A new paper is added to the collection of reproducible documents: Full waveform inversion and joint migration inversion with an automatic directional total variation constraint

As full waveform inversion (FWI) is a non-unique and typically ill-posed inversion problem, it needs proper regularization to avoid cycle-skipping. To reduce the non-linearity of FWI, Joint Migration Inversion (JMI) is proposed as an alternative, explaining the reflection data with decoupled velocity and reflectivity parameters. However, the velocity update may also suffer from being trapped in local minima. To optimally include geologic information, we propose FWI/JMI with directional total variation as an L1-norm regularization on the velocity. We design the directional total variation operator based on the local dip field, instead of ignoring the local structural direction of the subsurface and only using horizontal- and vertical- gradients in the traditional TV. The local dip field is estimated using plane-wave destruction based on a raw reflectivity model, which is usually calculated from the initial velocity model. With two complex synthetic examples, based on the Marmousi model, we demonstrate that the proposed method is much more effective compared to both FWI/JMI without regularization and FWI/JMI with the conventional TV regularization. In the JMI-based example, we also show that L1 directional TV works better than L2 directional Laplacian smoothing. In addition, by comparing these two examples, it can be seen that the impact of regularization is larger for FWI than for JMI, because in JMI the velocity model only explains the propagation effects and, thereby, makes it less sensitive to the details in the velocity model.

A new paper is added to the collection of reproducible documents: Five-dimensional seismic data reconstruction using the optimally damped rank-reduction method

It is difficult to separate additive random noise from spatially coherent signal using a rank-reduction method that is based on the truncated singular value decomposition (TSVD) operation. This problem is due to the mixture of the signal and the noise subspaces after the TSVD operation. This drawback can be partially conquered using a damped rank reduction method, where the singular values corresponding to effective signals are adjusted via a carefully designed damping operator. The damping operator works most powerfully in the case of a small rank and a small damping factor. However, for complicated seismic data, e.g., multi-channel reflection seismic data containing highly curved events, the rank should be large enough to preserve the details in the data, which makes the damped rank reduction method less effective. In this paper, we develop an optimal damping strategy for adjusting the singular values when a large rank parameter is selected so that the estimated signal can best approximate the exact signal. We first weight the singular values using optimally calculated weights. The weights are theoretically derived by solving an optimization problem that minimizes the Frobenius-norm difference between the approximated signal components and the exact signal components. The damping operator is then derived based on the initial weighting operator to further reduce the residual noise after the optimal weighting. The resulted optimally damped rank reduction method is nearly an adaptive method, i.e., insensitive to the rank parameter. We demonstrate the performance of the proposed method on a group of synthetic and real five-dimensional seismic data.