Linear Waveform Tomography Inversion Using Machine Learning Algorithms

A linear probabilistic waveform inversion strategy is proposed for crosshole tomographic data using machine learning algorithms that integrates a priori information described by Gaussian distributed slowness fields. A theoretical framework is outlined that combines an approximate linear forward operator describing the waveform with the ridge regression algorithm. The framework approximates arbitrary geostatistical a priori information with a Gaussian distribution, which makes it possible to obtain an analytic description of the posterior probability density, the solution of the inverse problem. The suggested inversion strategy is tested on synthetic tomographic crosshole ground-penetrating radar full-waveform data generated using multiple-point-based a priori information incorporating realistic noise. The benefits of the proposed strategy include: (I) Increased resolution of the posterior probability density compared to first arrival type inversion, due to using the wavefield. (II) Much faster execution than existing full waveform inversion algorithms based on Monte Carlo sampling or the adjoint method. (III) Greater efficiency in obtaining realizations from the posterior probability density. The main challenge in using the method is that it needs a quite large training data set from which the linear forward model can be inferred.