Distance field computation for geological slab surface data sets

Abstract

The three-dimensional shapes of tectonic plates that sink into the Earth's mantle (slabs) are the starting point for a range of geoscience studies, from determining the forces driving the motion of tectonic plates, to potential seismic and tsunami hazards, to the sources of magmas beneath active volcanos. For many of these applications finite element methods are used to model the deformation or fluid flow, and therefore the input model parameters, such as feature geometries, temperature or viscosity, must be defined with respect to a smooth, continuous distance field around the slab. In this paper we present a framework for processing sparse and noisy seismic data (earthquake locations), defining the shape of the slab and computing a continuous distance function on a mesh with variable node spacing. Due to the inhomogeneous volumetric distribution of earthquakes within the slab and significant inaccuracies in the locations of earthquakes occurring hundreds of kilometers below the Earth's surface, the seismicity data set is extremely noisy and incomplete. Therefore, the preprocessing is the major part of the framework consisting of several steps including a point based smoothing procedure, a powerful method to use other observational constraints on slab location (e.g., seismic tomography or geologic history) to extend of the slab shape beyond earthquake data set and continuous resampling using moving least squares method. For the preprocessed point data Communicated by Gabriel Wittum.we introduce approaches for finding the three-dimensional boundary of the slab and a subdivision of the slab into quadric implicit polynomials. The resulting distance field is then compiled from distances to the piecewise continuous approximation of the slab and distances to slab boundary.

Sensitivity of the short‐ to intermediate‐wavelength geoid to rheologic structure in subduction zones

“…The structure of the subducted slab is designed to create a smooth temperature distribution that approximates the conductive warming of the bottom of the slab and convective removal of the slab thermal boundary layer in the mantle wedge. We first calculate the 3‐D distance from the subducting plate and slab surface (including taking into account the free edges) using a method based on visualization algorithms to produce smooth, unaliased distances to the finite element mesh [ Vančo et al , 2012]. The temperature structure is defined by a constant‐age half‐space cooling model below the slab (80 Myr) and above the slab (10 Myr).…”