Full-waveform inversion in the time domain with an energy-weighted gradient

When applying full-waveform inversion to surface seismic reflection data, one difficulty is that the deep region of the model is usually not reconstructed as well as the shallow region. We develop an energy-weighted gradient method for the time-domain full-waveform inversion to accelerate the convergence rate and improve reconstruction of the entire model without increasing the computational cost. Three different methods can alleviate the problem of poor reconstruction in the deep region of the model: the layer stripping, depth-weighting and pseudo-Hessian schemes. The first two approaches need to subjectively choose stripping depths and weighting functions. The third one scales the gradient with only the forward propagation wavefields from sources. However, the Hessian depends on wavefields from both sources and receivers. Our new energy-weighted method makes use of the energies of both forward and backward propagated wavefields from sources and receivers as weights to compute the gradient. We compare the reconstruction of our new method with those of the conjugate gradient and pseudo-Hessian methods, and demonstrate that our new method significantly improves the reconstruction of both the shallow and deep regions of the model.