The Dulmage–Mendelsohn permutation in seismic tomography

Abstract

Seismic tomography inverse problems are among the largest high-dimensional parameter estimation tasks in Earth science. Although iterative algorithms can be used to efficiently solve these problems, their size gives rise to several issues such as the intractability of the computation of the model resolution and the model posterior covariance matrices that provide the means of assessing the robustness of the solution. In this work, we utilize methods from combinatorics and graph theory to study the structure of typical regional seismic body-wave tomography problems, and to effectively decompose them into subsets that can be solved efficiently by means of the least squares method. In combination with recent high performance direct sparse algorithms, this reduction in dimensionality allows for an efficient computation of the model resolution and covariance matrices using limited resources. We apply this methodology to a moderate size imaging of the structure of the crust and the upper mantle beneath Japan using deep local earthquakes recorded by the High Sensitivity Seismograph Network stations. Among the prominent features that are being imaged is a strong low-velocity region beneath the subducting Pacific slab along the entire Japan trench.

Advances in On- and Offshore Archaeological Prospection

“…In addition to the velocity model, the full model resolution matrix was calculated efficiently using direct sparse methods and the Dulmage Mendelsohn decomposition (Bogiatzis et al 2019) allowing to evaluate the robustness of the imaged features (Fig. 2 left).…”

Asthenospheric flow through the Izanagi-Pacific slab window and its influence on dynamic topography and intraplate volcanism in East Asia

“…Indeed, this process has been proposed in order to explain the intraplate volcanism (Zhou et al, 2018) and dynamic uplift in the western United States during the late Cenozoic, following the opening of tears in the Juan de Fuca slab and the Juan de Fuca-Pacific slab window. Furthermore, the asthenospheric build-up stage of this process may be invoked at circum-Pacific margins in the present day, and evidenced by seismically slow anomalies beneath subducting slabs in Japan (Ma J. et al, 2019;Bogiatzis et al, 2019), Cascadia (Hawley et al, 2016;Bodmer et al, 2018Bodmer et al, , 2020, and South America (Portner et al, 2017).…”