Seafloor topography estimation from Vertical Gravity Gradients using Particle Swarm Optimization

The Earth's Vertical Gravity Gradient (VGG) can be used to map seafloor topography but presents a challenging inverse problem. A promising approach is forward modeling, in which one searches over a set of candidate topographies and selects the one whose predicted VGG best fits the observed one. The main bottleneck here is solving the associated high-dimensional and non-linear optimization problem. Yang et al (2018) demonstrated a method in which the topography is parametrized by heights of mass elements on a rectangular grid and the $\approx 10^4$ dimensional optimization problem is tackled with simulated annealing (SA). We propose a computationally much cheaper method, using a stochastic optimization method known as Particle Swarm Optimization (PSO) and representing the topography as a linear combination of Radial Basis Functions (RBFs). First results, obtained without any tuning, show that the MATLAB code achieves an RMS error of 700 m with 500 RBFs (1500 parameters) and a 30 min run time. This is comparable to the error of 350 m from the much more expensive SA method that takes hours. Improvements to our method are likely to result in state of the art performance levels.