We present a general scheme for 3D geophysical inversion using a deep learning convolutional neural network that enables three-dimensional inversions of useful size to be solved on laptops and desktops. A priori constraints of maximum smoothness or compactness on model parameters used during conventional geophysical inversion are not necessary. In environments where a single stabilizing functional is not capable of adequately representing the subsurface variation (e.g., steel cased wells, buried pipes in smoothly varying geology), the method provides an attractive alternative. Projecting data to the Hilbert space of model parameters using the adjoint operator before training mitigates non uniqueness associated with the underdetermined nature of traditional 3D geophysical inverse problems. A field inversion example using magnetic data collected in Washington -on- Brazos state historic site to image buried pipe and other infrastructure is presented. While the training for a single inversion takes longer, the results show better resolution of the top of the structure and overall shape compared to conventional minimum structure inversion methods. For multiple inversions such as for systems with moving footprints, or time lapse surveys, neural networks can be substantially faster than traditional inversion as the network needs to be trained only once for several successive model predictions. The method can be applied to other geophysical data including seismic, electromagnetic and gravity, at various scales and resolution.

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