No abstract

Summary Full-waveform inversion (FWI) is a powerful seismic imaging methodology to estimate geophysical parameters that honor the recorded waveforms (observed data), and it is conventionally formulated as a least-squares optimization problem. Despite many successful applications, least-squares FWI suffers from cycle skipping issues. Optimal transport (OT) based FWI has been demonstrated to be a useful strategy for mitigating cycle skipping. In this work, we introduce a new Wasserstein metric based on q-statistics in the context of the OT distance. In this sense, instead of the data themselves, we consider the graph of the seismic data, which are positive and normalized quantities similar to probability functions. By assuming that the difference between the graphs of the modeled and observed data obeys the q-statistics, we introduce a robust q-generalized graph-space OT objective function in the FWI context namely q-GSOT-FWI, in which the standard GSOT-FWI based on l2-norm is a particular case. To demonstrate how the q-GSOT-FWI deals with cycle skipping, we present two numerical examples involving 2D acoustic wave-equation modeling. First, we investigate the convexity of q-GSOT objective function regarding different time shifts, and, secondly, we present a Brazilian pre-salt synthetic case study, from a crude initial model which generates significant cycle-skipping seismic data. The results reveal that the q-GSOT-FWI is a powerful strategy to circumvent cycle skipping issues in FWI, in which our objective function proposal presents a smoother topography with a wider attraction valley to the optimal minimum. They also show that q-statistics leads to a significant improvement of FWI objective function convergence, generating higher resolution acoustic models than classical approaches. In addition, our proposal reduces the computational cost of calculating the transport plan as the q-value increases.

The ocean-bottom-node (OBN) technology has been increasingly used to characterize the Brazilian pre-salt reservoirs. The independence between the geometries of seismic sources and receivers, enabled by an OBN survey, permits designing wide-aperture acquisition geometries that favour the recording of refracted waves from ultra-deep reservoirs. In this context, we present a target-oriented full-waveform inversion (FWI) methodology to evaluate the inversion of refracted waves simulated using a realistic velocity model inspired by typical Brazilian pre-salt oil fields. In our tests we compare three acquisition geometries, using the same node configuration on the seabed, but different source geometries: (i) circular shot geometry, (ii) conventional OBN geometry, (iii) long-offset OBN geometry. We perform a wavepath analysis to investigate the illumination of the target region promoted by the refracted waves of a circular shot OBN survey. The wavepath analysis suggests that Brazilian pre-salt reservoirs may be well illuminated using the much fewer source points in a circular shot acquisition geometry. The FWI results with synthetic data show that refracted waves bring important information from the ultra-deep reservoirs which are indispensable for obtaining a reliable final velocity model. We show that adding a low-cost circle shot geometry to a conventional OBN survey delivers improvements from the long-offset data that are comparable to those obtained from the much more expensive long-offset OBN geometry. Furthermore, these results suggest that the long-offset and multi-azimuth dataset has great potential to improve the reservoir characterization in deep-water exploration marine settings.