Description of the topic and the problematic

Cutting-edge numerical techniques for seismic imaging are considered at different scales. Among them,

advanced methods relates to full-waveform inversion (FWI) and to reverse time migration (RTM). They

are essential to obtain quantitative images of the sub-surface, for example for the identification and

placement of hydrocarbon reservoirs and for the characterisation of the subsurface material like poros-

ity, viscosity, acoustic velocity, localisation, dimensions, and others. Such applications are extremely

important for the efficiency of oil and gas exploration, such as in coastal regions where hydrocarbon

reservoirs are found a few kilometres deep under salt bodies. One single well drilled in the wrong location

can waste millions of euros and delay the production for weeks or months. Even after the production

starts, it is important to track how reservoirs evolve (i.e., the quantities of remaining hydrocarbon, the

flow and pressure of fluids in porous rocks, where to inject fluids to increase pressure, etc) to maximise

production. But there are other applications. Seismic imaging methods can also be employed for the

location of of both onshore and offshore sites for the storage of carbon dioxide storage. Studies on the

use of caves for the capture and storage of CO2 are recent but with great potential for environmental

sustainability [RCGI (2018)]. The topic is really active from both its importance and its potential of

cutting-edge research activities Operto and Virieux (2009); Igel (2017); Munk and Wunsch (1982); Wu

and Zhang (2018); Zhang et al. (2019); Operto et al. (2013); Shi et al. (2020); Thrastarson et al. (2020).

In the geotechnical context or for environmental studies, quantiative seismic approaches are not yet fully

developed.

Full-waveform inversion (FWI) is a data-fitting procedure based on full-wavefield modelling to extract

quantitative information from collected data. In conventional time-domain FWI

workflows, most of the time is spent in the computation of the forward and adjoint wave propagation. The

kernel of this process involves the numerical solution of partial differential equations (PDEs) that model

the propagation of acoustic waves in multi-layer subsurface materials. The FWI workflow minimises

both amplitude and phase differences between the signals that are recorded with a set of microphones

(or hydrophones) located near the surface. The model is incrementally modified so that the functional

that represents the error is sufficiently reduced [Virieux and Operto (2009)]. The final objective is to

reconstruct various parameters of the materials, such as the velocities of P-waves and S-waves, density,

anisotropy, and attenuation. The reverse-time migration (RTM) is a quite similar process which uses

least-squares minimisation of the misfit between recorded and modelled data. One difference between

RTM and FWI is that the seismic wavefield recorded at the receiver is back propagated in reverse time

migration, whereas the data misfit is back propagated in the waveform inversion. Besides their application

for the identification and placement of hydrocarbon reservoirs, FWI and RTM are important tools for

studies for the use of caves for the capture and storage of carbon.

As a numerically sensitive inversion problem, FWI is computationally challenging. For instance,

cycle-skipping (related to the intrinsic oscillating nature of seismic waves) and non-linearity will lead to

convergence toward a local minimum. To mitigate this issue, there is a strong need for: (1) multi-scale

strategies, which progressively incorporate shorter wavelengths in the parameter space; (2) differential

approaches, in which the gradient and the Hessian operators can be efficiently estimated even in the

presence of multi-layer materials with sharp interfaces and diverse geological shapes; (3) better modelling

of the wave propagation physics; (4) noise reduction, and (5) efficient absorbing techniques along the

domain boundaries to mitigate spurious reflections.

In summary, FWI tries to iteratively approximate synthetic data (produced by simu-

lating waves propagating through an estimated velocity model) of the subsurface to actual

reflection data that were acquired during a seismic survey.

FWI and RTM workflows are known to be computationally heavy. Typically, the execution of an FWI

scenario can take several months on a Petaflop/s cluster with data that are collected with a frequency

within the range from 2 to 10 Hz. If the desired frequency if multiplied by a factor 2, the CPU time is

typically 16 times larger in 3d. As better quality data can be collected and made available, and because

higher resolution images are requested (i.e., processing higher frequency data) to shorten the “time to first

oil” and improve the industry efficiency, the computational cost of FWI will keep increasing significantly

in the coming years.

