Parameterization of a ground model

The inversion principles are presented in chapter 2 as well as the particular method used in this work: the neighbourhood algorithm. Chapter 3 details the computation of dispersion, ellipticity and auto-correlation curves for a one-dimensional ground model, as well as the misfit calculation in each case. To perform an inversion of experimental data, it is also necessary to identify the physical unknowns of the problem. For most of the stochastic inversion methods, models are characterized by a set of uniform random deviates between 0 and 1. The objective of this chapter is to investigate the possible alternatives for transforming those random vectors into physical parameters of a one-dimensional ground model. In a first approach, it can be seen as a scaling of the interval $[0,1]$ to the prior uncertainty of a particular layer property. But things become more complicated when some combinations of parameter values are not physically acceptable. This problem is analysed in the first section. The efficiency of the inversion algorithm decreases with the number of parameters. When the number of layers increases, low velocity zones are likely to be present in the generated profiles. The second section reviews the problems encountered with models with a great number of layers. The third section proposes various solutions to handle velocity variations with a reduced number of parameters.