Learning to invert pseudo-spectral data for seismic waveforms

Abstract

Full-waveform inversion (FWI) is a widely adopted technique used in seismic processing to produce high resolution Earth models, that fully explain the recorded seismic data. FWI is a local optimisation problem which aims to minimise, using a least-squares approach, the misfit between recorded and modelled data. The inversion process begins with a best-guess initial model which is iteratively improved using a sequence of linearised local inversions to solve a fully non-linear problem. Deep learning has gained widespread popularity in the new millennium. At the core of these tools are Neural Networks (NN), in particular Deep Neural Networks (DNN), which are variants of these original NN algorithms with significantly more hidden layers, resulting in efficient learning of a non-linear function between input and output pairs. The learning process within DNN involves repeatedly updating network neuron weights to best approximate input-to-output mappings. There is clear similarity between FWI and DNN as both approaches attempt to solve non-linear mapping in an iterative sense. However, they are fundamentally different in that FWI is knowledge-driven, whereas DNN is data-driven. This article proposes a novel approach which learns pseudo-spectral data-driven FWI. We test this methodology by training a DNN on 1D multi-layer, horizontally-isotropic data and then apply this to previously unseen data to infer the surface velocity. Results are compared against a synthetic model and success and failures of this approach are hence identified.