On the relationship between volcanic pointlike features and the crust-mantle boundary at the Pinacate Volcanic Field, Sonora, México

Abstract

A description of numerical methods is presented, which applied to data from a digital elevation model, helps to enhance the presence of pointlike features in a volcanic field. It was assumed in the development of the method, that the scalar field representing the topography in a digital elevation model is the vertical gradient of a harmonic function u. The second derivatives of u, in orthogonal directions, x, y, z, are computed in the wavenumber domain, via the two-dimensional Fourier transform, to obtain the gradient tensor of u. At every point in the digital elevation model, the gradient tensor components form a 3 by 3 symmetric matrix. I use the singular value decomposition of these matrices to calculate its eigenvalues to obtain their principal invariants. The square of the second invariant is found as an excellent choice to select pointlike features, likely related to volcanic vents. The method is fully described and illustrated using a digital elevation model with a horizontal resolution of 25 m from the Pinacate volcanic field in northwestern Sonora, where we have selected 353 pointlike features. Fundamental statistical analysis of the azimuth and location of the central point between every two points was carried in the range (0–5] km to obtain a rose diagram, where the azimuth of maximum and minimum frequencies are separated apart 90°, suggesting that most of the magma, that built the Pinacate Volcanic Field, was emplaced along the N25 ± 5°W direction. This direction is nearly parallel to the trend of the Crust-Mantle interface, inferred by nonlinear inversion of isostatic residual gravity data, which lies at a depth of about 18.5 km beneath the Santa Clara Volcano. The magnetization between 18 and 21 km-depth, inferred by linear inversion of aeromagnetic data, may correspond with mafic rocks of gabbroic composition, which led to monogenetic volcanism of basaltic composition. It is suggested that monogenetic volcanic activity in the PVF was accommodated mainly in a direction normal to a major lateral change in density.