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Summary For macro-velocity-model building, the ray-based formulation of classic stereotomography is replaced by eikonal solvers with simultaneous introduction of adjoint-state method for an efficient matrix free optimization scheme. In this approach, named adjoint stereotomography, forward modelling is performed from sources and receivers, making the approach independent of the data complexity. In this work, the adjoint stereotomography is extended to anisotropic media where vertical velocity, Thomsen anisotropic parameters and scattering-point positions are inverted jointly. In this multi-parameter inversion, the matrix-free framework of optimization reduces drastically the computational burden of the workflow. The inversion is based on a weighted leastsquares misfit function as we mix different data. Explicit expressions of gradients for the different parameters are provided and are illustrated through sensitivity kernels. A very simple example of a circular anomaly will show how are recovered parameters when using a quasi-Newton lBFGS method of optimization, giving us the confidence that more realistic examples could be investigated in the future.

We apply 2D VTI acoustic FWI to wide-aperture OBC data from the Valhall field. Initial models for FWI are determined by VTI reflection traveltime tomography. Mono-parameter and multi-parameter VTI FWI are applied to the hydroacoustic component for reconstruction of seismic wavespeeds and Thomsen parameters, while density and attenuation are kept at their initial values during FWI. Two types of inversions are considered: in the first one, we invert only for one velocity and we keep fixed two Thomsen parameters. In the second one, we invert for two velocities, while the extra Thomsen pa- rameter is kept fixed during FWI. As long as the two Thomsen parameters describe the long wavelength content of the subsurface, the first type of inversion succeeds in reconstructing the wavespeed with a high resolution. The second type of inversion succeeds in reconstructing the two wavespeeds, vertical or normal moveout and horizontal velocities, but with a lower resolution for the horizontal velocities. Reverse time migrations and common image gathers, which are computed in the initial and final FWI models, show that FWI models do not allow us to improve the deep part of the migrated images, where the footprint of anisotropy is shown.

Backlund transform is applied to a seismogram in order to construct a new signal where the time is transformed in a pseudo‐time the square of its dimension is expressed in seconds. The Backlund transform links partial differential equations related to wave propagation to partial differential equations related to diffusion. Potential applications have been performed previously from magnetotelluric data to pseudo‐seismic signals by using the inverse of the Backlund transform. This transform could be applied to the seismic signal through real computations. Therefore, we propose to transform seismic data into pseudo‐CSEM signals for possible applications of these diffusive signals as the initial stage of the full waveform inversion of seismic data.

Modelling methods are nowadays at the heart of any geophysical interpretation approach. These are heavily relied upon by imaging techniques in elastodynamics and electromagnetism, where they are crucial for the extraction of subsurface characteristics from ever larger and denser datasets. While highfrequency or one-way approximations are very powerful and efficient, they reach their limits when complex geological settings and solutions of full equations are required for high resolution imaging. A review of three important formulations will be carried out during this presentation: the spectral method, which is very efficient and accurate but generally restricted to simple earth structures, and often layered earth structures; the pseudo-spectral, finite-difference and finite-volume methods based on strong formulation of the partial differential equations, which are easy to implement and currently represent a good compromise between accuracy, efficiency and flexibility; and the continuous or discontinuous Galerkin finite-element methods that are based on the weak formulation, which lead to more accurate earth representations and therefore to more accurate solutions, although with higher computational costs and more complex use. The choice between these different approaches is still difficult and depends on the applications. Guidelines are given here through discussion of the requirements for imaging/ inversion.

Here we assess the potential of the visco-acoustic frequency domain full-waveform inversion (FWI) to reconstruct P-wave velocity and P-wave attenuation factor (Qp) from onshore seismic data. We show that both the velocity and the attenuation factor can be reliably reconstructed with a comparable resolution and without trade-off for sufficiently attenuating media and sufficiently-accurate velocity starting model by non-linear inversion. We applied both the acoustic and visco-acoustic FWI to real wide-aperture onshore seismic data with a strong footprint of attenuation that were recorded in the Polish Basin. We show how a heuristic normalisation of the data with offset allows us to remove the effect of the attenuation from the data and reconstruct a reliable velocity model in the acoustic approximation. Alternatively, visco-acoustic FWI allows us to reconstruct jointly both a reliable velocity model and a Q model from the true-amplitude data. We find the recovered velocity and Q models consistent with the expected lithology and stratigraphy in the study area. We link high-attenuation zones with the increased clay content and the presence of the mineralized fluids.