Junzhe Sun

Elastic wave-vector decomposition in heterogeneous anisotropic media

ABSTRACT The goal of wave‐mode separation and wave‐vector decomposition is to separate a full elastic wavefield into three wavefields with each corresponding to a different wave mode. This allows elastic reverse‐time migration to handle each wave mode independently. Several of the previously proposed methods to accomplish this task require the knowledge of the polarisation vectors of all three wave modes in a given anisotropic medium. We propose a wave‐vector decomposition method where the wavefield is decomposed in the wavenumber domain via the analytical decomposition operator with improved computational efficiency using low‐rank approximations. The method is applicable for general heterogeneous anisotropic media. To apply the proposed method in low‐symmetry anisotropic media such as orthorhombic, monoclinic, and triclinic, we define the two S modes by sorting them based on their phase velocities (S1 and S2), which are defined everywhere except at the singularities. The singularities can be located using an analytical condition derived from the exact phase‐velocity expressions for S waves. This condition defines a weight function, which can be applied to attenuate the planar artefacts caused by the local discontinuity of polarisation vectors at the singularities. The amplitude information lost because of weighting can be recovered using the technique of local signal–noise orthogonalisation. Numerical examples show that the proposed approach provides an effective decomposition method for all wave modes in heterogeneous, strongly anisotropic media.

Strategies for stable attenuation compensation in reverse-time migration: Strategies for stable attenuation compensation in reverse-time migration

Attenuation in seismic wave propagation is a common cause for poor illumination of subsurface structures. Attempts to compensate for amplitude loss in seismic images by amplifying the wavefield may boost high-frequency components, such as noise, and create undesirable imaging artifacts. In this paper, rather than amplifying the wavefield directly, we develop a stable compensation operator using stable division. The operator relies on a constant-Q wave equation with decoupled fractional Laplacians, and compensates for the full attenuation phenomena by performing wave extrapolation twice. This leads to two new imaging conditions to compensate for attenuation in reverse-time migration (RTM). A time-dependent imaging condition is derived by applying Q-compensation in the frequency domain, while a time-independent imaging condition is formed in the image space by calculating image normalization weights. We demonstrate the feasibility and robustness of the proposed methods using three synthetic examples. We found that the proposed methods are capable of properly compensating for attenuation without amplifying high-frequency noise in the data. This article is protected by copyright. All rights reserved

Increasing resolution of reverse-time migration using time-shift gathers

Reverse-time migration (RTM) has become an industry standard imaging method for complex geological areas. We present an approach for increasing its imaging resolution by employing time-shift gathers. The method consists of two steps: 1) migrating seismic data with the extended imaging condition to get time-shift gathers; 2) accumulating the information from time-shift gathers after they are transformed to zero-lag time-shift by a post-stack depth migration on a finer grid. The final image is generated on a grid which is denser than that of the original image thus increasing its resolution. The proposed method is based on the observation that non-zero-lag time-shift images recorded by the regular computing grid contain the information of zero-lag time-shift image of a denser grid, and such information can be continued to zero-lag time-shift and refocused at the correct locations on the denser grid. The extra computational cost of the proposed method amounts to the computational cost of zero-offset migration, and is almost negligible compared to the cost of prestack shot-record RTM. Numerical tests on synthetic models demonstrate that the method can effectively improve RTM resolution. It can also be regarded as an approach to improve the effciency of RTM by performing wavefield extrapolation on a coarse grid and generating the final image on the desired fine grid. This article is protected by copyright. All rights reserved