Elastic isotropic and anisotropic full-waveform inversions using automatic differentiation for gradient calculations in a framework of recurrent neural networks

We have implemented multiparameter full-waveform inversions (FWIs) in the framework of recurrent neural networks in elastic isotropic and transversely isotropic media. A staggered-grid velocity-stress scheme is used to solve the first-order elastodynamic equations for forward modeling. The gradients of loss with respect to model parameters are obtained by automatic differentiation. Multiple elastic model parameters are simultaneously inverted with a minibatch optimizer. We prove the equivalency of full-batch automatic differentiation and the conventional adjoint-state method for inversions in elastic isotropic media. Synthetic tests on elastic isotropic models show that the minibatch configuration has a better convergence rate and higher inversion accuracy than full-batch elastic FWIs. Inversions with data that contain incoherent and coherent noise are tested, respectively. With automatic differentiation, we determine the ease of extension to anisotropic media with two parameterizations, and the potential to implement it for more general media.