Geophysical inversion and optimal transport

Sambridge, Malcolm; Jackson, Andrew; Valentine, Anne

doi:10.1093/gji/ggac151

Cited by 20 publications

(14 citation statements)

References 59 publications

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“…Like the KSdistance the Wasserstein defines a metric space, satisying the triangle inequality. Elsewhere in the Earth sciences, the Wasserstein distance is increasingly being used for solving non-linear geophysical inverse problems (e.g., Engquist and Froese 2014;Métivier et al 2016;Sambridge et al 2022). Full mathematical treatments of the Wasserstein distance and optimal transport are beyond the scope of this paper, but interested readers are referred to Villani (2003) or Peyré and Cuturi (2019).…”

Section: The Wasserstein Distancementioning

confidence: 99%

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Short Communication: The Wasserstein distance as a dissimilarity metric for comparing detrital age spectra, and other geological distributions

Lipp¹,

Vermeesch²

2023

Preprint

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Distributional data such as detrital age populations or grain size distributions are common in the geological sciences. As analytical techniques become more sophisticated, increasingly large amounts of distributional data are being gathered. These advances require quantitative and objective methods, such as multidimensional scaling (MDS), to analyse large numbers of samples. Crucial to such methods is choosing a sensible measure of dissimilarity between samples. At present, the Kolmogorov-Smirnov (KS) statistic is the most widely used of these dissimilarity measures. However, the KS statistic has some limitations. It is very sensitive to differences between the modes of two distributions, and relatively insensitive to differences between their tails. Here we introduce the Wasserstein-2 distance (W2) as an alternative to address this issue. Whereas the KS-distance is defined as the maximum vertical distance between two empirical cumulative distribution functions, the W2-distance is a function of the horizontal distances (i.e., age differences) between individual observations. Using a combination of synthetic examples and a published zircon U-Pb dataset, we show that the W2 distance produces similar MDS results to the KS-distance in most cases, but significantly different results in some cases. Where the results differ, the W2 results are geologically more sensible. For the case study, we find that the MDS map that is produced using W2 can be readily interpreted in terms of the shape and average age of the age spectra. The W2-distance has been added to the R package IsoplotR, for immediate use in detrital geochronology and other applications. The W2 distance can be generalised to multiple dimensions, which opens opportunities beyond distributional data.

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Section: The Wasserstein Distancementioning

confidence: 99%

“…Full mathematical treatments of the Wasserstein distance and optimal transport are beyond the scope of this paper, but interested readers are referred to Villani (2003) or Peyré and Cuturi (2019). A geophysical perspective is given in Sambridge et al (2022).…”

Section: The Wasserstein Distancementioning

confidence: 99%

Short Communication: The Wasserstein distance as a dissimilarity metric for comparing detrital age spectra, and other geological distributions

Lipp¹,

Vermeesch²

2023

Preprint

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“…This allows a structured approach to algorithm development, progressing from simpler to more complex test problems (Käufl et al, 2014(Käufl et al, , 2015(Käufl et al, , 2016. As such, pyprop8 underpins many of the examples presented in Sambridge et al (2022), which develops a novel optimal-transport based misfit function for waveform inversion.…”

Section: Applicationsmentioning

confidence: 99%

pyprop8: A lightweight code to simulate seismic observables in a layered half-space

Valentine¹,

Sambridge²

2022

JOSS

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The package pyprop8 enables calculation of the response of a 1-D layered halfspace to a seismic source, and also derivatives ('sensitivity kernels') of the wavefield with respect to source parameters. Seismograms, seismic spectra, and measures of static displacement (e.g. GPS, InSAR and field observations) may all be simulated. The method is based on a Thompson-Haskell propagator matrix algorithm, described in O'Toole & Woodhouse (2011) and O'Toole et al. ( 2012). The package is entirely written in Python, dependent only on the mainstream libraries numpy (Harris et al., 2020) and scipy (Virtanen et al., 2020). As such, it is lightweight and easy to deploy across a variety of platforms, making it particularly suited to use for teaching and outreach purposes.

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“…Originating from the work of Monge (1781) on Optimal Transport, calculation of Wasserstein distances have been developed by Kantorovich (1942) and Villani (2003). The Wasserstein distance has been applied to a range of problems in computing (Arjovsky et al., 2017), chemistry (Seifert et al., 2022), oceanography (Hyun et al., 2022; Nooteboom et al., 2020), climate science (Chang et al., 2015; Vissio et al., 2020), geophysics (Engquist & Froese, 2014; Métivier et al., 2016a, 2016b; Sambridge et al., 2022), sedimentology (A. Lipp & Vermeesch, 2023), and hydrology (Magyar & Sambridge, 2023). As far as we are aware it has not been used to invert landscapes for their properties (e.g., uplift histories, erosion rates, sedimentary fluxes).…”

Section: Introductionmentioning

confidence: 99%