Michael Afanasiev

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Afanasiev

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Michael

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0000-0002-5050-7454

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Publications1 - 10 of 12

Accelerating numerical wave propagation by wavefield adapted meshes, Part II: Full-waveform inversion
Thrastarson, Sölvi; van Driel, Martin; Krischer, Lion; et al. (2020)
Geophysical Journal International
We present a novel full-waveform inversion (FWI) approach which can reduce the computational cost by up to an order of magnitude compared to conventional approaches, provided that variations in medium properties are sufficiently smooth. Our method is based on the usage of wavefield adapted meshes which accelerate the forward and adjoint wavefield simulations. By adapting the mesh to the expected complexity and smoothness of the wavefield, the number of elements needed to discretize the wave equation can be greatly reduced. This leads to spectral-element meshes which are optimally tailored to source locations and medium complexity. We demonstrate a workflow which opens up the possibility to use these meshes in FWI and show the computational advantages of the approach. We provide examples in 2-D and 3-D to illustrate the concept, describe how the new workflow deviates from the standard FWI workflow, and explain the additional steps in detail.
Using optimal transport to mitigate cycle-skipping in ultrasound computed tomography
Boehm, Christian; Krischer, Lion; Ulrich, Ines; et al. (2022)
Proceedings of SPIE ~ Medical Imaging 2022 Ultrasonic Imaging and Tomography
Full-waveform inversion (FWI) for ultrasound computed tomography is an advanced method to provide quantitative and high-resolution images of tissue properties. Two main reasons hindering the widespread adoption of FWI in clinical practice are (1) its high computational cost and (2) the requirement of a good initial model to mitigate the non-convexity of the inverse problem. The latter is commonly referred to as “cycle-skipping", which occurs for phase differences between synthetic and observed signals and usually traps the inversion in a local minimum. Source-encoding strategies, which simultaneously activate several emitters and have been proposed to reduce the simulation cost, further contribute to this issue due to the multiple arrivals of the wavefronts. We present a time-domain acoustic full-waveform inversion strategy utilizing a recently proposed misfit functional based on optimal transport. Using a graph-space formulation, the discrepancy between simulated and observed signals can be computed efficiently by solving an auxiliary linear program. This approach alleviates the common need for either a good initial model and / or low-frequency data. Furthermore, combining this misfit functional with random source-encoding and a stochastic trust-region method significantly reduces the computational cost per FWI iteration. In-silico examples using a numerical phantom for breast screening ultrasound tomography demonstrate the ability of the proposed inversion strategy to converge to the ground truth even when starting from a weak prior and cycle-skipped data.
Full-waveform inversion of ultrasonic echo signals to evaluate grouting quality of tendon ducts in post-tensioned concrete structures
Krischer, Lion; Strobach, Elmar; Boehm, Christian; et al. (2022)
Accelerating numerical wave-propagation using wavefield adapted meshes, Part I: Forward and adjoint modelling
van Driel, Martin; Boehm, Christian; Krischer, Lion; et al. (2020)
Geophysical Journal International
An order of magnitude speed-up in finite-element modelling of wave propagation can be achieved by adapting the mesh to the anticipated space-dependent complexity and smoothness of the waves. This can be achieved by designing the mesh not only to respect the local wavelengths, but also the propagation direction of the waves depending on the source location, hence by anisotropic adaptive mesh refinement. Discrete gradients with respect to material properties as needed in full waveform inversion can still be computed exactly, but at greatly reduced computational cost. In order to do this, we explicitly distinguish the discretization of the model space from the discretization of the wavefield and derive the necessary expressions to map the discrete gradient into the model space. While the idea is applicable to any wave propagation problem that retains predictable smoothness in the solution, we highlight the idea of this approach with instructive 2-D examples of forward as well as inverse elastic wave propagation. Furthermore, we apply the method to 3-D global seismic wave simulations and demonstrate how meshes can be constructed that take advantage of high-order mappings from the reference coordinates of the finite elements to physical coordinates. Error level and speed-ups are estimated based on convergence tests with 1-D and 3-D models.
Accelerated full-waveform inversion using dynamic mini-batches
van Herwaarden, Dirk-Philip; Boehm, Christian; Afanasiev, Michael; et al. (2020)
