Enhancing Low-wavenumber Components Of Full-waveform Inversion Using Wavefield Decomposition Methods In The Timespace Domain

Full-waveform inversion(FWI)is a promising 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 low-wavenumber information of wavefields.If the initial model is far away from the true model,FWI will inevitably get trapped into meaningless local minima.Given that the properties of the low-wavenumber components can help construct the initial model and overcome cycle skipping,we propose a low-wavenumber update FWI method based on the Hilbert transform called the LWUH method.This method provides a new form of FWI in the time-space domain that appears to be capable to pick out the low-wavenumber components of the gradient and enhance the low-wavenumber updates iteratively.In this method,the updates of low wavenumbers and high wavenumbers are running in different steps.In the first step,a gradient formula based on the Hilbert transform plays a key role in updating the low-wavenumber components.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.Compared with the result of least-squares-reversetime-migration based on the low-wavenumber-updates method,the result of the LWUH method shows a better precision not only in ideal-condition tests but also in noisy-data and low-frequency missing tests.