3-D Least-Squares Reverse Time Migration in Curvilinear-τ Domain

Curvilinear-grid-based least-squares reverse time migration (LSRTM) can produce an accurate image of complex subsurface structures. However, a huge amount of computational cost of LSRTM makes it difficult in real data applications, especially in 3-D cases. We propose a wavefield continuation operator in a new curvilinear-
$\tau $
domain to make the sampling space in the vertical direction to be uniform by stretching and compressing the low- and high-velocity zones, respectively. An objective function based on a conical wave encoding and student’s
$T$
distribution is constructed to improve the computational efficiency and robustness of LSRTM. The gradient formula is derived based on the objective function, and to correct the unbiased random estimation error, the idea of random optimization is introduced to obtain a weighted gradient. Demigration and adjoint wave equations in the curvilinear-
$\tau $
domain are derived to calculate the synthetic records and the backward-propagated wavefields. Numerical examples on synthetic and field datasets suggest that the proposed 3-D LSRTM method produces better images with a higher signal-to-noise ratio (SNR), more improved resolution, and more balanced amplitude than the conventional 3-D LSRTM and greatly improves the computational efficiency of 3-D LSRTM.