Linear machine learning algorithms are used to perform a full-wavefield inversion of synthetic cross-hole tomographic data. A general method to invert geophysical data is proposed and tested on a specific problem of cross-hole tomography.

A linear mapping is learned between a tomographic image and the resulting wavefield, so an analytical inversion is possible to obtain the posterior on the tomographic image. This has the advantage that it is extremely fast.

The full wavefield is summarized by traveltime and Principal Component Analysis (PCA) reduction. The linear mapping is learned using ridge regression. The tomographic images are generated to show a channel structure and the wavefields are generated using finite-difference forward modeling.

The method is shown to perform better than traditional linear ray inversion methods, both qualitatively in that the posterior means have a higher resolution and quantitatively in that there is a higher correlation coefficient between the posterior mean and the true value.


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