Multi-parameter Full Waveform Inversions Based On Recurrent Neural Networks

Full waveform inversion(FWI)is a data fitting method that provides under ground high-resolution models with both phase and amplitude information in seismic data.The full waveform inversion is performed into two steps: forward modeling and inversion.In the process of forward modeling,taking the finite difference method as an example,the information of the wavefield at the t moment can be calculated from the value of the wave field at the t-1 moment and the value of the wave field at the t-2 moment.Therefore,the whole forward modeling process can be realized by a recurrent neural network,that is,the time t-1 and the value of the wave field at the time t-2 are remembered in the network,and the value of the wave field at the time can be output.A recurrent neural network is established to replace the forward process in full waveform inversion.The inversion process in full waveform inversion is the training process of neural network.In deep learning frameworks,such as Tensorflow,gradients are calculated using an automatic differentiation mechanism.In this paper,the gradient of the loss function for velocity and density parameters is derived,and the calculation result is the same as that of the adjoint state method used in the whole waveform inversion.In this paper,a recurrent neural network is established based on the constant density acoustic wave equation,and the single-parameter full waveform inversion of the velocity model is realized.Two model data(a homogeneous model and the Marmousi model)are used for verification.The accuracy and convergence rate of the inversions obtained by the two optimization algorithms(Adam optimization and L-BFGS-B)are compared.Secondly,based on the two-dimensional wave equation with heterogeneous density,a new recurrent neural network model is established,and the velocity model is fixed to perform the single-parameter full waveform inversion process to obtain the density model.The velocity and density gradients with respect to the loss function are derived theoretically,and the feasibility of the algorithm is demonstrated.In the experiments,two kinds of model data are used to verify the feasibility of the algorithm.Finally,simultaneous inversion of multi-parameter velocity and density was carried out.Due to the crosstalk effect of velocity and density in multi-parameter full waveform inversion,the precision of multi-parameter inversion is relatively low.In this paper,two inversion strategies(stepwise inversion and alternating inversion)are used to improve the accuracy of the inversion model of multi-parameter full waveform inversion.The improvement of the accuracy ofvelocity model and density model by different strategies is compared,and the best inversion strategy is selected to realize the multi-parameter full waveform inversion.