In summary, the existing computational methods for solving full-waveform inversion are

not only computationally expensive, but also yield low-resolution results because of the

ill-posedness and cycle skipping issues of FWI.

Main objectives

The main objective of this PhD proposal is to investigate high performance techniques for accelerating

seismic imaging applications such as FWI and RTM in the perspective of considering large-scale HPC

systems including exascale ones.

The expected focus and contribution of this PhD proposal is twofold. First, we will focus on stencil

codes (they are crucial for FWI and RTM problems), which are known to be computationally challenging

with high-performance processors [Tadonki (2017); Haggui et al. (2018)]. Stencil patterns can be fine-

grained for point-wise computations like in image processing or coarse-grained for macroscopic schemes

like what can be found with simulation codes in experimental physics [Tadonki (2017)]. The processing

power of modern processors is increasing, but their memory systems are more and more complex. Mapping

stencil codes efficiently on such processors is difficult and is still under intensive studies. Second, an

efficient parallelization of stencil codes on large cluster requires to skillfully program the compute nodes

and to minimize data exchanges. We will pay a particular attention on the non-uniform memory access

(NUMA) model, since most of large multi-core processors are of NUMA type. Efficient programming

for NUMA processors is a hot topic and the results of our achievements will certainly stand as an HPC

breakthrough, especially with exascale considerations. In addition, implementation of seismic imaging

codes on specific devices like GPUs and FPGAs still needs to be deeply explored for their potential

efficiency in terms of computing power and energy. The two main expected benefits are (1) to be able to

run FWI at higher frequencies for higher resolution images and (2) to possibly derive uncertainties on the

final result, instead of a unique deterministic solution. Such uncertainty maps are indeed not accessible

yet for computational reasons.

References

• Haggui, O., Tadonki, C., Lacassagne, L., Sayadi, F., and Ouni, B. (2018). Harris corner detection on a NUMA manycore. Future Generation Computer Systems, 88:442–452.
• Igel, H. (2017). Computational seismology: a practical introduction. Oxford University Press.
• Munk, W. H. and Wunsch, C. I. (1982). Observing the ocean in the 1990s. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 307(1499):439–464.
• Operto, S., Gholami, Y., Prieux, V., Ribodetti, A., Brossier, R., Metivier, L., and Virieux, J. (2013). A guided tour of multiparameter full-waveform inversion with multicomponent data: From theory to practice. The Leading Edge, 32(9):1040–1054.
• Operto, S. and Virieux, J. (2009). An overview of full-waveform inversion in exploration geophysics. Geophysics, 74(6):WCC1.
• RCGI (2018). Rcgi scientists study storage of carbon-rich nat. gas in underwater salt caves. https://www.rcgi.poli.usp.br/rcgi-scientists-study-storage-of-carbon-ri….
• Shi, J., Beretta, E., de Hoop, M. V., Francini, E., and Vessella, S. (2020). A numerical study of multi-parameter full waveform inversion with iterative regularization using multi-frequency vibroseis data. Computational Geosciences, 24(1):89–107.
• Tadonki, C. (2017). Scalable numa-aware wilson-dirac on supercomputers. pages 315–324.
• Thrastarson, S., van Driel, M., Krischer, L., Boehm, C., Afanasiev, M., van Herwaarden, D.-P., and Fichtner, A. (2020). Accelerating numerical wave propagation by wavefield adapted meshes. Part II: full-waveform inversion. Geophysical Journal International, 221(3):1591–1604.
• Virieux, J. and Operto, S. (2009). An overview of full-waveform inversion in exploration geophysics. Geophysics, 74(6).
• Wu, H. and Zhang, B. (2018). A deep convolutional encoder-decoder neural network in assisting seismic horizon tracking.
• Zhang, Y., Gao, J., Han, W., and He, Y. (2019). A discontinuous Galerkin method for seismic wave propagation in coupled elastic and poroelastic media. Geophysical Prospecting, 67(5):1392–1403.

Funding category: Contrat doctoral

Contrat doctoral classique

PHD title: Ingénierie des Systèmes, Matériaux, Mécanique, Energétique

PHD Country: France