The potential of machine learning to solve the single step inversion problem in ambient noise tomography

The two step inversion of ambient noise surface wave data is common practice due to its convenience and reliability of imaging structures that are consistent with other observations. It is performed by taking the inter station dispersion curves produced by cross-correlation of ambient noise and performing individual 2D travel time tomographic inversions to produce maps of phase and/or group velocity for Rayleigh and/or love waves and whichever frequencies and modes have been extracted from the ambient noise data. These maps are then sampled in discrete points to produce location based dispersion curves known as pseudo-dispersion curves. These pseudo-dispersion curves are then inverted for 1D velocity structure. The issue with this method is the many separate inversions that are performed are entirely separate from one another with no regularisation applied to the final 3D model only in the individual steps. This can lead to artefacts in the model, particularly in areas of low data coverage, as the pseudo-dispersion curves can have unphysical spikes and velocity changes and so often produce unrealistic 1D models. Post processing can partially remedy this, such as smoothing the final model, but it does not go all the way to solving the problem. Single step inversions are also possible. The forward problem involves taking the 3D model and sampling it in discrete locations and computing dispersion curves which can be converted into 2D maps of phase/group velocity etc. Then using some Eikonal solver the travel time between stations can be calculated. These calculated travel times are then used with the measured travel times extracted from ambient noise to perform an inversion. This obtains a 3D model directly from the observed dispersion curves with regularisation built into whichever inversion scheme being used. This is often much more computationally expensive than the two step as the forward problem is expensive and needs to be computed many times in a typical inversion scheme. In this preliminary study we investigate the potential of using neural networks to assist in the single step inversion process by training networks to perform the forward and inverse problems in single step tomography of interstation dispersion curves. This may result in significant speed ups in these processes or lead to different ways of approaching the one step process. To examine the potential of this we investigate possible efficient sampling algorithms to produce synthetic training data sets as well as network architectures that produce the most accurate mapping of model parameters to the data and vice versa.