My main professional interest is seismic imaging of the earth interior by tomography and full waveform inversion.
I am interested in theoretical, algorithmic and application aspects of full waveform inversion (FWI). FWI is a PDE-constrained optimization method which aims to estimate mechanical properties of the earth interior by fitting the waveforms of seismic records. The PDE constraint is the wave equation where the mechanical properties of the earth are embedded in its spatially-varying coefficients. In its conventional form the objective function to be minimized is the least-squares norm of the difference between the seismic observables and the restriction of the numerically-simulated wavefield at the receiver positions. We classically solve this optimization problem with local optimization techniques (gradient-based methods) and a reduced-space (variable projection) approach: we transform the PDE-constrained optimization problem into an unconstrained problem by enforcing the closed-form expression of the solution of the wave equation as a function of the subsurface parameters in the data misfit function and solve the unconstrained problem with Newton-type algorithm where the gradient of the objective function is computed with the so-called matrix-free adjoint-state method. It is well acknowledged that this inverse problem is highly nonlinear due to the oscillatory nature of seismic waves. The linearization of the FWI relies on the Born approximation which requires the initial subsurface model to allow for the fitting of the recorded traveltimes with an error that does not exceed half the period. This kinematic-accuracy condition is challenging to achieve for real-life problems in particular for long-offset acquisitions.
My current interestes are to overcome this pitfalls with two different approaches:
The first aims to improve the accuracy of the initial subsurface model that is built by slope tomography also referred to stereotomography. Slope tomography seeks to track in a semi-automatic way locally-coherent events in the seismic data volume to perform a dense picking of traveltimes and slopes (the horizontal component of the slowness vectors ideally at the source and receiver positions). This dense picking is amenable to high-resolution velocity model building. Traveltimes are sensitivie to the long-wavelength distribution of the velocity field, while the slopes carry out a complementary information on the velocity gradients. We have developed a new formulation of slope tomography based on eikonal solver and the adjoint-state method (Tavakoli et al., 2017, Tavakoli et al., 2019, Sambolian et al., 2019a) and extend it to first-arrival traveltime tomography (Sambolian et al., 2019b) and joint first-arrival and reflection tomography (Sambolian et al., 2019c) . We aim to apply this technology on towed-streamer data as well as to sparse multi-component ocean-bottom seismometer data.
These developments have been performed during the PhD of Borhan Tavakoli and continue during the ongoing PhD of Serge Sambolian.
The second approach seeks to extend the linear regime of the FWI by extending its search space with the Wavefield Reconstruction Inversion (WRI) method. WRI fosters the data fitting and prevent the cycle skipping pathology accordingly by relaxing the wave equation constraint (by allowing for extended sources) during wavefield reconstruction. Then, the subsurface parameters are updated by minimizing the source residuals or shrink the extended sources to their trough form (point source with a given temporal signature). We implement WRI with the alternating direction method of multipliers (ADMM) i.e., an augmented Lagrangian method with operator splitting (Aghamiry et al., 2019a) and with various regularization (nonsmooth, adaptive,...) (Aghamiry et al., 2019b,Aghamiry et al., 2019c). We work also on extension of ADMM_based WRI to multi-parameter imaging for anisotropic and attenuating media (Aghamiry et al., 2019d, Aghamiry et al., 2019e), adaptation to time domain (Aghamiry et al., 2019f), improvement with phase retrieval (Aghamiry et al., 2019g), ...
These developments are performed with Hossein Aghamiry (University Cote d'Azur | University of Tehran) and Professor Ali Gholami (University of Tehran).
From the algorithmic viewpoint, we are developing at Geoazur in-house slope tomography code as well as 3D time-domain and frequency-domain FWI codes. The time-domain FWI code is developed by L. Combe and the frequency domain code by A. Miniussi and myself. In this latter code, we use the MUMPS multifrontal solver to solve efficiently the time-harmonic wave equation with multiple right-hand sides. I am currebtly collaborating with V. Dolean, P. Jolivet and P.-H. Tournier to assess whether the GMRES iterative solver with multi-level domain decomposition preconditioner is a complementary linear algebra method to address large-scale problem.
We are working on different applications on OBC data from the North sea (Operto et al., 2015, Amestoy et al., 2016, Operto and Miniussi, 2018) and on OBS data from the eastern Nankai trough in Japan in collaboration with Andrzej Gorszczyk and Michal Malinowski (Institute of Geophysics of the Polish Academy of Science) (Gorszczyk et al., 2017; Gorszczyk et al., 2019).
I am also interested in application of FWI on earthquake data, in particular on teleseismic data.
Stephen Beller and Vadim Monteiller have developed a 3D FWI code for lithospheric imaging from teleseismic data. A sensitivity analysis of the data to the acquisition geometry, the subsurface parametrization and the initial model was performed as well as an application on the data from the CIFALPS experiment in the western Alps (Beller et al., 2010a, Beller et al., 2010b).
I launched in 2020 the WIND project which aims to develop the FWI technology for deep crustal imaging from multi-component OBS data. This raises three important challenges related to the acquisition design of OBS survey amenable to slope tomography and FWI, high-performance computing challenges to address FWI applications involving up to billions of parameters and methodological challenges related to the nonlinearity of the FWI for long-offset deep-crustal stationary recording geometries. The WIND project is currently supported by a consortium of oil companies. Visit the WIND site for more details.
I am also involved in the SEFASILS project which aims to perform a regional seismic exploration of the Northern Ligurian margin in November-December 2018.
