Parameterization of geophysical inversion model using particle clustering

Abstract

This paper presents a new method of constructing physical models in a geophysical inverse problem, when there are only a few possible physical property values in the model and they are reasonably known but the geometry of the target is sought. The model consists of a fixed background and many small "particles" as building blocks that float around in the background to resemble the target by clustering. This approach contrasts the conventional geometric inversions requiring the target to be regularly shaped bodies, since here the geometry of the target can be arbitrary and does not need to be known beforehand. Because of the lack of resolution in the data, the particles may not necessarily cluster when recovering compact targets. A model norm, called distribution norm, is introduced to quantify the spread of particles and incorporated into the objective function to encourage further clustering of the particles. As proof of concept, 1D magnetotelluric inversion is used as example. My experiments reveal that the particles, starting from a fully scattered distribution, are able to move towards the actual target location; the quality of recovery depends on whether there is enough material (vertical conductance in 1D) in the particles to build the target; and the use of distribution norm can help produce tightened clustering. When the inversion struggles to fit the data, it may indicate that the prior information about the particles' conductivity and size are incorrect.