Geologic provinces from unsupervised learning: synthetic experiments in clustering of localized topography/gravity admittance and correlation spectra
Authors: Pastorutti Alberto , Braitenberg Carla 
Published: March 2021

&lt;p&gt;Partitioning of the Earth surface in &quot;provinces&quot;: tectonic domains, outcropping geological units, crustal types, discrete classes extracted from age or geophysical data (e.g. tomography, gravity) is often employed to perform data imputation of ill-sampled observables (e.g. the similarity-based NGHF surface heat flow map [1]) or to constrain the parameters of ill-posed inverse problems (e.g. the gravimetric global Moho model GEMMA [2]).&lt;/p&gt;&lt;p&gt;We define provinces as noncontiguous areas where quantities or their relationships are similar. Following the goodness metric employed for proxy observables, an adequate province model should be able to significantly improve prediction of the extrapolated quantity. Interpolation of a quantity with no reliance on external data sets a predictivity benchmark, which a province-based prediction should exceed.&lt;br&gt;In a solid Earth modelling perspective, gravity, topography, and their relationship, seem ideal candidates to constrain a province clustering model. Earth gravity and topography, at resolutions of at least 100 km, are known with an incomparable sampling uniformity and negligible error, respect to other observables.&lt;/p&gt;&lt;p&gt;Most of the observed topography-gravity relationship can be explained by regional isostatic compensation. The topography, representing the load exerted on the lithosphere, is compensated by the elastic, thin-shell like response of the latter. In the spectral domain, flexure results in a lowpass transfer function between topography and isostatic roots. The signal of both surfaces, superimposed, is observed in the gravity field.&lt;br&gt;However, reality shows significant shifts from the ideal case: the separation of nonisostatic effects [3], such as density inhomogeneities, glacial isostatic adjustments, dynamic mantle processes, is nontrivial. Acknowledging this superposition, we aim at identifying clusters of similar topography-gravity transfer functions.&lt;/p&gt;&lt;p&gt;We evaluate the transfer functions, in the form of admittance and correlation [4], in the spherical harmonics domain. Spatial localization is achieved with the method by Wieczorek and Simons [5], using SHTOOLS [6]. Admittance and correlation spectra are computed on a set of regularly spaced sample points, each point being representative of the topo-gravity relationship in its proximity. The coefficients of the localized topo-gravity admittance and correlation spectra constitute each point features.&lt;/p&gt;&lt;p&gt;We present a set of experiments performed on synthetic models, in which we can control the variations of elastic parameters and non-isostatic contributions. These tests allowed to define both the feature extraction segment: the spatial localization method and the range of spherical harmonics degrees which are more sensible to lateral variations in flexural rigidity; and the clustering segment: metrics of the ground-truth clusters, performance of dimensionality reduction methods and of different clustering models.&lt;/p&gt;&lt;p&gt;[1] Lucazeau (2019). Analysis and Mapping of an Updated Terrestrial Heat Flow Data Set. doi:10.1029/2019GC008389&lt;br&gt;[2] Reguzzoni and Sampietro (2015). GEMMA: An Earth crustal model based on GOCE satellite data. doi:10.1016/j.jag.2014.04.002&lt;br&gt;[3] Bagherbandi and Sj&amp;#246;berg (2013). Improving gravimetric&amp;#8211;isostatic models of crustal depth by correcting for non-isostatic effects and using CRUST2.0. doi:10.1016/j.earscirev.2012.12.002&lt;br&gt;[4] Simons et al. (1997). Localization of gravity and topography: Constraints on the tectonics and mantle dynamics of Venus. doi:10.1111/j.1365-246X.1997.tb00593.x&lt;br&gt;[5] Wieczorek and Simons (2005). Localized spectral analysis on the sphere. doi:10.1111/j.1365-246X.2005.02687.x&lt;br&gt;[6] Wieczorek and Meschede (2018). SHTools: Tools for Working with Spherical Harmonics. doi:10.1029/2018GC007529&lt;/p&gt;