Using compositional fields to trace where material has come from or is going to has many advantages from a computational point of view. For example, the numerical methods to advect along fields are well developed and we can do so at a cost that is equivalent to one temperature solve for each of the compositional fields. Unless you have many compositional fields, this cost is therefore relatively small compared to the overall cost of a time step. Another advantage is that the value of a compositional field is well defined at every point within the domain. On the other hand, compositional fields over time diffuse initially sharp interfaces, as we have seen in the images of the previous section.
At the same time, the geodynamics community has a history of using particles for this purpose. Historically, this may have been because it is conceptually simpler to advect along individual particles rather than whole fields, since it only requires an ODE integrator rather than the stabilization techniques necessary to advect fields. They also provide the appearance of no diffusion, though this is arguable. Leaving aside the debate whether fields or particles are the way to go, ASPECT supports both: using fields and using particles.