Submitted as: model description paper
30 Nov 2021
Submitted as: model description paper | 30 Nov 2021
Status: a revised version of this preprint is currently under review for the journal GMD.

spyro: a Firedrake-based wave propagation and full waveform inversion finite element solver

Keith J. Roberts1, Alexandre Olender2, Lucas Franceschini2, Robert C. Kirby3, Rafael S. Gioria1, and Bruno S. Carmo2 Keith J. Roberts et al.
  • 1Dept. of Mining and Petroleum Engineering, Escola Politécnica, University of São Paulo
  • 2Dept. of Mechanical Engineering, Escola Politécnica, University of São Paulo
  • 3Dept. of Mathematics, Baylor University

Abstract. In this article, we introduce spyro, a software stack to solve acoustic wave propagation in heterogeneous domains and perform full waveform inversion (FWI) employing the finite element framework from Firedrake, a high-level Python package for the automated solution of partial differential equations using the finite element method. The capability of the software is demonstrated by using a continuous Galerkin approach to perform FWI for seismic velocity model building, considering realistic geophysics examples. A time-domain FWI approach is detailed that uses meshes composed of variably sized triangular elements to discretize the domain. To resolve both the forward and adjoint-state equations, and to calculate a mesh-independent gradient associated with the FWI process, a fully-explicit, variable higher-order (up to degree k = 5 in 2D and k = 3 in 3D) mass lumping method is used. We show that, by adapting the triangular elements to the expected peak source frequency and properties of the wavefield (e.g., local P-wavespeed) and by leveraging higher-order basis functions, the number of degrees-of-freedom necessary to discretize the domain can be reduced. Results from wave simulations and FWIs in both 2D and 3D highlight our developments and demonstrate the benefits and challenges with using triangular meshes adapted to the material properties.

Keith J. Roberts et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on gmd-2021-363', Anonymous Referee #1, 24 Jan 2022
  • RC2: 'Comment on gmd-2021-363', Anonymous Referee #2, 27 Jan 2022

Keith J. Roberts et al.

Data sets

Simulation scripts and data for full waveform inversion using spyro Keith J. Roberts

Model code and software

spyro V0.1.0 Keith J. Roberts; Alexandre Olender; Lucas Franceschini

Keith J. Roberts et al.


Total article views: 898 (including HTML, PDF, and XML)
HTML PDF XML Total BibTeX EndNote
676 205 17 898 10 6
  • HTML: 676
  • PDF: 205
  • XML: 17
  • Total: 898
  • BibTeX: 10
  • EndNote: 6
Views and downloads (calculated since 30 Nov 2021)
Cumulative views and downloads (calculated since 30 Nov 2021)

Viewed (geographical distribution)

Total article views: 850 (including HTML, PDF, and XML) Thereof 850 with geography defined and 0 with unknown origin.
Country # Views %
  • 1
Latest update: 20 May 2022
Short summary
Finite Element Methods (FEM), although permit the use of more flexible unstructured meshes, are rarely used in Full Waveform Inversions (FWI), an iterative process that reconstructs velocity models of earth’s subsurface, due to computational and memory storage costs. To reduce those costs, a novel software is presented allowing the use of high-order mass-lumped FEM on triangular meshes, together with a material-property mesh-adaptation performance enhancing strategy, enabling its use in FWI.