Enhancing low-wavenumber components of full-waveform inversion using an improved wavefield decomposition method in the time-space domain

摘要

Full-waveform inversion (FWI) is a successful technique that attempts to build high-resolution velocity models by minimizing the residuals between observed and calculated data after a series of iterations. However, its successful application still relies on the quality of the estimated initial velocity model, as well as on the design of a suitable hierarchical workflow. If the initial model is far away from the true model, the widely used gradient based FWI will inevitably get trapped into meaningless local minima. Given that the properties of the low-wave number components can help construct the initial model and overcome cycle skipping, we propose a low-wave number update FWI method based on the Hilbert transform called the hybrid method. This method provides a new form of FWI in the time-space domain that appears to be capable of enhancing the low-wavenumber updates. In this method, the updates of low wavenumbers and high wavenumbers are divided into two parts. In the first step, a gradient formula based on the Hilbert transform plays a key role in updating the low-wavenumber components. The gradient is formed by cross-correlation of upgoing and downgoing waves of source and residual wavefields. Instead of using the wavefield decomposition method in the frequency-wavenumber domain with high computational complexity, we apply a novel method to extract the upgoing and downgoing wavefields in the time-space domain. In addition to the acceptable computational burden, the memory is reduced greatly. The second step is the standard FWI, and its task is to update the high-wavenumber components. Numerical tests on an anomaly model and the Marmousi model demonstrate the effectiveness of the hybrid method for extracting low-wavenumber components even for noisy data or when low-frequency data are missing. (C) 2018 Elsevier B.V. All rights reserved.