  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.