Geophysical Journal International
We present an accelerated full-waveform inversion based on dynamic mini-batch optimization, which naturally exploits redundancies in observed data from different sources. The method rests on the selection of quasi-random subsets (mini-batches) of sources, used to approximate the misfit and the gradient of the complete data set. The size of the mini-batch is dynamically controlled by the desired quality of the gradient approximation. Within each mini-batch, redundancy is minimized by selecting sources with the largest angular differences between their respective gradients, and spatial coverage is maximized by selecting candidate events with Mitchell’s best-candidate algorithm. Information from sources not included in a specific mini-batch is incorporated into each gradient calculation through a quasi-Newton approximation of the Hessian, and a consistent misfit measure is achieved through the inclusion of a control group of sources. By design, the dynamic mini-batch approach has several main advantages: (1) The use of mini-batches with adaptive size ensures that an optimally small number of sources is used in each iteration, thus potentially leading to significant computational savings; (2) curvature information is accumulated and exploited during the inversion, using a randomized quasi-Newton method; (3) new data can be incorporated without the need to re-invert the complete data set, thereby enabling an evolutionary mode of full-waveform inversion. We illustrate our method using synthetic and real-data inversions for upper-mantle structure beneath the African Plate. In these specific examples, the dynamic mini-batch approach requires around 20 per cent of the computational resources in order to achieve data and model misfits that are comparable to those achieved by a standard full-waveform inversion where all sources are used in each iteration.
Fully parallel mesh I/O using PETSC DMPLEX with an application to waveform modelling
Hapla, Václav; Knepley, Matthew G.; Afanasiev, Michael; et al. (2021)
SIAM Journal on Scientific Computing
Large-scale PDE simulations using high-order finite-element methods on unstructured meshes are an indispensable tool in science and engineering. The widely used open-source PETSc library offers an efficient representation of generic unstructured meshes within its DMPlex module. This paper details our recent implementation of parallel mesh reading and topological interpolation (computation of intermediate codimensions from a cell-vertex mesh) into DMPlex. We apply these developments to seismic wave propagation scenarios on Mars as a sample application. The principal motivation is to overcome single-node memory limits and reach mesh sizes which were impossible before. Moreover, we demonstrate that scalability of I/O and topological interpolation goes beyond 12'000 cores, and memory imposed limits on maximum mesh size vanish.
Evolutionary full-waveform inversion
van Herwaarden, Dirk-Philip; Afanasiev, Michael; Thrastarson, Sölvi; et al. (2021)
Geophysical Journal International
We present a new approach to full-waveform inversion (FWI) that enables the assimilation of data sets that expand over time without the need to reinvert all data. This evolutionary inversion rests on a reinterpretation of stochastic Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS), which randomly exploits redundancies to achieve convergence without ever considering the data set as a whole. Specifically for seismological applications, we consider a dynamic mini-batch stochastic L-BFGS, where the size of mini-batches adapts to the number of sources needed to approximate the complete gradient. As an illustration we present an evolutionary FWI for upper-mantle structure beneath Africa. Starting from a 1-D model and data recorded until 1995, we sequentially add contemporary data into an ongoing inversion, showing how (i) new events can be added without compromising convergence, (ii) a consistent measure of misfit can be maintained and (iii) the model evolves over times as a function of data coverage. Though applied retrospectively in this example, our method constitutes a possible approach to the continuous assimilation of seismic data volumes that often tend to grow exponentially.
Full-Waveform Tomography of the African Plate Using Dynamic Mini-Batches
van Herwaarden, Dirk-Philip; Thrastarson, Sölvi; Hapla, Václav; et al. (2023)
Journal of Geophysical Research: Solid Earth
