Full waveform inversion

Full Waveform Inversion (FWI) estimates subsurface model attributes by minimizing the difference between observed and simulated data as well as incorporating structural prior information. It relies on the consistent implementation of acoustic and visco/poro-elastic wave propagation equations.

As exascale high-performance computing continues to evolve, FWI is becoming increasingly feasible.

Owing to its reliance upon substantiated theoretical grounds, the method promises to provide superior insights into the course of subsurface resource characterization.

Albert Akhriev Sasha Aravkin Haim Avron Saurav Basu Stephen Becker Alecio Binotto
Paul Borrel Renato Cerqueira Devi Chunduri Alberto Costa Nogueira Jr. Anshul Gupta Lior Horesh
Shivkumar Kalyanaraman Kiran Mantripragada Stephen Moore Andrew Rawlinson Yogish Sabharwal Nicole Sultanum
Tigran Tchrakian Leonardo Pondian Tizzei Ewout van den Berg Karthik Visweswariah Sergiy Zhuk

Natural resources: Industry challenges

Challenge 1 Challenge 1

Design, plan, build, optimize

Challenge 2 Challenge 3

Find, produce, optimize

Challenge 3 Challenge 3

Maximize recovery



Cumulative water volume


Off-shore drilling challenges

Imaging: Seismic inversion

Seismic inversion is the process of transforming seismic data into a quantitative rock-property description of the subsurface.

This has been performed hitherto primarily by means of approximated physics or heuristic methods.

Seismic inversion

Industry trends: Depth imaging challenges roadmap

The entire industry is moving towards imaging methods of higher fidelity, implying higher (exascale) computing.

Industry trends

From data to image

FWI solution 1

Robust seismic imaging

Full wave inversion is non-convex regardless of penalty choice because observation is nonlinear. Heavy-tailed models are less conservative with regard to outlier distributions. Subsurface images drive key acquisition and development decisions. Many major oil companies are making significant efforts to take their imaging capabilities to the next level.

The image (top right) shows full wave inversion recovery based on the conventional approach. The image (bottom right) demonstrates image recovery of the same noise-corrupted data when robust measures are considered.

Robust seismic imaging

Robust seismic imaging

Forward/adjoint modelling


A first outcome:


Source estimation

Source estimation is a fundamental ingredient of Full Waveform Inversion (FWI). In such seismic inversion methods, wavelet intensity and phase spectra are usually estimated statistically, although for the FWI formulation as a nonlinear least-squares optimization problem it can naturally be incorporated to the workflow.

Modern approaches for source estimation consider robust misfit functions leading to the well-known robust FWI method. The present work uses synthetic data generated from a high-order spectral element forward solver to produce observed data, which in turn are used to estimate the intensity and the location of the point seismic source term of the original elastic wave PDE. A min-max filter approach is used to convert the original source estimation problem into a state problem conditioned to the observations and a non-standard uncertainty description.

The resulting numerical scheme uses an implicit midpoint method to solve, in parallel, the chosen 2D and 3D numerical examples running on an IBM Blue Gene/Q using a grid defined by approximately 16,000 5th-order elements, resulting in a total of approximately 6.5 million degrees of freedom. Further details are available in [2].

Source locations

List of references

[1] A Spectral Element Solution of the Wave Equation in 3D
Sergiy Zhuk, Steve Moore, James Korte, Andrew Rawlinson, Tigran Tchrakian, Lior Horesh, Aleksandr Aravkin
SEG workshop on FWI, 2014.

[2] Source Estimation for Wave Equations with Uncertain Parameters
Sergiy Zhuk, Stephen Moore, Alberto Costa Nogueira Junior, Andrew Rawlinson, Tigran Tchrakian, Lior Horesh, Aleksandr Aravkin and Albert Akhriev
European Control Conference, 2015.