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The analysis of surface wave dispersion curves (DCs) is widely used for near-surface S -wave velocity (VS) reconstruction. However, a comprehensive characterization of the near-surface requires also the estimation of P -wave velocity (VP). We focus on the estimation of both VS and VP models from surface waves using a direct data transform approach. We estimate a relationship between the wavelength of the fundamental mode of surface waves and the investigation depth and we use it to directly transform the DCs into VS and VP models in laterally varying sites. We apply the workflow to a real data set acquired on a known test site. The accuracy of such reconstruction is validated by a waveform comparison between field data and synthetic data obtained by performing elastic numerical simulations on the estimated VP and VS models. The uncertainties on the estimated velocity models are also computed. [ABSTRACT FROM AUTHOR]

The SEISCOPE optimization toolbox is a set of FORTRAN 90 routines, which implement first-order methods (steepest-descent and nonlinear conjugate gradient) and second-order methods (l-BFGS and truncated Newton), for the solution of large-scale nonlinear optimization problems. An efficient line-search strategy ensures the robustness of these implementations. The routines are proposed as black boxes easy to interface with any computational code, where such large-scale minimization problems have to be solved. Traveltime tomography, least-squares migration, or full-waveform inversion are examples of such problems in the context of geophysics. Integrating the toolbox for solving this class of problems presents two advantages. First, it helps to separate the routines depending on the physics of the problem from the ones related to the minimization itself, thanks to the reverse communication protocol. This enhances flexibility in code development and maintenance. Second, it allows us to switch easily between different optimization algorithms. In particular, it reduces the complexity related to the implementation of second-order methods. Because the latter benefit from faster convergence rates compared to first-order methods, significant improvements in terms of computational efforts can be expected. [ABSTRACT FROM AUTHOR]

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]

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]

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]

Multiparameter elastic full waveform inversion (FWI) is a promising technology that allows inferences to be made on rock and fluid properties, which thus narrows the gap between seismic imaging and reservoir characterization. Here, we assess the feasibility of 2-D vertical transverse isotropic visco-elastic FWI of wide-aperture multicomponent ocean-bottom-cable data from the Valhall oil field. A key issue is to design a suitable hierarchical data-driven and model-driven FWI workflow, the aim of which is to reduce the nonlinearity of the FWI. This nonlinearity partly arises because the shear (S) wavespeed can have a limited influence on seismic data in marine environments. In a preliminary stage, visco-acoustic FWI of the hydrophone component is performed to build a compressional (P)-wave velocity model, a density model and a quality-factor model, which provide the necessary background models for the subsequent elastic inversion. During the elastic FWI, the P and S wavespeeds are jointly updated in two steps. First, the hydrophone data are inverted to mainly update the long-to-intermediate wavelengths of the S wavespeeds from the amplitude-versus-offset variations of the P–P reflections. This S-wave velocity model is used as an improved starting model for the subsequent inversion of the better-resolving data recorded by the geophones. During these two steps, the P-wave velocity model is marginally updated, which supports the relevance of the visco-acoustic FWI results. Through seismic modelling, we show that the resulting visco-elastic model allows several P-to-S converted phases recorded on the horizontal-geophone component to be matched. Several elastic quantities, such as the Poisson ratio, and the ratio and product between the P and S wavespeeds, are inferred from the P-wave and S-wave velocity models. These attributes provide hints for the interpretation of an accumulation of gas below lithological barriers. [ABSTRACT FROM AUTHOR]

The development of dense networks of broad-band seismographs makes teleseismic data amenable to full-waveform inversion (FWI) methods for high-resolution lithospheric imaging. Compared to scattered-field migration, FWI seeks to involve the full seismic wavefield in the inversion. We present a parametric analysis of 2-D frequency-domain FWI in the framework of lithospheric imaging from teleseismic data to identify the main factors that impact on the quality of the reconstructed compressional (P)-wave and shear (S)-wave speed models. Compared to controlled-source seismology, the main adaptation of FWI to teleseismic configuration consists of the implementation with a scattered-filed formulation of plane-wave sources that impinge on the base of the lithospheric target located below the receiver network at an arbitrary incidence angle. Seismic modelling is performed with a hp-adaptive discontinuous Galerkin method on unstructured triangular mesh. A quasi-Newton inversion algorithm provides an approximate accounting for the Hessian operator, which contributes to reduce the footprint of the coarse acquisition geometry in the imaging. A versatile algorithm to compute the gradient of the misfit function with the adjoint-state method allows for abstraction between the forward-problem operators and the meshes that are during seismic modelling and inversion, respectively. An approximate correction for obliquity is derived for future application to real teleseismic data under the two-dimension approximation. Comparisons between the characteristic scales involved in exploration geophysics and in teleseismic seismology suggest that the resolution gain provided by full waveform technologies should be of the same order of magnitude for both applications. We first show the importance of the surface-reflected wavefield to dramatically improve the resolving power of FWI by combining tomography-like and migration-like imaging through the incorporation of the forward-scattered and the backscattered wavefields in the inversion. The resolution of FWI is assessed through checkerboard tests and confirms a resolution of the order of the wavelength for both the P and S speeds, when the full wavefield is incorporated in the inversion. Secondly, we show that computationally efficient strategies, which consist of decimating the number of frequency components involved in the inversion, do not apply to teleseismic acquisitions, because the scattering-angle bandwidth sampled by plane-wave sources can be narrow and coarsely sampled, compared to that provided by dense profiles of point sources in exploration seismology. The waveform inversion is less sensitive to the band of incidence angles spanned by the plane-wave sources and to the sampling of this band. However, the deficit of vertically propagating plane waves hampers the vertical resolution of planar layers. Aliasing artefacts created by coarse arrays of receivers are illustrated. We show how taking into account the Hessian in the inversion and the suitable management of frequencies in the inversion help to mitigate these artefacts. Acceptable reconstructions are shown for both the P- and S-wave speeds for a receiver spacing of up to 20 km in the 0.1–0.4 Hz frequency range. Building a reliable initial model for FWI is a highly non-linear problem in exploration seismology. We show how the low-frequency content of the teleseismic sources allow us to build accurate P- and S-wave speed models starting from simple vertical-gradient velocity models. All of these results are derived using a 2-D realistic synthetic experiment that was performed with noise-free data. Most of conclusions of this parametric study should apply in three dimensions. The impact of noise and the footprint of other experimental parameters ... [ABSTRACT FROM AUTHOR]