelling reduces to the solution of a large and sparse system of linear equations, resulting from the discretization of the heterogeneous Helmholtz equation. Our approach to the high-performance, scalable solution of large sparse linear systems is to combine direct and iterative methods. Such a hybrid approach exploits the advantages of both direct and iterative methods. The iterative component uses a small amount of memory and provides a natural way for parallelization. The direct part has favourable numerical properties for multiple right-hand side modelling. The domain decomposition is based upon the algebraic Schur complement method, which allows for the iterative solution of a reduced system, the solution of which is the wavefield at the interfaces between the subdomains. Once the interface unknowns have been computed, the wavefield at the interior of each subdomain is efficiently computed by local substitutions. The reduced Schur complement system is solved with the generalized minimum residual method and is preconditioned by an algebraic additive Schwarz preconditioner. A direct solver is used to factorize local impedance matrices defined on each subdomain. Theoretical analysis shows that the time complexity of the hybrid solver is the same as that of iterative solver and time-domain approaches for single frequency modelling. Simulations are performed in the SEG/EAGE overthrust and the salt models for frequencies up to 12.5 Hz. The number of iterations increases linearly with the number of subdomains for a given computational domain but the elapsed time of the iterative resolution remains almost constant. The number of iterations also increases linearly with frequencies, when the grid interval is adapted to the frequencies and the size of the subdomains is kept constant over frequency. These results make the cost of the hybrid solver of the same order as that of finite-difference time-domain modeling for one-frequency modelling. Although the hybrid approach allows one to tackle larger problems than the direct-solver approach, further improvements are needed to mitigate the computational burden of the iterative component in the context of multisource modelling. On the numerical side, the use of block iterative solvers and of incremental two-level deflating preconditioners and on the parallel implementation side, the use of two levels of parallelism in the domain decomposition method should mitigate this computational burden. [ABSTRACT FROM AUTHOR]

In this study we present the workflow and results of 2D frequency domain waveform tomography applied to the global-offset seismic data acquired in central Poland along a 50-km long profile during the GRUNDY 2003 experiment. The waveform tomography method allows full exploitation of the wide-aperture content of these data and produces in a semi-automatic way both the detailed P-wave velocity model and the structural image (i.e., perturbations in respect to the starting model). Thirteen frequencies ranging from 4 to 16 Hz were inverted sequentially, gradually introducing higher wavenumbers and more details into the velocity models. Although the data were characterised by relatively large shot spacings (1.5 km), we obtained clear images both of the Mesozoic and Permian sedimentary cover. Velocity patterns indicated facies changes within the Jurassic and Zechstein strata. A high velocity layer (ca. 5500 m/s) was found near the base of Triassic (Scythian), which made the imaging of a deeper layer difficult. Nevertheless, we were able to delineate the base of the Permian (i.e., base of the Rotliegend), which was not possible to derive from conventional common-depth-point processing, as well as some deeper events, attributed to the Carboniferous. The sub-Permian events formed a syn-form which favoured our previous interpretation of a depression filled with Upper Carboniferous molasse. The validity of the waveform tomography-derived model was confirmed by well-log data. Forward ray-tracing modelling and synthetic seismograms calculations provided another justification for the key structures present in the waveform tomography model. [ABSTRACT FROM AUTHOR]

Double-difference tomographic methods use directly accurate time delays computed between similar signals. Such methods are designed to image very heterogeneous media, such as volcanoes or fault zones. In seismological applications, similar signals are recorded at a given station from earthquakes sharing similar and close-by sources. In seismic exploration experiments, similar signals are often recorded at neighbouring receivers. After a brief presentation of the tomographic algorithm used, a seismological application is summarized. The potential and limits of double-difference tomographic methods are explored using various numerical experiments. They show that two effects are competing in double-difference tomography: (i) the degradation of the stability of the inversion due to the geometrical proximity of the rays used in the differentiation and (ii) the decrease in modelling error, which allows improving the stability of the inversion and using smaller quantities of a priori information when data are sufficiently accurate. The best resolution is obtained for an optimal value of the inter-source or inter-receiver distance. For optimal values of these distances and a priori information, tomography using traveltime differences provides significantly better resolved results than using traveltimes. [ABSTRACT FROM AUTHOR]

Wavelet decomposition of the slowness model allows a multiscale description of the seismic first-arrival time tomography. We propose the introduction of the so-called second generation wavelets that could be used for any mesh structure and do not require a number of samples, such as the power of two in each direction for fast wavelet transform. A linearized procedure for inverting delayed travel-times considering either slowness coefficients or wavelet coefficients has been set up with an efficient ray tracing at each iteration of the inversion procedure. Wavelet decomposition over constant patches (Haar wavelet) or over linear patches (Battle-Lemarie wavelet) of coefficients at different scales are inverted as unknowns of the tomographic linearized system. Reconstruction of these coefficients depends dynamically on the local resolution when considering dense ray coverage. On simple synthetic examples, it has been found necessary to perform a local resolution analysis for specifying wavelet coefficients to be inverted. This resolution analysis could be performed for an initial smooth reconstructed medium and by designing a bit mask operator it allows fine scales to be inverted in specific areas of the model where the resolution is high while not being inverted in other areas where the resolution is poor: the wavelet decomposition will ease the multiscale reconstruction. A few synthetic examples, such as crosshole tomography or surface-surface tomography illustrate the multiscale feature of wavelet tomography. The second generation wavelet approach seems to be a flexible and rather promising tool for controlling the resolution variation of seismic first-arrival tomography. [ABSTRACT FROM AUTHOR]