Project:	Voronoi-Based Spatial Weighting for Robust Geocenter Motion Estimation from JTRF (JPL AO No. 16875)
Disciplines:	Geophysics, Space Geodesy, Aerospace Engineering
Mentor:	Claudio Abbondanza, (JPL), Claudio.Abbondanza@jpl.nasa.gov, Phone: (818) 354-1870
Background:	The center-of-mass (CM) of the total Earth system (solid Earth plus fluid envelope) is commonly referred to as geocenter. Geocenter motion describes the motion of the CM relative to the center-of-figure (CF) of the solid Earth surface. This quantity plays a fundamental role in satellite orbit determination, terrestrial reference frame realization, and studies of global mass redistribution. Geocenter motion is primarily driven by degree-1 loading processes and reflects large-scale mass transport in the Earth system. It is therefore critical for understanding sea level rise, atmospheric and ocean circulation, hydrology, glacial isostatic adjustment, and deep Earth processes. At JPL, geocenter motion can be estimated from station position time series derived from the JPL Terrestrial Reference Frame (JTRF), which is computed using a Square-Root Information Filter and Dyer–McReynolds smoother assimilating observations from GNSS, VLBI, SLR, and DORIS. A common approach to estimating time-variable CM–CF motion consists of computing the barycenter of the global station network at each epoch. However, this method assumes a homogeneous global station distribution. In practice, the network geometry is uneven, introducing spatial bias into geocenter estimates. Current mitigation strategies rely on carefully selecting subsets of stations with improved geographic balance. This project proposes a more rigorous alternative based on spherical Voronoi tessellation to derive spatial weights that account for an uneven network geometry in a mathematically consistent way.
Description:	## Project Description The objective of this project is to develop and test a Voronoi-based spatial weighting scheme for improving JTRF-derived geocenter motion estimates. The student will contribute to the following tasks: 1. Station Selection and Quality Control * Identify high-quality station time series based on: * Length of observing history * Repeatability metrics * Formal uncertainties * Exclude stations exhibiting significant nonlinear or poorly modeled motion 2. Spherical Voronoi Tessellation * Compute spherical Voronoi polygons for selected JTRF stations (using e.g. Python’s scipy.spatial.SphericalVoronoi) * Compute polygon areas on the sphere 3. Spatial Weight Computation * Derive normalized station weights based on spherical polygon area * Investigate regularization strategies to: * Enforce smoothness between neighboring polygons * Constrain adjacent weights toward equality within a prescribed variance 4. Integration into Geocenter Estimator * Modify the existing geocenter estimation code to incorporate spatial weights * Compare weighted and unweighted CM–CF solutions * Quantify reduction in geometric bias ## Expected Outcomes By the end of the internship, the student will: * Deliver a reproducible Python-based Voronoi weighting pipeline * Produce quantitative comparisons between classical and weighted geocenter estimates * Document the methodology and validation results * Present findings at an internal JPL seminar * Potentially contribute to a conference abstract
References:	## Key References - Rebischung et al. (2024), *ITRF2020 seasonal geocenter motion model*, Journal of Geodesy - Caroli et al. (2009), *Robust and Efficient Delaunay triangulations of points on or close to a sphere* - Wu et al. (2019), *Improved global nonlinear surface mass variation estimates from geodetic displacements and reconciliation with GRACE data*, JGR Solid Earth
Student Requirements:	- Coursework in applied mathematics, physics, aerospace engineering, planetary sciences, space geodesy or computer science - Exposure to numerical methods, linear algebra, and- basic estimation theory - Familiarity with spherical geometry concepts - Programming experience in Python, MATLAB, Fortran, or C++
Location / Safety:	Project building and/or room locations: . Student will need special safety training: .
Programs:	This AO can be done under the following programs:   Program    Available To        SURF@JPL    both Caltech and non-Caltech students  Click on a program name for program info and application requirements.