SALSA3D: A Tomographic Model of Compressional Wave Slowness in the Earth’s Mantle for Improved Travel‐Time Prediction and Travel‐Time Prediction Uncertainty

The Dulmage–Mendelsohn permutation in seismic tomography

“…It should be noted that the ability to calculate the model posterior covariance matrix, is a first step towards putting error bars in moderate size tomographic models, and thus allowing more accurate quantitative interpretation of the tomographic models. This further requires realistically determining the prior data errors and model covariance (e.g., Tarantola, 1987;Nolet et al, 1999;Rawlinson et al, 2014), and recently, significant effort has been focused on improving the determination of these priors (e.g., Bodin et al, 2012;Duputel et al, 2012Duputel et al, , 2014Rodi & Myers, 2013;Voronin et al, 2014;Ballard et al, 2016).Furthermore, we show that the matrix decomposition, in combination with a recently developed singular value decomposition algorithm, allow the computation of the entire range of singular values of both the well/over-determined and the under-determined subsystems giving insight into the problem. For example, it reveals the exact nature of the gradual decay of the singular values, which is of considerable interest for the efficient and accurate dimensionality reduction of the problem by means of low rank approximations (e.g., Voronin et al, 2014, 2015Gu 2015.…”

“…For example, parallel dense Cholesky factorization using such system has been utilized to solve large, at the time, seismic tomography inverse problems (Boschi 2003;Soldati & Boschi 2005;Soldati et al, 2006). More recently, a dense Cholesky solver that stores and fetches the matrices in significantly slower external memory such as hard drives (also known as out-of-the-core capability; D"Azevedo & Dongarra, 2000), has been used to calculate the resolution and covariance matrix for a global tomography model with ~230K parameters (Hipp et al, 2011;Ballard et al, 2016). This particular study required about 12 hours of computation time, using 400 threads distributed over 10 computational nodes, that had access to main memory that varied from 64 GB to 768 GB per node.…”

The lateral variation of Pn velocity gradient under Eurasia

“…Because of the highest P wave path coverage density in Eurasia, the velocity model SALSA3D is most reliable for the region. The uncertainty of the model travel time prediction for Eurasia is on the order of 0.3 to 0.9 s [Ballard et al, 2016b;Figure 9b]. As a result, I do not expect the error introduced by the uncertainty of the velocity model to be significant.…”

Illuminating the seismicity pattern of the October 8, 2005, M = 7.6 Kashmir earthquake aftershocks

“…Efforts to mitigate this have evolved from correction terms for individual paths (e.g. Murphy et al, 2005), to regionalized models for traveltime calculation (Myers et al, 2010), to global 3-dimensional models Ballard et al, 2016). We 55 now have at our disposal a 3-dimensional global P-and S-wave velocity model anticipated to improve significantly the representation of traveltimes in central Asia .…”