3D forward modeling of upgoing and downgoing wavefields using Hilbert transform

Abstract

The separation of upgoing and downgoing wavefields is an important technique in the processing of vertical seismic profiling data and ocean bottom cable data. It is also used in reverse time migration (RTM) based on the two-way wave equation to suppress low-frequency, high-amplitude noises and false images. Therefore, we model upgoing and downgoing wavefields directly in the wavefield propagation. There are several methods to obtain separated wavefields. The methods using the Fourier transform require storage of the wavefields, which is not practical due to the extremely high disk-space requirements. Methods using Poynting vectors have an ambiguity problem when crossing a peak or a trough of the wavefields. To improve the accuracy and stability of the modeled upgoing and downgoing wavefields in a complicated velocity model, we evaluate an efficient forward-modeling approach purely based on the Hilbert transform in 3D acoustic wavefield simulation. This method is implemented by the Hilbert transform along the time and depth axis, instead of the Fourier transform. We explicitly derive the formulas for upgoing and downgoing wavefield propagation and attach reproducible source codes. Applications to synthetic models indicate that this method can forward propagate upgoing and downgoing wavefields effectively and improve the imaging quality in migration. This method has various potential applications, e.g., 3D seismic imaging with high computation efficiency.