Source-independent least-squares reverse time migration in vertical transversely isotropic media based on the Student’s t-distribution

Abstract

Seismic anisotropy exists in various type of strata and should be considered in seismic imaging schemes. Seismic imaging algorithms based on isotropic assumption neglect the impacts of anisotropy on seismic data, which causes migration artifact and waveform distortion. To correct the effects of anisotropy on seismic wave propagation, we propose an imaging algorithm that performs least-squares reverse time migration in vertical transversely isotropic acoustic media. We derive the following operators to implement this algorithm, the de-migration operator, its adjoint migration operator and the corresponding gradient. However, an inaccurate estimated source wavelet will introduce the error in the seismic simulation, and thus increase the mismatch between observed and synthetic data for least-squares reverse time migration. In addition, the noises, especially the noises with abnormal amplitudes in the seismic data, damage the inversion convergence and reduce the imaging resolution. To improve the image quality, we propose to use convolved wavefields between observed and synthetic data so that such mismatch can be independent of the source wavelets. Also, we employ the student's t-distribution instead of L2 norm in our inversion scheme to better handle the seismic noise. Its implementation only modifies the gradient of the conventional least square reverse time migration scheme. Our numerical tests show a clear improvement using our proposed imaging algorithm when compared with the conventional isotropic migration scheme for the anisotropic data. Also, the synthetic examples demonstrate the feasibility and effectiveness of our proposed source-independent algorithm using the student's t-distribution.