Viscoacoustic reverse-time migration with a robust space-wavenumber domain attenuation compensation operator

Intrinsic attenuation gives rise to phase dispersion and amplitude loss during seismic wave propagation. Not correcting these effects in seismic imaging can result in inaccurate reflector locations, dimmed amplitudes and degraded spatial resolution. In reverse-time migration (RTM), attenuation compensation can be implemented by reversing the sign of the dissipation term and keeping the dispersion term unchanged for backward wavefield extrapolation. Although this Q-compensated RTM scheme can effectively correct attenuation effects, amplitude amplification during back-propagation might lead to numerical instabilities, especially for field data with strong high-frequency noise. To mitigate this problem, we develop a robust space-wavenumber compensation operator, and apply it to viscoacoustic RTM. By analyzing the dispersion-only and viscoacoustic Green’s functions, we obtain an analytical solution for the attenuation compensation operator in a homogeneous medium. Because it is a time-frequency operator, to apply it directly in viscoacoustic RTM requires access to the extrapolated wavefields within a certain time window. To avoid storing the wavefields and improve computational efficiency, we use an approximated dispersion relation and convert the time-frequency operator to an equivalent space-wavenumber operator, which allows us to implement attenuation compensation on the fly during wavefield extrapolation. The hybrid-domain property of the operator enables us to account for the wavenumber-dependent compensation. A similar strategy can also be applied to the migrated images as a poststack processing approach, which is more efficient than the prestack compensation. Two synthetic and one land field dataset examples demonstrate the feasibility and adaptability of the proposed method.

Depth Migration Based on Two-Way Wave Equation to Image OBS Multiples: A Case Study in the South Shetland Margin (Antarctica)

With the development of marine seismic exploration, the ocean bottom seismometer (OBS) as a new seismic acquisition technology has been widely concerned. Although multiple waves are frequently viewed as noises, they may carry a wealth of subsurface information and produce a broader illumination than primary waves. To perform multiple wave imaging, we propose to utilize a two-way wave equation depth wavefield extrapolation method which is rarely used in this field. A simple dipping model is imaged by using primary and multiple waves, which proves the superiority of multiple waves in imaging over the primary waves and lays a foundation for practical application. Moreover, the comparison of multiple imaging results by reverse time migration and those by our proposed method demonstrates that our proposed method requires less storage space. In this study, we apply this migration method to actual OBS data collected in the South Shetland margin (Antarctica), where gas hydrates have been well documented. Firstly, the wavefield separation method is adopted to process the OBS data, so as to produce reliable primary and multiples waves; secondly, the ray-tracing method is used to derive the velocity field; and finally, the depth wavefield extrapolation method based on the two-way wave equation is applied to image primary and multiple waves. Migration results show that multiple waves provide a broader illumination and a clearer sediment structure than primary waves, especially for the highly shallow reflections.

Exact extrapolation and immersive modelling with finite-difference injection

SUMMARY In numerical modelling of wave propagation, the finite-difference (FD) injection method enables the re-introduction of simulated wavefields in model subdomains with machine precision, enabling the efficient calculation of waveforms after localized model alterations. By rewriting the FD-injection method in terms of sets of equivalent sources, we show how the same principles can be applied to achieve on-the-fly wavefield extrapolation using Kirchhoff–Helmholtz (KH)-like integrals. The resulting extrapolation methods are numerically exact when used in conjunction with FD-computed Green’s functions. Since FD injection only relies on the linearity of the wave equation and compactness of FD stencils in space, the methods can be applied to both staggered and non-staggered discretizations with arbitrary-order spatial operators. Examples for both types of discretizations show how these extrapolators can be used to truncate models with exact absorbing or immersive boundary conditions. Such immersive modelling involves the evaluation of KH-type extrapolation and representation integrals in the same simulation, which include the long-range interactions missing from conventional FD injection.

An implicit stabilization strategy for Q-compensated reverse time migration

Reverse time migration with [Formula: see text] compensation ([Formula: see text]-RTM) is an effective approach to enhance the resolution of seismic images because it retrieves the amplitude loss and phase distortion induced by the viscosity of media. According to the crosscorrelation imaging condition, [Formula: see text]-RTM requires compensation for the amplitude loss in the propagation paths of source and receiver wavefields, which can be realized by solving an amplitude-boosted wave equation. However, the amplitude-boosted simulations suffer from numerical instability due to the amplification of high-frequency noise. We have developed a robust stabilization strategy for [Formula: see text]-RTM by incorporating a time-variant filter into the amplitude-boosted wavefield extrapolation step. We modify the Fourier spectrum of the operator that controls the amplitude compensation to be time variant, and we add to the spectrum a stabilization factor. Doing so, we integrate the time-variant filter into the viscoacoustic wave propagator implicitly, and we avoid any explicit filtering operation in [Formula: see text]-RTM. We verify the robustness of this stabilized [Formula: see text]-RTM with two synthetic data examples. We also apply this technique to a field data set to demonstrate the imaging improvements compared to an acoustic RTM and a more traditional [Formula: see text]-RTM method.

PROPERTIES OF WAVEFIELD EXTRAPOLATION OPERATORS (ON THE EXAMPLE OF PREDICTION OF GHOST REFLECTIONS)

Seismic deghosting algorithms involve wavefield extrapolation. The operator of such a transformation is integral, and when applied to discrete seismic data, its approximation is used, which corresponds to a method of numerical integration. The paper examines the limits of applicability of the approximation by the method of cells and the method of rectangles. It is shown that when processing 3D seismograms recorded using traditional survey geometries, correct ghost prediction is possible only after interpolation. When processing 2D seismic gathers, it is possible to predict and remove ghost waves for deep and shallow streamers. The streamer shape can be arbitrary. The results of the study and the conclusions made are valid not only for ghost prediction operators, but also for all seismic exploration tasks that involve wavefield extrapolation.