An explicit stabilization scheme for Q-compensated reverse time migration

Abstract

Attenuation compensation in prestack depth migration typically requires nonphysical frequency-dependent energy amplification, which may lead to numerical instability. An explicit stabilization approach is developed for seismic [Formula: see text] compensation after deriving the [Formula: see text]-space Green’s function of the compensated constant-[Formula: see text] wave equation, which has decoupled fractional Laplacians. At high wavenumbers, as time increases, the time propagator of [Formula: see text]-space Green’s function increases exponentially. Therefore, an exponential window function is introduced to stabilize the exponentially divergent time propagator. Unlike the conventional low-pass filtering approach in the frequency or wavenumber domain, the proposed method assumes that the exponent of the chosen window is a power function of the wavenumber magnitude, which only involves explicit stabilization terms in the time-space domain. An explicit stabilization form helps to perform seismic data [Formula: see text] compensation more conveniently. We outline the basic structure of the proposed approach with explicit stabilization and highlight some numerical details using compute unified device architexture-based implementations. The strong scaling analysis justifies the good performance of the developed code package in terms of computational efficiency and scalability. In addition, we further analyze the optimal scheme parameter selection and the influence of parameters on filtering performance. The proposed [Formula: see text]-compensated reverse time migration is applied on the Marmousi model and synthetic and real crosswell examples to verify its feasibility and numerical stability.