We present a seismic model of the Africa Plate, constructed with the technique of full-waveform inversion. The purpose of our model is to serve as a foundation for quantitative geodynamic and geochemical interpretation, earthquake-induced ground motion predictions, and earthquake source inversion. Starting from the first-generation Collaborative Seismic Earth Model, we invert seismograms filtered to a minimum period of 35 s and compute gradients of the misfit function with respect to the model parameters using the adjoint state method. We use dynamically changing mini-batches of the complete data set to compute approximate gradients at each iteration. This approach has three significant advantages: (a) it reduces computational costs for model updates and the inversion, (b) it enables the use of larger datasets without increasing iteration costs, and (c) it makes it trivial to assimilate new data since we can extend the data set without changing the misfit function. We invert data from 397 unique earthquakes and 184,356 unique source-receiver pairs. We clearly image tectonic features such as the Afar triple junction and low-velocity zones below the Hoggar, Air, and Tibesti Mountains, pronounced more than in earlier works. Finally, we introduce a new strategy to assess model uncertainty. We deliberately perturb the final model, perform additional mini-batch iterations, and compare the result with the original final model. This test uses actual seismic data instead of artificially generated synthetic data and requires no assumptions about the linearity of the inverse problem.
First generation of a three-dimensional tomographic model for the uppermost mantle beneath the Zagros collision zone-constraints from full-waveform inversion
Masouminia, Neda; van Herwaarden, Dirk-Philip; Thrastarson, Sölvi; et al. (2025)
Acta Geophysica
We construct a three-dimensional model of seismic velocity structure beneath the Zagros collision zone by analyzing phase measurements of seismic waveform recordings from earthquakes. We used entire waveforms from 37 earthquakes and followed a multi-scale approach for periods between 20 and 80 s. As a starting model, we used the first generation of the Collaborative Seismic Earth Model, applied the adjoint method to compute model gradients, and utilized the Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimization algorithm to reconstruct the uppermost mantle seismic velocity structure. The Zagros collision zone consists of the margin of the Arabian platform (the Zagros Fold-and-Thrust Belt) and the margin of the Eurasian plate (the Iranian microplates). The retrieved model reveals a strong shear wave velocity contrast at a depth of approximately 180 km along the Zagros mountain belt, and topography at the surface is a piece of evidence that the deformation of the transition zone stops along the Zagros. We interpret this as an interaction between the two continental lithospheres that end at this depth. We observe that the sub-crustal lithosphere of the studied region was constructed from relatively high shear velocity structures beneath Central Iran as well as the Lut block at 80-150 km depth and continuity of high-velocity structure throughout the margin of the Arabian lithosphere from 70- to 200-km depth. It explains continental collision caused earlier thickening during the convergence of the Arabian platform toward the northeast. This observation indicates that the lithosphere of Iranian microplates has a relatively warm structure. It also shows the non-uniform distribution of a sharp velocity contrast between this structure and the strong low-velocity structure underlying it, marking the lithosphere and asthenosphere boundary (LAB). Our results locate this boundary at approximately 119-km depth. On the other hand, we observed a thickened and cold lithosphere for the margin of the Arabian lithosphere.
The EU Center of Excellence for Exascale in Solid Earth (ChEESE): Implementation, results, and roadmap for the second phase
Folch, Arnau; Abril, Claudia; Afanasiev, Michael; et al. (2023)
Future Generation Computer Systems
The EU Center of Excellence for Exascale in Solid Earth (ChEESE) develops exascale transition capabilities in the domain of Solid Earth, an area of geophysics rich in computational challenges embracing different approaches to exascale (capability, capacity, and urgent computing). The first implementation phase of the project (ChEESE-1P; 2018–2022) addressed scientific and technical computational challenges in seismology, tsunami science, volcanology, and magnetohydrodynamics, in order to understand the phenomena, anticipate the impact of natural disasters, and contribute to risk management. The project initiated the optimisation of 10 community flagship codes for the upcoming exascale systems and implemented 12 Pilot Demonstrators that combine the flagship codes with dedicated workflows in order to address the underlying capability and capacity computational challenges. Pilot Demonstrators reaching more mature Technology Readiness Levels (TRLs) were further enabled in operational service environments on critical aspects of geohazards such as long-term and short-term probabilistic hazard assessment, urgent computing, and early warning and probabilistic forecasting. Partnership and service co-design with members of the project Industry and User Board (IUB) leveraged the uptake of results across multiple research institutions, academia, industry, and public governance bodies (e.g. civil protection agencies). This article summarises the implementation strategy and the results from ChEESE-1P, outlining also the underpinning concepts and the roadmap for the on-going second project implementation phase (ChEESE-2P; 2023–2026).

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Michael Afanasiev

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